The Eighth Congress of Romanian Mathematicians

THE EIGHTH CONGRESS OF ROMANIAN MATHEMATICIANS

PROGRAMME and ABSTRACT BOOK

ALEXANDRU IOAN CUZA UNIVERSITY OF IASI http://www.math.uaic.ro/cmr2015/ IAȘI, 2015 ORGANIZING INSTITUTIONS

The Section of Mathematical Sciences of the Romanian Academy

The Simion Stoilow Institute of Mathematics of the Romanian Academy

The Faculty of Mathematics of "Alexandru Ioan Cuza" University of Iasi

The Faculty of Mathematics and Computer Science of the University of Bucharest

"Octav Mayer" Institute of Mathematics of the Romanian Academy, Iasi

The Romanian Mathematical Society

"Alexandru Myller" Mathematical Seminary Foundation

ORGANIZING COMMITTEE

Romanian Academy Viorel Barbu, Marius Iosifescu, Solomon Marcus, Ioan Tomescu, Gabriela Marinoschi - Simion Stoilow Institute of Mathematics of the Romanian Academy Lucian Beznea, Dan Timotin University of Bucharest Victor Tigoiu Faculty of Mathematics of "Alexandru Ioan Cuza" University of Iasi "Octav Mayer" Institute of Mathematics of the Roumanian Academy, Iasi Cătălin-George Lefter The Romanian Mathematical Society Radu Gologan

THE CONGRESS IS ORGANIZED WITH FINANCIAL SUPPORT FROM:

Dedeman Fundaţia Familiei Menachem H. Elias - the Romanian Academy Fundaţia Patrimoniu - the Romanian Academy Fundaţia Seminarului Matematic Alexandru Myller SOFTWIN Group

The organizing institutions contributed with both financial and logistic support to the Congress.

SECTIONS

1. ALGEBRA AND NUMBER THEORY

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu

2. ALGEBRAIC, COMPLEX AND DIFFERENTIAL GEOMETRY AND TOPOLOGY

Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties

3. REAL AND COMPLEX ANALYSIS, POTENTIAL THEORY 4. ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS, VARIATIONAL METHODS, OPTIMAL CONTROL

Special session: Optimization and Games Theory

5. FUNCTIONAL ANALYSIS, OPERATOR THEORY AND OPERATOR ALGEBRAS, MATHEMATICAL PHYSICS

Special sessions: Spectral Theory and Applications in Mathematical Physics Dynamical Systems and Ergodic Theory

6. PROBABILITY, STOCHASTIC ANALYSIS, AND MATHEMATICAL STATISTICS 7. MECHANICS, NUMERICAL ANALYSIS, MATHEMATICAL MODELS IN SCIENCES

Special sessions: Mathematical Modeling of Some Medical and Biological Processes Mathematical Models in Astronomy

8. THEORETICAL COMPUTER SCIENCE, OPERATIONS RESEARCH AND MATHEMATICAL PROGRAMMING

Special session: Logic in Computer Science

9. HISTORY AND PHILOSOPHY OF MATHEMATICS

CONTENTS

Short programme Full programme Abstract 34 Index 159

FULL PROGRAMME OF THE CONGRESS

FRIDAY, June 26, 2015

9:00 - CONGRESS OPENING – Aula Magna “Mihai Eminescu”

SECTION 1: Algebra and Number Theory – room III.11

Chairman: Șerban Raianu 11:30 – 12:30 CAENEPEEL Stefaan Hopf Categories 12:30 – 13:00 POP Horia Heisenberg algebras and coefficient rings 13:00 – 15:00 LUNCH Chairman: Ghiocel Groza 15:00 – 15:30 DEACONESCU Marian Operator Theory for Finite Groups 15:30 – 16:00 POPESCU Sever - Angel On the v-extensions of a valued field (coautor Victor Alexandru) 16:00 – 16:30 COFFEE BREAK Chairman: Marian Deaconescu 16:30 – 17:00 BREAZ Simion Pure semisimple rings and direct products 17:00 – 17:30 PANAITE Florin Hom-structures 17:30 – 18:00 STAIC Mihai Operations on the Secondary Hochschild Cohomology Chairman: Viviana Ene 18:00 – 18:30 RAICU Claudiu The syzygies of some thickenings of determinantal varieties 18:30 – 19:00 ICHIM Bogdan How to compute the Stanley depth of a module 19:00 – 19:30 URSU Vasile Commutators theory in language congruences for modular algebraic system

SECTION 2 - Algebraic, Complex and Differential Geometry and Topology – room Myller

Chairman: Vasile Brînzănescu 11:30 – 12:30 MOSCOVICI Henri Modular geometry on noncommutative tori 12:30 – 13:00 ANASTASIEI Mihai Some foliations on the cotangent bundle 13:00 – 15:00 LUNCH Chairman: Marian Aprodu 15:00 – 16:00 BURGHELEA Dan Refinements of homology provided by a real or angle valued map 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 RASDEACONU Rares Counting real rational curves on K3 surfaces 17:30 – 18:00 DAMIAN Florin Hyperbolic manifolds and their representations by lens polytopes 18:00 – 18:30 BEJAN Cornelia - Livia Parallel second order tensors on Vaisman manifolds

SECTION 3 - Real and Complex Analysis, Potential Theory – room II.7

Chairman: Grigore Ștefan Salagean 11:30 – 12:00 BAYINDIR Hilal Z Approximation by generalized deferred Cesàro means in the space H p 12:00 – 12:30 BERISHA Faton On some I p -type inequalities involving quasi monotone and quasi lacunary sequences 12:30 – 13:00 KOHR Gabriela The generalized Loewner differential equation in higher dimensions. Applications to extremal problems for biholomorphic mappings 13:00 – 15:00 LUNCH Chairman: Victor Lie 15:00 – 16:00 BRACCI Filippo Univalent mappings, Horosphere boundary and prime end theory in higher dimension 16:00 – 16:30 COFFEE BREAK Chairman: Gabriela Kohr 16:30 – 17:00 IANCU Mihai Compactness and density of certain reachable families of the Loewner ODE in Cn 17:00 – 17:30 IONITA George - Ionut q-completeness and q-completeness with corners of unbranched Riemann domains 17:30 – 18:00 SALAGEAN Grigore Some characteristic properties of analytic functions Stefan 18:00 – 18:30 BUCUR Gheorghe Generalized Arzela-Ascoli theorem and applications 18:30 – 19:00 BUCUR Ileana Fixed point theory and contractive sequences

SECTION 4 - Ordinary and Partial Differential Equations, Variational Methods, Optimal Control – room I.1

Chairman: Petru Jebelean 11:30 – 12:30 MAWHIN Jean Periodic solutions of relativistic-type systems with periodic nonlinearities 12:30 – 13:00 IGNAT Radu Kinetic formulation for vortex vector fields 13:00 – 15:00 LUNCH Room II.4 Chairman: Radu Ignat 15:00 – 15:30 GAUDIELLO Antonio Homogenization of highly oscillating boundaries with strongly contrasting diffusivity 15:30 – 16:00 BEREANU Cristian Prescribed mean curvature of manifolds in Minkowski space 16:00 – 16:30 COFFEE BREAK Chairman: Antonio Gaudiello 16:30 – 17:00 KRISTALY Alexandru Gagliardo-Nirenberg inequalities on manifolds: the influence of the curvature 17:00 – 17:30 VARGA Csaba Symmetry and multiple solutions for certain quasilinear elliptic equations Chairman: Cristian Bereanu 17:30 – 18:00 MIHAILESCU Mihai On the asymptotic behavior of some classes of nonlinear eigenvalue problems involving the $p$-Laplacian 18:00 – 18:20 SERBAN Calin- Existence results for discontinuous perturbations of singular ㊾- Constantin Laplacian operator 18:20 – 18:40 FARCASEANU Maria On the spectrum of some eigenvalue problems 18:40 – 19:00 MARICA Aurora Numerical meshes ensuring uniform observability of 1d waves

SECTION 5 - Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics – room II.5

Joint Section 2 – room Myller 11:30 – 12:30 MOSCOVICI Henri Modular geometry on noncommutative tori Chairman: Marius Dadarlat 12:30 – 13:30 VASILESCU Florian - Square Positive Functionals in an Abstract Setting Horia 13:30 – 15:00 LUNCH Special session: Spectral Theory and Applications in Mathematical Physics Chairman: Stefan Teufel 15:00 – 16:00 PILLET Claude - Alain Conductance and AC Spectrum 16:00 – 16:30 COFFEE BREAK Chairman: Pavel Exner 16:30 – 17:30 TEUFEL Stefan Peierls substitution for subbands of the Hofstadter model 17:30 – 18:30 CORNEAN Horia On the construction of composite Wannier functions Chairman: Gheorghe Nenciu 18:30 – 19:00 RASMUSSEN Morten Analytic Perturbation Theory of Embedded Eigenvalues Grud 19:00 – 19:30 SAVOIE Baptiste A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit

SECTION 6 - Probability, Stochastic Analysis, and Mathematical Statistics – room III.9

Chairman: Mădălina Deaconu 11:30 – 12:30 PIRVU Traian Cumulative Prospect Theory with Skewed Return Distribution 13:00 – 15:00 LUNCH Chairman: Lucian Beznea 15:00 – 16:00 DEACONU Madalina Brownian and Bessel hitting times: new trends in their approximation 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 BALLY Vlad Asymptotic behavior for PDMP's with three regime 17:30 – 18:00 MATICIUC Lucian Viscosity solutions for functional parabolic PDEs. A stochastic approach via BSDEs with time-delayed 18:00 – 18:30 ROTENSTEIN Eduard Anticipated BSVIs with generalized reflection

Parallel session – Faculty Conference room Chairman: Anna Soos 11:30 – 12:30 MARRON, J. S. Object Oriented Data Analysis 12:30 – 13:30 PATRANGENARU Vic Two Sample Tests for Means on Lie Groups and Homogeneous Spaces with Examples 13:00 – 15:00 LUNCH

SECTION 7 - Mechanics, Numerical Analysis, Mathematical Models in Sciences – room I.3

Joint Section 2 – room I.1 11:30 – 12:30 MAWHIN Jean Periodic solutions of relativistic-type systems with periodic nonlinearities 13:00 – 15:00 LUNCH Chairman: Gabriela Marinoschi 15:00 – 15:30 MIRANVILLE Alain Some generalizations of the Cahn-Hilliard equation 15:30 – 16:00 CAVATERRA Cecilia Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions 16:00 – 16:30 COFFEE BREAK Chairman: Victor Ţigoiu 16:30 – 17:00 KOHR Mirela Boundary value problems of transmission type for the Navier- Stokes and Darcy-Forchheimer-Brinkman systems in weighted Sobolev spaces 17:00 – 17:30 POLISEVSCHI Dan The flow through fractured porous media along Beavers-Joseph interfaces 17:30 – 18:00 PASA Gelu Saffman-Taylor instability for a non-Newtonian Fluid 18:00 – 18:30 ION Stelian Water flow on vegetated hill. Shallow water equations model

Special session: Mathematical Modeling of Some Medical and Biological Processes – room II.6 Chairman: Narcisa Apreutesei 15:00 – 15:30 PRECUP Radu Mathematical models of stem cell transplantation 15:30 – 16:00 NEAMTU Mihaela Hopf bifurcation analysis for the model of the hypothalamic- pituitary-adrenal axis with distributed time dela 16:00 – 16:30 COFFEE BREAK 16:30 – 17:00 BALAN Vladimir Spectral aspects of anisotropic metric models in the Garner oncologic framework 17:00 – 17:30 RADULESCU Anca Dynamic Networks: From Connectivity to Temporal Behavior 17:30 – 18:00 ION Anca Veronica Qualitative and numerical study of a system of delay differential equations modeling leukemia 18:00 – 18:30 LITCANU Gabriela About patterns driven by chemotaxis 18:30 – 19:00 DIMITRIU Gabriel Numerical simulations of a two noncompeting species chemotaxis model 19:00 – 19:30 BADRALEXI Irina Stability analysis of some equilibrium points in a complex model for blood cells’ evolution in CML

SECTION 8 - Theoretical Computer Science, Operations Research and Mathematical Programming – room III.12

Chairman: Henri Luchian 11:30 – 12:30 ISTRAIL Sorin On Humans, Plants and Disease: Algorithmic Strategies for Haplotype Assembly Problems 13:00 – 15:00 LUNCH Special session: Logic in Computer Science Chairman: Laurentiu Leustean 15:00 – 16:00 ROSU Grigore Matching Logic 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 LUCANU Dorel Proving Reachability Properties by Circular Coinduction 17:30 – 18:30 RUSU Vlad The flow through fractured porous media along Beavers-Joseph interfaces 18:30 – 19:00 SERBANUTA Traian Pushdown Model Checking in the K Frammework

SATURDAY, June 27, 2015

SECTION 1: Algebra and Number Theory – room III.11

Chairman: Dorin Popescu 9:00 – 10:00 WELKER Volkmar Ideals of orthogonal graph representations 10:00 – 10:30 VLADOIU Marius Bouquet Algebra of Toric Ideals 10:30 – 11:00 CONSTANTINESCU Castelnuovo-Mumford regularity and triangulations of manifolds Alexandru 11:00 – 11:30 COFFEE BREAK Chairman: Volkmar Welker 11:30 – 12:00 SECELEANU Alexandra Polynomial growth for Betti numbers 12:00 – 12:30 OLTEANU Anda - Classes of path ideals and their algebraic properties Georgiana 12:30 – 13:00 ENE Viviana Ideals of 2-minors 13:00 – 15:00 LUNCH Chairman: Dragoș Ștefan 15:00 – 15:30 BOTNARU Dumitru The duality (σ,τ) 15:30 – 16:00 CERBU Olga About B-inductive semireflexive spaces 16:00 – 16:30 COFFEE BREAK 16:30 – 17:00 CHIS Mihai Some properties of autocommutator subgroups of certain p-groups 17:00 – 17:30 SZOLLOSI Istvan Computation of Hall polynomials in the Euclidean case 17:30 – 18:00 COJUHARI Elena Skew ring extensions and generalized monoid rings 18:00 – 18:30 BALAN Adriana When Hopf monads are Frobenius 18:30 – 19:00 NICHITA Florin Nonassociative Structures, Yang-Baxter Equations and Applications

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu room 2.1 Chairman: Dumitru Stamate 15:00 – 15:30 Remember Nicolae Radu 15:30 – 16:00 POPESCU Dorin A theorem of Ploski's type 16:00 – 16:30 COFFEE BREAK 16:30 – 17:00 ENESCU Florian The Frobenius complexity of a local ring 17:00 – 17:30 VRACIU Adela Totally reflexive modules for Stanley-Reisner rings of graphs 17:30 – 18:00 VELICHE Oana Intersections and Sums of Gorenstein ideals 18:00 – 18:30 IACOB Alina Gorenstein projective precovers 18:30 – 19:00 CONSTANTINESCU Towards longer-range topological properties for finite generation Adrian of subalgebras

SECTION 2 - Algebraic, Complex and Differential Geometry and Topology – room Myller

Chairman: Răzvan Liţcanu 9:00 – 10:00 MIRON Radu Lagrangian and Hamiltonian Geometries. Applications to Analytical Mechanics 10:00 – 11:00 VAISMAN Izu Generalized para-Kähler manifolds 11:00 – 11:30 COFFEE BREAK Chairman: Izu Vaisman 11:30 – 12:30 BUCATARU Ioan Projective deformations for Finsler functions 12:30 – 13:00 CONSTANTINESCU Oana Geometric inverse problems in Lagrangian mechanics 13:00 – 15:00 LUNCH Chairman: Henri Moscovici 15:00 – 16:00 CALDARARU Andrei Towards a new algebraic proof of the Barannikov-Kontsevich theorem 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 TIMOFEEVA Nadezhda A compactification of moduli of stable vector bundles on a surface by locally free sheaves 17:30 – 18:30 SABAU Sorin Convexity on Finsler manifolds

SECTION 3 - Real and Complex Analysis, Potential Theory – room II.7

Chairman: Nicolae Popa 9:00 – 10:00 LIE Victor Extremizers for the 2D Kakeya problem 10:00 – 11:00 MUSCALU Camil Iterated Fourier series 11:00 – 11:30 COFFEE BREAK Joint Section 6 – room III.9 11:30 – 12:30 TRUTNAU Gerald Recurrence criteria for diffusion processes generated by divergence free perturbations of non-symmetric energy forms 13:00 – 15:00 LUNCH Joint Section 6 – room III.9 15:00 – 16:00 HSU Elton P Brownian Motion on Complex Structures 16:00 – 16:30 COFFEE BREAK Chairman: Gheorghe Bucur 16:30 – 17:00 ATANASIU Dragu A Cauchy Functional Inequality 17:00 – 17:30 SYMEONIDIS Harmonic families of closed surfaces Eleutherius 17:30 – 18:00 OPRINA Andrei - George Perturbations with kernels of the generator of a Markov process 18:00 – 18:30 VLADOIU Speranta Markov Processes on the Lipschitz Boundary for the Neumann and Robin Problems 18:30 – 19:00 MITROI - SYMEONIDIS On some properties of Tsallis hypoentropies and hypodivergences Flavia - Corina

SECTION 4 - Ordinary and Partial Differential Equations, Variational Methods, Optimal Control – room I.1

Chairman: Viorel Barbu 9:00 – 10:00 TATARU Daniel Long time dynamics for water waves 10:00 – 11:00 TURINICI Gabriel Mathematical models of vaccination: societal and invididual views 11:00 – 11:30 COFFEE BREAK Chairman: Ioan I. Vrabie 11:30 – 12:00 GILARDI Gianni Sliding modes for a phase field system 12:00 – 12:30 GRASSELLI Maurizio Nonlocal Cahn-Hilliard equations 12:30 – 13:00 FAVINI Angelo Inverse problems from control theory 13:00 – 15:00 LUNCH Chairman: Gianni Gilardi 15:00 – 15:30 GUIDETTI Davide On recostruction of a source term depending on time and space variables in a parabolic mixed problem 15:30 – 16:00 CERNEA Aurelian Existence results for a class of quadratic integral inclusions 16:00 – 16:30 COFFEE BREAK Chairman: Maurizio Grasselli 16:30 – 17:00 COLLI Pierluigi Non-smooth regularization of a forward-backward parabolic equation 17:00 – 17:30 RADU Petronela Oscillational blow-up of traveling solutions in models for suspension bridges Chairman: Aurelian Cernea 17:30 – 18:00 VICOL Vlad Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations 18:00 – 18:30 BOCIU Lorena Controlling Turbulence in Fluid-Elasticity Interactions 18:30 – 19:00 LUCA TUDORACHE Positive solutions for a system of singular second-order integral

Rodica boundary value problems

Special session: Optimization and Games Theory – Faculty Conference Room Chairman: Constantin Zalinescu 15:00 – 15:30 BOT Radu Ioan Primal-dual algorithms for complexly structured nonsmooth convex optimization problems 15:30 – 16:00 CSETNEK Ernoe Robert An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions 16:00 – 16:30 COFFEE BREAK Chairman: Radu Ioan Boţ 16:30 – 17:00 VOISEI Mircea The local equicontinuity of a maximal monotone operator and consequences 17:30 – 18:00 LOZOVANU Dmitrii Determining the Saddle Points for Antagonistic Positional Games in Markov Decision Processes 18:00 – 18:30 TKACENKO Alexandra The fractional multi-objective transportation problem of fuzzy type 18:30 – 19:00 UNGUREANU Valeriu Strategic Games, Information Leaks, Corruption, and Solution Principles

SECTION 5 - Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics – room II.5

Special session: Spectral Theory and Applications in Mathematical Physics Chairman: Claude-Alain Pillet 9:00 – 10:00 EXNER Pavel Approximating quantum graphs by Schrödinger operators on thin networks 10:00 – 11:00 NENCIU Irina On some criteria for quantum and stochastic confinement 11:00 – 11:30 COFFEE BREAK Chairman: Horia Cornean 11:30 – 12:30 SPARBER Christof Weakly nonlinear time-adiabatic theory 12:30 – 13:00 ANGHEL Nicolae Fredholmness vs. Spectral Discreteness for First-Order Differential Operators 13:00 – 15:00 LUNCH Chairman: Christof Sparber 15:00 – 16:00 NISTOR Victor Essential spectrum of N-body Hamiltonians with asymptotically homogeneous interactions 16:00 – 16:30 COFFEE BREAK Chairman: Florin Rădulescu 16:30 – 17:30 DADARLAT Marius A generalized Dixmier-Douady theory 17:30 – 18:00 DEACONU Valentin Symmetries of graph C*-algebras Chairman: Valentin Deaconu 18:00 – 18:30 DUMITRASCU A direct proof of K-amenability for a-T-menable groups Constantin Dorin 18:30 – 19:00 FURUICHI Shigeru Some inequalities related to operator means 19:00 – 19:30 POPA Ioan - Lucian Nonuniform Exponential Trichotomies in Terms of Lyapunov Functions

SECTION 6 - Probability, Stochastic Analysis, and Mathematical Statistics – room III.9

Chairman: Vic Patrangenaru 8:00 – 9:00 HUCKEMANN Stephan On Relations Between Statistics and Geometry Chairman: Vlad Bally 9:00 – 10:00 GRADINARU Mihai Nonlinear Langevin type equation driven by stable Levy process 10:00 – 11:00 LOECHERBACH Eva Propagation of chaos for systems of interacting neurons 11:00 – 11:30 COFFEE BREAK Chairman: Mihai Grădinaru 11:30 – 12:30 TRUTNAU Gerald Recurrence criteria for diffusion processes generated by divergence free perturbations of non-symmetric energy forms 12:30 – 13:00 ROBE - VOINEA Elena - On the recursive evaluation of a certain multivariate compound Gratiela distribution 13:00 – 15:00 LUNCH Chairman: Ionel Popescu 15:00 – 16:00 HSU Elton P Brownian Motion on Complex Structures 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 BARBU Vlad - Stefan Survival analysis for semi-Markov systems Chairman: Lucian Maticiuc 17:30 – 18:00 CIUIU Daniel Bayesian good-of-fit tests: past, present and future 18:00 – 18:30 ANTON Cristina Statistical Analysis of a Cytotoxicity Model 18:30 – 19:00 CANEPA Elena Modeling and calibrating banks' demand deposits versus asset sizes

SECTION 7 - Mechanics, Numerical Analysis, Mathematical Models in Sciences – room I.3

Chairman: Viorel Barbu Joint Section 4 – room I.1 9:00 – 10:00 TATARU Daniel Long time dynamics for water waves 10:00 – 11:00 TURINICI Gabriel Mathematical models of vaccination: societal and invididual views 11:00 – 11:30 COFFEE BREAK Joint Section 4 – room I.1 11:30 – 12:00 GILARDI Gianni Sliding modes for a phase field system 12:00 – 12:30 GRASSELLI Maurizio Nonlocal Cahn-Hilliard equations 12:30 – 13:00 FAVINI Angelo Inverse problems from control theory 13:00 – 15:00 LUNCH Chairman: Liviu Marin 15:00 – 15:30 DELVARE Franck Fading regularization method for Cauchy problems associated with elliptic operators 15:30 – 16:00 PASCAN Raisa Elastoplastic models with continuously distributed defects: dislocations and disclinations, for finite and small strains 16:00 – 16:30 COFFEE BREAK Chairman: Sanda Ţigoiu 16:30 – 17:00 STRUGARU Magdalena Simulation of necking phenomenon in a polyconvex material 17:00 – 17:30 CRACIUN Eduard - Cracks propagation in prestressed and prepolarized piezoelectric Marius materials 17:30 – 18:00 CAPATINA Anca A quasistatic frictional contact problem with normal compliance and unilateral constraint

Special session: Mathematical Modeling of Some Medical and Biological Processes – room II.6 Chairman: Andrei Halanay 15:00 – 15:30 POPOVICI Irina Border-Collision Bifurcations in A Piece-Wise Smooth Planar Dynamical System Associated with Cardiac Potential 15:30 – 16:00 KASLIK Eva Dynamical analysis of a fractional-order Hindmarsh-Rose model 16:00 – 16:30 COFFEE BREAK 16:30 – 17:00 RADULESCU Rodica Optimal control of Imatinib treatment in a competition model of Chronic Myelogenous Leukemia with immune response 17:00 – 17:30 TARFULEA Nicoleta A hybrid mathematical model for cell motility in angiogenesis 17:30 – 18:00 GEORGESCU Paul Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito

SECTION 8 - Theoretical Computer Science, Operations Research and Mathematical Programming – room III.12

Special session: Logic in Computer Science Chairman: Grigore Roșu 9:00 – 10:00 MARDARE Radu Stone Dualities for Markov Processes 10:00 – 11:00 POPESCU Andrei A Conference Management System with Verified Document Confidentiality 11:00 – 11:30 COFFEE BREAK 11:30 – 12:00 BARONI Marian Order locatedness and strong extensionality in constructive Alexandru mathematics 12:00 – 12:30 SIPOS Andrei Codensity and Stone spaces 13:00 – 15:00 LUNCH Chairman: Adrian Iftene 15:00 – 16:00 BAZGAN Cristina Most vital elements of graphs 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 ZARA Catalin Tolerance Distances on Minimal Coverings 17:30 – 18:00 MANDRESCU Eugen The independence polynomial of a well-covered graph at -1 18:00 – 18:30 SIMION Emil Statistical tests in cryptographic evaluation 18:30 – 19:00 BARONI Mihaela Phylogenetic networks: mathematical models and algorithms Carmen

MONDAY, June 29, 2015

SECTION 1: Algebra and Number Theory – room III.11

Joint Section 3 – room II.7 9:00 – 10:00 DEMETER Ciprian Decouplings and applications to Number Theory and PDEs Chairman: Daniel Bulacu 10:00 – 11:00 CHINDRIS Calin On the invariant theory of string algebras 11:00 – 11:30 COFFEE BREAK Chairman: Mihai Cipu 11:30 – 12:00 GROZA Ghiocel On the analytic functions with p-adic coefficients 12:00 – 12:30 BONCIOCAT Nicolae Ciprian Some applications of the resultant to factorization problems 12:30 – 13:00 COCONET Tiberiu Module covers and the Green correspondence 13:00 – 15:00 LUNCH Chairman: Călin Chindriș 15:00 – 16:00 STANCU Radu Extentions of cohomological Mackey functors 16:00 – 16:30 COFFEE BREAK Chairman: Stefaan Caenepeel 16:30 – 17:00 RAIANU Serban A Coring Version of External Homogenization for Hopf Algebras 17:00 – 17:30 BULACU Daniel Frobenius and separable functors for the category of generalized entwined modules 17:30 – 18:00 MILITARU Gigel The factorization problem and related questions Chairman: Radu Stancu 18:00 – 18:30 BURCIU Sebastian On the irreducible representations of Drinfeld doubles 18:30 – 19:00 AGORE Ana Jacobi and Poisson algebras 19:00 – 19:30 TODEA Constantin - Cosmin Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups

SECTION 2 - Algebraic, Complex and Differential Geometry and Topology – room Myller

Chairman: Liviu Ornea 9:00 – 10:00 MUNTEANU Ovidiu Four dimensional Ricci solitons 10:00 – 11:00 SUVAINA Ioana Asymptotically Locally Euclidean Complex Surfaces 11:00 – 11:30 COFFEE BREAK Chairman: Ioan Suvaina 11:30 – 12:30 VILCU Costin Baire categories for Alexandrov surfaces 12:30 – 13:00 CIOBAN Mitrofan Distances, boundedness and fixed point theory 13:00 – 13:30 COSTINESCU Cristian An equivariant generalization of the Segal's finiteness theorem 13:30 – 15:00 LUNCH Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties Chairman: Ștefan Papadima 15:00 – 16:00 MAXIM Laurentiu Motivic infinite cyclic covers 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 BURGHELEA Dan Monodromy / Alexander rational function of a circle valued map 17:30 – 18:30 NICOLAESCU Liviu A stochastic Gauss-Bonnet-Chern formula

SECTION 3 - Real and Complex Analysis, Potential Theory – room II.7

Chairman: Camil Muscalu 9:00 – 10:00 DEMETER Ciprian Decouplings and applications to Number Theory and PDEs 10:00 – 11:00 IORDAN Andrei Non existence of Levi flat hypersurfaces with positive normal bundle in compact K 11:00 – 11:30 COFFEE BREAK Chairman: Andrei Iordan 11:30 – 12:00 JOITA Cezar Finite coverings of complex spaces by connected Stein open sets 12:00 – 12:30 PREDA Ovidiu Locally Stein Open Subsets in Normal Stein Spaces 13:00 – 15:00 LUNCH Chairman: Elona Agora 15:00 – 15:30 MARCOCI Anca Nicoleta Improved Sobolev inequalities in the classical Lorentz spaces 15:30 – 16:00 MARCOCI Liviu Gabriel On some factorization results 16:00 – 16:30 COFFEE BREAK Chairman: Liviu Florescu 16:30 – 17:00 AGORA Elona Weak and strong type boundedness of Hardy-Littlewood maximal operator on weighted Lorentz spaces 17:00 – 17:30 MOCANU Marcelina Cheeger differentiable Orlicz-Sobolev functions on metric spaces 17:30 – 18:00 CRISTEA Mihai Some properties of open discrete ring mappings 18:00 – 18:30 APREUTESEI Gabriela Semiliniarity of space of sn-bounded multifunctions 18:30 – 19:00 DEGER Ugur On Approximation by Matrix Means of the Multiple Fourier Series in the Hölder 19:00 – 19:30 YASEMIN GOLBOL Sibel On Some Spaces of Sequences of Interval Numbers

SECTION 4 - Ordinary and Partial Differential Equations, Variational Methods, Optimal Control – room I.1

Chairman: Gabriel Turinici 9:00 – 10:00 MOSCO Umberto Time, grids, similarity 10:00 – 11:00 MARIS Mihai On some minimization problems in RN: the concentration- compactness principle revisited 11:00 – 11:30 COFFEE BREAK Chairman: Daniel Tataru 11:30 – 12:00 TARFULEA Nicolae On Constrained Wave Propagation 12:00 – 12:30 KIRR Eduard - Wilhelm Large Solitary Waves via Global Bifurcation Methods 13:00 – 15:00 LUNCH Chairman: Mihai Mariș 15:00 – 15:30 IGNAT Liviu Dispersion property for Schrödinger equations 15:30 – 16:00 GUTU Valeriu Shadowing pseudo-orbits in set-valued dynamics 16:00 – 16:30 COFFEE BREAK Chairman: Liviu Ignat 16:30 – 17:00 SEREA Oana Discontinuous control problems and optimality conditions via occupational measures 17:00 – 17:20 SATCO Bianca Mild solutions for functional semilinear evolution equations Chairman: Valerian Gutu 17:20 – 17:40 RUSU Galina Some singularly perturbed Cauchy problems for abstract linear differential equations with positive powers of a positive defined operator 17:40 – 18:00 CIUBOTARU Stanislav Transvectants and Lyapunov quantities for bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree 18:00 – 18:20 STANCU - DUMITRU Denisa A Baouendi-Grushin type operator in Orlicz-Sobolev spaces and applications to PDEs 18:20 – 18:40 BAKSI Ozlem Some inequalities about the eigenvalues of a two terms differential operator and the sum of the eigenvalues of that operator

SECTION 5 - Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics – room II.5

Special session: Dynamical Systems and Ergodic Theory Chairman: Florian-Petre Boca 9:00 – 9:30 MIHAILESCU Eugen Ergodic and metric properties of certain invariant measures on fractals 9:30 – 10:00 FALK Kurt Conformal ending measures on limit sets of Kleinian groups 10:00 – 10:30 RADU Remus Semi-indifferent dynamics 10:30 – 11:00 TANASE Raluca Stability and continuity of Julia sets in C2 11:00 – 11:30 COFFEE BREAK Chairman: Eugen Mihăilescu 11:30 – 12:30 BOCA Florin - Petre The distribution of rational numbers and ergodic theory 12:30 – 13:00 DUTKAY Dorin Fourier series on fractals 13:00 – 15:00 LUNCH Chairman: Nicolae Danet 15:00 – 15:30 PALTANEA Radu On equivalence of K-functionals and weighted moduli of continuity 15:30 – 16:00 TALPAU DIMITRIU Maria On some second order moduli of continuity 16:00 – 16:30 COFFEE BREAK Chairman: Florian-Horia Vasilescu 16:30 – 17:00 DANET Nicolae Closure sublinear operators and their use to the Dedekind completion of a Riesz space 17:00 – 17:30 DANET Rodica - Mihaela The most important challenge in the interval analysis. Historical notes and how we can overcome the barrier via extension results 17:30 – 18:00 POPESCU Marian - Valentin Collectively coincidence results in some classes of topological spaces Chairman: Cezar Joiţa 18:00 – 18:30 CATANA Viorel An example of twisted bi-Laplacian and its spectral properties 18:30 – 19:00 DZHUNUSHALIEV Vladimir Supersymmetry, nonassociativity, and Big Numbers 19:00 – 19:30 SAH Ashok Kumar Irregular Weyl-Heisenberg wave packet frames generated by hyponormal operators

SECTION 6 - Probability, Stochastic Analysis, and Mathematical Statistics – room III.9

Chairman: Mihai Grădinaru 9:00 – 10:00 GOREAC Dan Asymptotic Control of Switch Processes in Systems Biology 10:00 – 11:00 PASCU Mihai N. Brownian Couplings and Applications 11:00 – 11:30 COFFEE BREAK 11:30 – 12:30 MATZINGER Henry Sample Size Needed for Estimating Principal Component 12:30 – 13:00 VON DAVIER Alina A. Psychometric Applications: Parameter Estimation and Comparability of Test Performance in Multistage Testing 13:00 – 15:00 LUNCH Chairman: Mihai Pascu 15:00 – 15:30 CIMPEAN Iulian A new approach to the existence of invariant measures for Markovian semigroups 15:30 – 16:00 CLIMESCU - HAULICA Voiculescu's free entropy and spectral analysis of random Adriana graphs 16:00 – 16:30 COFFEE BREAK Chairman: Traian Pîrvu 16:30 – 17:00 MOCIOALCA Oana Stochastic modeling of compositional data with diffusions 17:00 – 17:30 DE LA CRUZ CABRERA Stochastic aspects of Single Cell Analysis Omar 17:30 – 18:00 UNGUREAN Viorica Stabilizing solution for modified algebraic Riccati equations in infinite dimensions 18:00 – 18:30 SOOS Anna Stochastic spline fractal interpolation functions

SECTION 7 - Mechanics, Numerical Analysis, Mathematical Models in Sciences – room I.3

Joint Section 4 – room I.1 9:00 – 10:00 MOSCO Umberto Time, grids, similarity 10:00 – 11:00 MARIS Mihai On some minimization problems in RN: the concentration- compactness principle revisited 11:00 – 11:30 COFFEE BREAK Chairman: Pierluigi Colli 11:30 – 12:00 IANNELLI Mimmo A model for describing the structure and growth of epidermis 12:00 – 12:30 CASCAVAL Radu Optimization and Control in Vascular Networks 13:00 – 15:00 LUNCH Chairman: Alain Miranville 15:00 – 15:30 POPA Constantin On Single Projection Kaczmarz Extended-Type Algorithms 15:30 – 16:00 GALES Catalin Bogdan Dynamics of space debris: resonances and long term orbital effects 16:00 – 16:30 COFFEE BREAK Chairman: Cecilia Cavaterra 16:30 – 17:00 PETCU Madalina Parallel matrix function evaluation via initial value ODE modelling 17:00 – 17:30 DRAGANESCU Andrei Optimal Order Multigrid Preconditioners for Linear Systems Arising in the Semismooth Newton Method Solution Process of a Class of Control-Constrained Problems 17:30 – 18:00 GHEORGHIU Calin - Ioan From Separation of Variables to Multiparameter Eigenvalue Problems. Numerical Aspects

SECTION 8 - Theoretical Computer Science, Operations Research and Mathematical Programming – room III.12

Special session: Logic in Computer Science Chairman: Radu Mardare 9:00 – 10:00 DIMA Catalin The automata-logic duality for temporal epistemic frameworks 10:00 – 11:00 TIPLEA Ferucio Laurentiu Symbolic and computational models for security policies and protocols 11:00 – 11:30 COFFEE BREAK Joint Section 9 – room II.6 11:30 – 12:30 MARCUS Solomon Arrow and Conway in spectacle: the impossibilitytheorem and the cosmological theorem 13:00 – 15:00 LUNCH Special session: Logic in Computer Science Chairman: Cătălin Dima 15:00 – 16:00 MINEA Marius Modeling and verification of security for web applications and services 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 CIOBANU Gabriel Probabilistic Logic for Timed Migration 17:30 – 18:00 ARUSOAIE Andrei Language Independent Symbolic Execution 18:00 – 18:30 CIOBACA Stefan Proving Program Equivalence

SECTION 9 - History and Philosophy of Mathematics – room II.6

Chairman: Christophe Eckes 9:00 – 9:30 BARBOSU Mihai Mathematics: Current State and Future Direction 9:30 – 10:00 STEFANESCU Doru Petre Sergescu and the rebirthing of Bret's theorems 10:00 – 11:00 BRECHENMACHER Frederic The 1874 controversy between Camille Jordan and Leopold Kronecker 11:00 – 11:30 COFFEE BREAK Chairman: Dragoș Vaida 11:30 – 12:30 MARCUS Solomon Arrow and Conway in spectacle: the impossibilitytheorem and the cosmological theorem 13:00 – 15:00 LUNCH Chairman: Doru Ștefănescu 15:00 – 16:00 CIOBANU Gabriel Axiom of Choice in Finitely Supported Mathematics 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 VAIDA Dragos Dan Barbilian at the 120 years anniversary.The contribution of Dan Barbilian in the history and philosophy of mathematics 17:30 – 18:00 VERNESCU Andrei Some Aspects in the History of Mathematics in Romania

TUESDAY, June 30th

SECTION 1: Algebra and Number Theory – room III.11

Chairman: Adrian Diaconu 9:00 – 10:00 JONES Nathan The distribution of class groups of imaginary quadratic fields 10:00 – 11:00 COJOCARU Alina Arithmetic properties of the Frobenius traces of an abelian variety Carmen 11:00 – 11:30 COFFEE BREAK Chairman: Nathan Jones 11:30 – 12:00 NASTASESCU Constantin Are graded semisimple algebras symmetric? 12:00 – 12:30 RUDEANU Sergiu Most general forms in the study of Boolean equations 12:30 – 13:00 STEFANESCU Doru Irreducibility criteria for polynomials over discrete valuation domains 13:00 – 15:00 LUNCH Chairman: Alina Cojocaru 15:00 – 16:00 LENART Cristian A combinatorial model for Kirillov-Reshetikhin crystals and applications 16:00 – 16:30 COFFEE BREAK Chairman: Cristian Lenart 16:30 – 17:00 CIPU Mihai Recent advances in the study of Diophantine quintuples 17:00 – 17:30 ANTON Marian From class field to arithmetic group cohomology Chairman: Doru Ștefănescu 17:30 – 18:00 STAMATE Dumitru Ungraded strongly Koszul rings 18:00 – 18:30 CIMPOEAS Mircea On intersections of complete intersection ideals 18:30 – 19:00 ZAROJANU Andrei On the Stanley Depth

POSTER SESSION - Sala Pașilor pierduţi POPOVICI Florin A Simple Proof of Fermat's Last Theorem for n=4 and n=6 19:00 – 19:30 SMITH - TONE Daniel Quantum-Resistant Public Key Cryptography YARAHMADI Zahra Ideal cimaximal graph and its application

SECTION 2 - Algebraic, Complex and Differential Geometry and Topology – room Myller

Chairman: Dan Burghelea 9:00 – 10:00 BERCEANU Barbu De la alfabetul Artin la alfabetul Garside Rudolf 10:00 – 11:00 SUCIU Alexandru Topology of complex line arrangements 11:00 – 11:30 COFFEE BREAK Chairman: Alexandru Suciu 11:30 – 12:30 PAUNESCU Laurentiu Proof of Whitney fibering conjecture 12:30 – 13:30 TIBAR Mihai Topology of real polynomial maps 13:30 – 15:00 LUNCH Chairman: Barbu Berceanu 15:00 – 16:00 MACINIC Anca (Multi)nets and monodromy 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 SECELEANU Alexandra Symbolic powers and line arrangements 17:30 – 18:30 POPESCU Clement Radu Flat connections and resonance varieties of rank larger than 1

POSTER SESSION - Sala Pașilor pierduţi CUZUB Stefan Andrei Models of Belyi Covers MASCA Ioana Monica On the geometry of Finsler manifolds with reversible geodesics 18:30 – 19:30 MUNTEANU Marius Nonhomogeneous Metric Foliations POPA Alexandru Space duality as instrument for construction of new geometries POPOVICI Elena On the volume of complex indicatrix

SECTION 3 - Real and Complex Analysis, Potential Theory – room II.7

Chairman: Liviu Ignat 9:00 – 9:30 CIRSTEA Florica Existence and classification of singular solutions to nonlinear elliptic equations with a gradient term 9:30 – 10:00 CAZACU Cristian Optimal Hardy constants for Schrodinger operators with multi- singular inverse-square potentials Joint Section 6 – room I.1 10:00 – 11:00 ROECKNER Michael A new approach to stochastic PDE 11:00 – 11:30 COFFEE BREAK Chairman: Constantin Niculescu 11:30 – 12:30 NISHIO Masaharu Harmonic Bergman spaces with radial measure weight on the ball 13:00 – 15:00 LUNCH Chairman: Nicolae Pascu 15:00 – 15:30 BREAZ Nicoleta Mocanu and Serb univalence criteria for some integral operators 15:30 – 16:00 BREAZ Daniel Some new classes of analytic functions 16:00 – 16:30 COFFEE BREAK Chairman: Masaharu Nishio 16:30 – 17:00 FLORESCU Liviu Direct methods through convergence in measure 17:00 – 17:30 BENFRIHA Habib Nearly saturation, balayage and fine carrier in excessive structures 17:30 – 18:00 ANDREI Anca On Loewner domains in metric spaces 18:00 – 18:30 PASCU Nicolae Univalence Criteria for analytic functions defined in non-convex domains 18:30 – 19:00 MINCULETE Nicusor An improvement of Gruss inequality

SECTION 4 - Ordinary and Partial Differential Equations, Variational Methods, Optimal Control – room II.4

Chairman: Sorin Micu 9:00 – 9:30 BOCEA Marian Relaxation and Duality for the L∞ Optimal Mass Transport Problem 9:30 – 10:00 CASTRO Carlos Null controllability of coupled systems of PDE's Joint Section 6 – room I.1 10:00 – 11:00 ROECKNER Michael A new approach to stochastic PDE 11:00 – 11:30 COFFEE BREAK Chairman: Radu Precup 11:30 – 12:00 GAL Ciprian G On reaction-diffusion equations with anomalous diffusion and various boundary conditions 12:00 – 12:30 PERJAN Andrei Singularly perturbed problems for abstract differential equations of second order in Hilbert spaces 12:30 – 13:00 DRAGAN Vasile On the bounded and stabilizing solution of a generalized Riccati differential 13:00 – 15:00 LUNCH Chairman: Carlos Castro 15:00 – 15:30 SHIRIKYAN Armen Global stabilisation for damped-driven conservation laws 15:30 – 16:00 ZARNESCU Arghir Partial regularity and smooth topology-preserving approximations of rough domains 16:00 – 16:30 COFFEE BREAK Chairman: Andrei Perjan 16:30 – 17:00 VARVARUCA Eugen Global bifurcation of steady gravity water waves with critical layers

POSTER SESSION – Sala Pașilor pierduţi ARAMA Bianca - Elena The cost of approximate controllability and an unique continuation result at initial time for the Ginzburg-Landau equation ISAIA Florin Non-existence results of higher-order regular solutions for the p(x)- Laplacian KIZILBUDAK CALISKAN Calculated of regularized trace of a fourth order regular differential Seda equation 17:00 – 18:00 MUNTEANU Laura An Algorithm for Generating Maximal Simulation Relations in Geometric Control Theory NEGRESCU Alexandru Controllability for the vibrating string equation with Neumann boundary conditions OMAR Benniche Approximate viability on graphs OZCUBUKCU Zerrin Calculated the regularized trace of a fourth order regular differential equation

SECTION 5 - Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics – room II.5

Chairman: Nicolae Popa 9:00 – 9:30 COSTARA Constantin Complex analysis and spectral isometries 9:30 – 10:00 GOK Omer On Boolean Algebras of Projections of Finite Multiplicity 10:00 – 10:30 GHEONDEA Aurelian Interpolation for completely positive maps 10:30 – 11:00 OLTEANU Cristian Octav On Markov moment problem and its applications 11:00 – 11:30 COFFEE BREAK Chairman: Constantin Costara 11:30 – 12:00 VALUSESCU Ilie On the maximal function model of a contraction operator 12:00 – 12:30 POPA Nicolae Abel-Schur multipliers on Banach spaces of infinite matrices 12:30 – 13:00 BADEA Gabriela On the summing properties of the multilinear operators on a cartezian product of c{0}(X) spaces 13:00 – 15:00 LUNCH Chairman: Serban Stratila 15:00 – 16:00 ZSIDO Laszlo Hilbert Space Geometry problems occurring in the Tomita-Takesaki Theory 16:00 – 16:30 COFFEE BREAK Chairman: Laszlo Zsido 16:30 – 17:30 STRATILA Serban Commutation and Splitting Theorems for von Neumann Algebras 17:30 – 18:00 PAUNESCU Liviu Almost commuting permutations are near commuting permutations 18:00 – 18:30 JOITA Maria Pro-C*-correspondences Chairman: Radu Purice 18:30 – 19:00 MUNTEANU Radu Non singular automorphisms and dimension spaces 19:00 – 19:30 MORADI Sirous On a generalization of Ciric fixed point in best approximation

SECTION 6 - Probability, Stochastic Analysis, and Mathematical Statistics – III.9

Chairman: Gerald Trutnau 9:00 – 10:00 LUPASCU Oana Branching processes and the fragmentation equation 10:00 – 11:00 ROECKNER Michael A new approach to stochastic PDE 11:00 – 11:30 COFFEE BREAK Chairman: Oana Lupașcu 11:30 – 12:00 NOVAC Ludmila Approach of the Currency Exchange Risk 17:00 – 17:30 LAZARI Alexandru Geometric Programming Models for Dynamical Decision Stochastic Systems with Final Sequence of States 13:00 – 15:00 LUNCH 15:00 – 15:30 TONE Cristina A new approach to the existence of invariant measures for Markovian semigroups 16:00 – 16:30 COFFEE BREAK

SECTION 7 - Mechanics, Numerical Analysis, Mathematical Models in Sciences – room I.3

Chairman: Mădălina Petcu 9:00 – 9:30 OPREA Iuliana Spatiotemporal compex dynamics in anisotropic fluids 9:30 – 10:00 CARABINEANU Aerodynamics coefficients of a thin oscillating airfoil in subsonic flow Adrian 10:00 – 10:30 BIRSAN Mircea On the 6-parameter shell model derived from the three-dimensional Cosserat theory of elasticity 11:00 – 11:30 COFFEE BREAK Chairman: Doru Suran 11:30 – 12:00 BARBOSU Mihai RIT's Cubesat Project 12:00 – 12:30 CHIRUTA Ciprian Rein's Model for the Restricted Eliptic Three-Body Problem with drag 13:00 – 15:00 LUNCH Chairman: Ciprian Chiruţă 15:00 – 15:30 PRICOPI Dumitru Modelling of pulsations of giant stars 15:30 – 16:00 SURAN Marian Doru Exploring the Space of Stellar Parameters for PLATO2 Space Mission Targets Using CESAM2k and LNAWENR/ROMOSC Codes 16:00 – 16:30 COFFEE BREAK

POSTER SESSION - Sala Pașilor pierduţi BUCUR Andreea - Some non-standard problems related with the mathematical model of Valentina thermoviscoelasticity with voids CONSTANTIN Diana The Black Hole Effect and theGravitational Redshift Computation in Rodica the Frame of Post – Newtonian Type Garavitational Fields DMITRIEVA Irina Investigation of Specific Electromagnetic Field Problems Using Systems of Partial Differential Equations SECRIERU Ivan The stable approximate schemes for the evolution equation of the plane fractional diffusion process MIGDALOVICI Marcel On the separation property between stable and unstable zones of the dynamical systems and it implications MOROSANU Costică Well-posedness for a phase-field transition system endowed with a polynomial nonlinearity and a general class of nonlinear dynamic boundary conditions NEDELCU Dan Alin The J5:2 mean motion resonance as a new source of H-chondrites 16:30 – 18:30 MUNTEAN Angela On the raindrop motion NICOLESCU Bogdan Some considerations on Reynolds' equation for the lubricant thin films POP Nicolae Quasistatic contact problems for viscoelastic bodies POPESCU Emil Two-body problem associated to Buckingham potential POPESCU Nedelia Fractional kinetic equations as a model of intermittent bursts in solar Antonia wind turbulence RIBACOVA Galina Computational scheme for drift-diffusion equations in multiply connected domain SADIKU Murat Algorithms for Accelerating Convergence of Power Series by means of Euler Type Operators SEICIUC Vladislav Direct-approximate methods in solving some classes of singular integral equations defined on arbitrary smooth closed contours VLAD Serban E. Asynchronous flows: the technical condition of proper operation and its generalization

SECTION 8 - Theoretical Computer Science, Operations Research and Mathematical Programming – room III.12

Special session: Logic in Computer Science Chairman: Gabriel Ciobanu 9:00 – 10:00 PRUNESCU Mihai Recurrent many-dimensional sequences over finite alphabets 10:00 – 11:00 PETRE Luigia A Theory of Service Composition 11:00 – 11:30 COFFEE BREAK 11:30 – 12:00 DIACONESCU Denisa Automata, Logic and Stone Duality 12:00 – 12:30 POPOVICI Matei Semantic variants of (truely) perfect recall in Alternating-Time Temporal Logic 13:00 – 15:00 LUNCH Chairman: Cristina Bâzgan 15:00 – 16:00 PETRE Ion Modeling with Exploration Systems 16:00 – 16:30 COFFEE BREAK 16:30 – 17:30 AMAN Bogdan Mobility Types for Cloud Computing 17:30 – 18:00 TACHE Rozica - Maria Extremal cacti graphs for general sum-connectivity index and Narumi-Katayama index

SECTION 9 - History and Philosophy of Mathematics – room II.6

Chairman: Frederic Brechenmacher 9:00 – 9:30 GIURGESCU Patricia Aspects of parameter estimation 9:30 – 10:30 ECKES Christophe The correspondence between Hermann Weyl and Erich Hecke 10:30 – 11:00 NICULESCU Constantin Tiberiu Popoviciu and his contribution to convex functions theory 11:00 – 11:30 COFFEE BREAK Chairman: Constantin Niculescu 11:30 – 12:30 DEACONESCU Marian Mathematical archaeology: Art Nouveau 12:30 – 13:00 IONITA Cătălin The Concept of a Real Definition and that of Real Numbers 13:00 – 15:00 LUNCH

WEDNESDAY, July 1st

SECTION 1: Algebra and Number Theory – room Myller

Chairman: Andrei Marcus 9:00 – 10:00 POPA Alexandru On the trace formula for Hecke operators Anton 10:00 – 11:00 DIACONU Adrian Non-vanishing of quadratic twists of automorphic L-functions 11:00 – 11:30 COFFEE BREAK Chairman: Alexandru Popa 11:30 – 12:00 PASOL Vicentiu p-adic Analytic Functions from Recurrence Sequences 12:00 – 12:30 COBELI Cristian On the Dew Line in Circle Packings

SECTION 3 - Real and Complex Analysis, Potential Theory – room II.7

Chairman: Marcelina Mocanu 9:00 – 9:30 NEAGU Vasile On the algebra of singular operators with shift 9:30 – 10:00 GHISA Dorin On the Location of the Zeros of Bohr Functions 10:00 – 10:30 OROS Georgia Irina Strong differential superordination and Sandwich theorem obtained with some new integral operators 11:00 – 11:30 COFFEE BREAK

SECTION 5 - Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics – room II.5

Chairman: Aurelian Gheondea 9:00 – 9:30 SEZER Yonca About The Regularized Trace Of A Self Adjoint Differential Operator 9:30 – 10:00 NOMURA Takaaki Realizing homogeneous cones through oriented graphs 10:00 – 10:30 CROITORU Anca On weak linear spaces 10:30 – 11:00 STAMATE Elena - Vector integrals for multifunctions Cristina 11:00 – 11:30 COFFEE BREAK Chairman: Dan Timotin 11:30 – 12:00 POSTOLICA Vasile Isac's cones 12:00 – 12:30 SHARMA Preeti On approximation properties of generalization of Kantorovich-type discrete q-Beta operators

ABSTRACT

Section 1 Algebra and Number Theory

Jacobi and Poisson algebras

AGORE Ana

Vrije Universiteit Brussel, Belgium Coauthors: G. Militaru

Jacobi/Poisson algebras are algebraic counterparts of Jacobi/Poisson manifolds. We introduce representations of a Jacobi algebra A and Frobenius Jacobi algebras as symmetric objects in the category. A characterization theorem for Frobenius Jacobi algebras is given in terms of integrals on Jacobi algebras. For a vector space V a non-abelian cohomological type object JH2, (V,,A) is constructed: it classiﬁes all Jacobi algebras containing A as a subalgebra of codimension equal to dim(V ). Representations of A areusedinorderto give the decomposition of JH2, (V,,A) as a coproduct over all Jacobi A-module structures on V . The bicrossed product P bowtieQ of two Poisson algebras recently introduced by Ni and Bai appears as a special case of our construction. A new type of deformations of a given Poisson algebra Q is introduced and a cohomological type object HA2(P,,Q | (,,,,,,)) is explicitly constructed as a classifying set for the bicrossed descent problem for extensions of Poisson algebras. Several examples and applications are provided.

From class ﬁeld to arithmetic group cohomology

ANTON Marian

Central Connecticut State University and IMAR, USA and Romania

There are a few known examples of arithmetic groups for which the mod p cohomology is a free module over the ring of Chern classes. A. D. Rahm and M. Wendt have recently conjectured that this property is true for a class of arithmetic groups if the rank of the group is smaller than p and each cohomology class is detected on some ﬁnite subgroup. In this talk we present a preliminary report on the current status of their conjecture.

When Hopf monads are Frobenius

BALAN Adriana

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

Under suitable exactness assumptions, a Hopf monad T on a monoidal category C having as right adjoint a Hopf comonad G is shown to be also a Frobenius monad, if TI and GI are isomorphic (right) Hopf T -modules (in particular, TI is a Frobenius algebra), where I denotes the unit object of C. If additionally the underlying base category is autonomous, then a Hopf monad T becomes also a Frobenius monoidal functor.

37 38

Some applications of the resultant to factorization problems

BONCIOCAT Nicolae Ciprian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We present a method to obtain information on the factorization of two polynomials using the canonical decomposition of their resultant. In particular we obtain irreducibility criteria for pairs of polynomials whose resultant is a prime number. As another application we provide irreducibility conditions for polynomials that take a prime value, and for polynomials obtained by expressing prime numbers by quadratic forms. The use of the resultant in the study of linear combinations of relatively prime polynomials is also discussed. Similar results will be provided for multivariate polynomials over an arbitrary ﬁeld. We will ﬁnally give a method to compute the resultant using linear recurrence sequences.

The duality (σ, τ )

BOTNARU Dumitru

State University from Tiraspol, Moldova

In the category C2V of the locally convex topological vector Hausdorff spaces we denote by B the class of bijective morphisms ε b :(E,u) −→ (F, v)forwhich(E,u) =(F, v) and Rε(S) the class of all reflective subcategories R is closed under B-subobjects and B-factorobjects. Let S be the subcategory of the spaces with weak topology, Γ0 - the subcategory of locally complete spaces, and R the lattice of all nonzero reflective subcategories. ε Theorem 1. For any element R∈Rε(S) there is an element Γ ∈ R so that Γ0 ⊂ Γ and R = S∗sr Γ0,whereS∗sr Γ0 is the semireflexive product of the elements S and Γ (see [1]). For any morphism f :(E,u) −→ (F, v) we take in correspondence the morphism f : Fτ −→ Eτ , where the dual spaces possess the Mackey topology. There was defined a contravariant functor dτ : C2V−→C2V. Theorem 2. The functor dτ is right exact and transfers the products into sums. Denote by M the coreflective subcategory of the spaces with Mackey topology, K(M) the class of the coreflective subcategories that is contained in the M subcategory. For any A⊂C2V subcategory we denote by δ(A) the full subcategory from C2V defined on the class of object {dτ (X) | X ∈| A |}. −1 If A∈K(M)denotebyδ (A) the full subcategory from C2V defined by the class of objects {X ∈| C2V|,dτ (X) ∈| A |}. Theorem 3. 1. If R∈R, then δ(R) ∈ K(M). −1 ε 2. If A∈K(M), then δ (A) ∈ Rε(S). 3. Let C⊂Rand R∈R.Thenδ(R)=M. −1 4. Let R∈R.ThenM∗d R = δ δ(R),whereM∗d R is the right product of the M and R elements (see [2]). −1 ε 5. Let R∈R.Thenδ δ(R) is the first element of the class Rε(S) that contains the R element. ε ε 6. The maple δ sets an isomorphism of the Rε(S) and K(M) − δ : Rε(S) −→ K(M) lattices. ε 7. The lattices Rε(S) and M contains a proper class of elements. References 1. Botnaru D., Cerbu O. – Semireflexive product of two subcategories, Proc. of the 6th Congress of Romanian Math., Bucharest, 2007, v.1, p. 5-19. 2. Botnaru D., Turcanu A. – The factorization of the right product of two subcategories, ROMAI J., 2010, v.VI, Nr.2, p. 41-53.

Pure semisimple rings and direct products

BREAZ Simion

Babes-Bolyai University, Romania 39

We present some characterizations for pure-semisimple rings which involve direct products of modules. One of them depends on the (non-)existence of some large cardinals: Let R be a ring and let W be the direct sum of all finitely presented right R-modules. Under the set theoretic hypothesis (V = L), the ring R is right pure semisimple if and only if there exists a cardinal λ such that Add(W ) ⊆ Prod(W (λ)). Moreover, there is a set theoretic model such that for every ring R there exists a cardinal λ such that Add(W ) ⊆ Prod(W (λ)). On the other side, we will see that a left pure-semisimple ring R is of finite representation type (i.e. it is right pure-semisimple) if and only if for every finitely presented left R-module M the right R-module HomZ(M, Q/Z ) is Mittag-Leffler.

Frobenius and separable functors for the category of generalized entwined modules

BULACU Daniel

University of Bucharest, Romania Coauthors: S. Caenepeel and B. Torrecillas

The explicit structure of a cowreath in a monoidal category C leads to the notion of generalized entwined module in a C-category. A cowreath can be identiﬁed with a coalgebra X in the Eilenberg-Moore category EM(C)(A), for some algebra A in C, and the Frobenius or separable property of the forgetful functor from the category of generalized entwined modules to the category of representations over A is transferred to the coalgebra X and vice-versa.

On the irreducible representations of Drinfeld doubles

BURCIU Sebastian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

A description of all the irreducible representations of generalized quantum doubles associated to skew pairings of semisimple Hopf algebras is given. In particular, a description of the irreducible representations of semisimple Drinfeld doubles is obtained in this way. We also give a formula for the tensor product of any two such irreducible representations. Using this formula new information on the structure of the Grothendieck rings of these generalized quantum doubles is obtained.

Hopf Categories

CAENEPEEL Stefaan

Vrije Universiteit Brussel, Belgium Coauthors: Eliezer Batista, Joost Vercruysse

We introduce Hopf categories enriched over braided monoidal categories. The notion is linked to several recently developed notions in Hopf algebra theory, such as Hopf group (co)algebras, weak Hopf algebras and duoidal categories. We generalize the fundamental theorem for Hopf modules and some of its applications to Hopf categories. 40 About B-inductive semireﬂexive spaces

CERBU Olga

Moldova State University, Moldova Coauthors: Dumitru Botnaru, Alina Turcanu Let C2V be the category of the locally convex topological vector Hausdorff spaces. We denote by M the subcategory of the spaces with Mackey topology, N orm - the subcategory of normed spaces, Γ0 - the subcategory of complete spaces, lΓ0 - the subcategory of locally complete spaces (D. Ra¨ıcov) or b-complete (W. Slovikovski), and S - the subcategory of the spaces with weak topology. For an object (E,t) the absolute convex and bounded set A is defined as a Banach sphere, if the normed space (EA,nA) is the Banach space, where EA is the linear coverage of the set A, and nA - the Minkowski functional of the set A.WedenotewithB the set of all Banach spheres in the space Eβ (β - the topology of the uniform convergence on all the bounded sets from (E,t)). The inductive topology j(t)onE is defined as the most fine locally convex topology for which the following applications jA : (EA,nA) −→ (E ,j(t)) are continuous, A ∈B. Definition [V. Sekevanov]. Thespace(E,t) is called semireflexive B - inductive if (E,j(t)) = E. Let iR be the subcategory of the semireflexive inductive spaces [1], and B−iR - of the semireflexive B-inductive spaces. Then iR⊂B−iR (V. Sekevanov). We denote A the class of all bijective morphisms b :(E,u) −→ (F, v) ∈C2V for which (E,u) =(F, v). For a subcategory C⊂C2V we denote by QA(C) the subcategory A-factor objects of the objects from C. Theorem 1. Let be L and Γ two reflective subcategories S⊂L, Γ0 ⊂ Γ . Further let be R the semireflexive product of the subcategories L and Γ : R = L∗sr Γ (see [2]).Then: 1.QA(M∩R) is a reflective subcategory. 2. R⊂QA(M∩R). 3. The subcategory QA(M∩R) is closed under the A-subobjects and A-factorobjects. Theorem 2. 1. B−iR = QA(M∩iR). 2. lΓ0 = QA(M∩Γ0)=QA(N orm). References 1. Berezanschi I.A. – The inductive reflexive locally convex spaces, DAN SSSR,1968, T.182, Nr.1, p.20-22. 2. Botnaru D., Cerbu O. – Semireflexive product of two subcategories, Proc. of the Sixth Congress of Romanian Math., Bucharest, 2007, v.1, p.5-19.

On the invariant theory of string algebras

CHINDRIS Calin

University of Missouri-Columbia, United States Coauthors: Andrew Carroll

This talk is based on joint work with Andy Carroll. It is about studying the module category of a finite-dimensional algebra within the general framework of invariant theory. Our objective is to describe the tameness of an algebra in terms of its moduli spaces of modules. Specifically, we will show that for an acyclic string algebra, the irreducible components of any moduli space of modules are just products of projective spaces. Along the way, we will describe a decomposition result for moduli spaces of modules of arbitrary finite-dimensional algebras.

Some properties of autocommutator subgroups of certain p-groups

CHIS Mihai

West University of Timisoara, Romania Coauthors: Codruta Chis

We investigate some properties of autocommutator subgroups of certain classes of p-groups. 41 On intersections of complete intersection ideals

CIMPOEAS Mircea

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Dumitru Stamate

We present a class of complete intersection toric ideals whose intersection is a complete intersection, too.

Recent advances in the study of Diophantine quintuples

CIPU Mihai

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

Apparently motivated by Heron’s formula for triangle area, Diophantus has asked to ﬁnd sets of numbers with the property that increasing by one the product of any two elements results in a perfect square. Such sets are called nowadays Diophantine or D(1)-sets. A lot of work has been prompted by the conjecture (put forward in 1978 by P. E. Gibbs and independently by J. Arkin, V. E. Hoggatt, and E. G. Strauss) that any Diophantine triple has a unique extension to a Diophantine quadruple. Clearly, this implies a weaker conjecture, predicting that there exists no Diophantine quintuple. The talk will contain a survey of very recent ideas and results, many of them still unpublished, which bring us closer to solution of these problems. Several results are obtained in common with A. Filipin (Croatia), Y. Fujita (Japonia), M. Mignotte (Franta), T. Trudgian (Australia).

On the dew line in circle packings

COBELI Cristian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Alexandru Zaharescu

Let A be a ﬁxed arc of a selected circle in a circle packings P.Thedew line associated to A is a curve DA(h), which is parallel to A and lies at a distance h>0awayfromA, on the same side with the other circles of P. Denote by CA the set of circles in P that are tangent to A and let PA(h) be the probability that a point on the dew line DA(h) is inside a circle of CA. We present a few problems and results concerning the following questions: Is there a limit probability lim PA(h)? If the answer is positive, does this limit depends h→0 on the arc and on the packing?

Module covers and the Green correspondence

COCONET Tiberiu

Babes-Bolyai University, Romania Coauthors: Andrei Marcus

The Green correspondence can be expressed as an equivalence between certain quotient categories of modules over group algebras. M.E. Harris combined this categorical version with the Nagao-Green theorem on block induction, obtaining a version with blocks of the mentioned equivalence. We investigate this approach with respect to module covers and block covers and discover more general results that imply well-known correspondences. 42 Arithmetic properties of the Frobenius traces of an abelian variety

COJOCARU Alina Carmen

University of Illinois at Chicago, Institutul de Matematica al Academiei Romane, USA, Romania Coauthors: R. Davis, K.E. Stange, A. Silverberg

Given an abelian variety A/Q, with a trivial endomorphism ring (over the algebraic closure of Q), we investigate the arithmetic properties of the coeﬃcients of the p-Weil polynomials of A,asp varies.

Skew ring extensions and generalized monoid rings

COJUHARI Elena

Technical University of Moldova, Republic of Moldova

Given a ring A with identity and a multiplicative monoid G,aD-structure is defined as a collection σ of self-mappings of A indexed by elements of G satisfying certain demanding but quite natural conditions [1, 2]. D-structures are used to define various skew and also twisted monoid rings which in turn being confined in a general construction of a ring A G, σ named as a generalized monoid ring (e.g. [2]). Weyl algebras, skew polynomial rings and others related to them [3] become special concrete realizations of such monoid rings. Among many others we examine the relationships between generalized monoid rings, especially skew monoid rings, and normalizing and subnormalizing extensions. Relations between the existence of a D-structure and gradability of the ring by a cyclic group are also studied. The talk is based on joint work with Barry J. Gardner. Reference 1. Cojuhari E.P., Gardner B.J. – Generalized Higher Derivations, Bull. Aust. Math. Soc. 86, no. 2 (2012), 266-281. 2. Cojuhari E.P. – Monoid algebras over non-commutative rings, Int. Electron. J. Algebra, 2 (2007), 28-53. 3. Cohn P.M. – Free rings and their relations, London Mathematical Society Monographs, No. 2. Academic Press, London-New York, 1971, 346 pp.

Towards longer-range topological properties for ﬁnite generation of subalgebras

CONSTANTINESCU Adrian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

Let A be a reduced subalgebra of an algebra A of finite type over a field k. The problem of the finite generation of A is a restatement of the renowned 14-th Hilbert Problem, representing an interplay of Algebra with Geometry and Topology. According to some author’s results, there exists a complete topological control about the finite generation of such a subalgebra A when k = C,aswellwhenk is arbitrary and A is Noetherian. Passing to the associated geometric objects X∗ = SpecA,resp.X = SpecA (see [2]), we have a canonical dominant morphism f : X → X∗ of affine k-schemes with X an algebraic k-variety and then we are naturally guided to the more general situation of a similar dominant morphism f : X → X∗ of arbitrary (not necessarily affine) k-schemes. The problem of the algebraization of the k-scheme X∗ (i.e. X∗ to be exactly an algebraic k-variety) is close related to the ”good” topological properties of the k-schemes morphism f. In this talk we review a class of such topological properties and center on a possible new situation, suggested by the central Hilbert- Mumford-Nagata Theorem of the Invariant Theory (see [3]), as by a topological result due to Prof. M. Ciobanu: namely the case when f is a universally topological quotient morphism. References 1. A. Constantinescu – Schemes dominated by algebraic varieties and some classes of scheme morphisms.I.II,III:I,ActaUniv.Apu- lensis, Math.-Info., 16 (2008), 37 - 51; II, Preprint Ser. in Math., IMAR, Bucharest, ISSN 0250 - 3638, 8 (2010), 36 p. ; III, to appear 2. A. Grothendieck – Elements de geometrie algebrique. I,II, Publ. Math. IHES, 4 (1960); 8 (1961). 43

3. D. Mumford – Geometric Invariant Theory, Springer, 1965.

Castelnuovo-Mumford regularity and triangulations of manifolds

CONSTANTINESCU Alexandru

Freie Universitaet Berlin, Germany

We show that for every positive integer r there exist monomial ideals generated in degree two, with linear syzygies, and regularity of the quotient equal to r. For Gorenstein ideals we prove that the regularity of their quotients can not exceed four, thus showing that for d>4every triangulation of a d-manifold has a hollow square or simplex. We also show that for most monomial ideals generated in degree two and with linear syzygies the regularity is O(log(log(n)), where n is the number of variables.

Operator theory for ﬁnite groups

DEACONESCU Marian

Kuwait University, Kuwait Coauthors: G.L. Walls

My talk will present a handful of recent results obtained jointly with G.L. Walls. These results are quite general since they are related to the following situation: an arbitrary finite group G is operated (acted) upon by an arbitrary finite group A. In older terminology, A is “a group of operators of G”. The newer terminology is that A “acts on G via automorphisms”. This kind of an action, as general as it is (no other conditions are imposed here) comes with a set of “invariants” attached to it. The first is the subgroup F of all of the fixed points of A in G. The second is the “autocommutator subgroup” [G, A], which is the subgroup of G generated by the elements g−1gα for g ∈ G, α ∈ A. Finally, the orbits of the elements in G under the action of A are also of interest. Particular cases are important, of course; we where able to solve, among other things, the old well-known problem of characterizing (via a simple, compact, alternative group-theoretical condition) those finite groups whose automorphism group is abelian. The first example of a finite non-abelian group G whose group Aut(G) of automorphisms is abelian was given by G.A. Miller in 1913. Infinitely many more examples were produced since. Whenever the subgroup F is nontrivial it turns out that the sequence of the lengths of the orbits of A in G behaves in a very orderly manner. In particular, it is true that if p is a prime dividing the order of F , then the number of orbits of A in G whose length is co-prime to p must be a multiple of p. When H is an A-invariant subgroup of G, then we can determine the number of pairs (g, α)withg ∈ G and α ∈ A such that g−1gα ∈ H. This is a far reaching extension of a classic result of Frobenius (who determined this number when A = G acts on G via conjugation and when H = 1 is the trivial subgroup of G) and it has several important consequences.

Non-vanishing of quadratic twists of automorphic L-functions

DIACONU Adrian

University of Minnesota, USA Coauthors: Ben Brubaker, Ian Whitehead

In this talk, I will discuss a novel approach in understanding the important problem of the non-vanishing of some of the quadratic twists of an L-function attached to a ﬁxed cuspidal automorphic representation on GL(n). 44 Ideals of 2-minors

ENE Viviana

Universitatea Ovidius din Constanta, Romania

In this talk we survey recent results on binomial edge ideals defined on generic (Hankel) matrices. Given a simple graph G on the vertex set [n], one may associate with it a binomial ideal JG in the polynomial ring K[X]overa x1 x2 ... xn field K, where X = . The ideal JG is generated by maximal minors of X, fij = xiyj − xj yi with {i, j} edge of G, and y1 y2 ... yn is called the binomial edge ideal of G. Later on, the notion of binomial edge ideal was generalized to a pair of graphs. The interest in studying (generalized) binomial edge ideals partially comes from the fact that they turned out to have applications in statistics. In our talk, we discuss various algebraic and homological properties of binomial edge ideals. Similar constructions can be done by considering binomial edge ideals on Hankel matrices associated with (pairs of) graphs. They generalize the well known defining ideals of rational normal curves. We mainly focus on some recent results obtained in joint papers with F. Chaudhry, A. Dokuyucu, J. Herzog, T. Hibi, A. Qureshi, A. Zarojanu.

The Frobenius complexity of a local ring

ENESCU Florian

Georgia State University, United States

The talk will outline the notion of Frobenius complexity of a local ring of prime characteristic and discuss various examples. This is joint work with Yongwei Yao.

On the analytic functions with p-adic coeﬃcients

GROZA Ghiocel

Technical University of Civil Engineering Bucharest, Romania

|| Q | | 1 Let p be a fixed prime and the normalized p-adic absolute value defined on ,thatis p = p .IfR is a positive real number and Qp is the completion of Q with respect to ||,wedenotebyB(R)={x ∈ Qp : |x|≤R} and S(R)={x ∈ Qp : |x| = R} the ball with circumference and the sphere, with center 0 and radius R, respectively. For a fixed non-negative integer t let ∞ i f = ciX ,ci ∈ Qp, (0.1) i=0 be a convergent series on B(p−t). We study the analytic functions of the form (0.1) which define a mapping from S(p−t)intoS(1). Hence we get a result concerning entire functions with p-adic coefficients which are bounded on Qp. Finally we study infinite interpolation by means of entire functions with p-adic coefficients.

Gorenstein projective precovers

IACOB Alina

Georgia Southern University, USA 45

We consider a right coherent and left n-perfect ring R. We prove that the class of Gorenstein projective complexes is special precovering in the category of unbounded complexes, Ch(R). As a corollary, we show that the class of Gorenstein projective modules is special precovering over such a ring. This is joint work with Sergio Estrada and Sinem Odabasi.

How to compute the Stanley depth of a module

ICHIM Bogdan

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Lukas Katthan, Julio Moyano

We introduce an algorithm for computing the Stanley depth of a ﬁnitely generated multigraded module M over the polynomial ring K[X1,...,Xn]. As an application, we give an example of a module whose Stanley depth is strictly greater than the depth of its syzygy module. In particular, we obtain complete answers for two open questions raised by Herzog.

The distribution of class groups of imaginary quadratic ﬁelds

JONES Nathan

University of Illinois at Chicago, USA Coauthors: S. Holmin, P. Kurlberg, C. Macleman and K. Petersen

Which abelian groups occur as the class group of some imaginary quadratic field? Inspecting tables of M. Watkins on imaginary quadratic fields of class number up to 100, one finds that some abelian groups do not occur as the class group of any imaginary quadratic field (for instance (Z/3Z)3 does not). In this talk, I will combine heuristics of Cohen-Lenstra together with a refinement of a conjecture of Soundararajan to make precise predictions about the asymptotic distribution of imaginary quadratic class groups, partially addressing the above question. I will also present some numerical evidence of the resulting conjectures.

A combinatorial model for Kirillov-Reshetikhin crystals and applications

LENART Cristian

State University of New York at Albany, USA Coauthors: S. Naito, D. Sagaki, A. Schilling, M. Shimozono

Crystals are colored directed graphs encoding information about Lie algebra representations. Kirillov-Reshetikhin (KR) crystals correspond to certain finite-dimensional representations of affine Lie algebras. I will present a combinatorial model which realizes tensor products of (column shape) KR crystals uniformly across untwisted affine types. Some computational applications are discussed. A corollary states that the Macdonald polynomials (which generalize the irreducible characters of semisimple Lie algebras), upon a certain specialization, coincide with the graded characters of tensor products of KR modules. 46 The factorization problem and related questions

MILITARU Gigel

University of Bucharest, Romania Coauthors: Ana Agore

Let A ≤ G be a subgroup of a group G.AnA-complement of G is a subgroup H of G such that G = AH and A ∩ H =1.The classifying complements problem asks for the description and classiﬁcation of all A-complements of G. We shall give the answer to this problem in three steps. Let H be a given A-complement of G and (, ) the canonical left/right actions associated to the factorization G = AH. To start with, H is deformed to a new A-complement of G, denoted by Hr, using a certain map r : H → A called a deformation map of the matched pair (A, H, , ). Then the description of all complements is given: H is an A-complement of G if and only if H is isomorphic to Hr, for some deformation map r : H → A. Finally, the classiﬁcation of complements proves that there exists a bijection between the isomorphism classes of all A-complements of G and a cohomological object D, (H, A, |, (, )). As an application we show that the theoretical formula for computing the number of isomorphism types of all groups of order n arises only from the factorization Sn = Sn−1Cn.

Are graded semisimple algebras symmetric?

NASTASESCU Constantin

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: S. Dascalescu, L. Nastasescu

We study graded symmetric algebras, which are the symmetric monoids in the monoidal category of vector spaces graded by a group. We show that a finite dimensional graded division algebra whose dimension is not divisible by the characteristic of the base field is graded symmetric. Using the structure of graded simple (semisimple) algebras,we extend the results to these classes. In particular, in characteristic zero any graded semisimple algebra is graded symmetric. We show that the center of a finite dimensional graded division algebra is often symmetric.

Nonassociative structures, Yang-Baxter equations and applications

NICHITA Florin

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Radu Iordanescu

Several of our books, papers, talks and posters (since 1979 until now) treated topics on Jordan Algebras, Nonassociative Structures, Yang-Baxter Equations, Hopf Algebras and Quantum Groups. For example, we list the papers presented at previous congresses:

1. F.F. Nichita – Lie algebras and Yang-Baxter equations, Bull. Trans. Univ. Brasov, Series III, Vol. 5 (54), 2012, Special Issue: Proceedings of the 7-th Congress of Romanian Mathematicians, Brasov, 2011, 195-208. 2. F.F. Nichita and D. Parashar – Coloured bialgebras and nonlinear equations, Proceedings of the 6-th Congress of Romanian Math- ematicians, Bucharest, 2007, Editura Academiei, vol. 1, 65-70, 2009.

Recently, we published some joint works on the above mentioned topics:

3. Radu Iordanescu, Florin F. Nichita, Ion M. Nichita – The Yang-Baxter equation, (quantum) computers and unifying theories, Axioms, 2014; 3(4):360-368. 4. Radu Iordanescu, Florin F. Nichita, Ion M. Nichita – Non-associative algebras, Yang-Baxter equations, and quantum computers, Bulg. J. Phys., vol.41, n.2, 2014, 71-76.

Motivated by the above achievements we would like to present new results and directions of study. 47 Classes of path ideals and their algebraic properties

OLTEANU Anda - Georgiana

University Politehnica of Bucharest and , Romania

Given a directed graph G, the path ideal of the graph G (of length t ≥ 2) is the monomial ideal It(G) generated by the squarefree monomials which correspond to the directed paths of length t in G. Classes of directed graphs arise from posets. We consider path ideals associated to special classes of posets such as tree posets and cycles. We express their property of being sequentially Cohen– Macaulay in terms of the underlying poset. For Alexander dual of cycle posets, we compute the Castelnuovo–Mumford regularity and, as a consequence, we get the projective dimension of path ideals of cycle posets. We also pay attention to path ideals of powers of the line graph and study the property of being sequentially Cohen–Macaulay and having a linear resolution. The results are expressed in terms of the combinatorics of the underlying poset.

Hom-structures

PANAITE Florin

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

Hom-structures (Hom-associative algebras, Hom-Lie algebras etc) are generalizations of classical algebraic structures in which the deﬁning identities are twisted by certain homomorphisms. We will present some recently introduced concepts, constructions and properties involving Hom-structures (such as twisted tensor products, smash products etc).

p-adic analytic functions from recurrence sequences

PASOL Vicentiu

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: A. Zaharescu

B. Berndt, S. Kim and A. Zaharescu, in their study of the diophantine approximation of e2/a have constructed certain p-adic functions, naturally arising from the sequence of convergents of e. They prove that for certain primes p, these functions are continuous. They raised the question if those functions are in fact rigid analytic. We prove that in fact this question has a positive answer for all primes p.

Heisenberg algebras and coeﬃcient rings

POP Horia

Mt San Antonio College, USA

In the noncommutative theory of local rings, the existence of coefficient fields is not always granted. We study a counter-example constructed using an enveloping algebra of a Heisenberg algebra to see how to describe a good coefficient ring for a non-commutative local ring, with commutative residue field. Further, dealing with the case of a noncommutative residue division algebra, we use a theorem of Hochschild on the Brauer group to describe a canonical coefficient ring in the case when the exponent of the residue division algebra is prime to the characteristic of the residue field. 48 On the trace formula for Hecke operators

POPA Alexandru Anton

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We present a new, simple proof of the trace formula for Hecke operators on modular forms for congruence subgroups. It is based on an approach for the full modular group sketched by Don Zagier more than 20 years ago, by computing the trace of Hecke operators on the space of period polynomials associated with modular forms. This algebraic proof has been recently sharpened in a joint work with Zagier, and we show that it generalizes to congruence subgroups as well. We use the theory of period polynomials for congruence subgroups, developed jointly with Vicentiu Pasol.

A theorem of Ploski’s type

POPESCU Dorin

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

N Let Cx, x =(x1,...,xn), f =(f1,...,fs) be some convergent power series from Cx, Y , Y =(Y1,...,YN ) and y in C[[x]] with y(0) = 0 be a solution of f = 0. Then Ploski proved that the map v : B = Cx, Y /(f) → C[[x]] given by Y → y factors through an A-algebra of type B = Cx, Z for some variables Z =(Z1,...,Zs), that is v is a composite map B → B → C[[x]]. Now, let (A, m) be an excellent Henselian local ring, A its completion, B a ﬁnite type A-algebra and v : B → A an A-morphism. h h Then we show that v factors through an A-algebra of type A[Z] for some variables Z =(Z1,...,Zs), where A[Z] is the Henselization of A[Z](m,Z).

On the v-extensions of a valued ﬁeld

POPESCU Sever-Angel

Technical University of Civil Engineering Bucharest, ROMANIA

Let (K, v) be a perfect nontrivial Krull valued field of rank 1 and let w be an extension of v to a fixed algebraic closure Ω of K. An intermediate valued field (L, w)iscalledav-extension of (K, v)ifv does not split in L.If(L, v) is maximal with this property, we say that it is a v-maximal extension of (K, v). For instance, if (K, v) is a henselian field, then the only v-maximal extension of (K, v)is L = Ω. We prove in this note that if (K, v) is a (finite) algebraic number field, then any v-maximal extension of it cannot be a normal extension of K. On the other hand, in the case of the rational function field, with coefficients in a field k of characteristic zero, endowed with the X-adic valuation, we give a constructive example of an X-adic maximal extension L of K which is also a normal extension of K.

A simple proof of Fermat’s last theorem for n =4and n =6

POPOVICI Florin

Colegiul National de Informatica Grigore Moisil din Brasov, Romania Coauthors: Dorin Dutkay

We give a simple elementary and natural proof of Fermat’s Last Theorem for the exponents n = 4 and n =6. 49 A coring version of external homogenization for Hopf algebras

RAIANU Serban

California State University, Dominguez Hills, USA

We give a coring version for the external homogenization for Hopf algebras, which is a generalization of a construction from graded rings, called the group ring of a graded ting. We also provide a coring version of a Maschke-type theorem.

The syzygies of some thickenings of determinantal varieties

RAICU Claudiu

University of Notre Dame, USA Coauthors: Jerzy Weyman

The space of mxn matrices admits a natural action of the group GLm × GLn via row and column operations on the matrix entries. The invariant closed subsets are the determinantal varieties deﬁned by the (reduced) ideals of minors of the generic m × n matrix. The minimal free resolutions for these ideals are well-understood by work of Lascoux and others. There are however many more invariant ideals which are non-reduced, and whose syzygies are quite mysterious. These ideals correspond to nilpotent structures on the determinantal varieties, and they have been completely classiﬁed by De Concini, Eisenbud and Procesi. In my talk I will recall the classical description of syzygies of determinantal varieties, and explain how this can be extended to a large collection of their thickenings.

Most general forms in the study of Boolean equations

RUDEANU Sergiu

Faculty of Mathematics and Computer Science, University of Bucharest, Romania

TBA

Polynomial growth for Betti numbers

SECELEANU Alexandra

University of Nebraska-Lincoln, USA Coauthors: L.L. Avramov, Y. Zheng

It is well known that the asymptotic patterns of the Betti sequences of the finitely generated modules over a local ring R reflect the structure of R. For instance, these sequences are eventually zero if and only if R is regular (Auslander and Buchsbaum, Serre) and they are eventually constant if and only if R is a hypersurface (Shamash, Gulliksen, Eisenbud). We consider the problem of characterizing the rings R such that every R-module has Betti numbers eventually given by some polynomial. We give necessary and sufficient conditions for R to have this property. In some important cases, for example when R is homogeneous, these conditions coincide and therefore characterize R. 50 Quantum-resistant public key cryptography

SMITH-TONE Daniel

University of Louisville and National Institute of Standards and Technology, United States of America

Multivariate public key cryptosystems form a family of purported quantum-resistant cryptosystems, schemes which remain secure even if an adversary is assumed to have access to a large scale quantum computer. Such cryptosystems publish a public key consisting of a large collection of low degree polynomials in several variables over a finite field. Many cryptographic tasks can be accomplished if the system of equations is unfeasible to invert for an illegitimate user while being efficiently invertible to a legitimate user. We derive several new techniques for determining the security (or insecurity) of multivariate public key cryptosystems. The author presents new security criteria which are practical and are readily proven for a multitude of multivariate schemes. We further demonstrate an attack utilizing a subspace differential invariant illustrating a sharp contrast between cryptosystems which provably have a trivial differential structure and those for which an attack can be realized.

Operations on the secondary hochschild cohomology

STAIC Mihai

Bowling Green State University, USA Coauthors: Alin Stancu

Secondary cohomology is associated to a triple (A, B, ε), and was introduced in order to describe all the B-algebra structures on A[[t]] at the same time. We present some results related to this cohomology: the cup and bracket product, the Hodge decomposition, the bar complex, and the secondary cyclic cohomology associated to the triple (A, B, ε).

Ungraded strongly Koszul rings

STAMATE Dumitru

University of Bucharest, Romania Coauthors: Juergen Herzog

Various methods have been designed for checking that a standard graded algebra is Koszul, some being more eﬃcient than the others. We are interested in semigroup rings R = K[H], which are not usually standard graded. In this context we introduce the strongly Koszul property, extending in a natural way the similar concept of Herzog, Hibi and Restuccia for standard graded K-algebras. We show that if K[H] is strongly Koszul, then its associated graded ring grK[H] is a Koszul ring in the classical sense and that the two rings have the same Poincare series. Our toolbox includes sequentially Cohen- Macaulayness and shellability for posets. This is a preliminary report on work in progress with Juergen Herzog, Essen, Germany.

Extentions of cohomological Mackey functors

STANCU Radu

LAMFA, Universite de Picardie, France Coauthors: Serge Bouc

Let k be a field of characteristic p and G a finite group. The cohomological Mackey functors for G over k are modules over a specific finitely generated algebra coμk(G), called the cohomological Mackey algebra. This algebra shares many properties with the usual group 51 algebra, and most questions about modules over the group algebra and methods used for them can be extended to Mackey functors: e.g. relative projectivity, vertex and source theory, Green correspondence, the central role played by the elementary abelian p-groups. These resemblances raise some natural questions, whether, a given theorem on kG admits an analogue for coμk(G). This was the main motivation in a previous work of Serge Bouc, where the question of complexity of cohomological Mackey functors was solved (in the only non-trivial case where p divides the order of G). It was also shown there how this question can be reduced to the consideration of elementary abelian p-groups E appearing as subquotients of G, and to the knowledge of enough information on the ∗ E E E algebra Extcoμk(E)(S1 ,S1 ) of self-extensions of a particular simple functor S1 for these groups. The aim of the talk I give - which is based on a joint work with Serge Bouc - is to recall the basic properties of cohomological Mackey ∗ G G functors and give insight into how one can get an explicit presentation of the algebra Extcoμk(G)(S1 ,S1 ), when G is an elementary abelian p-group.

Irreducibility criteria for polynomials over discrete valuation domains

STEFANESCU Doru

University of Bucharest, Romania

We study properties of the Newton polygon of a product of two polynomials over a discrete valuation domain (A, v) and we establish corresponding properties of the Newton index of a polynomial in A[X] . There are deduced factorization properties of polynomials over A and there are obtained new irreducibility criteria. The results are used for generating classes of irreducible polynomials over various discrete valuation domains. In particular we obtain criteria for quasi-generalized diﬀerence polynomials, for univariate polynomials over Z and for polynomials over formal power series.

Computation of Hall polynomials in the Euclidean case

SZOLLOSI Istvan

Babes-Bolyai University, Romania Coauthors: Csaba Szanto

Let kQ be the path algebra of the acyclic quiver Q =(Q0,Q1) over the finite field k (here Q0 is the set of vertices and Q1 the set of arrows). We will consider the category mod-kQ of finite k-dimensional right modules over kQ, which can be identified with the category rep-kQ of the finite dimensional k-representations of the quiver Q. Denote by [X] the isomorphism class of a module X in mod-kQ. The Ringel-Hall algebra H(kQ) associated to the algebra kQ is the rational space having as basis the isomorphism classes in M M 1 2 mod-kQ together with a multiplication defined by [N ][N ]= [M] FN1N2 [M], where the structure constant FN1N2 is the number of submodules U of M such that U is isomorphic to N2 and M/U is isomorphic to N1. These structure constants are also called Ringel-Hall numbers. One can see that H(kQ) is an associative rational algebra with identity [0]. In case of Dynkin and Euclidean (tame) quivers the Ringel-Hall numbers are polynomials in the number of elements of the base field. These are the Hall polynomials, which appear in various contexts: they are the structure constants of quantum groups, they are used in the theory of cluster algebras and they can also be used successfully to investigate the structure of the module category. Apart from Ringel’s famous list of Hall polynomials in the Dynkin case and a limited number of special cases, our knowledge on Hall polynomials is scarce. We present some of the theoretical and computational challenges one has to deal with, when trying to compute Hall polynomials. Deep theoretical results, unusual techniques, complex algorithms and huge computing power are all required in the process of obtaining these polynomials. We focus on the computational aspect of the problem and also present the first results of our quest. 52 Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups

TODEA Constantin - Cosmin

Technical University of Cluj-Napoca, Romania

The Bockstein homomorphism in group cohomology is the connecting homomorphism in the long exact sequence associated to some short exact sequence of coefficients. It appears in the Bockstein spectral sequence, which is a tool for comparing integral and mod p cohomology (p is a prime), and has applications for Steenrod operations. We will define the Bockstein homomorphisms for the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use and additive decomposition and a product formula for the Hochschild cohomology HH∗(kG), given by Siegel and Witherspoon in 1999, where G is a finite group and k is an algebraically closed field of characteristic p. We obtain similar results for the cohomology algebra of a defect group of B with coefficients in the source algebra of a block algebra B of kG.

Commutators theory in language congruences for modular algebraic system

URSU Vasile

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania and Technical University of Moldova

In [1] V.A. Gorbunov asked a different definition of congruence on an algebraic system that is determined before. In this definition, congruence is associated not only with the basic operations and the basic relationships that would greatly extend the results and methods for universal algebra in the theory of algebraic systems. Following Gunma [2], in this work we were able to describe the theory of the switches in the language of the congruence of the algebraic system. It is possible to introduce the notion of Abelian, nilpotent and solvable algebraic systems which generalize concepts in universal algebra. References

1. V.. Gorbunov. Algebraic theory of quasivarieties, Siberian school of algebra and logic, Novosibirsk “Science Book“, 1999. 2. H.P. Gumm. An easy way to the commutator in modular varieties, Arch. Math., 1980, 34, 220-228.

Intersections and sums of Gorenstein ideals

VELICHE Oana

Notheastern University, USA Coauthors: Lars Winther Christensen

A complete local ring of embedding codepth 3 has a minimal free resolution of length 3 over a regular local ring. Such resolutions carry a diﬀerential graded algebra structure, based on which one can classify local rings of embedding codepth 3. The Gorenstein rings of embedding codepth 3 belong to the class called G(r), which was conjectured not to contain any non Gorenstein rings. In a previous work with Lars W. Christensen and Jerzy Weyman we gave examples and constructed non Gorenstein rings in G(r), for any r ≥ 2. We show now that one can get such rings generically, from intersections of Gorenstein ideals. The class of the rings obtained from sums of such ideals will also be discussed. 53 Bouquet algebra of toric ideals

VLADOIU Marius

University of Bucharest, Romania Coauthors: Sonja Petrovic, Apostolos Thoma

To any toric ideal (encoded by an integer matrix A) we associate a matroid structure called the bouquet graph of A, and introduce another toric ideal called the bouquet ideal of A, which captures the essential combinatorics of the initial toric ideal. The new bouquet framework allows us to answer some open questions about toric ideals. For example, we provide a characterization of toric ideals forwhich the following sets are equal: the Graver basis, the universal Groebner basis,any reduced Groebner basis and any minimal generating set. Moreover, we show that toric ideals of hypergraphs encode all toric ideals.

Totally reﬂexive modules for Stanley-Reisner rings of graphs

VRACIU Adela

University of South Carolina, U.S.A. Coauthors: Cameron Atkins

For a Cohen-Macaulay non-Gorenstein ring it is known that either there are inﬁnitely many isomorphism classes of indecomposable totally reﬂexive modules, or else there are none except for the free modules. However it is not known how to determine which of this situations holds for a given ring. We investigate this question for the case of Stanley-Reisner rings of graphs.

Ideals of orthogonal graph representations

WELKER Volkmar

Universtaet Marburg, Germany Coauthors: J. Herzog, A. Macchia, S. Madani

We describe algebraic properties of an ideal associated to an undirected graph by Lovasz, Saks and Schrijver. Over the reals it describes orthogonal representations of graphs in Euclidian space.

Ideal cimaximal graph and its application

YARAHMADI Zahra

Islamic Azad University, Iran

Let R be a commutative ring and G(R) be a graph with vertices as proper and non-trivial ideals of R. Two distinct vertices I and J are said to be adjacent if and only if I + J = R. In this paper we study a graph constructed from a subgraph of G(R) which consists of all ideals I of R such that contained in Jacobson radical of R. In this paper we study about the relation between the number of maximal ideal of R and the number of partite of this subgraph. Also we study on the structure of ring R by some properties of vertices of this subgraph. In another section, it is shown that under some conditions on the G(R), the ring R is Noetherian or Artinian. Finally we characterize clean rings and then study on diameter of this constructed graph. 54 On the stanley depth

ZAROJANU Andrei

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Dorin Popescu

Let I ⊃ J be two squarefree monomial ideals of a polynomial algebra over a ﬁeld generated in degree ≥ d,resp.≥ d +1.Ifthe Stanley depth of I/J is ≤ d + 1 then the usual depth of I/J is ≤ d +1ifI has at most four generators of degree d. Section 2 Algebraic, Complex and Diﬀerential Geometry and Topology

Some foliations on the cotangent bundle

ANASTASIEI Mihai

Octav Mayer Institute of Mathematics and The University Alexandru Ioan Cuza from Iasi, Romania

A Cartan space is a manifold whose cotangent bundle is endowed with a smooth function K which is positively homogeneous of degree 1 in momenta. Then the vertical distribution (the kernel of the diﬀerential of the projection of the cotangent bundle on its base manifold) becomes a semi Riemannian foliation whose transversal distribution is completely determined by K and is orthogonal on the vertical distribution with respect to a semi Riemannian metric of Sasaki type. In the same framework there exist and another foliations on the cotangent bundle. One is that deﬁned by the level surfaces of the function K. One determines various connections associated to these two foliations and some properties of them are pointed out.

Parallel second order tensors on Vaisman manifolds

BEJAN Cornelia-Livia

Seminarul Matematic “Al. Myller”, Romania Coauthors: Mircea Crasmareanu

We present some aspects on Ricci solitons from our recent works.

De la alfabetul Artin la alfabetul Garside

BERCEANU Barbu Rudolf

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

Schimbind generatorii Artin {x1,x2,...,xn−1} ai grupului braid Bn cu generatorii {δ|Δn} se obtine un sistem ﬁnit de relatii derivate ale lui Bn.

55 56 Projective deformations for Finsler functions

BUCATARU Ioan

“Alexandru Ioan Cuza” University of Iasi, Romania

The geometry of a systems of second order ordinary differential equations (SODE) 2 i d x i dx +2G x, =0, dt2 dt on some configuration manifold M, is determined by the (differential) properties of functions Gi, and it can be: affine, Riemannian, Finslerian or Lagrangian. A Finsler function, F (x, x˙), is given by a family of Minkowski norms in each tangent space of the manifold. In the Finslerian case, the functions Gi are 2-homogeneous inx ˙ = dx/dt, and this property allows for reparameterizations of the system. Such reparameterization (projective deformation) can change substantially the geometry of the system. In this talk, I will discuss the behaviour of a (SODE) under projective deformations, regarding some geometric properties: Finsler metrizability, curvature and isotropy. A special attention will pe paid to Hilbert’s fourth problem, which asks to determine and study all Finsler metrics that are projectively equivalent to the standard flat metric.

Reﬁnements of homology provided by a real or angle valued map

BURGHELEA Dan

Ohio State University, United States

To any pair (X, f),X compact ANR and f a real (angle) valued map defined on X and any nonnegative integer r we assign: f (1) a finite configuration of points z with multiplicities δr (z) located in the complex plane and f (2) a finite configuration of vector spaces δˆr (z) indexed by the same z s in analogy with (1) the configuration of eigenvalues and of (2) generalized eigenspaces of a linear operator in a finite dimensional complex vector space. The analogy goes quite far as long as the formal properties are concerned and becomes particularly subtle in the case of an angle valued map (involving L-2 topology). The basic properties /implications are discussed. f The configurations δr ’s are effectively computable in case that X is a finite simplicial complex and f a simplicial map and enjoy remarkable properties promising application in and outside mathematics.

Monodromy/Alexander rational function of a circle valued map

BURGHELEA Dan

Ohio State University, U.S.A.

I will provide an alternative presentation of the monodromy of (X; xiinH1(X; Z) based on the linear algebra of “linear relations”. This presentation is a source of new invariants derived from any homology/ cohomology type of vector valued homotopy functor. The Alexander polynomial of a knot is a particular example. 57 Towards a new algebraic proof of the Barannikov-Kontsevich theorem

CALDARARU Andrei

University of Wisconsin–Madison, USA Coauthors: Dima Arinkin, Marton Hablicsek

We present a new approach to an algebraic proof of a claim of Barannikov-Kontsevich, which was ﬁrst proved with analytic methods by Sabbah. This result is conceptually the analogue of the Hodge-de Rham degeneration statement (which applies for complex Kahler manifolds), but applied to a dg category of matrix factorizations. Our proof relies on reducing to positive characteristic and then applying our earlier results on formality of derived intersections in Azumaya spaces (spaces endowed with an Azumaya algebra).

Distances, boundedness and ﬁxed point theory

CIOBAN Mitrofan

Tiraspol State University, Republic of Moldova

We consider general distance d on a space X with the condition: d(x, y)+d(y, x) = 0 if and only if x = y. The distance d is called: an H-distance if any convergent sequence has a unique limit; a wH-distance if any Cauchy convergent sequence has a unique limit. If g is a mapping of X into itself, the distance d is g-bounded if for any point x from X there exists a number k(x) > 0 such that d(x, gn(x)) + d(gn(x),x)

Geometric inverse problems in Lagrangian mechanics

CONSTANTINESCU Oana

Alexandru Ioan Cuza University of Iasi, Romania Coauthors: Ioan Bucataru

The classic inverse problem of Lagrangian mechanics requires to find the necessary and sufficient conditions, which are called emphHelmholtz conditions, such that a given system of second order ordinary differential equations (SODE) is equivalent to the Euler- Lagrange equations of some regular Lagrangian function. In this talk we discuss the inverse problem of Lagrangian systems with non-conservative forces. Locally, the problem can be formulated as follows. We consider a SODE in normal form

2 i d x i +2G (x, x˙) = 0 (0.2) dt2 i and an arbitrary covariant force ﬁeld σi(x, x˙)dx . We will provide necessary and suﬃcient conditions, which we will call emphgeneralized Helmholtz conditions, for the existence of a Lagrangian L such that the system eqrefsode is equivalent to the Lagrange equations d ∂L ∂L − = σi(x, x˙). (0.3) dt ∂x˙ i ∂xi

The general theory is applied to some particular cases, for dissipative and respectively gyroscopic forces. One main result is that any SODE on a 2-dimensional manifold is of dissipative type. We provide examples where the proposed generalized Helmholtz conditions, expressed in terms of a semi-basic 1-form, can be integrated and the corresponding Lagrangian and Lagrange equations can be found. 58 An equivariant generalization of the Segal’s ﬁniteness theorem

COSTINESCU Cristian

Technical University of Civil Engineering Bucharest, Romania

A very useful result for calculations in equivariant K-theory is the following (due to Segal): Theorem. If X is a locally G contractible compact G space such that the orbit space X/G has finite covering dimension, then ∗ KG(X) is a finite R(G)-module; here G is a compact Lie group and by R(G) one denotes the representation ring of G. In this paper we consider a generalization of the Segal’s finiteness theorem to G-cohomology theories defined on a suitable category ∗ of G-spaces. For obtaining that we are led to consider G-cohomology theories hG which are “complete” with respect to a family S of closed subgroups of G. The completeness allows us to induct up from conditions on the associated H-cohomology theories (where H ∈ S), to obtain ∗ conclusions about hG . The appropriated generalization of the Segal’s finiteness theorem can then be stated in terms of conditions ∗ concerning the associated cohomology theories hH . The tool used is the generalized Atiyah-Hirzebruch spectral sequence.

Models of Belyi covers

CUZUB Stefan Andrei

“Alexandru Ioan Cuza” University of Iasi, Romania

The aim of this talk is to describe some results regarding semi-stable models of Belyi morphisms over rings of integers of number ﬁelds.

Hyperbolic manifolds and their representations by lens polytopes

DAMIAN Florin

Moldova State University, Republic of Moldova Coauthors: V. Makarov, P. Makarov

In topology a three-dimensional (n-dimensional) manifold is often given by the indication of the way how to identify pairwise faces of polytopes of some homogeneous complex. Poincare noticed that one polytope is suﬃcient. In [1] and in the present work, we discuss an ”intermediate” way to represent the manifold by lens polytopes. We start with cells complexes over regular (semiregular or k-regular) maps on totally geodesic hyperbolic submanifolds, named compact lens polytopes, and indicate the pairwise faces of lens polytope that lead to hyperbolic manifolds. This geometric construction will be illustrated by examples. References 1. F. L. Damian, V. S. Makarov – On lens polytopes, International Seminar on Discrete Geometry. State Univ. Moldova, Chisinau. P. 32–35, 2002.

(Multi)nets and monodromy

MACINIC Anca

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

The existence of non-trivial monodromy for the comomology of the Milnor ﬁber F associated to a complex hyperplane arrangement seems to be connected to the existence of a symmetric structure on the intersection lattice of the arrangement. We present instances of this occurence and describe the (combinatorial) monodromy action on H1(F ), in relation to Aomoto-Betti numbers. 59

On the geometry of Finsler manifolds with reversible geodesics

MASCA Ioana Monica

Colegiul “Nicolae Titulescu”, Brasov, Romania

A Finsler space is said to have reversible geodesics if for any of its oriented geodesic path, the same path traversed in the opposite sense is also a geodesic. We present the conditions for a Finsler space endowed with an (α, β) metric to be with reversible geodesics, and the classes of (α, β) metrics with reversible geodesics. In [1] the structure of a Finsler manifold of nonnegative weighted Ricci curvature including a straight line is investigated, and the classical Cheeger-Gromoll-Lichnerowicz splitting theorem is extended. We are going to extend these results for Finsler manifolds with reversible geodesics including a line. References [1] Shin-ichi Ohta – Splitting theorems for Finsler manifolds, arXiv:1203.0079v1.

Motivic inﬁnite cyclic covers

MAXIM Laurentiu

University of Wisconsin-Madison, USA Coauthors: Manuel Gonzalez Villa, Anatoly Libgober

To an infinite cyclic cover of a punctured neighborhood of a simple normal crossing divisor on a complex quasi-projective manifold we associate (assuming certain finiteness conditions are satisfied) an element in the equivariant Grothendieck ring of varieties, called motivic infinite cyclic cover, which satisfies birational invariance. Our construction provides a unifying approach for the Denef-Loeser motivic Milnor fibre of a complex hypersurface singularity germ, and the motivic Milnor fiber of a rational function, respectively. This is joint work with M. Gonzalez Villa and A. Libgober.

Lagrangian and Hamiltonian Geometries. Applications to analytical mechanics

MIRON Radu

Octav Mayer Institute of Mathematics, Romania

The purpose of this talk is to provide a short presentation of the geometrical theory of Lagrange and Hamilton spaces as well as to define and investigate some new Analytical Mechanics. It is largely recognized that a rigorous geometrical theory of conservative and nonconservative mechanical systems can not be constructed without the use of the geometry of the tangent and cotangent bundle of the configuration space. Such a theory can be raised based on the Lagrangian and Hamiltonian geometries. And conversely, the construction of these geometries relies on the mechanical principle and on the Legendre transformation. In the last thirty five years, geometers, mechanicians and physicists from all over the world worked in the field of Lagrange or Hamilton geometries and their applications. We mention only few names: P.L. Antonelli, M. Anastasiei, G. S. Asanov, A. Bejancu, I. Buc˘ataru, M. Crampin, R.S. Ingarden, S. Ikeda, M. de Leon, M. Matsumoto, H. Rund, H. Shimada, P. Stavrinos, L. Tamassy. The Lagrangian and Hamiltonian geometries are useful also for applications in Variational calculus, Mechanics, Physics, Biology etc. Finsler geometry as well as the Riemannian geometry are the geometries of particular Lagrangians whose dual by the Legendre transformation define interesting geometries on the cotangent bundle. The following topics are reviewed: 1◦ A solution of the problem of geometrization of the classical nonconservative mechanical systems, whose external forces depend on velocities, based on the differential geometry of velocity space. 2◦ The introduction of the notion of Finslerian mechanical system. 60

3◦ The deﬁnition of Cartan mechanical system. 4◦ The study of theory of Lagrangian and Hamiltonian mechanical systems by means of the geometry of tangent and cotangent bundles. 5◦ The geometrization of the higher order Lagrangian and Hamiltonian mechanical systems. 6◦ The determination of the fundamental equations of the Riemannian mechanical systems whose external forces depend on the higher order accelerations.

Modular geometry on noncommutative tori

MOSCOVICI Henri

The Ohio State University, USA

The concept of intrinsic curvature, which lies at the very core of classical geometry, has only lately begun to be understood in the noncommutative framework. I will present recent results in this direction for noncommutative tori, obtained in joint works with A. Connes and with M. Lesch, which illustrate both the challenges and the rewards of doing geometry on noncommutative spaces.

Nonhomogeneous metric foliations

MUNTEANU Marius

State University of New York at Oneonta, U.S.A.

We introduce a new way of constructing (nonhomogeneous) metric foliations on Lie groups endowed with a left invariant metric, and present several examples of such foliations.

Four dimensional Ricci solitons

MUNTEANU Ovidiu

University of Connecticut, USA

Shrinking Ricci solitons are self similar solutions of the Ricci flow and arise as Type I singularities of the flow. They are classified in dimension two and three, by Hamilton, Ivey and Perelman’s work. I will present some recent results about the asymptotic geometry of four dimensional complete noncompact shrinking Ricci solitons. This is based on joint work with Jiaping Wang.

A stochastic Gauss-Bonnet-Chern formula

NICOLAESCU Liviu

University of Notre Dame, USA

A Gaussian ensemble of smooth sections of a smooth vector bundle E determines a metric and a compatible connection on E.If the bundle is oriented, and the base manifold M is compact and oriented, then the zero locus of a random section in the ensemble is a random current in M and we prove that the expectation of this current is equal to the current determined by the Euler form associated to the above connection by the Chern-Weil construction. 61 Proof of Whitney ﬁbering conjecture

PAUNESCU Laurentiu

The University of Sydney, Australia Coauthors: Adam Parusinski

In this paper we show Whitney fibering conjecture in the real and complex, local analytic and global algebraic cases. For a given germ of complex or real analytic set, we show the existence of a stratification satisfying a strong (real arc-analytic with respect to all variables and analytic with respect to the parameter space) trivialization property along each stratum. We call such a trivialization arc-wise analytic and we show that it can be constructed under the classical Zariski algebro-geometric equisingularity assumptions. Using a slightly stronger version of Zariski equisingularity, we show the existence of Whitney stratified fibration, satisfying the conditions (b) of Whitney and (w) of Verdier. Our construction is based on Puiseux with parameter theorem and a generalization of Whitney interpolation. For algebraic sets our construction gives a global stratification.

Connections theory on modules and (pseudo)metrizability of generalized algebraic spaces

PEYGHAN Esmaeil

Arak university, Iran

We consider the generalized Lie algebras introduced by the same authors in [5] and using them we introduce the concept of linear ρ-connection for a module over pseudoring. Also, we extend linear ρ-connection to tensor algebra of a module and considering a free module, we express it with respect to a basis of the module. Moreover, we obtain formulas of Ricci and Bianchi type using ρ-connections. Then we deﬁne the ρ-torsion and ρ-curvature associated to the linear ρ-connection and using them we introduce torsion and curvature forms and we obtain identities of Cartan and Bianchi type. Finally, we introduce collineation and (pseudo)metrizable generalized algebraic spaces and we obtain interesting results on these spaces.

Space duality as instrument for construction of new geometries

POPA Alexandru

Institute of Mathematics and Computer Science of The Acadmy of Sciences of Moldova, Moldova

At different levels of geometry arise different kinds of duality. Duality plays an important role in projective geometry. It is also easy to observe duality of regular polyhedra of each dimension. Duality is a powerful tool for construction of new figures. Duality plays fundamental role also in study of homogeneous spaces. In this case with the power of duality one can produce not new figures in a space, but whole new spaces with completely new geometry. In the presentation the anti-hyperbolic geometry will be constructed by applying duality to hyperbolic plane.

Flat connections and resonance varieties of rank larger than 1

POPESCU Clement Radu

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

A way of studying the topological and geometrical properties of a connected CW-complex X, is to study the representation variety of the fundamental group π1(X) into a linear algebraic group G. 62

The set of g - valued flat connections, g - being the Lie algebra of the group G, an infinitesimal version of the representation variety has a filtration by resonance varieties associated to a representation of g. I present results concerning these resonance varieties of rank larger than 1.

On the volume of complex indicatrix

POPOVICI Elena

Transilvania University of Brasov, Romania

Following the study of volume of unit tangent spheres, i.e. indicatrices, in a real Finsler manifold, we investigate some properties of the volume of the complex indicatrix in a complex Finsler space. Since the complex indicatrix is an embedded CR - hypersurface of the holomorphic tangent bundle in a ﬁxed point, by means of its normal vector, the volume element of the indicatrix is determined. Thus, the volume function is pointed out and its variation is studied. Also, conditions under which the volume is constant are determined and some classes of complex Finsler spaces with constant indicatrix volume are given. Moreover, the length of the complex indicatrix of Riemann surfaces is found to be constant. In addition, considering submersions from the complex indicatrix onto almost Hermitian surfaces, we obtain that the volume of the submersed manifold has also constant value.

Counting real rational curves on K3 surfaces

RASDEACONU Rares

Vanderbilt University, SUA Coauthors: Viatcheslav Kharlamov

Real enumerative invariants of real algebraic manifolds are derived from counting curves with suitable signs. Based on a joint work with V. Kharlamov, I will discuss the case of counting real rational curves on simply connected complex projective surfaces with zero ﬁrst Chern class (K3 surfaces), equipped with an anti-holomorphic involution. An adaptation to the real setting of a formula due to Yau and Zaslow will be presented. The proof passes through results of independent interest: a new insight into the signed counting, and a formula computing the Euler characteristic of the real Hilbert scheme of points on a K3 surface, the real version of a result due to G”ottsche.

Convexity on Finsler manifolds

SABAU Sorin

Tokai University, Japan

We will discuss some convexity related problems on Finsler manifolds. In special we will focus on the geometrical and topological information provided by a convex function deﬁned on a Finsler manifold.

Symbolic powers and line arrangements

SECELEANU Alexandra

University of Nebraska-Lincoln, USA 63

Symbolic powers of ideals play a signiﬁcant part in algebraic geometry and in commutative algebra, where containment relations between symbolic powers and ordinary powers of ideals have become a focus of interest. In this talk, we consider new algebraic invariants that measure this containment. Examples will focus on the case of ideals of points arising as the singular locus of a planar line arrangement.

Topology of complex line arrangements

SUCIU Alexandru

Northeastern University, USA

I will discuss some recent advances in our understanding of the relationship between the topology, group theory, and combinatorics of an arrangement of lines in the complex plane.

Asymptotically locally euclidean complex surfaces

SUVAINA Ioana

Vanderbilt University, USA

Asymptotically locally Euclidean (ALE) scalar flat Kahler surfaces play an important role in the study of the moduli space of constant scalar curvature Kahler metrics on compact complex surfaces. In this talk, we present the classification of ALE Ricci-flat Kahler surfaces, and we also discuss the classification of ALE scalar flat Kahler surfaces.

Topology of real polynomial maps

TIBAR Mihai

Universite de Lille 1, France

The topology of fibres of a real polynomial function may change due to the behavior at infinity. We focus on the detection of those fibres which are asymptotically atypical.

A compactiﬁcation of moduli of stable vector bundles on a surface by locally free sheaves

TIMOFEEVA Nadezhda

Yaroslavl State University, Russian Federation

The compactification mentioned is obtained when families of Gieseker-stable vector bundles on the surface S are comleted by Gieseker-semistable vector bundles satisfying some additional requirement, on projective schemes of some certain class. We give functorial interpretation of this compactification as moduli space of objects we call semistable admissible pairs. The target result of the talk is the isomorphism of (main components of) the functor of moduli of semistable admissible pairs and (main conponents of) the classical functor of semistable torsion-free coherent sheaves on the surface S which leads to the Gieseker – Maruyama compactification obtained 64 by adding nonlocally free semistable torsion-free sheaves. This implies the isomorphism of corresponding moduli schemes with possibly nonreduced scheme structures and interprets Gieseker – Maruyama compactification as a compactification of moduli of semistable vector bundles by locally free sheaves only.

Generalized para-Kahler manifolds

VAISMAN Izu

University of Haifa, Israel

We define a generalized almost para-Hermitian structure to be a commuting pair (F, J ) of a generalized almost para-complex structure and a generalized almost complex structure with an adequate non-degeneracy condition. If the two structures are integrable the pair is called a generalized para-K”ahler structure. This class of structures contains both the classical para-K”ahler structure and the classical K”ahler structure. We show that a generalized almost para-Hermitian structure is equivalent to a triple (gamma,psi,F), where gamma is a (pseudo) Riemannian metric, psi is a 2-form and F is a complex (1, 1)-tensor field such that F 2 = Id, gamma(FX,Y)+ gamma(X, FY ) = 0. We deduce integrability conditions similar to those of the generalized K”ahler structures and give several examples of generalized para-K”ahler manifolds. We discuss submanifolds that bear induced para-K”ahler structures and, on the other hand, we define a reduction process of para-K”ahler structures.

Baire categories for Alexandrov surfaces

VILCU Costin

IMAR, Romania

An Alexandrov surface is a compact 2-dimensional Alexandrov space with curvature bounded below, without boundary, as defined in [2]. It is known that these surfaces are 2-dimensional topological manifolds. The set A(κ) of all Alexandrov surfaces with curvature bounded below by κ is a Baire space, and it has a dense subset of Riemannian surfaces, and a dense subset of κ-polyhedra [1]. The talk is mainly based on joint works with Joël Rouyer, and will present properties of most surfaces in A(κ), see [2], [3], [4], [5], [6]. Here most means “all, except those in a first category set”. References 1. K. Adiprasito and T. Zamfirescu – Few Alexandrov surfaces are Riemann, J. Nonlinar Convex Anal., to appear 2. A.D. Aleksandrov and V.A. Zalgaller – Intrinsic geometry of surfaces, Transl. Math. Monographs, Providence, RI, Amer. Math. Soc., 1967 3. Y. Burago, M. Gromov and G. Perelman – A. D. Alexandrov spaces with curvature bounded below, Russian Math. Surveys 47 (1992), 1-58 4. J. Itoh, J. Rouyer and C. Vˆılcu – Moderate smoothness of most Alexandrov surfaces,Int.J.Math.,toappear 5. J. Rouyer and C. Vˆılcu – The connected components of the space of Alexandrov surfaces, in D. Ibadula and W. Veys (eds.), Bridging Algebra, Geometry and Topology, Springer Proc. Math. Stat. 96 (2014), 249-254 6. J. Rouyer and C. Vˆılcu – Simple closed geodesics on most Alexandrov surfaces, Adv. Math., to appear 7. J. Rouyer and C. Vˆılcu – Farthest points on most Alexandrov surfaces, arXiv:1412.1465 [math.MG] Section 3 Real and Complex Analysis, Potential Theory

Weak and strong type boundedness of Hardy-Littlewood maximal operator on weighted Lorentz spaces

AGORA Elona

University of Crete, Greece Coauthors: J. Antezana, M. J. Carro, J. Soria

In this presentation we will discuss the weak and strong type boundedness of Hardy-Littlewood maximal operator, M, on weighted Lorentz spaces. In fact, we will show that they are equivalent whenever p>1. The weighted Lorentz spaces generalize weighted Lebesgue spaces, as well as the classical Lorentz spaces, where the boundedness of M is characterized by the Ap and Bp conditions, respectively. Thus, our characterization extends and uniﬁes these results. Moreover, since the boundedness of M is involved in the boundedness of the Hilbert transform, H, the aforementioned results over M lead to a complete characterization of H on weighted Lorentz space. The results are based on joint works with J. Antezana, M. J. Carro, and J. Soria.

On Loewner domains in metric spaces

ANDREI Anca

National Computer Science College “Spiru Haret” Suceava, Romania

This presentation continues my results that were presented in [1], [2], [3] and [4]. The main purpose is to give some properties of a Loewner domain in a Q - Ahlfors regular space, Q>1. First, we shall prove that, in a locally path connected and Q - Ahlfors regular space, a bounded Q - Loewner domain is locally arc connected on the boundary and weakly quasiconformal accessible at each boundary point. Eventually, we deal with the extension theorems to boundary for quasiconformal mappings on domains in Q - Ahlfors regular spaces, when one of domain is a Q -Loewner domain. In [1], we have proved that if X and Y are complete Q - Ahlfors regular spaces, f : D → D is a metrically quasiconformal mapping, D ⊂ X and D ⊂ Y are bounded Q - Loewner domains, then f can be extended to a homeomorphism f ∗ : D → D. We shall prove that, instead of complete spaces, we can assume proper spaces. In this case, f is a quasiconformal mapping in any sense. References 1. A. Andrei – Extension theorems for quasiconformal mappings in Ahlfors regular spaces, Math Reports, 7(57), 3(2005), 167-178. 2. A. Andrei – Quasiconformal mappings in Ahlfors regular spaces, Rev. Roumaine Math. Pures Appl., 54 (2009), 5-6, 361-373. 3. A. Andrei – Quasiconformal mappings on certain classes of domains in metric spaces, Buletin of the Univ. of Brasov, 5(54), 2012. 4. A. Andrei – On quasiextremal distance domains in metric spaces, Math. Reports 15(65), 4 (2013), 319-329. 5. I. Heinonen – P. Koskela, Quasiconformal spaces with controlled geometry, Acta Math, 181 (1998), 1-61. 6. O. Martio, V. Ryazanov, U. Srebro and E. Yakubov – Moduli in the modern mapping theory, Springer, New York, 2009.

65 66 Semiliniarity of space of sn-bounded multifunctions

APREUTESEI Gabriela

“Alexandru Ioan Cuza” University of Ia¸si, Romania Coauthors: Anca Croitoru

In this presentation we study a metric structure on the space of sn-bounded set-valued functions. Thus we introduce a metric d1 of supremum type and a near metric d2 deﬁned by a Sugeno integral, and compare the induced topologies τ1 and τ2. We also study the translated topology τ3 of τ1 and establish suﬃcient and characteristic conditions for τ3 to be semi-linear.

A Cauchy functional inequality

ATANASIU Dragu

University of Bor˚as, Sweden Coauthors: Lucian Beznea

In this presentation we give a solution to a moment problem related to the Cauchy Functional Equation on commutative semigroups. A result related to potential theory is also obtained.

ω Approximation by generalized deferred Ces´aro means in the space Hp

BAYINDIR Hilal

Mersin University, Department of Mathematics, Turkey Coauthors: Deger Ugur

The deferred Cesáro transformations which have useful properties not possessed by the Cesáro transformation was considered by R.P. Agnew in [1]. In [2], Deˇger and Kü¸cükaslan introduced a generalization of deferred Cesáro transformations by taking account of some well known transformations such as Woronoi-Nörlund and Riesz, and considered the degree of approximation by the generalized deferred Cesáro means in the space H(α, p), p ≥ 1, 0 <α≤ 1 by concerning with some sequence classes. In 2014, Nayak et al. studied ω the rate of convergence problem of Fourier series by Deferred Cesáro Mean in the space Hp introduced by Das et al. in [2]. ω In this presentation, we shall give the degree of approximation by the generalized deferred Cesáro means in the space Hp . Therefore the results given in [4] are generalized according to the summability method. References 1. R. P. Agnew – On deferred Cesáro means, Ann. Math., 33 (1932), 413–421. 2. G. Das, A. Nath and B. K. Ray – An estimate of the rate of convergence of Fourier series in generalized Hölder metric, Analysis and Applications (Ujjain, 1999), Narosa (New Delhi, 2002), 43–60. 3. U. De˘ger and M. Kü¸cükaslan – A generalization of deferred Cesaro means and some of their applications, Journal of Inequalities and Applications, 2015 (2015), 1–16. 4. L. Nayak, G. Das and B. K. Ray – An estimate of the rate of convergence of Fourier series in the generalized Hölder metric by Deferred Cesáro Mean, Journal of Mathematical Analysis and Applications, 420 (2014), 563–575.

Nearly saturation, balayage and ﬁne carrier in excessive structures

BENFRIHA Habib

Universite d’Oran 1, Algeria Coauthors: Ileana Bucur 67

We give minimal conditions on the space X, such that a good part of potential theory in the frame of excessive structure, associated with a proper submarkovian resolvent family of kernels on X, may be developed. We characterize the regular excessive elements as being those excessive functions for which the pseudobalayages associated with, are balayages and we construct a ﬁne carrier theory without use any kind of compactiﬁcation.

On some lp-type inequalities involving quasi monotone and quasi lacunary sequences

BERISHA Faton

University of Prishtina, Kosovo Coauthors: Nimete Berisha, Murat Sadiku

We give some lp-type inequalities about sequences satisfying certain quasi monotone and quasi lacunary type properties. As special cases, reverse lp-type inequalities for non-negative decreasing sequences are obtained. The inequalities are closely related to Copson’s and Leindler’s inequalities, but the sign of the inequalities is reversed. We also give an application of the inequalities in Foruier analysis.

Univalent mappings, horosphere boundary and prime end theory in higher dimension

BRACCI Filippo

Universit`a di Roma “Tor Vergata”, Italia

We give an account of the theory of univalent mappings in the ball of higher dimension, highlighting the diﬀerence between the one dimensional case and the higher dimensional one (density of automorphisms, existence of bounded support functions in the class S0). We also describe an new approach on complete hyperbolic complex manifolds in order to deﬁne an abstract boundary by means of suitable sequences which can be seen as “horosphere sequences”, and that can be considered a prime end type theory in higher dimension. All biholomorpisms extend to homeomorphisms on such horosphere boundaries. As a consequence we give some applications of this construction to study the boundary behavior of univalent mappings in the unit ball.

Some new classes of analytic functions

BREAZ Daniel

1 Decembrie 1918 University of Alba Iulia, Romania

In this talk I present some new classes of analytic functions. Some suﬃcient conditions are proved and some connections with other known classes are presented. 68 Mocanu and Serb univalence criteria for some integral operators

BREAZ Nicoleta

1 Decembrie 1918 University of Alba Iulia, Romania Coauthors: Virgil Pescar

We obtain Mocanu and Serb type univalence criteria for two general integral operators deﬁned by analytic functions in the open unit disk.

Generalized Arzela-Ascoli theorem and applications

BUCUR Gheorghe

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

For any two arbitrary sets X and Y and any function f deﬁned on the cartesian product X × Y with values in a metric space, we state a very general Arzela-Ascoli result. The function f has some compact property with respect to X if and only if it has this property with respect to Y . We give several applications of this general result.

Fixed point theory and contractive sequences

BUCUR Ileana

Universitatea Tehnic˘a de Construct¸ii Bucure¸sti, Romania

In an abitrary metric space X we introduce the notion of contractive sequence and we show that if X is complete then such sequences are convergent. Some applications to the ﬁxed point theory are given.

Optimal Hardy constants for Schr¨odinger operators with multi-singular inverse-square potentials

CAZACU Cristian

University Politehnica of Bucharest and Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania |∇ |2 2 In this presentation we consider the optimization problem μ (Ω):=inf Ω u dx Ω Vu dx ,where V is a multi-singular potential with n singular poles (n ≥ 2) which arise either in the interior or on the boundary of a smooth bounded domain Ω ⊂ RN , N ≥ 2. First we prove that whenever Ω contains all the singularities in the interior, then μ(Ω) >μ(RN )ifn ≥ 3 and μ(Ω)=μ(RN ) when n = 2 (It is known that μ(RN )=(N − 2)2/n2). Furthermore, we also analyze the situation in which all the poles are located on the boundary. In this case, we obtain a new critical barrier for the best Hardy constant corresponding to V ,whichisμ(Ω)=N 2/n2. In addition, we also discuss the attainability of μ(Ω). A special case for the non-attainability of μ(Ω) corresponds to the bipolar case n =2. 69 Existence and classiﬁcation of singular solutions to nonlinear elliptic equations with a gradient term

CIRSTEA Florica

The University of Sydney, Australia Coauthors: Joshua Ching

In this talk, we present a complete classification of the behavior near 0 (and at ∞ when Ω = RN ) of all positive solutions of Δu = uq|∇u|m in Ω \{0},whereΩ is a domain in RN (N ≥ 2) and 0 ∈ Ω. Here, q ≥ 0 and min(0, 2) satisfy m + q>1. Our N−m,(N−1) ∞ classification depends on the position of q relative to the critical exponent q∗ := N−2 (with q∗ = if N = 2). We prove the following: If q2), then 0 is a removable singularity for all positive solutions. Furthermore, any positive solution in RN \{0} is either constant or has a weak/strong singularity at 0. The latter is possible only for q1when all solutions decay to 0. We also provide sharp existence results, emphasizing the more difficult case of min(0, 1) where new phenomena arise. This is joint work with Joshua Ching (The University of Sydney).

Some properties of open discrete ring mappings

CRISTEA Mihai

University of Bucharest, Faculty of Mathematics and Computer Sciences, Romania

We study the properties of open, discrete ring mappings satisfying generalized modular inequalities, namely the equicontinuity, the distortion and the limit mapping of certain homeomorphisms from these classes. Such mappings generalize the known class of quasiregular mappings and their extensions known as mappings of ﬁnite distortion. We apply our results to open discrete ring mappings n n q f : D ⊂ R → Df ⊂ R satisfying condition (N) and having local ACL inverses, and we focus especially on the case n−1

On approximation by matrix means of the multiple Fourier series in the H¨older metric

DEGER Ugur

Mersin University, Department of Mathematics, Turkey

Suppose that f(x, y) is integrable in the sense of Lebesgue over the square S2 := S(−π, π; −π, π) and of period 2π in x and in y. In [1] and [2], A. I. Stepanets has been investigated the problem of the approximation of functions f(x, y) by the partial sums of their Fourier sums under the some conditions. S. Lal has been studied the approximation of functions belonging to Lipschitz class by matrix summability method for double Fourier series under the uniform norm in [3]. Naturally, there has arisen the problem of considering similar questions also in the case of periodic functions of two variables in the Hölder metric. In this talk, we shall give the degree of approximation to functions belonging to Hölder class by matrix summability method of multiple Fourier series in the Hölder metric. References

1. A. I. Stepanets – The approximation of certain classes of diferentiable periodic functions of two variables by Fourier sums, Ukrainian Mathematical Journal(Translated from Ukrainskii Matematieheskii Zhurnal, Vol. 25, No. 5, pp. 599-609, September-October, 1973), 26 (1973) 498–506. 2. A. I. Stepanets – Approximation of certain classes of periodic functions of two variables by linear methods of summation of their Fourier series, Ukrainian Mathematical Journal(Translated from Ukrainskii Matematieheskii Zhurnal, Vol. 26, No. 2, pp. 205-215, March-April, 1974), 26 (1974) 168–179. 70

3. S. Lal – On the approximation of function f(x, y) belonging to Lipschitz class by matrix summability method of double Fourier series, Journal of the Indian Math. Soc. (78)1-4 (2011), 93–101.

Decouplings and applications to number theory and PDEs

DEMETER Ciprian

Indiana University, Bloomington, USA

We discuss a new Fourier analytic approach to estimating a wide variety of exponential sums. Applications include estimates for the number of solutions to various Diophantine inequalities, Vinogradov mean value-type theorems and progress on the Lindelof hypothesis. Among the consequences in PDEs, we will mention the sharp Strichartz estimates on the higher dimensional torus and progress on the local smoothing equation.

Direct methods through convergence in measure

FLORESCU Liviu

Faculty of Mathematics, “Al. I. Cuza” University of Iasi, Romania

Tonelli’s direct method provides conditions on H and f that ensure the existence of a solution for the problem (P )inff(t, u(t), ∇u(t))dt, u∈H Ω where, generally, H is equipped with a weak topology. In this contribution we study the continuity of integral and the compactness of minimizing sequences for the above problem with respect to the topology of convergence in measure on H.

On the location of the zeros of Bohr functions

GHISA Dorin

York University, Canada

Given a general Dirichlet series, a basis is attached to the sequence of exponents. With the corresponding Bohr matrix, a Bohr function is deﬁned. We are studying the location of the zeros of such a function.

Compactness and density of certain reachable families of the Loewner ODE in Cn

IANCU Mihai

Babes-Bolyai University, Cluj-Napoca, Romania

In this presentation we focus on the control-theoretic approach to the Loewner ODE, developed by O. Roth in C and by I. Graham, H. Hamada, G. Kohr, M. Kohr in Cn. We present some results concerning compactness and density of certain normalized time-T -reachable 71 families of the Loewner ODE in Cn,whereT ∈ [0, ∞]. Then we study some generalizations suggested by the last mentioned authors. In particular, we prove a generalization to Cn of a well-known result due to Loewner from 1923.

q-completeness and q-completeness with corners of unbranched Riemann domains

IONITA George - Ionut

University Politehnica of Bucharest and Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

In 2007, Colt¸oiu and Diederich showed that if p : Y → X is a Riemann domain between complex spaces with isolated singularities such that X is Stein and p is a Stein morphism, then Y is Stein. We improve the above mentioned result in two ways: - we suppose that X is q-complete and we obtain that Y is q-complete; - we suppose that the morphism p is locally q-complete with corners and we obtain that Y is q-complete with corners.

Non existence of Levi ﬂat hypersurfaces with positive normal bundle in compact K¨ahler manifolds of dimension ≥ 3

IORDAN Andrei

Institut de Mathematiques de Jussieu, Univ. Pierre et Marie Curie, France

In 1993, D. Cerveau conjectured the non existence of smooth Levi flat real hypersurfaces in the complex n-dimensional projective space CP n, n ≥ 2. The conjecture was proved for n ≥ 3 by A. Lins Neto in 1999 for real analytic Levi flat hypersurfaces and by Y.-T. Siu in 2000 for C12 smooth Levi flat hypersurfaces. It is still open for n =2. A principal element in the proof of the non existence of smooth Levi flat hypersurfaces in CP n for n ≥ 3 is that the Fubini-Study metric induces a metric with positive curvature on every quotient of the tangent space. In 2008, M. Brunella proved that the normal bundle to the Levi foliation of a closed real analytic Levi flat hypersurface in a compact Kähler manifold of dimension n ≥ 3 does not admit any Hermitian metric with leafwise positive curvature. He conjectured that this is also true for C∞ Levi flat hypersurfaces. In this talk, we will give a proof to this conjecture of M. Brunella.

Finite coverings of complex spaces by connected Stein open sets

JOITA Cezar

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania Coauthors: Mihnea Coltoiu

We prove that every connected complex space has a ﬁnite covering by connected Stein open subsets. Joint work with Mihnea Colt¸oiu. 72 The generalized Loewner diﬀerential equation in higher dimensions. Applications to extremal problems for biholomorphic mappings

KOHR Gabriela

Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania Coauthors: : Ian Graham, Hidetaka Hamada, and Mirela Kohr

In this presentation we survey classical and also recent results related to the generalized Loewner diﬀerential equation on the n n 0 n Euclidean unit ball B in C . We also present applications in the study of extreme points and support points for the family SA(B ) of mappings with A-parametric representation, i.e. normalized biholomorphic mappings f on Bn which can be imbedded in normal tA n Loewner chains f(z, t)=e z + ··· such that f = f(·, 0), where A ∈ L(C )withk+(A) < 2m(A). Here k+(A) is the Lyapunov index of A and m(A)=min{ A(z),z : z =1}. We also use some control theoretical methods to discuss the case of reachable families of biholomorphic mappings generated by the generalized Loewner diﬀerential equation on Bn. Certain open problems and conjectures are also considered. Finally, we point recent related results due to F. Bracci, O. Roth, and S. Schleissinger. Joint work with Ian Graham (Toronto), Hidetaka Hamada (Fukuoka), and Mirela Kohr (Cluj-Napoca)

Extremizers for the 2D Kakeya problem

LIE Victor

Purdue University, United States Coauthors: Michael Bateman

Our talk will adress the following theme: 2n Formulation of the problem. Let Q0 be the unit square and let T be a collection of M separated tubes inside Q having length one and −2n ∈ N ∪ − − 9 width M for some large M, n . Assume that T = T1 T2 with T1 consisting of tubes that have slopes between [ 1, 10 ]and 9 T2 having tubes with slopes in [ 10 , 1]. Our goal is to understand both the structure and the size of the level sets

{F>α} τ τ where α>0 and F := ( τ∈T1 χ )( τ∈T2 χ ) stands for the bilinear Kakeya function. Our analysis will involve additive combinatorics (e.g. Plunnecke sum-set estimate) and incidence geometry (e.g. Szemeredi-Trotter inequality) techniques and relates with a class of problems including Bourgain’s sum-product theorem and Katz-Tao ring conjecture. This is a joint work with Michael Bateman.

Improved Sobolev inequalities in the classical Lorentz spaces

MARCOCI Anca Nicoleta

Technical University of Civil Engineering Bucharest, Romania

In this contribution we present reﬁned Sobolev inequalities using as base space classical Lorentz spaces associated to a weight from the Arino-Muckenhoupt class. This class of weights appeared in a paper of M. A. Arino and B. Muckenhoupt from 1990, in connection with the Hardy inequality with weights for non-increasing functions. This talk is based on a joint work with D. Chamorro and L. Marcoci. 73 On some factorization results

MARCOCI Liviu Gabriel

Technical University of Civil Engineering Bucharest, Romania

G. Bennett in 1996 studied some classical inequalities from the point of view of factorization between some spaces of sequences. In this talk we present some factorizations in the case of weighted function spaces. In particular, we derive the best constants in some weighted inequalities.

An improvement of Gruss inequality

MINCULETE Nicusor

Transilvania University of Brasov, Romania

The aim of this presentation is to show a reﬁnement of Gruss inequality using several inequalities in an inner product space. We also present several remarks to the Cauchy-Schwarz inequality.

On some properties of Tsallis hypoentropies and hypodivergences

MITROI-SYMEONIDIS Flavia-Corina

Lumina - University of South-East Europe, Bucharest, Romania Coauthors: Eleutherius Symeonidis, Shigeru Furuichi

The aim of this presentation is to extend Ferreri’s hypoentropy to the Tsallis statistics. We introduce the Tsallis hypoentropy and the Tsallis hypodivergence and describe their mathematical behavior. Fundamental properties like nonnegativity, the chain rule and subadditivity are established.

Cheeger diﬀerentiable Orlicz-Sobolev functions on metric spaces

MOCANU Marcelina

“Vasile Alecsandri” University of Bacau, Romania

We prove sufficient conditions for the Cheeger differentiability a.e. of the functions in the Orlicz-Sobolev space N 1,Φ (X), where (X, d, μ) is a doubling metric measure space and Φ is a Young function. We also study the LΦs −differentiability of the functions in 1,Φ N (X), where Φ satisfies some Calderón-type growth conditions. Here Φs denotes the Sobolev conjugate of Φ with respect to the homogeneous dimension s of X. In the special case where Φ (t)=tp with 1 ≤ p<∞ and p>s− 1 we prove that every monotone 1,Φ function in Nloc (X) (in particular, every continuous quasiminimizer for the p−Dirichlet energy integral) is Cheeger differentiable a.e. Our main tool is the extension of Stepanov’s differentiability theorem to metric measure spaces, proved by Balogh, Rogovin and Zürcher. 74 Iterated Fourier series

MUSCALU Camil

Cornell University, USA

The goal of the lecture is to describe a natural bridge which connects the KdV equation to the absolute Galois group. The “pillars” of this bridge turned out to be the analytical objects from the title.

On the algebra of singular operators with shift

NEAGU Vasile

Moldova State University, Republic of Moldova

As it is known, the Noether theorems play an important role in the theory of singular integral equations. A singular integral operator with a Carleman shift is defined to be the operator of the form n bk(t) ϕ(τ) (Mϕ)(t)= ak (t) ϕ (αk (t)) + dτ , (0.4) − k=0 πi Γ τ αk (t) where ak,bk are function given on the contour Γ . In the present talk on the least subalgebra of the algebra L(Lp(Γ,ρ)), containing all operators of the form (0.4) with piecewise continuous coefficients, is studied. It is necessary to consider separately the case, when α preserves the orientation on Γ , and the case, when α reverses the orientation. The algebra contains the set 0 of all sums of compositions of operators of the form (0.4), and also operators, which are limits (in the sense of convergence by the norm of operators) of a sequence of operators from 0 . The research of the set 0 is based on the suggested by I. Gohberg and N.Krupnik method of the study of complicated operators, which allows to receive necessary and sufficient conditions of Noetherian property of operators from . In the talk the existence of such an isomorphism between and some algebra A of singular integral operators with a Cauchy kernel that an arbitrary operator from and its image are simultaneously Noetherian or not Noetherian is proved. It allows us to introduce the concept of a symbol for all operators from and, using known results for algebra A, in terms of a symbol to receive conditions of Noetherian property for all operators from , including for \ 0. Through the symbol the index of operators A ∈ can be also expressed. The set of values of the determinant of a symbol A(t, ξ) represents a closed continuous curve, which can be oriented in natural way. The index of this curve (i.e. the number of turns about the origin), taken with the opposite sign, is equal to the index of the operator A.

Harmonic Bergman spaces with radial measure weight on the ball

NISHIO Masaharu

Osaka City University, Japan Coauthors: Kiyoki Tanaka

We consider harmonic Bergman spaces on the ball. In this talk, we deal with space with radial measure weight. For two radial measures, we introduce an averaging function, to give the conditions for corresponding Toeplitz operators to be bounded and compact. We also discuss the boundary behavior of the harmonic Bergman kernels. 75 Perturbations with kernels of the generator of a Markov process

OPRINA Andrei-George

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania Coauthors: Lucian Beznea

We present the perturbation with kernels of the generator of a Markov process. Our approach avoids any transience hypothesis and it is motivated by recent applications in inﬁnite dimensional situations: measure-valued branching processes and the associated nonlinear equations, quasi-regular generalized Dirichlet forms. The talk is based on joint works with Lucian Beznea.

Strong diﬀerential superordination and sandwich theorem obtained with some new integral operators

OROS Georgia Irina

University of Oradea, Faculty of Sciences, Romania Coauthors: Gheorghe Oros

The concept of strong differential subordination was introduced in by J.A. Antonino and S. Romaguera using the classical notion of differential subordination introduced by S.S. Miller and P.T. Mocanu. This concept was developed by the authors of the present talk in a series of papers. The concept of strong differential superordination was introduced by G.I.Oros, like a dual concept of the strong differential subordination and developed by the authors in other papers. In this talk, we study certain strong differential superordinations, obtained by using a new integral operator previously introduced in the paper G.I. Oros, Gh. Oros, R. Diaconu, Differential subordinations obtained with some new integral operators, J. Computational Analysis and Application, 19(2015), no. 5, 904-910.

Univalence criteria for analytic functions deﬁned in non-convex domains

PASCU Nicolae

Kennesaw State University, USA

We consider two general classes of non-convex domains: the ﬁrst class consists of simply connected planar domains characterized by a certain deformation from convexity given by the convexity constant of the domain, the second being the class of ϕ-convex domains introduced by M. O. Reade. We derive new univalence criteria for analytic functions deﬁned on these classes of non-convex domains which generalize some well known univalence criteria (Ozaki - Nunokawa univalence criterion).

Locally stein open subsets in normal Stein spaces

PREDA Ovidiu

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

We present a result related to the local Steinness problem: if Ω is a locally Stein open subset of a Stein space X,doesitfollowthat Ω is itself Stein? We will prove that if X is normal, then for every sequence of points (xn)n which tends to a limit x ∈ ∂Ω \ Sing(X), there exists a holomorphic function f on Ω which is unbounded on (xn)n. Then, we will use this result to obtain a characterization theorem for a particular case of the Serre problem. 76 Some characteristic properties of analytic functions

SALAGEAN Grigore Stefan

Babes-Bolyai University Cluj-Napoca, Romania

We consider a class of analytic functions defined in the open unit disk satisfying a certain subordination condition where is used a differential operator We obtain some characteristic properties giving the coefficient inequality, radius and subordination results, and an inclusion result for the above class. Sharp bounds for the initial coefficient and for the Fekete-Szegö functional are determined, and also some integral representations are given.

Harmonic families of closed surfaces

SYMEONIDIS Eleutherius

Katholische Universitaet Eichstaett-Ingolstadt, Germany

The mean value property of harmonic functions and other quadrature identities result by passing to the limit in families of surfaces, over which every harmonic function has the same mean value.

Markov processes on the Lipschitz boundary for the Neumann and Robin problems

VLADOIU Speranta

University of Bucharest, Romania Coauthors: L. Beznea

We investigate the Markov process on the boundary of a bounded Lipschitz domain associated to the Neumann and Robin boundary value problems. We ﬁrst construct Lp-semigroups of sub-Markovian contractions on the boundary, generated by the boundary conditions and we show that they are induced by the transition function of the forthcoming processes. As in the smooth boundary case the process on the boundary is obtained by the time change with the inverse of a continuous additive functional of the reﬂected Brownian motion. The talk is based on joint work with Lucian Beznea.

On some spaces of sequences of interval numbers

YASEMIN GOLBOL Sibel

Mersin University, Department of Mathematics, Turkey Coauthors: Ugur Deger

Interval arithmetic was first suggested by Dwyer in [3]. In [2], Chiao introduced the sequences of interval numbers and defined usual convergence of sequences of interval number. Esi and Yasemin Gölbol in [1] defined the metric spaces c0(f,p,s), c(f,p,s), l∞(f,p,s) and lp(f,p,s) of sequences of interval numbers by a modulus function. In this study, we consider a generalization of these metric spaces. Forthisaim,letψ(k)beapositivefunctionforallk ∈ N such that

lim ψ(k)=0, (0.5) k→∞

Δ2ψ(k)=ψ(k − 1) − 2ψ(k)+ψ(k +1)≥ 0. (0.6) 77

Therefore, according to class of functions which satisfying the conditions (0.16) and (0.6) we deal with the metric spaces c0(f,p,ψ), c(f,p,ψ), l∞(f,p,ψ) and lp(f,p,ψ) of sequences of interval numbers deﬁned by a modulus function and state some topological and inclusion theorems related to these spaces. References

1. A. Esi and S. Yasemin G¨olbol – Some spaces of sequences of interval numbers deﬁned by a modulus function, Global Journal of Mathematical Analysis, 2 (2014), 11–16. 2. K. P. Chiao – Fundamental properties of interval vector max-norm, Tamsui Oxford Journal of Mathematics., 18 (2002), 219–233. 3. P. S. Dwyer – Linear Computation, Wiley, New York, 1951.

Section 4 Ordinary and Partial Diﬀerential Equations, Variational Methods, Optimal Control

The cost of approximate controllability and an unique continuation result at initial time for the Ginzburg-Landau equation

ARAMA˘ Bianca-Elena

”Alexandru Ioan Cuza” University, Ia¸si, Romania

We reconsider the Carleman inequalities for the Ginzburg-Landau equation obtained by Rosier and Zhang and we focus on determining precise estimates for the constants involved, i.e., the explicit dependence on T , where [0,T]isthemaximumintervaloftimewe consider for the systems. We then study the cost of approximate controllability for the linearized equation, i.e., of the minimal norm of a control needed to steer the system in a ε-neighborhood of a given target. In order to obtain explicit bounds of the cost of approximate controllability, we ﬁrst have to obtain sharp bounds on the cost of controlling to zero. The key point in proving the cost of approximate controllability is to understand how observability inequalities may be used to obtain sharper results on the coercivity of the functional J. Of course, sharp coercivity estimates yield sharp upper bounds on the norms of the minimizer.Another interesting consequence of the explicit dependence of the constants in Carleman estimates is an unique continuation result at initial time.

Some inequalities about the eigenvalues of a two terms diﬀerential operator and the sum of the eigenvalues of that operator

BAKSI Ozlem

Yildiz Technical University, Turkey

In this work, we ﬁnd an asymptotic formula for the sum of the eigenvalues of a diﬀerential operator L in the space L2(0π; H). Here, H is a separable Hilbert space.

Prescribed mean curvature of manifolds in Minkowski space

BEREANU Cristian

University of Bucharest and IMAR, Romania

In this talk we present existence and multiplicity of classical positive solutions for Dirichlet problems with the mean curvature operator in Minkowski space. We use a combination of degree arguments, critical point theory for lower semicontinuous functionals and the upper and lower solutions method.

79 80 Relaxation and duality for the L∞ optimal mass transport problem

BOCEA Marian

Loyola University Chicago, U.S.A.

The original mass transport problem, formulated by Gaspard Monge in 1781, asks to ﬁnd the optimal volume preserving map between two given sets of equal volume, where optimality is measured against a cost functional given by the integral of a cost density. After reviewing some aspects of this classical problem, I will describe recent joint work with Nick Barron and Robert Jensen (Loyola University Chicago) leading to a duality theory for the case of relaxed L∞ cost functionals acting on probability measures with prescribed marginals.

Controlling turbulence in ﬂuid-elasticity interactions

BOCIU Lorena

NC State University, United States

Reducing and controlling turbulence inside the fluid flow in fluid-structure interactions is particularly relevant in the design of small- scale unmanned aircrafts and morphing aircraft wings, and is also of great interest in the medical community (for example, blood flow in a stenosed or stented artery). Existing literature on control problems in fluid-structure interactions is predominantly focused on the assumption of small but rapid oscillations of the solid body, so that the common interface is assumed static. In comparison, we address the issue of minimizing turbulence inside the fluid in the case of a moving boundary interaction between a viscous, incompressible fluid and an elastic body. The PDE model consists of the Navier-Stokes equations coupled with the nonlinear equations of elastodynamics. Due to the strong nonlinearity of the model and the moving domains, the minimization problem requires a combination of tools from optimal control and sensitivity/shape analysis. In this talk, we will discuss the existence of an optimal control and the derivation of the first order necessary optimality conditions.

Primal-dual algorithms for complexly structured nonsmooth convex optimization problems

BOT¸ Radu Ioan

University of Vienna, Austria

In this talk we address the solving of a primal-dual pair of convex optimization problems with complex and intricate structures, by actually solving the corresponding system of optimality conditions, which involves mixtures of linearly composed, Lipschitz single- valued and parallel-sum type monotone operators. The proposed numerical schemes have as common feature the fact that the set-valued maximally monotone operators are processed individually via backward steps, while the single-valued ones are evaluated via explicit forward steps. The performances of the primal-dual algorithms are illustrated by numerical experiments on real-life problems arising in image and video processing, optimal portfolio selection and machine learning.

Null controllability of coupled systems of PDE’s

CASTRO Carlos

Universidad Politecnica de Madrid, Espana Coauthors: Luz de Teresa 81

We present a new strategy for the control of coupled systems of PDE’s. The main idea is to write the solutions and controls of the system in series form where each term satisfies a new control problem, still coupled, but that can be written in cascade form. This means that the coupling term appears only in one of the equations and the controllability can be deduced from suitable observability inequalities for the uncoupled equations. The control for the fully coupled system is then obtained combining the controllability of this reduced system with the convergence of the series. We apply this technique to the linear system of thermoelastic plates when we consider two different controls supported in some, possibly different, open sets.

Existence results for a class of quadratic integral inclusions

CERNEA Aurelian

University of Bucharest, Romania

We are concerned with the following integral inclusion

t x(t) ∈ (fx)(t) k(t, s)F (s, x(s))ds, t ∈ I := [0,T], 0 where f : C(I,Rn) → C(I,Rn), k : I × I → Rn, F : I × Rn →P(Rn) is a set-valued map and, for simplicity, by k(t, s)F (s, x(s)) we mean the set {; v ∈ F (s, x(s))} with <, > the scalar product on Rn. InthecasewhenF (·, ·) has convex values and is Carath´eodory, using a sort of Leray-Schauder nonlinear alternative for set-valued maps we prove the existence of solutions for the integral inclusion considered. Another existence result is obtained in the case when the set-valued map has non convex values and is lower semicontinuous. The proof is based on the Leray-Schauder alternative for single-valued maps and Bressan-Colombo-Fryszkowski selection theorem.

Transvectants and Lyapunov quantities for bidimensional polynomial systems of diﬀerential equations with nonlinearities of the fourth degree

CIUBOTARU Stanislav

Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, Republic of Moldova Coauthors: Iurie Calin

Let us consider the bidimensional polynomial system of diﬀerential equations with nonlinearities of the fourth degree

dx dy = P1(x, y)+P4(x, y), = Q1(x, y)+Q4(x, y), (0.7) dt dt where Pi(x, y),Qi(x, y) are homogeneous polynomials of degree i with real coefficients. The GL(2, R)-comitants of the first degree with respect to the coefficients of the system (0.7) have the form 1 ∂Pi(x, y) ∂Qi(x, y) Ri = Pi(x, y)y − Qi(x, y)x, Si = + ,i=1, 4. (0.8) i ∂x ∂y

By using the comitants Ri and Si (i =1, 4), system (0.7) can be written in the form

dx 1 ∂R1 1 1 ∂R4 4 dy 1 ∂R1 1 1 ∂R4 4 = + S1x + + S4x, = − + S1y − + S4y. (0.9) dt 2 ∂y 2 5 ∂y 5 dt 2 ∂x 2 5 ∂x 5

Let f and ϕ be polynomials in the coordinates of the vector (x, y) ∈ R2 of degrees r and ρ, respectively. The polynomial

− − k k k (k) (r k)!(ρ k)! − h k ∂ f ∂ ϕ (f,ϕ) = ( 1) k−h h h k−h r!ρ! h=0 h ∂x ∂y ∂x ∂y is called the transvectant of the index k of the polynomials f and ϕ. Using system (0.7) written in the form (0.9), the comitants (0.8) and the notion of the transvectant for the system (0.7) the recurent ∗ formulas for the Lyapunov quantities: G8, G14, G20, ..., G6m+2, ...,wherem ∈ N were constructed. 82

An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions

CSETNEK Ern¨o Robert

University of Vienna, Austria

We present a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.

On the bounded and stabilizing solution of a generalized Riccati diﬀerential

DRAGAN Vasile

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

On the bounded and stabilizing solution of a generalized Riccati differential equation with periodic coefficients arising in connection with a zero sum linear quadratic stochastic differential game. We consider a system of coupled matrix nonlinear differential equations arising in connection with the solution of a zero sum two players linear quadratic differential game for a system modeled by an Ito differential equation subject to random switching according with a standard homogeneous Markov process with a finite number of state. The system of differential equations under consideration contains as special cases the game theoretic Riccati differential equations arising in the solution of the H∞ control problem from the deterministic and stochastic cases. Among the global solution of the generalized game theoretic Riccati equation, an important role in the construction of the solution of the zero sum two players linear quadratic differential game is played by the so called stabilizing solution. In this work we present a set of conditions which guarantee the existence and uniqueness of the bounded and stabilizing solution of the Riccati differential equation under consideration. Also, we shall provide a method for numerical computation of this bounded and stabilizing solution. It is worth mentioning that we do not know a priori neither an initial value nor a boundary value of the bounded and stabilizing solution of the Riccati differential equation under investigation. That is why, the numerical methods applicable for the approximation of the solution of a Cauchy problem or of a boundary value problem associated to a differential equation cannot be used to compute the bounded and stabilizing solution of a Riccati differential equation. The bounded and stabilizing solution of the generalized game theoretic Riccati differential equation is obtained as a limit of a sequence of bounded and stabilizing solutions of some Riccati differential equations with defined sign of the quadratic parts. For this kind of Riccati differential equation already exits reliable iterative procedures to obtain the stabilizing solution. References 1. V. Dragan – Stabilizing solution of periodic game theoretic Riccati differential equation of stochastic control, IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnu026, (2014).

On the spectrum of some eigenvalue problems

FARCASEANU Maria

University of Craiova, Romania 83

The goal of this presentation is to emphasize diﬀerent situations regarding the nature of the spectrum of some eigenvalue problems involving elliptic diﬀerential operators. More precisely, we will show that the spectrum of such an eigenvalue problem can be either discrete or continuous or a combination of the above two cases involving a continuous part plus an isolated point.This is a joint work with Mihai Mihailescu and Denisa Stancu-Dumitru.

Inverse problems from control theory

FAVINI Angelo

University of Bologna, Italy Coauthors: Mohammed Al Horani

Some inverse problems for abstract diﬀerential equations are discussed. The motivation comes from relevant equations of interest from control theory.

On reaction-diﬀusion equations with anomalous diﬀusion and various boundary conditions

GAL Ciprian G

Florida International University, Miami, Florida, USA

We wish to present recent developments concerning the long term behavior (as time goes to infinity) in terms of finite dimensional global attractors and (global) asymptotic stabilization to steady states of solutions to non-local semi-linear reaction-diffusion equation associated with the fractional Laplace operator on non-smooth domains subject to Dirichlet, fractional Neumann and Robin boundary conditions.

Homogenization of highly oscillating boundaries with strongly contrasting diﬀusivity

GAUDIELLO Antonio

DIEI - Universit`a degli Studi di Cassino e del Lazio Meridionale, Italia

I shall discuss a joint work with A. Sili (Département de Mathématiques, Université du Toulon, and Centre de Mathématiques et Informatique, Aix Marseille Université). In this paper, we consider a linear diffusion problem, with strongly contrasting diffusivity, in a medium having highly oscillating boundary. The problem is characterized by two small positive parameters: a parameter ε describing the periodicity of the oscillating boundary and a parameter αε describing the contrasting diffusivity. As ε and αε vanish, we pinpoint three different limit regimes αε ∞ ∞ depending on ratio l = lim ε , according to l =0,0

GILARDI Gianni

University of Pavia, Italy

The talk regards the modification of a Caginalp type phase field system obtained by introducing suitable feedback control terms in the equations in order that the trajectories reach a prescribed manifold of the phase space in a finite time and then lie there with a sliding mode. More precisely, two problems are considered. In the first one, the feedback control law is added to the energy balance equation and a linear relationship between temperature and order parameter is forced. In the second case, the modification is inserted in the phase dynamics in order that a prescribed distribution of the order parameter is reached. In both cases, well-posedness and regularity of the solution are discussed and it is shown that the desired sliding actually occurs in a finite time. The results we present regard a recent joint research project with V. Barbu, P. Colli, G. Marinoschi and E. Rocca.

Nonlocal Cahn-Hilliard equations

GRASSELLI Maurizio

Politecnico di Milano, Italy

I intend to present some results on nonlocal Cahn-Hilliard equations I have obtained in collaboration with several authors.

On reconstruction of a source term depending on time and space variables in a parabolic mixed problem

GUIDETTI Davide

Dipartimento di Matematica, University of Bologna, Italy

We determine a factor depending on both time and one of the spaces variables in a mixed parabolic system in a cylindrical domain. In order to do this, we employ a certain supplementary information, concerning a space-time measurement of the solution.

Shadowing pseudo-orbits in set-valued dynamics

GUTU Valeriu

Moldova State University, Republic of Moldova Coauthors: Vasile Glavan

We are concerned with dynamical systems, generated by finite families of continuous mappings, not necessarily contractive, in metric spaces, called also Iterated Function Systems (IFS). In case of affine mappings and under suitable cone condition, we localize the maximal compact viable on Z subset and prove the Shadowing property of the IFS on this subset. 85 Dispersion property for Schrödinger equations

IGNAT Liviu

Simion Stoilow Institute of Mathematics of the Romanian Academy and Faculty of Mathematics, University of Bucharest, ROmania

In this talk we analyze the dispersion property of some models involving Schrodinger equations. First we focus on the discrete case and then we present some results on graphs.

Kinetic formulation for vortex vector ﬁelds

IGNAT Radu

Universit´e Paul Sabatier - Toulouse III, France Coauthors: Pierre Bochard

We will focus on vortex gradient ﬁelds of unit-length. The associated stream function solves the eikonal equation, more precisely it is the distance function to a point. We will prove a kinetic formulation characterizing such vector ﬁelds in any dimension. This characterization is useful in many variational models such as the study of zero energy states in a Ginzburg-Landau type model.

Non-existence results of higher-order regular solutions for the p(x)-Laplacian

ISAIA Florin

Transilvania University of Brasov, Romania

This talk is devoted to present several non-existence results for higher-order regular solutions to the following nonlinear Dirichlet problem −Δp(x)u = d (x) f (u)inΩ,

u|∂Ω =0, n 1,h(·) where Ω is a smooth bounded open set in R , n ≥ 2, p : Ω → R is a Lipschitz function with minx∈Ω p (x) > 1, d ∈ W (Ω)with h : Ω → [1, ∞) log-H¨older continuous, f : R → R is a Borel measurable and locally Lebesgue integrable function. These results are subjected to the following natural principle: the stronger (respectively weaker) are the assumptions on the given data f,thelarger (respectively smaller) is the variable exponent Sobolev space W m,q(·) (Ω) in which no nontrivial strong solutions can be found. To do this, we use some recent developments on superposition operators between higher-order Sobolev spaces.

Large Solitary Waves via Global Bifurcation Methods

KIRR Eduard-Wilhelm

University of Illinois, USA Coauthors: Vivek Natarajan

We will show how the now classical Global Bifurcation Theory can be enhanced by determining the limit points of solitary wave branches at the boundary of the domain inside which the theory applies. From these limit points we can track the branches back into the domain, and, in the examples we have analyzed so far, determine all the branches i.e., all solitary waves regardless of their size. 86 Calculated of regularized trace of a fourth order regular diﬀerential equation

KIZILBUDAK CALISKAN Seda

Yildiz Technical University, Turkey Coauthors: Zerrin Ozcubukcu

We shall obtain a formula for the regularized trace of a fourth order regular diﬀerential equation

Gagliardo-Nirenberg inequalities on manifolds: the inﬂuence of the curvature

KRISTALY Alexandru

Babes-Bolyai University, Romania

In this talk we discuss the validity of the Gagliardo-Nirenberg inequality (shortly, GN inequality) and its limit cases on Riemannian manifolds. First, when the manifold has non-negative Ricci curvature and the GN inequality holds, we shall provide a sharp, quantitative volume growth of geodesic balls. Second, when the manifold has non-positive sectional curvature, we establish a sharp GN inequality whenever the Cartan-Hadamard conjecture holds (e.g., the dimension of the manifold is 2, 3 or 4).

Determining the saddle points for antagonistic positional games in Markov decision processes

LOZOVANU Dmitrii

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Republic of Moldova

A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore, algorithms for determining the optimal stationary strategies of the players are proposed and grounded.

Positive solutions for a system of singular second-order integral boundary value problems

LUCA TUDORACHE Rodica

“Gheorghe Asachi” Technical Universiy of Iasi, Romania Coauthors: Johnny Henderson

We investigate the existence of positive solutions of a system of second-order nonlinear diﬀerential equations subject to Riemann- Stieltjes integral boundary conditions, where the nonlinearities do not possess any sublinear or superlinear growth conditions and may be singular. In the proof of our main results, we use the Guo-Krasnosel’skii ﬁxed point theorem. 87 Numerical meshes ensuring uniform observability of 1d waves

MARICA Aurora

Universitatea Politehnica Bucuresti & Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania Coauthors: Sylvain Ervedoza, Enrique Zuazua

In this talk, we build non-uniform numerical meshes for the finite difference and finite element approximations of the 1-d wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, in the sense that the full discrete energy can be observed by means of boundary measurements, uniformly with respect to the mesh-size. The construction of the nonuniform mesh is achieved by means of a concave diffeomorphic transformation of a uniform grid into a non-uniform one, making the mesh finer and finer when approaching the right boundary. For uniform meshes it is known that high-frequency numerical wave packets propagate very slowly without never getting to the boundary. Our results show that this pathology can be avoided by taking suitable non-uniform meshes. This also allows to build convergent numerical algorithms for the approximation of boundary controls of the wave equation.

On some minimization problems in RN : the concentration-compactness principle revisited

MARIS Mihai

Universite Paul Sabatier - Toulouse 3, France

We present recent improvements of the concentration-compactness principle and show that they give a new insight in some old minimization problems leading to the existence of solitary waves for nonlinear dispersive equations.

Periodic solutions of relativistic-type systems with periodic nonlinearities

MAWHIN Jean

Universit´e Catholique de Louvain, Belgium Coauthors: P. Jebelean, C. Serban

The lecture surveys recent results on the multiplicity of periodic solutions of diﬀerential systems of the type u + ∇uV (t, u)=e(t) 1 −|u|2 when the potential V is periodic in each component of u and e has mean value zero over the time period.

On the asymptotic behavior of some classes of nonlinear eigenvalue problems involving the p-Laplacian

MIHAILESCU Mihai

University of Craiova “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

The goal of this talk is to present recent results concerning two diﬀerent PDEs which can be regarded as the limiting equations of some families of nonlinear eigenvalue problems. First, eigenvalue problems involving the p-Laplacian and rapidly growing operators in divergence form are studied in an Orlicz-Sobolev setting. An asymptotic analysis of these problems leads to a full characterization of 88 the spectrum of an exponential type perturbation of the Laplace operator. Next, the issue of existence of nonnegative solutions for a class of problems depending on a real parameter and involving the ∞-Laplacian is considered. It is shown that nontrivial nonnegative viscosity solutions for this class of problems exist if and only if the parameter is greater than or equal to the reciprocal of the maximum of the distance to the boundary of the domain. This is a joint work with Marian Bocea (Loyola University Chicago).

Time, grids, similarity

MOSCO Umberto

Worcester Polytechnic Institute, USA

We construct certain discrete dynamical systems governed by ODEs on syncronized time-space inﬁnite grids, which give rise asymptotically to ﬁlling space attractors. The role of time-space grid syncronization in the description of fast short-range dynamics will also be discussed.

An Algorithm for Generating Maximal Simulation Relations in Geometric Control Theory

MUNTEANU Laura

State University of New York at Oneonta, U.S.A.

A relatively recent problem in geometric control theory is the study of simulation relations between nonlinear control systems. In this presentation, we introduce an algorithm for generating simulation relations between certain nonlinear control systems that are aﬃne in inputs and disturbances, and prove that, under appropriate conditions, the algorithm leads to a maximal simulation relation.

Controllability for the vibrating string equation with Neumann boundary conditions

NEGRESCU Alexandru

Universitatea Politehnica Bucuresti, Romania

In this presentation we study the controllability in T = π for the vibrating string equation with Neumann boundary conditions using the moment problem approach.

Approximate viability on graphs

OMAR Benniche

Department of Mathematics, Energy and Smart Systems Laboratory (L.E.S.I) Khemis Miliana University, 442500, Algeria, Algeria Coauthors: Ovidiu Carja

Let X be a real Banach space and I ⊂ R a nonempty and bounded interval. Let K : I X be a multi-function with the graph K. In this talk we present some results concerning approximate viability for the graph K with respect to the quasi-autonomous semilinear 89

diﬀerential inclusion x (t) ∈ Ax(t)+F (t, x(t)) where A : D(A) ⊂ X → X is the inﬁnitesimal generator of a C0-semigroup and F : I × X X is a given multi-function. As applications, we give some results concerning Lipshitz regularity of the solution set and a relaxation result for x(t) ∈ Ax(t)+F (t, x(t)).

Calculated the regularized trace of a fourth order regular diﬀerential equation

OZCUBUKCU Zerrin

Yildiz Technical University, Turkey

Coauthors: Seda KIZILBUDAK

We shall obtain a formula for the regularized trace of a fourth order regular diﬀerential equation.

Singularly perturbed problems for abstract diﬀerential equations of second order in Hilbert spaces

PERJAN Andrei

Moldova State University, Republic of Moldova

Let H and V be two real Hilbert spaces such that V ⊂ H continuously and densely. Let A : V = D(A) ⊂ H → H be a self-adjoint positive deﬁnite operator and let B : D(B) ⊂ H → H be a nonlinear operator. Consider the following abstract hyperbolic system εuε (t)+δuε(t)+Auε(t)+B uε(t) = fε(t),t∈ (0,T), uε(0) = v0ε,uε(0) = v1ε.

Under some conditions on operators A and B we study the behavior of solutions uε as ε → 0,δ → 0.

Oscillational blow-up of traveling solutions in models for suspension bridges

RADU Petronela

University of Nebraska-Lincoln, USA Coauthors: Daniel Toundykov, Jeremy Trageser

The study of fourth order diﬀerential equations has recently intensiﬁed in the context of studying the behavior of traveling waves for nonlinear suspension bridges. I will present a blow-up result for the equation

(4) u + ku + f(u)=0 where f is super linear with f(u)u>0 and when k>0. Previous work by Gazzola and his collaborators solved the case kleq0. The case k>0 is physically significant as it corresponds to k = c2 with c being the speed of propagation of the traveling wave. 90 Some singularly perturbed Cauchy problems for abstract linear differential equations with positive powers of a positive defined operator

RUSU Galina

Moldova State University, Republic of Moldova

In a real Hilbert space H consider the following Cauchy problem: ε uε (t)+A1uε(t) + uε(t)+A0uε(t)=fε(t),t∈ (0,T), (Pε) uε(0) = u0ε,uε(0) = u1ε, where Ai : D(Ai) ⊂ H → H, i =0, 1, are two linear self-adjoint operators, ε>0 is a small parameter (ε 1), uε,fε :[0,T) → H. Supposing that the operator A1 is subordinated to a positive power of the operator A0, the behavior of solutions uε to the problems (Pε), when u0ε → u0,fε → f as ε → 0, is investigated. We establish a relationship between solutions to the problems (Pε) and the corresponding solution to the following unperturbed problem: v (t)+A0v(t)=f(t),t∈ (0,T), (P0) v(0) = u0.

Mild solutions for functional semilinear evolution equations

SATCO Bianca

Stefan cel Mare University of Suceava, Romania

We study the matter of existence of mild solutions for functional semilinear evolution equations with a non-necessarily absolutely integrable function on the right-hand side. We make use of the properties of Kurzweil integrals and of Kurzweil-Stieltjes integrals for operators.

Existence results for discontinuous perturbations of singular φ-Laplacian operator

SERBAN Calin - Constantin

West University of Timisoara, Romania

Systems of diﬀerential inclusions of the form

−(φ(u )) ∈ ∂F(t, u),t∈ [0,T],

N N where φ = ∇Φ,withΦ strictly convex, is a homeomorphism of the ball Ba ⊂ R onto R , are considered under Dirichlet, periodic and Neumann boundary conditions. Here, ∂F(t, x) stands for the generalized Clarke gradient of F (t, ·)atx ∈ RN . Using nonsmooth critical point theory, we obtain existence results under some appropriate conditions on the potential F . The talk is based on joint work with Petru Jebelean and Jean Mawhin. Acknowledgements. The work of the speaker was supported by the strategic grant POSDRU/159/1.5/S/137750, ”Project Doctoral and Postdoctoral programs support for increased competitiveness in Exact Sciences research”. 91 Discontinuous control problems and optimality conditions via occupational measures

SEREA Oana

Universite de Perpignan, France

We present a linearization method for control problems in deterministic and stochastic case. This method allows us to transform a nonlinear control problem with a minimal cost into a maximization of a linear problem over occupational measures. This formulation is very useful because it allows for instance to obtain approximation results for the values functions using Dirac measures. We consider deterministic and stochastic control problems with discontinuous cost. Using the occupation measures we handle a diﬃcult problem: the characterization of semi-continuous value functions. The value function is the generalized viscosity solution for the associated Hamilton-Jacoby-Bellman equation. A dual formulation of the problem is obtained. Naturally, under certain assumptions, the primal value and dual value coincide. This formulation is used to derive optimality conditions. Moreover, we describe examples where this method is used in a theoretical framework as well as into a more applied one.

Global stabilisation for damped-driven conservation laws

SHIRIKYAN Armen

University of Cergy-Pontoise, France Coauthors: Sergio Rodrigues

We consider a multidimensional conservation law with a damping term and a localized control. Our main result proves that any (non-stationary) solution u(t, x) can be exponentially stabilized in the following sense: for any initial state one can ﬁnd a control such that the diﬀerence between the corresponding solution and the function u(t) goes to zero exponentially fast in an appropriate norm. As a consequence, we prove global exact controllability to solutions of the problem in question. We also establish global approximate controllability to solutions with the help of low-dimensional localized controls.

A Baouendi-Grushin type operator in Orlicz-Sobolev spaces and applications to PDEs

STANCU - DUMITRU Denisa

“Babes-Bolyai” University, Cluj-Napoca and “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania

We introduce a Baouendi-Grushin operator in the setting of Orlicz-Sobolev spaces and we establish a sharp result regarding the spectrum of this operator. More exactly, we show that the spectrum is continuous. The proofs are based on the critical point theory combined with adequate variational methods. This presentation is a joint work with Mihai Mih˘ailescu (University of Craiova and “Simion Stoilow” Institute of Mathematics of the Romanian Academy) and Csaba Varga (“Babes-Bolyai” University).

On constrained wave propagation

TARFULEA Nicolae

Purdue University Calumet, USA

Many important applications lead to hyperbolic systems of differential equations supplemented by constraint equations on infinite domains (e.g., Maxwell’s equations and Einstein’s field equations in various hyperbolic formulations). In general, for the pure Cauchy 92 problem one can prove that the constraints are preserved by the evolution. That is, the solution satisfies the constraints for all time whenever the initial data does. Frequently, the numerical solutions to such evolution problems are computed on artificial space cutoffs because of the necessary boundedness of computational domains. Therefore, well-posed boundary conditions are needed at the artificial boundaries. Moreover, these boundary conditions have to be chosen in such a way that the numerical solution of the cutoff system approximates as best as possible the solution of the original problem on infinite domain, including the preservation of constraints. In this talk, I will present a general technique for finding constrained preserving boundary conditions, and its application to a system of wave equations in a first-order formulation subject to divergence constraints.

Long time dynamics for water waves

TATARU Daniel

University of California, Berkeley, USA Coauthors: Mihaela Ifrim

The water wave equation describes the motion of the free surface of an inviscid, incompressible irrorational ﬂuid, moving under the inﬂuence of gravity, surface tension, etc. The goal of the talk will be to present several recent ideas and results concerning long time dynamics for such problems.

The fractional multi-objective transportation problem of fuzzy type

TKACENKO Alexandra

State University of Moldova, Republic of Moldova

In the presentation is developed an iterative fuzzy programming approach for solving the multi-objective fractional transportation problem of “bottleneck” type [1] with some imprecise data. Minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound for each objective function iterative, we find the set of efficient solutions for all time levels [3]. The mathematical model of the proposed problem is the follows: m n k c˜ij xij k i=1 i=1 min Z = (0.10) max{tij |xij > 0} ij

k+1 min Z =max{tij |xij > 0 } (0.11) ij n n xij = ai,i=1, 2,...,m; xij = ai,j =1, 2,...,n; (0.12) j=1 i=1

xij ≥ 0,i=1, 2,...,m,j =1, 2,...,n,k =1, 2,...,r. (0.13) k 1 2 k k where: Z (x)= Z (x),Z (x),...,Z (x) is a vector of r objective functions;c ˜ij , k =1, 2 ...r,i =1, 2,...m,j =1, 2,...n are unit costs or other amounts of fuzzy type, tij - necessary unit transportation time from source i to destination j, ai - disposal at source i, bj -requirement of destination j, xij - amount transported from source i to destination j. In order to solve the model (1)-(4) we proposed to reduce it to one of linear type, equivalent in terms of the set of solutions. Since the parameters and coeﬃcients of transportation multi-criteria models have real practical signiﬁcances such as unit prices, unit costs and many other, all of them are interconnected with the same parameter of variation, which can be calculated by applying of various statistical methods. Thus, the model (1)-(4) can be transformed in one with deterministic type of data. It can be solved using fuzzy techniques: ⎧ k ⎪1, if Z (x) ≤ Lk ⎨ k k Uk − Z (x) k μk(Z )) = , if Lk

The main part of this paper develops an iterative algorithm for solving the model (1)-(4) with deterministic data, which builds its set of eﬃcient solutions for every level of allowable time. The proposed algorithm was tested on some concrete examples and has proven to be quite eﬀective.

References 1. A. Tkacenko – The Multiobjective Fractional Transportation Problem, Computer Science Journal of Moldova 12 (2004), No. 3 (36), 397–405. 2. R. Belmann, L. Zadeh – Decision making in a fuzzy environment, Management Science 17 (1970), 141-164. 3. W.F. Abd El-Wahed, S.M. Lee – Interactive fuzzy goal programming for multi-objective transportation problems, Omega. The International Journal of Management Science 34 (2006), 158–166.

Mathematical models of vaccination: societal and invididual views

TURINICI Gabriel

CEREMADE, Universit´e Paris Dauphine and Institut Universitaire de France (IUF), FRANCE

The mathematical models of vaccination is a relatively old subject. Initial works focused mostly on the overall, societal optimums; on the contrary recent works can now treat the more difficult individual reactions. These reactions can be mathematically described in a Mean Field Games framework (introduced by P.L. Lions and J.M. Lasry) as a Nash equilibrium in a game with an infinity of players. We present several recent works on the subject and applications to H1N1 2009/10 vaccination in France along with discussions on the cost-effectiveness of public health interventions.

Strategic games, information leaks, corruption, and solution principles

UNGUREANU Valeriu

State University of Moldova, Republic of Moldova

We consider strategic games with rules violated by information leaks (corruption of simultaneity). As a result of corruption, various para/pseudo sequential games appear. The classiﬁcation of such games is provided on the base of the applicable solution principles. Conditions for solution existence are highlighted, formulated and analyzed.

Symmetry and multiple solutions for certain quasilinear elliptic equations

VARGA Csaba

University of Babes-Bolyai, Romania Coauthors: Roberta Filippucci, Patrizia Pucci

We present some symmetrization results which we apply to the same abstract eigenvalue problem in order to show the existence of three different solutions which are invariant by Schwarz symmetrization. In particular, we introduce two different methods in order to prove the existence of multiple symmetric solutions. The first is based on the symmetric version of the Ekeland variational principle and the mountain pass theorem, while the latter consists of an application of a suitable symmetric version of the three critical points theorem due to Pucci and Serrin. Using the second method, we are able to improve some recent results of Arcoya and Carmona and Bonnano and Candito. The methods we present work also for different types of symmetrization. 94 Global bifurcation of steady gravity water waves with critical layers

VARVARUCA Eugen

University of Reading, United Kingdom

I will present some recent results on the problem of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. By means of a conformal mapping and an application of Riemann-Hilbert theory, the free-boundary problem is equivalently reformulated as a one-dimensional pseudodifferential equation which involves a modified Hilbert transform and, moreover, has a variational structure. Using the new formulation, existence is established, by means of real-analytic global bifurcation theory, of a family of solutions which includes waves of large amplitude, even in the presence of critical layers in the flow. This is joint work with Adrian Constantin (King’s College London, UK) and Walter Strauss (Brown University, USA).

Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations

VICOL Vlad

Princeton University, United States Coauthors: Peter Constantin and Igor Kukavica

We consider the incompressible Euler equations on Rd, where dim 2, 3. We prove that: (a) In Lagrangian coordinates the real-analyticity radius (more generally, the Gevrey-class radius) is conserved, locally in time. (b) In Lagrangian coordinates the equations are well-posed in highly anisotropic spaces, e.g. Gevrey-class regularity in the label a1 and Sobolev regularity in the labels a2, ..., ad. (c) In Eulerian coordinates both results (a) and (b) above are false!

The local equicontinuity of a maximal monotone operator and consequences

VOISEI Mircea

Towson University, USA

∗ The local equicontinuity of an operator T : X ⇒ X with proper Fitzpatrick function ϕT and deﬁned in a barreled locally convex space X has been shown to hold on the algebraic interior of PrX (dom ϕT )) (see [MR3252437, Theorem 4]). The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator deﬁned in a barreled locally convex space including a new proof of James’s Theorem and the universality of the normal cone in the sum theorem for maximal monotone operators.

Partial regularity and smooth topology-preserving approximations of rough domains

ZARNESCU Arghir

IMAR and University of Sussex, Romania and UK

We consider domains whose boundary can be locally represented as the graph of a continuous function and construct smooth approximations that preserve topological properties (in particular the fundamental group, for instance). The main tool for doing this is a notion of (multivalued) map of “good directions at a point”, that is a map that associates to a point in the neighborhood of the boundary the directions along which the boundary can be locally represented as the graph of a continuous function. 95

We study various properties of the map of good directions and also use it to show that there must be points on the the boundary of the domain, in a neighborhood of which the domain is in fact smoother, it is locally Lipschitz. This is joint work with John M. Ball.

Section 5 Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

Fredholmness vs. spectral discreteness for ﬁrst-order diﬀerential operators

ANGHEL Nicolae

University of North Texas, United States

In this talk we show that for essentially self-adjoint first-order differential operators D, acting on sections of bundles over complete (non-compact) manifolds, Fredholmness vs. Spectral Discreteness is the same as ‘∃c>0, D is c-invertible at infinity’ vs. ‘∀c>0, D is c-invertible at infinity’. An application involving the spectral theory of electromagnetic Dirac operators is then given.

On the summing properties of the multilinear operators on a cartezian product of c0 (X) spaces

BADEA Gabriela

Ovidius University of Constanta, Romania Coauthors: Dumitru Popa

In this talk we discuss the necessary and suﬃcient conditions for an operator deﬁned on a Cartesian product of c0 (X)tobesumming, dominated or multiple s-summing. These three concepts are some possible extensions of the summing linear operators to the multilinear settings. Also, we consider the relationship with the nuclear multilinear operators, which is related to Schwartz’s theorem from the linear case. Some examples of such operators are also presented.

The distribution of rational numbers and ergodic theory

BOCA Florin-Petre

University of Illinois Urbana-Champaign, USA

Rational numbers in [0,1), or equivalently roots of unity on the unit circle, can be naturally ordered either by the size or their denominators, or by the sum of digits in their continued fraction representation. Their distribution is not random and appears to be controlled by four important types of measure-preserving transformations (Gauss, Farey, BCZ, Newman), with very diﬀerent ergodic properties. Our talk will discuss connections between number theory and ergodic theory along these lines.

97 98 An example of twisted bi-Laplacian and its spectral properties

CATANA˘ Viorel

University Politehnica of Bucharest, Romania

R2 − 1 2 2 − Let L be the twisted Laplacian on , which is the second-order partial differential operator given by L = Δ + 4 (x + y ) 2 2 ∂ ∂ ∂ ∂ 1 2 2 ∂ ∂ i x − y ,whereΔ = + is the Laplace operator, H = −Δ + (x + y ) is the Hermite operator and N = x − y ∂y ∂x ∂x2 ∂y2 4 ∂y ∂x is the rotation operator. It follows that the twisted Laplacian L = H − iN is the Hermite operator perturbed by the partial differential operator −iN. 1 Now, we introduce the renormalization of the twisted Laplacian L to be the partial differential operator given by Pm = (L+2m−1), 2 ∗ 1 t ∗ t 1 2 2 m ∈ N . So, the transpose Qm of Pm is given by Qm = (L +2m − 1), m ∈ N ,whereL = −Δ + (x + y )+iN is the 2 4 ∗ transpose of the twisted Laplacian L. The aim of this talk is to analyze the twisted bi-Laplacian Mm,n, m, n ∈ N defined by 1 − − − Mm,n = QnPm = PmQn = 4 (H + iN +2n 1)(H iN +2m 1), where Pm and Qn commute because it can be shown easy that H and N commute. Based on the well-known spectral properties of the twisted Laplacian L (see [2]) we can prove that the spectrum of Mm,n is given by a sequence of isolated eigenvalues of finite multiplicity each of them. This fact is a consequence of the compactness of the resolvent of the twisted bi-Laplacian as an operator from L2(R2)intoL2(R2). Moreover, the essential self-adjointness and global hypoellipticity in terms of a new two-parameter family of Hilbert spaces (in fact Sobolev spaces) are studied. Let us remark that when we take m = n = 1 we recover the results in the paper [3] and that we can also state and prove similar assertions as above in an abstract setting (see [1]). References

1. V. Catan˘a–The Heat Kernel and Green Function of the Generalized Hermite Operator, and the Abstract Cauchy Problem for the Abstract Hermite Operator, in Pseudo-Diﬀerential Operators: Analysis, Applications and Computations, Operator Theory: Advances and Applications, 213 (2011), 155-171. 2. A. Dasguspta and M.W. Wong – Essential self-adjointness and global hypoellipticity of the twisted Laplacian, Rend. Sem. Mat. Univ. Pol. Torino, 66 (2008), 75-85. 3. T. Gramchev, S. Pilipovic, L. Rodino, M.W. Wong – Spectral properties of the twisted bi-Laplacian, Arch. Math., 93 (2009), 565-575.

On the construction of composite Wannier functions

CORNEAN Horia

Aalborg University, Denmark

We give a constructive proof for the existence of an N-dimensional Bloch basis which is both smooth (real analytic) and periodic with respect to its d-dimensional quasi-momenta, when 1 ≤ d ≤ 2 and N ≥ 1. The constructed Bloch basis is conjugation symmetric when the underlying projection has this symmetry, hence the corresponding exponentially localized composite Wannier functions are real. This is joint work with G. Nenciu (Bucharest) and I. Herbst (Charlottesville)

Complex analysis and spectral isometries

COSTARA Constantin

Ovidius University of Constanta, Romania

In this talk, we shall present some ideas and methods from complex analysis which can be used to obtain new results on linear maps on Banach algebras preserving the spectral radius. 99 On weak linear spaces

CROITORU Anca

“Alexandru Ioan Cuza” University of Ia¸si, Romania Coauthors: Dan-Mircea Bors

Non-linear spaces have been introduced and studied related to various problems in optimization, functional analysis, computer science, set-valued analysis. In this talk we present some properties of weak linear spaces and comparison results on diﬀerent types of non-linear spaces.

A generalized Dixmier-Douady theory

DADARLAT Marius

Purdue University, USA Coauthors: Ulrich Pennig

We show that the Dixmier-Douady theory of continuous field C∗-algebras with compact operators K as fibers extends significantly to a more general theory of fields with fibers A ⊗ K where A is a strongly self-absorbing C*-algebra. An important feature of the general theory is the appearance of characteristic classes in higher dimensions. We give the following application of these results. Let X be a locally compact space of finite covering dimension. Let MQ be the the universal UHF algebra. Any separable continuous field of C*-algebras over X with all fibers abstractly isomorphic to MQ ⊗ K is locally trivial. The set of isomorphism classes of these fields becomes an abelian group with multiplication given by the tensor product. This group is isomorphic to

1 × 3 5 H (X, Q+) ⊕ H (X, Q) ⊕ H (X, Q) ⊕··· .

Closure sublinear operators and their use to the Dedekind completion of a Riesz space

DANET˘ ¸ Nicolae

Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, 124, Lacul Tei Blvd., 020396 Bucharest, Romania

A closure sublinear operator on a Riesz space (vector lattice) F is a sublinear operator U : F −→ F, which is also a closure operator (that is, (a) U is extensive: f ≤ U(f); (b) U is idempotent: U(U(f)) = U(f); and (c) U is increasing: f1 ≤ f2 ⇒ U(f1) ≤ U(f2)) that commutes with the finite supremums, U(f1 ∨ f2)=U(f1) ∨ U(f2). Using U we define a new operator L : F → F by putting L(f)=−U(−f). The operator L is a dual closure operator (the property (a) becomes: L(f) ≤ f), supralinear, and commutes with finite infimums, L(f1 ∧ f2)=L(f1) ∧ L(f2). The aim of this talk is to study the properties of this pair (U, L) of operators and to show how they can be used to construct the Dedekind completion of a Riesz space G, if this is a Riesz subspace of a Dedekind complete Riesz space E. References 1. D˘anet¸, N. – Riesz spaces of normal semicontinuous functions, Mediterr. J. Math. DOI 10.1007/s00009-014-0466-2, published online 23 September 2014. 2. Kaplan, S. – The second dual of the space of continuous functions, IV. Trans. Amer. Math. Soc. 113 (1964), 512-546. 3. Kaplan, S. – The bidual of C(X) I, North-Holland Mathematics Studies 101, Amsterdam, 1985. 100 The most important challenge in the interval analysis. Historical notes and how we can overcome the barrier via extension results

DANET˘ ¸ Rodica-Mihaela

Technical University of Civil Engineering Bucharest, Department of Mathematics and Computer Science, 124, Lacul Tei Blvd., 020396 Bucharest, Romania

The talk brings into question the most important challenge in the Interval Analysis, namely that the existence of an opposite for some closed intervals in an arbitrary ordered vector space ceases to be true and the second distributive law for the usual algebraic operations remains true only under a restrictive condition. Firstly some historical notes related to the Interval Analysis are given. Secondly we show how we can overcome the limits imposed to the above mentioned challenge. We shall illustrate this with some extension results. In a previous paper we gave a theorem of the Mazur-Orlicz type. Now we give new results concerning some applications of this theorem in the Interval Analysis. We also give a new example that shows how we can correct the “defect” of the addition that we mentioned above. References 1. Anguelov, R. – The algebraic structure of spaces of intervals-Contributions of Svetoslav Markov to interval analysis and its applications, International Conference on Mathematical Methods and Models in Bioscience, 16-21 June, Soﬁa, Bulgaria, Biomath 2013, Conference Book, 22-24 (2013). 2. Aseev, S.M. – Quasilinear operators and their application in the theory of multivalued mappings, Proceedings of the Steklov Institute of Mathematics 2, 23-52 (1986). 3. D˘anet¸, N., D˘anet¸, R.-M. – Existence and extensions of positive linear operators, Positivity 13, 89-106 (2009). 4. D˘anet¸, R-M. – A Mazur-Orlicz Type Theorem in Interval Analysis and its Applications, Proceedings of the seventh Positivity conference, July 22-26, Leiden, 2013 (to appear).

Symmetries of graph C*-algebras

DEACONU Valentin

University Of Nevada, Reno, USA

0 1 ∗ Given a discrete locally finite graph E =(E ,E ,r,s), we consider symmetries of the associated C -correspondence HE and of the graph algebra C∗(E), defined using actions and representations of a group G. Examples include self-similar actions of groups on trees. We study the fixed point algebra C∗(E)G and the crossed product C∗(E) G. The group G acts also on the AF -core C∗(E)T ∗ T ∼ ∗ T ∗ ∗ ∗ and C (E) G = (C (E) G) . If G is finite, then C (E) G is isomorphic to the C -algebra of a graph of C -correspondences, constructed using orbits and characters of the stabilizer groups. Some of the results can be extended to actions and representations of groupoids.

A direct proof of K-amenability for a-T-menable groups

DUMITRASCU Constantin Dorin

Adrian College, USA

∗ ∗ ∗ ∗ For amenable groups, the maximal group C -algebra C (G) and the reduced groups C -algebra Cr (G) are isomorphic. In the early 1980’s, Cuntz, for discrete groups, then Julg and Valette, for non-discrete groups, introduced a weaker concept of K-amenability, which implies the isomorphism of these two group C∗-algebras at the level of K-theory. In the late 1990’s, Higson and Kasparov proved the Baum-Connes conjecture for all the a-T-menable groups. These are groups that admit a continuous aﬃne isometric and metrically proper action on some real Hilbert space H. As a consequence of the Baum-Connes conjecture, it follows that the a-T-menable groups are K-amenable. In this presentation we give a new proof of this result. Our approach is new in at least two aspects. First, we construct a homotopy between the unit 1G in the representation ring of G and a Fredholm G-module whose representations are weakly contained in the left-regular representation. Second, we perform our computations in the new bivariant K-theory for C∗-algebras, called KE-theory, constructed by the presenter. This is joint work with Nigel Higson. 101 Fourier series on fractals

DUTKAY Dorin

University of Central Florida, United States

We present some recent results and open questions on the harmonic analysis and Fourier series on fractal measures.

Supersymmetry, nonassociativity, and big numbers

DZHUNUSHALIEV Vladimir

Al Farabi Kazakh National University, Kazakhstan

The nonassociative generalization of supersymmetry is considered. Using a special choice of the parameters, it is shown that the associator of the product of four supersymmetry generators is connected with the angular momentum operator. The associator of four 2 −2 supersymmetry generators has the coeﬃcient ∼ /0 where 0 is some characteristic length. Two cases are considered: (a) 0 coincides with the cosmological constant; (b) 0 is the classical radius of electron. It is also shown that the scaled constant is of the order of 10−120 for the ﬁrst case and 10−30 for the second case. The possible manifestation and smallness of nonassociativity is discussed. The connection of operator decomposition to the hidden variables theory and alternative quantum mechanics is discussed.

Approximating quantum graphs by Schr¨odinger operators on thin networks

EXNER Pavel

Czech Academy of Sciences, Czech Republic

Quantum graph models are extremely useful but they also have some drawbacks. One is related to the physical meaning of the vertex coupling. The self-adjointness requirement alone leaves a substantial freedom expressed through parameters appearing in the conditions matching the wave function at the graph vertices. It is a longstanding problem whether one can motivate their choice by approximating the graph Hamiltonian by operators on a family of networks, i.e. systems of tubular manifolds the transverse size of which tends to zero. It appears that the answer depends on the conditions imposed on tube boundaries. In this talk we present a complete solution for Neumann networks: we demonstrate that adding properly scaled potentials and changing locally the graph topology, one can approximate any admissible vertex coupling. The result comes from a common work with Taksu Cheon, Olaf Post, and Ondˇrej Turek.

Conformal ending measures on limit sets of Kleinian groups

FALK Kurt

University of Bremen, Germany

The dynamics of geometrically finite hyperbolic manifolds is well understood by means of Patterson-Sullivan theory. For geometrically infinite manifolds, or manifolds given by infinitely generated Kleinian groups, nonrecurrent dynamics becomes the “thick part” of dynamics, not only in the sense of measure but often also Hausdorff dimension. Patterson-Sullivan measures work well for divergence type groups at the critical exponent. Conformal measures of exponent above the critical one were known to exist by earlier work of Sullivan using methods from Harmonic Analysis, but were explicitely constructed only a few years ago by Anderson, Tukia and myself. Such conformal ending measures naturally work well when the Poincare series converges and are thus suitable for studying nonrecurrent dynamics in hyperbolic manifolds. In my talk I will present the construction, properties and some first applications of such conformal ending measures. 102

Some inequalities related to operator means

FURUICHI Shigeru

Nihon University, Japan

We give some operator inequalities between arithmetic mean, geometric mean and harmonic mean. In addition, we show some unitarily invariant norm inequalities, which give tight bound for the logarithmic mean.

Interpolation for completely positive maps

GHEONDEA Aurelian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We obtain necessary and suﬃcient conditions for solvability, as well as a parametrization of all solutions, for a problem of interpolation for completely positive maps between matrix spaces. Numerical approximation methods are also discussed.

On Boolean algebras of projections of ﬁnite multiplicity

GOK Omer

Yildiz Technical University, ISTANBUL, TURKEY

Let X be a Banach C(K)-module, where K is a compact Hausdorff space and the homomorphism map is continuous. In this talk, we give equivalent conditions for reflexivity of the dual space X. References 1. A. Kitover, M. Orhon – Reflexivity of Banach C(K)-modules via the reflexivity of Banach lattices, Positivity, 18 (2014), 475–488.

Pro-C*-correspondences

JOIT¸A Maria

University Politehnica of Bucharest and “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We associate a pro-C∗-algebra to a pro-C∗-correspondence and show that this construction generalizes the construction of crossed products by Hilbert pro-C∗-bimodules and the construction of pro-C∗-crossed products by strong bounded automorphisms. This is a joint work with I. Zarakas (University of Athens). 103 Ergodic and metric properties of certain invariant measures on fractals

MIHAILESCU Eugen

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

I will give several recent results about invariant measures on fractals, obtained either from non-invertible dynamical systems with some hyperbolicity, or from conformal (ﬁnite or inﬁnite) iterated function systems with overlaps.

On a generalization of Ciric ﬁxed point in best approximation

MORADI Sirous

Arak University, Iran

In this talk at first Ciric fixed point theorem is extended, then common fixed point for Banach operator pairs satisfying extended Ciric type contraction conditions are obtained without the assumption of linearity or affinity of either T or I. In particular we extend the main theorem due to Hussain. We also provide an application to an integral equation.

Nonsingular automorphisms and dimension spaces

MUNTEANU Radu

University of Bucharest, Romania

We show that if T is (measure theoretically isomorphic to) an adic transformation deﬁned on a Bratteli diagram endowed with a Markov measure then we can associate explicitly a matrix valued random walk and a dimension space. We explain how certain properties of nonsingular automorphisms can be translated in terms of dimension spaces and we give concrete examples. This talk is part of a joint work with Thierry Giordano and David Handelman.

On some criteria for quantum and stochastic conﬁnement

NENCIU Irina

University of Illinois, Chicago, USA Coauthors: G. Nenciu

In this talk we will present several recent results concerning criteria ensuring the confinement of a quantum or a stochastic particle to a bounded domain in Rn. These criteria are given in terms of explicit growth and/or decay rates for the diffusion matrix and the drift potential close to the boundary of the domain. As an application of the general method, we will discuss several cases, including some where the background Riemannian manifold (induced by the diffusion matrix) is geodesically incomplete. These results are part of an ongoing joint project with G. Nenciu (IMAR, Bucharest, Romania). 104 Essential spectrum of N-body Hamiltonians with asymptotically homogeneous interactions

NISTOR Victor

Universite de Lorraine and Pennsylvania State University, France Coauthors: Vladimir Georgescu

We prove a HWZ-type theorem for the essential spectrum of N-body type Hamiltonians with two-body interactions that are asymptotically homogeneous of order zero at inﬁnity. This generalizes the classical case of Coulomb potentials (for which the homogeneous part at inﬁnity is zero). The techniques of proof use representations of certain associated C∗-algebras.

Realizing homogeneous cones through oriented graphs

NOMURA Takaaki

Kyushu University, Japan Coauthors: Takashi Yamasaki

In this talk, we realize any homogeneous convex cone by assembling uniquely determined subcones. These subcones are realized in the cones of positive-deﬁnite real symmetric matrices of minimal possible sizes. The subcones are found through the oriented graphs drawn by the data of the given homogeneous cones. Several interesting examples of our realizations of homogeneous convex cones will be also presented.

On Markov moment problem and its applications

OLTEANU Cristian Octav

Politehnica University of Bucharest, Romania

We give necessary and sufficient conditions for the existence of a solution of a multidimensional real classical Markov moment problem, in an unbounded subset which is a Cartesian product of closed intervals. One obtains a characterization in terms of quadratic forms. To this end, we apply polynomial approximation results on such a Cartesian product. Next, we consider applications of a sufficient condition to approximating geometrically the solutions of some nonlinear systems with infinite many equations and unknowns (inverse problems solved starting from the moments). Thus, one solves problems studied in the literature by some other methods. Our way of treating these problems works in several dimensions. In the end, one considers a problem not necessarily involving polynomials. 105 On equivalence of K-functionals and weighted moduli of continuity

PALT˘ ANEA˘ Radu

“Transilvania” University of Brasov, Romania

We study the best constants which can appear in the inequalities between the weighted modulus of continuity and the corresponding K-functional, in special case where the weight functions are convex or concave. References 1. R. De Vore, G.G. Lorentz – Constructive approximation, Springer, Berlin, New York, 1993. 2 Z. Ditzian, V. Totik – Moduli of smousness, Springer, Berlin, New York, 1987. 3. H.H. Gonska – On approximation in spaces of continuous functions, Bull. Austral. Math. Soc., 28 (1983), 411432. 4. H. Johnen, K. Scherer – On the equivalence of the K -functional and moduli of continuity and some applications, Constructive Theory of Functions of Several Variables, Vol. 571 (1977) of Lecture Notes in Mathematics, Springer, Berlin, 119–140. 5. N.P. Korneichuk – The best uniform approximation of certain classes of continuous functions, Dokl., 141 (1961), 304–307, (AMS Transl., 2, 1254–1259). 6. B.S. Mitjagin, E.M. Semenov – Lack of interpolation of linear operators in spaces of smooth functions, (Russian), Math. USSR-Izv., 41 (1977), 1289-1328. 7. R. P˘alt˘anea – Approximation theory using positive linear operators, Birkhauser, Boston, 2004.

Almost commuting permutations are near commuting permutations

PAUNESCU Liviu

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Goulnara Arzhantseva

We prove that the commutator is stable in permutations endowed with the Hamming distance, that is, two permutations that almost commute are near two commuting permutations.

Conductance and AC spectrum

PILLET Claude-Alain

Universit´e de Toulon, France Coauthors: L. Bruneau, V. Jaksic, Y. Last

2 We characterize the absolutely continuous spectrum of the one-dimensional Schrödinger operators h = −Δ + v acting on (Z+)in terms of the limiting behaviour of the Landauer-Büttiker and Thouless conductances of the associated finite samples. The finite sample is defined by restricting h to a finite interval [1,L] ∩ Z+ and the conductance refers to the charge current across the sample in the open quantum system obtained by attaching independent electronic reservoirs to the sample ends. Our main result is that the conductances associated to an energy interval I are non-vanishing in the limit L →∞iff spac(h) ∩ I = ∅.

Nonuniform exponential trichotomies in terms of Lyapunov functions

POPA Ioan-Lucian

1 Decembrie 1918 University of Alba Iulia, Romania Coauthors: Mihail Megan, Traian Ceausu 106

The aim of this talk is to give characterizations in terms of Lyapunov functions for nonuniform exponential trichotomies of nonau- tonomous and noninvertible discrete-time systems.

Abel-Schur multipliers on Banach spaces of inﬁnite matrices

POPA Nicolae

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We consider a class of multipliers extending the Schur multipliers class of matrices. We get some similar results with those of [1] and [9]. In particular we obtain a new proof of the necessity of a well-known theorem of Hardy-Littlewood (see [14], [13], [10].) References

1. J.M. Anderson, J. Clunie and Ch. Pommerenke – On Bloch function and normal functions, J. Reine Angew. Math. 270 (1974), 1237. 2. J.M. Anderson and A. Shields – Coefficient multipliers of Bloch functions, Trans. Amer. Math. Soc. 224 (1976), 255265. 3. S. Barza, L. E. Persson and N. Popa – A Matriceal Analogue of Fejer’s theory, Math. Nach. 260 (2003), 1420. 4. G. Bennett – Schur multipliers, Duke Math. J., 44 (1977), 603-639. 5. I. C. Gohberg, M. G. Krein – Introduction to the theory of linear nonselfadjoint operators, Translations of mathematical Monographs, Vol. 18 American mathematical Society, providence, R. I. 1969. 6. G.H. Hardy, J. E. Littlewood – Theorems concerning mean values of analytic and harmonic functions, Quart. J. of Math. Oxford Ser. 12 (1941), 221-256. 7. D. Krtinic – A matricial analogue of Fejers theory for different types of convergence, Math. Nachr., 280 (2007), no. 13-14, 1537 1542. 8. M. Jevti and M. Pavlovi – OnmultipliersfromHptoq,0¡q¡p¡1,Arch. Math., 56 (1991), 174180. 9. A. Matheson – A multiplier theorem for analytic functions of slow mean groth, Proc. Amer. Math.Soc., 77 (1979), 53-57. 10. M. Mateljevic, M. Pavlovic – Multipliers of H p and BM OA, Pacific J. Math. 146 (1990), 71-84. 11. L.E. Persson and N. Popa – Matrix Spaces and Schur Multipliers: Matriceal Harmonic Analysis, World Scientific, 2014. 12. N. Popa – Matriceal Bloch and Bergman-Schatten spaces, Rev. Roumaine Math. Pures Appl., 52 (2007), 459478. 13. W. T. Sledd – On Multipliers of H p Spaces, Indiana Univ. Math. J., 27 (1978), 797-803. 14. E. M. Stein and A. Zygmund – Boundedness of translation invariant operators on Hoelder spaces and LP-spaces, Ann. Math., 85 (1967), 337-349. 15. K. Zhu – Operator theory in Banach function spaces, Marcel Dekker, New York, 1990.

Collectively coincidence results in some classes of topological spaces

POPESCU Marian-Valentin

Technical University of Civil Engineering Bucharest, Romania Coauthors: Rodica-Mihaela Danet, Nicoleta Popescu

In this talk we investigate some collectively fixed-point and coincidence results for multimaps defined on some topological spaces. Firstly we refer to results obtained with convexity assumptions in the Fréchet space setting (which obviously includes the Banach space setting). Secondly we refer to results obtained without convexity assumptions, in the acyclic finite dimensional ANR setting. Thirdly we consider some results also obtained without convexity assumptions, in the finite dimensional Riemannian manifolds and, in particular, in the finite dimensional Hadamard manifolds. References 1. Aliprantis, C. D. and Border, K. C. – Infinite dimensional analysis, a Hitchhiker’s Guide, Third ed. Springer Verlag, Berlin, Heidelberg, New York 2006. 2. Andres, J. and Górniewicz, L. – Topological Fixed Point Principles for Boundary Value Problems, Kluwer Academic Publishers, Dordrecht 2003. 3. do Carmo, M. P. – Riemannian Geometry (translated by F. Flaherty), in Mathematics; Theory and Applications (Eds. R.V. Kadison, I.M. Singer) Birkhäuser, Boston, Basel, Berlin 1992. 4. D˘anet¸, R.-M., Popescu, M.-V. and Popescu, N. – Coincidence results with compactness assumptions for families of correspondences containing upper semi-continuous multimaps, and their applications, Romanian Journal of Mathematics and Computer Science, Vol 3, Issue 2, 164-184 (2013). 107

5. D˘anet¸, R.-M.; Popescu, M.-V., Popescu, N. – From Fr´echet Spaces to Riemannian Manifolds via Equilibrium Results with and without Convexity Assumptions, Proceedings of the International Conference Riemannian Geometry and Applications in Engineering and Economics – RIGA 2014, Bucharest, May 19-21 (Eds. A. Mihai, I. Mihai), Bucharest University Press, 65-86 (2014). 6. Hu, S.-T. – Theory of Retracts, Wayne State Univ. Press. Detroit 1965.

ISAC’S CONES

POSTOLICA˘ Vasile

“Vasile Alecsandri” University of Bac˘au, ROMANIA

This is a very short research work representing an homage to the regretted Professor George Isac, Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. 17000, Kingston, Ontario, Canada, K7K 7B4. Professor Isac introduced the notion of “nuclear cone” in 1981, published in 1983 and called later as “supernormal cone” since it appears stronger than the usual concept of “normal cone”. For the first time, we named these convex cones as “Isac’s Cones” in 2009 , after the acceptancetextbf on professor Isac’s part. This study is devoted to Isac’s cones, including significant examples, comments and several pertinent references, with the remark that this notion has its real place in Hausdorff locally convex spaces not in the normed linear spaces, having strong implications and applications in the efficiency and optimization. Isac’s cones represent the largest class of convex cones in separated locally convex spaces ensuring the existence and important properties for the efficient points under completeness instead of compactness. References 1. Isac, G. – Points critiques des systmes dinamiques. Cônes nucléaires et optimum de Pareto, Research Report, Royal Military College of St. Jean, Québec, Canada, 1981. 2. Isac, G. – Sur l’existence de l’optimum de Pareto, Riv. Mat. Univ. Parma, 4(9),1983, p. 303 - 325. 3. Postolic˘aV.–Approximate Efficiency in Infinite Dimensional Ordered Vector Spaces. International Journal of Applied Management Science (IJAMS), Vol. 1, No. 3, 2009, p. 300 – 314. 4. Postolic˘aV.–Isac’s Cones in General Vector Spaces. Published as Chapter 121, Category: Statistics, Probability, and Predictive Analytics, vol.3, p.1323-1342, in Encyclopedia of Business Analytics and Optimization – 5 Vols., 2014.

Semi-indiﬀerent dynamics

RADU Remus

Stony Brook University, U.S.A.

We consider complex Hénon maps that have a semi-indifferent fixed point with eigenvalues λ and μ,where|λ| = 1 and |μ| < 1. At a semi-parabolic parameter (i.e. when λ is a root of unity) we have a good understanding of this family: for small Jacobian, the dynamics of the Julia set of the Hénon map fibers over the dynamics of a certain polynomial Julia set. This is joint work with R. Tanase. The situation when λ =exp(2πiα) and α is irrational is more complex as it depends on the arithmetic properties of α.Whenα is the golden mean, we show that the Hénon map with small Jacobian has a Siegel disk whose boundary is homeomorphic to a circle; the proof is based on renormalization of commuting pairs. This is joint work with D. Gaydashev and M. Yampolsky. We will explain where these maps sit in the whole parameter space of complex Hénon maps and explore other directions.

Analytic perturbation theory of embedded eigenvalues

RASMUSSEN Morten Grud

Aalborg University, Denmark

We are interested in the behavior of embedded eigenvalues of (analytic) families of self-adjoint operators {H(ξ)}ξ as a function of the parameter ξ. Kato’s analytic perturbation theory does not apply directly on embedded eigenvalues. The investigation of the essential 108 spectrum of a Schr¨odinger operator via spectral deformation techniques such as dilation analyticity is well-developed. In this talk, we present some new abstract results in which analytic perturbation theory for embedded eigenvalues is made available by the aid of a Mourre estimate and local spectral deformation. In particular, we show that given certain conditions on {H(ξ)}ξ, embedded eigenvalue clusters are branches of analytic functions. The conditions are veriﬁable in non-trivial cases; as an example an abstract two-body system is considered.

Irregular Weyl-Heisenberg wave packet frames generated by hyponormal operators

SAH Ashok Kumar

University of Delhi, India

Abstract. In this talk we study frame-like properties of a wave packet system by using hyponormal operators on L2(R). We present necessary and suﬃcient conditions in terms of relative hyponormality of operators for a system to be a wave packet frame in L2(R). We illustrate our results with several examples and counter-examples.

A rigorous proof of the Bohr-van Leeuwen theorem in the semiclassical limit.

SAVOIE Baptiste

DIAS-STP Dublin, Ireland

The original formulation of the Bohr-van Leeuwen (BvL) theorem states that, in a uniform magnetic field and in thermal equilibrium, the magnetization of an electron gas in the classical Drude-Lorentz model vanishes identically. This stems from classical statistics which assign the canonical momenta all values ranging from −∞ to ∞ what makes the free energy density magnetic-field-independent. When considering the classical Maxwell-Boltzmann electron gas, it is often admitted that the BvL theorem holds on condition that the potentials modeling the interactions are particle-velocities-independent and do not cause the system to rotate after turning on the magnetic field. From a rigorous viewpoint, when treating large macroscopic systems one expects the BvL theorem to hold provided the thermodynamic limit of the free energy density exists (and the equivalence of ensemble holds). This requires suitable assumptions on the many-body interactions potential and on the possible external potentials to prevent the system from collapsing or flying apart. Starting from quantum statistical mechanics, the purpose of this article is to give within the linear-response theory a proof of the BvL theorem in the semiclassical limit when considering a dilute electron gas subjected to a class of translational invariant external potentials.

About the regularized trace of a self adjoint diﬀerential operator

SEZER Yonca

Yildiz Technical University, Turkey

We ﬁnd a regularized trace formula of the Sturm Liouville operator with a bounded operator coeﬃcient. 109 On approximation properties of generalization of Kantorovich-type discrete q-Beta operators

SHARMA Preeti

Sardar Vallabhbhai National Institute, Surat Gujarat, India Coauthors: Vishnu Narayan Mishra

We discuss the Stancu type generalization of the Kantorovich discrete q-Beta operators. We establish some direct results, which include the asymptotic formula and error estimation in terms of the modulus of continuity and weighted approximation. 110 Weakly nonlinear time-adiabatic theory

SPARBER Christof

University of Illinois at Chicago, USA

We revisit the time-adiabatic theorem of quantum mechanics and show that it can be extended to weakly nonlinear situations. That is, to nonlinear Schr¨odinger equations in which, either, the nonlinear coupling constant or, equivalently, the solution is asymptotically small. To this end, a notion of criticality is introduced at which the linear bound states stay adiabatically stable, but nonlinear eﬀects start to show up at leading order in the form of a slowly varying nonlinear phase modulation. In addition, we prove that in the same regime a class of nonlinear bound states also stays adiabatically stable, at least in terms of spectral projections.

Vector integrals for multifunctions

STAMATE Elena-Cristina

“Octav Mayer” Institute of Mathematics, Iasi, Romania Coauthors: Anca Croitoru

In this talk we present a new Pettis-Sugeno type integral of vector mutifunctions relative to a vector multisubmeasure and present several classic properties. Some comparative results with other generalization for the integrals of Pettis-Lebesgue, Aumann-Sugeno and Choquet-Pettis type are also established.

Commutation and splitting theorems for von Neumann algebras

STRATIL˘ AS˘ ¸erban

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Laszlo Zsido

The Splitting Theorem for factors of Ge & Kadison (Inventiones Math., 1996) is extended for von Neumann Algebras and the Tomita Commutation Theorem is extended for tensor products over commutative subalgebras. Both these results appear as direct consequences of a general commutation theorem for tensor products over (arbitrary) subalgebras.

On some second order moduli of continuity

TALPAU DIMITRIU Maria

“Transilvania” University of Brasov, Romania

We study the equivalence of two second order moduli of continuity deﬁned for the Lipschitz continuous functions and a suitable generalized K-functional. Acknowledgement. This work is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), ﬁnanced from the European Social Fund and by the Romanian Government under the project number POSDRU/159/1.5/S/134378. References

1. Censor, E. – Quantitative results for positive linear approximation operators, J. Approx. Theory, 4 (1971), 442-450. 2. DeVore, R. A. – Optimal convergence of positive linear operators, Proceedings of the Conference on the Constructive Theory of Functions, Budapest, 1969. 3.Gonska,H.H.–On approximation of continuously diﬀerentiable functions by positive linear operators, Bull. Austral. Math. Soc., 27(1983), 73-81. 111

4. Gonska, H. H., Meier, J. – On approximation by Bernstein-type operators: best constants, Studia Sci. Math. Hungar., 22 (1987), 287297. 5. Johnen, H., Scherer, K. – On the equivalence of the K -functional and moduli of continuity and some applications, Constructive Theory of Functions of Several Variables, 571 (1977) of Lecture Notes in Mathematics, Springer, Berlin, 119–140. 6. P˘alt˘anea, R. – New second order moduli of continuity, In: Approximation and optimization (Proc. Int. Conf. Approximation and Optimization, Cluj-Napoca 1996; ed. by D.D. Stancu et al.), vol I, Transilvania Press, Cluj-Napoca, (1997), 327-334. 7. P˘alt˘anea, R. – Approximation theory using positive linear operators, Birkh¨auser, 2004. 8. Talp˘au Dimitriu, M. – Estimates with optimal constants using Peetre’s K-functionals, Carpathian J. Math., 26 (2010), No. 2, 158-169.

Stability and continuity of Julia sets in C2

TANASE Raluca

Stony Brook University, U.S.A.

We discuss some continuity results for the Julia sets J and J+ of the complex Hénon map, which is a polynomial automorphism of C2. We look at the parameter space of strongly dissipative Hénon maps which have a fixed point with one eigenvalue (1 + t)λ,whereλ is a root of unity and t is real and sufficiently small. These maps have a semi-parabolic fixed point when t is 0, and we use techniques that we have developed for the semi-parabolic case to describe nearby perturbations. We prove a two-dimensional analogue of radial convergence for polynomial Julia sets and show that the Hénon map is stable on J and J+ when t is nonnegative. This is joint work with Remus Radu.

Peierls substitution for subbands of the Hofstadter model

TEUFEL Stefan

University of Tuebingen, Germany Coauthors: Abderraman Amr, Silvia Freund

I start with a brief review of recent results on Peierls substitution for magnetic Bloch bands obtained jointly with Silvia Freund. Then I will show how these results can be applied to subbands of the Hofstadter model.

On the maximal function model of a contraction operator

VALUS¸ESCU Ilie

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

The maximal function of a contraction operator T ∈L(H) arises in the factorization process of an operator valued semispectral 2 ∗ −1 measure, i.e. it is the L -bounded analytic function attached to T and has the form MT (λ)=DT ∗ (I − λT ) ,whereλ ∈ D and DT is the defect operator of T . In the particular C.0 case, the Sz.-Nagy–Foias functional model reduces to the functional representation given by the maximal function 2 ∗ MT (λ), i.e. H = MT H⊂H (DT ∗ ), where (MT h)(λ)=MT (λ)h. In this case MT becomes an isometry, and the functional model for T ∗ 1 − is given by the restriction of the backward shift to H, and can be expressed with the maximal function of T as T = λ [MT (λ)h MT (0)h]. ∗ −1 Analogously, the maximal function of T has the form MT ∗ (λ)=DT (I − λT ) , and for the discrete linear system generated by the TDT ∗ rotation operator RT = ∗ the operators MT and MT ∗ become the controllability and the observability operators, respectively. DT −T Some other properties of the maximal function are analyzed, and partial results on a functional model of the maximal function are given. 112 Square positive functionals in an abstract setting

VASILESCU Florian-Horia

University of Lille 1, France

In the framework of spaces of functions on measurable spaces, and using techniques from the theory of ﬁnite-dimensional commutative Banach algebras, as well as Hilbert space methods, we discuss integral representations of square positive functionals, extending and completing some older results concerning the positive Riesz functionals in ﬁnite-dimensional spaces of polynomials.

Hilbert space geometry problems occurring in the Tomita-Takesaki theory

ZSIDOL´´ aszl´o

University of Rome “Tor Vergata”, Italia

Each normal weight on a von Neumann algebra is (by a result of U. Haagerup) the pointwise least upper bound of the majorized bounded linear functionals. This is a basic ingredient in the treatment of the fundamental facts of the Tomita-Takesaki Theory, but is not enough to reduce the case of general faithful, semi-finite, normal weights to the case of (everywhere defined) faithful normal linear functionals. In the talk we propose a “spatial” approximation of an arbitrary faithful, semi-finite, normal weight ϕ on a von Neumann algebra M with bounded normal functionals. Essentially we approximate ϕ with its (bounded) restrictions ϕe to the reduced von Neumann algebras eMe ,wheree ∈ M are projections with ϕ(e) < +∞ . Difficulties arise because in general we don’t have ϕ(eae) ≤ ϕ(a) for every a ∈ M +, and because the family of all projections of finite weight is not upward directed. We are approximating appropriately the identity operator on the Hilbert space Hϕ of the GNS representation of ϕ with the orthogonal projections onto the Hilbert spaces of the GNS representations of the functionals ϕe (considered subspaces of Hϕ) and succeed to reduce the fundamentals of the Tomita-Takesaki Theory for general faithful, semi-finite, normal weights to the case of bounded functionals. Section 6 Probability, Stochastic Analysis, and Mathematical Statistics

Statistical analysis of a cytotoxicity model

ANTON Cristina

Grant MacEwan University, Canada Coauthors: Yau Shu Wong, Jian Deng, Stephan Gabos, and Weiping Zhang Recently there is a big interest to develop innovative toxicity profiling programs based on large data sets obtained through experimental studies. In this talk we develop a mathematical model representing the effect of chemical compounds on the growth/death of different kinds of cells. This model is represented by a non-linear state-space model. To estimate the parameters of the model we use the expectation maximization (EM) algorithm. Since the state equation is non-linear, an approximation is needed during the E-step. The likelihood and the conditional likelihood are approximated based on a linearization, and the unscented filter is used for filtering, smoothing and prediction. The model is validated using experimental cytotoxicity data.

Asymptotic behavior for PDMP’s with three regime

BALLY Vlad

Universite Paris Est Marne la Valle, France Coauthors: Victor Rabiet We consider a sequence of Picewise Deterministic Markov Process (PDMP) with three regimes: a rapid one

(of CLT type), a medium one (of Law of Large Numbers type) and a slow one and we study the asymptotic behavior of such a sequence. At the limit the rapid regime gives rise to a diffusion component, the medium one to a drift component and the slaw one to a finite variation jump process. So the limit equation is no more a PDMP but an equation with diffusive behavior between the jump times and with an infinity of jumps in each finite time interval. This type of equation seems new in the literature. We prove existence and uniqueness for it and we study the regularity of the semigroup. Finally we prove the convergence result and we obtain estimates of the rate of convergence.

Survival analysis for semi-Markov systems

BARBU Vlad-Stefan

Universite de Rouen, Laboratoire de Mathematiques Raphael Salem, France

Semi-Markov processes and Markov renewal processes represent a class of stochastic processes that generalize Markov and renewal processes. As it is well known, for a discrete-time (respectively continuous-time) Markov process, the sojourn time in each state is geometrically (respectively exponentially) distributed. In the semi-Markov case, the sojourn time distribution can be any distribution on ... (respectively on ...). This is the reason why the semi-Markov approach is much more suitable for applications than the Markov one.

113 114

The purpose of our talk is threefold: (i) to make a general introduction to semi-Markov processes; (ii) to investigate some survival analysis and reliability problems for this type of system and (iii) to address some statistical topics. We start by brieﬂy introducing the discrete-time semi-Markov framework, giving some basic deﬁnitions and results. These results are applied in order to obtain closed forms for some survival or reliability indicators, like survival/reliability function, availability, mean hitting times, etc; we also discuss the particularity of working in discrete time. The last part of our talk is devoted to the nonparametric estimation of the main characteristics of a semi-Markov system (semi-Markov kernel, semi-Markov transition probabilities, etc) and to the asymptotic properties of these estimators. Statistical issues for the reliability indicators are also presented. References 1. V. Barbu, N. Limnios – Some algebraic methods in semi-Markov processes, In Algebraic Methods in Statistics and Probability, volume 2, series Contemporary Mathematics edited by AMS, Urbana, 19-35, 2010. 2. V. Barbu, N. Limnios – Semi-Markov Chains and Hidden Semi-Markov Models toward Applications - Their use in Reliability and DNA Analysis, Lecture Notes in Statistics, vol. 191, Springer, New York, 2008. 3. V. Barbu, N. Limnios – Reliability of semi-Markov systems in discrete time: modeling and estimation, In Handbook on Performability Engineering (ed. K. B. Misra), Springer, 369-380, 2008.

Modeling and calibrating banks’ demand deposits versus asset sizes

CANEPA Elena

University Politehnica of Bucharest, Romania

We model and calibrate U.S. banks’ demand deposits and we study the relationship between banks’ asset sizes and the estimated parameters of the deposit processes. Assuming that the banks’ demand deposits evolve as a Brownian motion (geometric Brownian motion/ Ornstein-Uhlenbeck process/ geometric Ornstein- Uhlenbeck process, respectively) between March 1991 and December 2000, we estimate the corresponding drifts and volatilities. The goodness-of-ﬁt tests show that the best model among the proposed ones is the geometric Ornstein-Uhlenbeck process, followed by the Ornstein-Uhlenbeck process, the geometric Brownian motion and the Brownian motion with drift, respectively. Regarding the connection between the asset sizes and deposits, we give the parameters of the deposits as functions of the mean asset sizes, using a regression line.

A new approach to the existence of invariant measures for Markovian semigroups

CIMPEAN Iulian

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Lucian Beznea and Michael Rockner

We present a result concerning the existence of invariant measures for a Markovian semigroup (Pt)t consisting of two steps: first we identify a convenient auxiliary measure m and then we study the existence of a non-zero co-excessive function for (Pt)t regarded as a semigroup on L∞(m). As an application we provide short proofs for the theorems of Lasota and Harris, and we answer to an open problem mentioned by Tweedie, concerning the sufficiency of the generalized drift condition for the existence of an invariant measure. We improve several results on the existence of invariant measures for small perturbations of Dirichlet forms, due to V. Bogachev, M. Röckner, and T.S. Zhang. The talk is based on joint works with Lucian Beznea and Michael Röckner.

Bayesian good-of-ﬁt tests: past, present and future

CIUIU Daniel

Technical University of Civil Engineering Bucharest; Romanian Institute for Economic Forecasting, Romania Coauthors: Carlos Mate 115

We will build the Bayesian version for the good-of-fit tests χ2 and Kolmogorov—Smirnov. Because for the last test the theoretical distribution must be totally specified, we will divide first the sample in two parts: the first part is for inference, and the second part is for test. The completely specified theoretical cdf for the second part of the sample is the Bayesian forecasted cdf from the first part. This is unique if the prior distribution is fixed. For the χ2 test, we do the same Bayesian inference in the first part, and we perform the Bayesian forecasts for the probability such 2 that X belongs to the involved intervals (the values of pi). The parameters of the prior distribution are chosen such that the χ statistics is minimum, and the number of degrees of freedom is k − 1 − npar,wherek is the number of intervals, and npar is the number of parameters of X. Of course, we can fix the prior distribution as for Kolmogorov—Smirnov test, but the number of degrees of freedom is k − 1. For the last test we can consider the whole sample, and the parameters that characterise the distribution of X are the Bayesian estimators. The number of degrees of freedom are the same as above, and npar is again the number of parameters of the distribution of X. When we estimate the values of forecasted cdf/ forecasted probabilities of the intervals or when we estimate the parameters for the chi square test we apply analytical formulae if they exist. Otherwise, we generate a sample according the forecasted distribution of X| S (or the posterior distribution of θ| S), and next we apply the Monte Carlo method. The way we generate the values of X is to use the mixture method: we generate θ according the posterior distribution, and X is generated for each θ.

Voiculescu’s free entropy and spectral analysis of random graphs

CLIMESCU-HAULICA Adriana

Bioclinome, France

Using the free probability calculus initiated by Dan Voiculescu we study the spectral measures of diﬀerent random graphs. Some examples from network communications and computational physiology are presented.

Stochastic aspects of single cell analysis

DE LA CRUZ CABRERA Omar

Case Western Reserve University, U.S.A.

New technologies in molecular biology have made it possible, in the last few years, to accurately measure the levels of gene activity, of epigenetic modiﬁcations, and even the sequencing of whole genomes, using the nuclear material of a single cell. At this level of detail, statistical analysis needs to take into account not only measurement error but also stochastic variation from cell to cell in order to obtain sensible inferences. We will survey some of the work done in this cutting-edge ﬁeld of research.

Brownian and Bessel hitting times: new trends in their approximation

DEACONU Madalina

Inria Centre de Recherche - Nancy Grand-Est, France Coauthors: Samuel Herrmann and Sylvain Maire

A new method for the simulation of the exit time and position, of the δ-dimensional Brownian motion and general Bessel processes, from a domain is constructed. This method avoids splitting time schemes as well as inversion of complicated series. We introduce ﬁrst the walk on moving spheres algorithm for approximating hitting times of Bessel processes with integer dimension. This new method couples the method of images for the ﬁrst hitting time, of a non-linear boundary for the Brownian motion, and the random walk on the spheres method, for the heat equation. After, the hitting time of a non-integer Bessel process is approximated by using the additivity property of the distributions of squared Bessel processes. Each simulation step is split in two parts : one is using the integer dimension case and the other one considers hitting times for a Bessel process starting from zero. 116

By using the connexion between the δ-dimensional Bessel process and the δ-dimensional Brownian motion we construct a fast and accurate numerical scheme for approximating the exit time and position from a boundary for the δ-dimensional Brownian motion. This is a joint work with Samuel Herrmann (University of Burgundy, France) and Sylvain Maire (University of Toulon, France).

Asymptotic control of switch processes in systems biology

GOREAC Dan

Universite Paris-Est, France Coauthors: Oana Silvia Serea

We begin by recalling the construction of a class of hybrid stochastic processes (piecewise deterministic diﬀusive Markov processes). This is done in connection to stochastic gene networks (e.g. moderate viruses). We discuss nonexpansive conditions guaranteeing the existence of long-run averaged value functions and generalized Abel/Tauberian results.

Nonlinear Langevin type equation driven by stable Levy process

GRADINARU Mihai

Universite de Rennes 1, France Coauthors: Ilya Pavlyukevich, Richard Eon

β The speed vt of a particle is a solution of a sde driven by a small α-Levy process × lt with non-linear drift coeﬃcient −sgn(v)|v| , β>2 − α/2. One studies the asymptotics of the position xt of the particle, under appropriate normalization, when tends to 0 and diﬀerent limits are emphasized. The talk is based on joint works with Ilya Pavlyukevich (Jena) and with Richard Eon (Rennes).

Brownian motion on complex structures

HSU Elton P

Northwestern University, U.S.A.

There is a well developed theory of Brownian motion on Riemannian manifolds. In this talk, we will study properties of Brownian motion on a complex domain or a complex manifold under various Riemannian metrics related to the complex structure of the underlying spaces. In particular, we will clarify probabilistic meanings of the Kaehler property and pseudo convexity and show how they aﬀect the behavior of Brownian motion on complex structures with these properties. The cases of the unit ball and a polydisc can be studied by explicit computations.

On relations between statistics and geometry

HUCKEMANN Stephan

University of G¨ottingen, Germany 117

Multivariate statistics takes great advantage from linearization due to the linear structure of the data space. If data reside in non-linear spaces, which, for instance, occurs in shape analysis, already the most basic statistical concepts such as means or principal components can no longer be simply defined as arithmetic averages or eigenspaces of covariance matrices. For suitable data descriptors living on manifolds or stratified spaces we investigate asymptotic properties to allow for statistical inference. It turns out that rates and forms of central limit theorems may reflect the topological and geometric structure of the underlying space.

Geometric programming models for dynamical decision stochastic systems with ﬁnal sequence of states

LAZARI Alexandru

Moldova State University, Republic of Moldova

This paper describes several classes of dynamical stochastic systems, that represent an extension of classical Markov decision processes. The Markov stochastic systems with given final sequence of states, over a finite or infinite state space, are studied. Such dynamical system stops its evolution as soon as given sequence of states in given order is reached. The evolution time of the stochastic system with fixed final sequence of states depends on initial distribution of the states and probability transition matrix. We are seeking for the optimal initial distribution and optimal probability transition matrix, that provide the minimal evolution time for the dynamical system. We show that this problem can be solved using the geometric programming approach. These geometric programming models are developed and theoretically grounded.

Propagation of chaos for systems of interacting neurons

LOCHERBACH¨ Eva

Universit´e de Cergy-Pontoise, France Coauthors: A. De Masi, N. Fournier, A. Galves, E. Presutti

We study the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electrical synapses. This system can be informally described as follows. Each neuron spikes randomly following a point process with rate depending on its membrane potential. At its spiking time, the membrane potential of the spiking neuron is reset to the value 0 and, simultaneously, the membrane potentials of the other neurons are increased by an amount of sl energy frac1N. This mimics the effect of chemical synapses. Additionally, the effect of electrical synapses is represented by a deterministic drift of all the membrane potentials towards the average value of the system. We show that, as the system size N diverges, the distribution of membrane potentials becomes deterministic and is described by a limit density which obeys a non linear PDE which is a conservation law of hyperbolic type.

Branching processes and the fragmentation equation

LUPAS¸CU Oana

Institute of Mathematical Statistics and Applied Mathematics and Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, and the Research Institute of the University of Bucharest, Romania

We investigate branching properties of the solution of a stochastic diﬀerential equation of fragmentation and we properly associate a continuous time cadlag Markov process on the space of all fragmentation sizes, introduced by J. Bertoin. The construction and the proof of the path regularity of the Markov processes are based on several newly developed potential theoretical tools, in terms of excessive functions and measures, compact Lyapunov functions, and some appropriate absorbing sets. The talk is based on joint works with Lucian Beznea and Madalina Deaconu. 118 Object oriented data analysis

MARRON J. S.

University of North Carolina, U.S.A.

Object Oriented Data Analysis is the statistical analysis of populations of complex objects. In the special case of Functional Data Analysis, these data objects are curves, where standard Euclidean approaches, such as principal components analysis, have been very successful. In non-Euclidean analysis, the approach of Backwards PCA is seen to be quite useful. An overview of insightful mathematical statistics for object data is given

Viscosity solutions for functional parabolic PDEs. A stochastic approach via BSDEs with time-delayed

MATICIUC Lucian

“Gheorghe Asachi” Technical University of Iasi, Romania

We provide a probabilistic representation of a viscosity solution for the path dependent nonlinear Kolmogorov equation: ⎧ ⎨−∂tu(t, φ) −Lu(t, φ) − f(t, φ, u(t, φ),∂xu(t, φ)σ(t, φ), (u(·,φ))t)=0, ⎩ (0.15) u(T,φ)=h(φ),t∈ [0,T),φ∈C([0,T]; Rd), where L is a second order diﬀerential operator and (u(·,φ))t := (u(t + θ, φ))θ∈[−δ,0] . We show that the functional u :[0,T] ×C([0,T]; Rd) → R, u(t, φ):=Y t,φ(t), is a viscosity solution for (1), where (Y t,φ,Zt,φ)isthe unique solution of a BSDE with time delayed–generators.

Sample size needed for estimating principal component

MATZINGER Henry

Georgia Institute of Technology, Atlanta, U.S.A.

We show how we can get a detailed description of the estimation error of certain eigenvectors of a covariance matrix even in the high-dimensional case. This allows in may cases to get smaller bounds for the sample size needed to retrieve these eigenvectors precisely.

Stochastic modeling of compositional data with diﬀusions

MOCIOALCA Oana

Kent State University, U.S.A. Coauthors: Lu Chen, Omar De la Cruz C.

Here we present a class of stochastic processes in continuous time which take as values vectors with non-negative values adding up to 1, and show their use as models for continuously changing compositions. They are defined as solutions of a stochastic differential equation, in such a way that the marginal distributions are Dirichlet. The aggregation property of the Dirichlet distribution is exploited to allow the study of microbial compositions at different taxonomic levels in microbiome surveys. 119 Approach of the currency exchange risk

NOVAC Ludmila

Moldova State University, Republic of Moldova

In this article we analyze the problem of Currency Exchange. The main goal is to approach the risk of loss for this problem (so called Currency Exchange Risk). Currency changes affect us, whether we are actively trading in the foreign exchange market, planning our next vacation, shopping online for goods from another country or just buying food or other things imported from abroad. More exactly, we can define this risk (also known as ”currency risk” or ”exchange-rate risk”) as the risk that an investor will have to close out a long or short position in a foreign currency at a loss due to an adverse movement in exchange rates. In order to analyze some multistage interactive situations of this problem, we will use the theory of extensive games and we will construct a dinamical model. Every such a situation can be represented by a strategic game. Representing a model as a multistage interactive situation, we can construct a dynamical model for the problem of the Currency Exchange. This risk usually affects businesses that export and/or import, but it can also affect investors making international investments. For example, if money must be converted to another currency to make a certain investment, then any changes in the currency exchange rate will cause that investment’s value to either decrease or increase when the investment is sold and converted back into the original currency. There are many factors that could cause the fluctuation of the currency rate. The supply and demand of a country’s money is reflected in its foreign exchange rate. It is not simple to determine the risk of the not adequate business. Consumer spending is influenced by a number of factors: the price of goods and services (inflation), employment, interest rates, government initiatives, and so on. There are many economic factors we can follow to identify economic trends and their effect on currencies. Keywords: dynamical model, problem of currency exchange, minimum loss, profit, loss risk, currency exchange risk, currency risk, exchange-rate risk.

Brownian couplings and applications

PASCU Mihai N.

Transilvania University of Brasov, Faculty of Mathematics and Computer Science, Romania

Brownian motion is invariant under the three basic geometric transformation: translation, scaling and rotation/symmetry. In this talk we will show that corresponding to each of these invariance properties one can construct couplings of (reflecting) Brownian motions: scaling coupling ([7]), mirror coupling ([1], [2], [9]), and recently the “translation” coupling ([10]). Aside from the intrinsic interest of the construction (existence of a pair of RBM with specified properties), the existence and the properties of these couplings can be used to prove various results for certain functionals associated with the RBM. For example, as an application of the scaling coupling, we will prove a monotonicity of the lifetime of reflecting Brownian motion with killing, which implies the validity of the Hot Spots conjecture of J. Rauch for a certain class of domains. As applications of the mirror coupling, we will present the proof of the Laugesen-Morpurgo conjecture ([8]), and a unifying proof of the results of I. Chavel and W. Kendall on Chavel’s conjecture. Time-permitting, we will discuss the recent results (joint with I. Popescu, [10]) on fixed-distance couplings, a particular case of shy coupling (as introduced and studied in [3], [4], [5]), and some of its applications. For example, in the particular case of a sphere, the existence of this coupling gives a resolution for a stochastic version of the celebrated Lion and Man problem of Radó ([6]). References

1. R. Atar, K. Burdzy – On Neumann eigenfunction in Lip domains, JAMS, 17 (2004), No. 2, 243–265. 2. R. Atar, K. Burdzy – Mirror couplings and Neumann eigenfunctions, Indiana Univ. Math. J., 57 (2008), 1317–1351. 3. I. Benjamini, K. Burdzy, Z.Q. Chen – Shy couplings, Probab. Theory Related Fields, 137 (2007), No. 3-4, 345–377. 4. M. Bramson, K. Burdzy, W.S. Kendall – Shy couplings, CAT(0) spaces, and the lion and man, Ann. Probab., 41 (2013), No. 2, 744–784. 5. W.S. Kendall – Brownian couplings, convexity, and shy-ness, Electron. Commun. Probab., 14 (2009), 66–80. 6. J.E. Littlewood – Littlewood’s miscellany, Cambridge University Press, Cambridge, 1986, Edited and with a foreword by Béla Bollobás. 7. M.N. Pascu – Scaling coupling of reflecting Brownian motions and the hot spots problem, Trans. Amer. Math. Soc., 354 (2002), No. 11, 4681–4702. 8. M.N. Pascu – Monotonicity properties of Neumann heat kernel in the ball, J. Funct. Anal., 260 (2011), No. 2, 490–500. 9. M.N. Pascu – Mirror coupling of reflecting Brownian motion and an application to Chavel’s conjecture, Electron. J. Probab., 16 (2011), No. 18, 504–530. 10. M.N. Pascu, I. Popescu – Shy and Fixed-Distance Couplings of Brownian Motions on Manifolds, preprint (http://arxiv.org/abs/1210.7217Arxiv link). 120 Two sample tests for means on lie groups and homogeneous spaces with examples

PATRANGENARU Vic

Florida State University, U.S.A.

This presentation focuses on recent advances in Data Analysis on Homogeneous Spaces, including two sample tests and MANOVA for means of random objects on homogeneous spaces with examples from 3D high level image analysis

Cumulative prospect theory with skewed return distribution

PIRVU Traian

McMaster University, Canada Coauthors: Minsuk Kwak

We investigate a one-period portfolio optimization problem of a cumulative prospect theory (CPT) investor with multiple risky assets and one risk-free asset. The returns of multiple risky assets follow multivariate generalized hyperbolic (GH) skewed t distribution. We obtain a three-fund separation result of two risky portfolios and risk-free asset. Furthermore, we reduce the high dimensional optimization problem to two 1-dimensional optimization problems and derive the optimal portfolio. We show that the optimal portfolio composition changes as some of investor-speciﬁc parameters change. It is observed that the consideration of skewness of stock return distribution has considerable impact on the distribution of CPT investor’s wealth deviation, and leads to less total risky investment.

On the recursive evaluation of a certain multivariate compound distribution

ROBE-VOINEA Elena-Gratiela

University of Bucharest, Romania Coauthors: Raluca Vernic

Abstract In this talk we extend to a multivariate setting the bivariate model introduced by Jin and Ren (2014) to model insurance aggregate claims in the case when diﬀerent types of claims simultaneously aﬀect an insurance portfolio. We obtain an exact recursive formula for the probability function of the multivariate compound distribution corresponding to the model A of Jin and Ren (2014), under the assumption that the conditional multivariate counting distribution (conditioned by the total number of claims) is multinomial. Our formula extends the corresponding one from Jin and Ren (2014). Key words: insurance model, multivariate aggregate claims, multinomial distribution, recursion.

A new approach to stochastic PDE

ROCKNER¨ Michael

Bielefeld University, Germany Coauthors: Viorel Barbu

We develop a new general approach to the existence and uniqueness theory of infinite dimensional stochastic equations of the form dX + A(t)Xdt = XdW in (0,T) × H,whereA(t) is a nonlinear monotone and demicontinuous operator from V to V , coercive and with polynomial growth. Here, V is a reflexive Banach space continuously and densely embedded in a Hilbert space H of (generalized) functions on a domain O⊂Rd and V is the dual of V in the duality induced by H as pivot space. Furthermore, W is a Wiener process in H. The new approach is based on an operatorial reformulation of the stochastic equation which is quite robust under perturbation of A(t). This leads to new existence and uniqueness results of a larger class of equations with linear multiplicative noise than the one 121 treatable by the known approaches. In addition, we obtain regularity results for the solutions with respect to both the time and spatial variable which are sharper than the classical ones. New applications include stochastic partial differential equations, as e.g. stochastic transport equations.

Anticipated BSVIs with generalized reﬂection

ROTENSTEIN Eduard

“Alexandru Ioan Cuza” University of Ia¸si, Romania Coauthors: Lucian Maticiuc

We present existence and uniqueness results for anticipated backward stochastic variational inequalities with generalized reﬂecting directions. In these equations the generator includes not only the values of solutions of the present, but also the future. Numerical approximation schemes are also envisaged.

Stochastic spline fractal interpolation functions

SOOS Anna

Babe¸s-Bolyai University, Romania Coauthors: Ildiko Somogyi

The spline interpolation method is the most important and well-known classical real data interpolation method. It has a lot of applications especially in computer geometric design. But the classical method can be generalized with fractal interpolation. These fractal interpolation functions provide new methods of approximation of exprimental data. We extend the spline fractal interpolation method to stochastic case.

Functional central limit theorem for empirical processes under a strong mixing condition

TONE Cristina

University of Louisville, U.S.A.

We introduce a functional central limit theorem for empirical processes endowed with real values from a strictly stationary random field satisfying an interlaced mixing condition. We proceed by first obtaining the limit theorem for the uniformly distributed case. We then generalize the result to the case where the absolutely continuous marginal distribution function is no longer uniform. In this case we show that the empirical process endowed with values from the rho-mixing stationary random field, due to the strong mixing condition, doesn’t converge in distribution to a Brownian bridge,but to a continuous Gaussian process with mean zero and the covariance given by the limit of the covariance of the empirical process. 122 Recurrence criteria for diffusion processes generated by divergence free perturbations of non-symmetric energy forms

TRUTNAU Gerald

Seoul National University, South Korea Coauthors: Minjung Gim

On a metric space E, we consider a generalized Dirichlet form 0 E(f,g)=E (f,g)+ fNgdμ, E where (E0,D(E0)) is a sectorial Dirichlet form on L2(E,dμ), (N,D(N)) is a linear operator on L2(E,dμ) and E0(f,f) ≤E(f,f). We find a criterion for recurrence of E. Namely, if the generalized Dirichlet form E is strictly irreducible and if there exists a sequence of functions (χn)n≥1 with 0 ≤ χn ≤ 1, limn→∞ χn =1μ-a.e. satisfying 0 lim E (g, χn)+ gNχn dμ = 0 (0.16) n→∞ E for any non-negative bounded g in the extended Dirichlet space of D(E0), then E is recurrent. As application, we consider E ⊂ Rd, E open or closed and a strictly irreducible generalized Dirichlet form 1 E(f,g)= A(∇f) ·∇gdμ− (B ·∇f)gdμ, 2 E E where the diffusion matrix A =(aij ) is not necessarily symmetric but its antisymmetric part consists of bounded functions and B is a locally μ-square integrable μ-divergence free vector field. Then using volume growth conditions of B and of the sectorial part of E on Euclidean balls w.r.t. μ, we construct explicitly (χn)n≥1 satisfying (0.16). One astonishing observation is that there may exist a sequence of functions (χn)n≥1 in the Dirichlet space with 0 ≤ χn ≤ 1, limn→∞ χn =1μ-a.e. and such that limn→∞ E(χn,χn) = 0, but recurrence does not hold for E in contrast to the symmetric case. Finally, as a concrete example, we consider a whole class of singular diffusions associated to E,whereμ = ρdx, ρ is continuous and in a certain Muckenhoupt class. Here, we discuss non-explosion (in particular existence of a pathwise and weakly unique strong solution) and recurrence for any initial condition x ∈{ρ>0}.

Stabilizing solution for modiﬁed algebraic Riccati equations in inﬁnite dimensions

UNGUREANU Viorica

Constantin Brancusi University, Targu-Jiu, Romania

The study of optimal control problems associated to stochastic systems with Markovian regime switching are of particular interest to researchers due to their various applications in finance, biology, engineering etc. In particular, infinite horizon linear quadratic (LQ) optimal control problems for stochastic systems with Markovian jumps has been recently investigated for both finite and infinite- dimensional cases. Their solvability is closely related to the existence of mean-square stabilizing (MSS) solutions for a class of modified Riccati equations (MREs). Most existing works, prove the existence of MSS solutions for these MAREs under either detectability or observability conditions. Some others give necessary and sufficient conditions are formulated in terms of linear matrix inequalities (LMIs). In this talk we consider a class of infinite-dimensional algebraic MREs associated with time-invariant linear stochastic systems affected simultaneous by multiplicative white noise(MN) and Markovian jumps(MJs). These algebraic MREs are defined on ordered Banach spaces of sequences of linear and bounded operators. Using spectral properties of positive operators and the general theory of compact (in particular, of trace-class operators), we provide necessary and sufficient conditions for the existence of MSS solutions for infinite-dimensional algebraic MREs in terms of system parameters. and of trace class and compact operators. mean-square stabilizing solution in terms of stabilizability and observability. Our results generalize similar ones obtained for finite-dimensional MREs associated with stochastic linear systems without MJs. 123 Psychometric applications: parameter estimation and comparability of test performance in multistage testing

VON DAVIER Alina A.

Educational Testing Service, U.S.A.

In a Multistage adaptive Test (MST), all test takers take first a set of items (called the routing module), and then, based on their performance there are administered different sets of items (or modules). Parameter estimation, calibration, linking, scoring, and equating are statistical processes required for any practical implementation of an MST design. This presentation discusses the types of parameter estimation and linking necessary at different stages in the life of an operational MST program. Item response theory (IRT) has traditionally provided the framework for these processes in analyzing test data. Justification is provided for application of conventional estimation methods for IRT to an MST. Calibration and linking involve an initial phase for data collection in which conventional test administrations are used to build modules and routing rules to begin use of MST administrations. Once MST administrations begin, data are collected to establish scoring rules, develop new test modules, equate the cut-scores for routing, and ensure comparability of tests over time. Discussion involves both direct use of estimated examinee proficiency in routing and scoring and use of sum scores for these purposes. When many administrations are involved, special procedures are considered for maintenance of stable linkage.

Section 7 Mechanics, Numerical Analysis, Mathematical Models in Sciences

Stability analysis of some equilibrium points in a complex model for blood cells’ evolution in CML

BADRALEXI Irina

University Politehnica of Bucharest, Romania Coauthors: Andrei Halanay

The complex model considers the competition between the populations of healthy and leukemic stem-like short-term and mature leukocytes and the influence of the T-lymphocytes on the evolution of leukemia. Delay differential equations are used in a modified Mackey-Glass approach, with the consideration of asymmetric division and feedback functions for the action of the immune system. This research is focused on the linear stability analysis of equilibrium points. As the characteristic equations for some equilibrium points are very complex, the existence of a Lyapunov-Krasovskii functional is investigated. Also, treatment with Imatinib is introduced in the model and new stability properties are investigated. This research is supported by the CNCS Grant PNII-ID-PCE-3-0198 and by POSDRU/159/1.5/S/132395.

Spectral aspects of anisotropic metric models in the Garner oncologic framework

BALAN Vladimir

University Politehnica of Bucharest, Romania Coauthors: Jelena Stojanov

The present talk discusses three natural Finsler models, which naturally relate to the classical Garner dynamical system, which describes the evolution of the active and quiescent cancer cell populations. The statistically fit metric structures are determined from the energy of the deformed field of the biological model, assuming that severe disease circumstances occur, and it is shown that the subsequently derived geometric objects are able to provide an evaluation of the overall cancer cell population growth. The spectral characteristics of the Cartan tensor, the comparison between the Z− and H−eigendata of the constructed Randers, m−th root and Euclidean structures, and the applicative advantages of the developed geometric models, are discussed. 2010 Mathematics Subject Classification: 53B40, 53C60, 37C75, 65F30, 15A18, 15A69.

RIT’s Cubesat Project

BARBOSU Mihai

RIT (Rochester Institute of Technology), USA Coauthors: Dorin Patru, Jennifer Connelly, Oesa Weaver, Anthony Hennig, David Sawyer Elliot, Andrew Hin

125 126

Students and faculty members of the Space Exploration group (SPEX) at the Rochester Institute of Technology (RIT) have worked together on a CubeSat project focused on laser communications. Laser communications represent a major change in how spacecraft communications could be handled in the future and this is an important area of research in the space community. Our plan is to launch a satellite through the NASA CubeSat Launch Initiative and we have two main scientiﬁc goals: testing laser uplink technologies and developing better tracking algorithms. We will discuss the scientiﬁc merit of the proposal and the technical challenges regarding this mission.

On the 6-parameter shell model derived from the three-dimensional Cosserat theory of elasticity

BIRSAN Mircea

University Duisburg-Essen and University “Al.I. Cuza” of Iasi, Germany and Romania Coauthors: P. Neﬀ, D.I. Ghiba, O. Sander

In order to obtain a refined shell model, we start from a nonlinear Cosserat model for three-dimensional elastic bodies, with a specific form of the strain energy functional (see [1]). We perform the dimensional reduction by integration through the thickness and using a generalized plane stress condition, which allows to determine in closed form the expression for the thickness stretch and the nonsymmetric shift of the midsurface in bending. Thus, we derive a two-dimensional shell model which takes full account of initial curvature effects and involves 6 parameters (kinematical degrees of freedom) for each material point: 3 for translations and 3 for rotations. Within this new model we can express the strain measures with the help of shell strain and bending-curvature tensors which were previously introduced in the general nonlinear theory of 6-parameter shells (see e.g., [2,3]). In our model we obtain a specific form for the shell strain energy density and show that this functional satisfies the invariant properties required by the local symmetry group of isotropic solid shells, as stated in [2]. We also prove the existence of minimizers for 6-parameter elastic shells, in a general case including anisotropic behavior, under certain convexity assumptions on the energy functional [3]. An important special case of the general shell theory is the case of shells without drilling rotations, where the in-plane rotations (i.e. rotations about the shell filament) are neglected. For this type of shells one obtains a 5-parameter model (3 translational and 2 transverse-rotational degrees of freedom, i.e. a Reissner-type kinematics) which is widely used in engineering, since it covers most of the practical situations. In order to characterize this type of shells in the framework of the general shell theory, we prove a representation theorem for the strain energy functional of shells without drilling rotations [4]. Finally, we show that this new model can be successfully applied to describe and solve numerically some complex mechanical problems, such as the formation of wrinkles in a thin elastic sheet under shear [5]. References 1. P. Neff, M. Bˆırsan, F. Osterbrink (2015) – Existence theorem for geometrically nonlinear Cosserat micropolar model under uniform convexity requirements, Journal of Elasticity, DOI 10.1007/s10659-015-9517-6. 2. V.A. Eremeyev, W. Pietraszkiewicz (2006) – Local symmetry group in the general theory of elastic shells, Journal of Elasticity, vol. 85, 125-152. 3. M. Bˆırsan, P. Neff (2014) – Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations, Mathematics and Mechanics of Solids, vol. 19, 376-397. 4. M. Bˆırsan, P. Neff (2014) – Shells without drilling rotations: A representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory, International Journal of Engineering Science, vol. 80, 32-42. 5. O. Sander, P. Neff, M. Bˆırsan (2015) – Numerical treatment of a geometrically nonlinear planar Cosserat shell model, published first on arXiv: 1412.3668v2 , submitted.

Some non-standard problems related with the mathematical model of thermoviscoelasticity with voids

BUCUR Andreea-Valentina

“Alexandru Ioan Cuza” University of Iasi, Romania

In this presentation, we consider the constrained motion of a prismatic cylinder made of a thermoviscoelastic material with voids and subjected to ﬁnal given data that are proportional, but not identical, to their initial values. We show how certain cross-sectional integrals of the solution spatially evolve with respect to the axial variable. Some conditions are derived upon the proportionality coeﬃcients in order to show that the integrals exhibit alternative behavior. 127

A quasistatic frictional contact problem with normal compliance and unilateral constraint

CAPATINA Anca

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We consider a mathematical model describing the quasistatic process of frictional contact between an elastic body and a foundation. The contact is modeled by normal compliance and unilateral constraints, and the friction by a slip-dependent version of Coulomb’s law. A weak formulation of the problem is derived and an existence result is proved by using arguments of incremental formulations, compactness and lower semicontinuity.

Aerodynamics coeﬃcients of a thin oscillating airfoil in subsonic ﬂow

CARABINEANU Adrian

University of Bucharest & Institute of Mathematical Statistics and Applied Mathematics of Romanian Academy, Romania

We linearize the equations of aerodynamics and express the jump of the pressure past the airfoil in terms of the solution of a hypersingular integral equation (the lifting surface equation). The great advantage of the lifting surface equation is that the domain of integration is the airfoil (more precisely its projection onto the Oxy - plane) and the influence of the vortex sheet is taken into account by means of the expresion of the kernel. After solving the lifting surface equation we calculate the aerodinamic coefficients (lift, drag and moment coefficients) and the pressure field.

Optimization and control in vascular networks

CASCAVAL Radu

University of Colorado Colorado Springs, USA

The cardiovascular system is designed to be a very robust system, meant to function under a wide range of external conditions. Understanding its dynamics in basal condition as well as in such dynamic states is desirable and several mathematical models have been developed to achieve this goal. In this talk we present a Boussinesq-type system for modeling the dynamics of pressure-flow in arterial networks, considered as a 1d spatial network. Numerical solutions of the system of PDE are obtained via discontinuous Galerkin schemes and are compared with simplified models based on particle-tracking arguments. We present several flow optimization studies, which include the geometry and size of the network as well as boundary control. Physiologically realistic control mechanisms are also tested in the context of these simplified models.

Non-isothermal viscous Cahn-Hilliard equation with inertial term and dynamic boundary conditions

CAVATERRA Cecilia

Universit`a degli Studi di Milano, Italy Coauthors: Maurizio Grasselli and Hao Wu 128

We consider a non-isothermal modified viscous Cahn-Hilliard equation. Such an equation is characterized by an inertial term and it is coupled with a hyperbolic heat equation from the Maxwell-Cattaneo’s law. We analyze the case in which the order parameter is subject to a dynamic boundary condition. This assumption requires a more refined strategy to extend the previous results to the present case. More precisely, we first prove the well-posedness for solutions with finite energy as well as for weak solutions. Then we establish the existence of a global attractor. Finally, we prove the convergence of any given weak solution to a single equilibrium by using a suitable Lojasiewicz-Simon inequality.

Rein’s Model for the restricted eliptic three-body problem with drag

CHIRUTA Ciprian

Universitatea de Stiinte Agricole si Medicina Veterinara “Ion Ionescu de la Brad” Iasi, Romania Coauthors: Mihai Barbosu, Tiberiu Oproiu

We present a generalization of Rein’s model for the elliptic restricted three-body problem (ERTBP) by taking into account of a drag force. The equations of motion and the sationary points were established, and the linear stability of the equilibrium points were studied. Applications to the Earth-Moon system are considered, with the traiectories computed around the stable Lagrangian points.

Non-smooth regularization of a forward-backward parabolic equation

COLLI Pierluigi

University of Pavia, Italy

A variation of the Cahn-Hilliard equation is discussed. In the concerned system, a viscosity term, with a maximal monotone graph acting on the time derivative of the phase variable, replaces the usual diﬀusive contribution. The phase variable stands for the concentration of a chemical species and it evolves under the inﬂuence of a non-convex free energy density. For the chemical potential a non-homogeneous Dirichlet boundary condition is assumed. Existence and continuous dependence results are discussed. The talk reports on a joint work with E. Bonetti and G. Tomassetti.

The black hole eﬀect and thegravitational redshift computation in the frame of post newtonian type garavitational ﬁelds

CONSTANTIN Diana Rodica

Astronomical Institute of the Romanian Academy, Romania Coauthors: Dumitru Pricopi

We analyze the gravitational redshift in the two-body problem associated to some post-Newtonian type gravitational fields. We start from the general relativistic metric and we discuss the black hole effect associated to each of the gravitational potentials. Also, the mathematical expression of the gravitational redshift is written down for all the considered potentials. Comparing with the Newtonian potential case, we are able to offer a deeper insight about the gravitational redshift problem in the relativistic (both general and special) theory. Our results may contribute to a better understanding of mechanisms involved in gravitationally lensed galaxies at high redshift. 129 Cracks propagation in prestressed and prepolarized piezoelectric materials

CRACIUN Eduard - Marius

Universitatea OVIDIUS Constanta, Romania

The considered problem is the antiplane deformation in prestressed and prepolarized piezoelectric crystals in equilibrium. The representation of the general solution is derived in terms of complex potentials for all piezoelectric crystal classes in which an antiplane state is possible. This generalizes earlier results obtained in respect of a speciﬁc crystal class. The general formulae are specialized to ﬁnd the antiplane state generated by a Mode-III crack.

Fading regularization method for Cauchy problems associated with elliptic operators

DELVARE Franck

Universit´e de Caen, France

Data completion problems, also known as Cauchy problems, associated with elliptic equations are investigated. These problems consist of recovering the missing data on a part of the boundary of the solution domain from over-speciﬁed data on the remaining boundary. A regularization method is introduced based on an iterative algorithm whose regularization eﬀect vanishes with respect to increasing the number of iterations. The principle, the continuous and discrete formulations of the method and numerical simulations are presented.

Numerical simulations of a two noncompeting species chemotaxis model

DIMITRIU Gabriel

“Grigore T. Popa” University of Medicine and Pharmacy of Iasi, Romania

We present the results of the numerical simulations of a two-species chemotaxis model. This model represents a regularized extension of the Patlak-Keller-Segel (PKS) system to the case of the chemotaxis motion of two noncompeting species that produce the same chemoattractant. We perform several experiments by applying a strong stability preserving (SSP) implicit-explicit Runge-Kutta method to study the behaviour of the obtained spiky solutions.

Investigation of specific electromagnetic field problems using systems of partial differential equations

DMITRIEVA Irina

Odessa National Academy of Telecommunications (ONAT), Ukraine

Specific case of the differential Maxwell system is studied as original mathematical model of electromagnetic wave propagation in heterogeneous lines under expofunctional excitations. It is shown, that this system is equivalent to the general wave PDE (partial differential equation) with respect to all electromagnetic field intensities. Solvability criterion of this system in the class of non generalized functions is proved, and all main types of corresponding boundary problems are proposed and solved explicitly in the unified manner. 130 Optimal order multigrid preconditioners for linear systems arising in the semismooth Newton method solution process of a class of control-constrained problems

DRAGANESCU Andrei

University of Maryland Baltimore County, USA Coauthors: Jyoti Saraswat

We present a new multigrid preconditioner for the linear systems arising in the semismooth Newton method solution process of certain control-constrained, quadratic distributed optimal control problems. Using a piecewise constant discretization of the control space, each semismooth Newton iteration essentially requires inverting a principal submatrix of the matrix entering the normal equations of the associated unconstrained optimal control problem, the rows (and columns) of the submatrix representing the constraints deemed inactive at the current iteration. Previously developed multigrid preconditioners by Draganescu [Optim. Methods Softw., 29 (2004), pp. 786-818] for the aforementioned sub matrices were based on constructing a sequence of conforming coarser spaces, and proved to be of suboptimal quality for the class of problems considered. Instead, the multigrid preconditioner introduced in this work uses non-conforming coarse spaces, and it is shown that, under reasonable geometric assumptions on the constraints that are deemed inactive, the preconditioner approximates the inverse of the desired submatrix to optimal order. The preconditioner is tested numerically on a classical elliptic- constrained optimal control problem and further on a constrained image-deblurring problem.

Dynamics of space debris: resonances and long term orbital eﬀects

GALES Catalin Bogdan

“Alexandru Ioan Cuza” University of Ia¸si, Romania

Since the beginning of space exploration a large number of space debris accumulated in the vicinity of the Earth, from near atmosphere to the geosynchronous region. The impact of operative spacecraft or satellites with large enough space debris could result in a dramatic situation. Understanding the overall orbital evolution of space debris is essential for maintenance and control strategies, as well as for space debris mitigation. In this talk, we present a description of the dynamics of space debris in various resonances by using the Hamiltonian formalism. We consider a model including the geopotential contribution and we compute the secular and the resonant parts of the Hamiltonian function for each resonance. Determining the leading terms of the expansions in speciﬁc resonant regions, we explain the main dynamical features of each resonance in a very eﬀective way. Then, by computing the Fast Lyapunov Indicators, we provide a cartographic study of each resonance, yielding the regular and chaotic behavior of the resonant regions. The study allows to determine easily the location of the equilibrium points, the amplitudes of the libration islands and the main dynamical stability features of each resonance. The results are validated by a comparison with a model developed in Cartesian coordinates, including the geopotential, the lunar and solar gravitational attractions and the solar radiation pressure.

Mathematical insights and integrated strategies for the control of Aedes aegypti mosquito

GEORGESCU Paul

Technical University of Iasi, Romania Coauthors: Hong Zhang, Hassan Adamu Shitu

We propose and investigate a delayed model for the dynamics and control of a mosquito population which is subject to an integrated strategy that includes pesticide release, the use of mechanical controls and the use of the sterile insect technique (SIT). The existence of positive equilibria is characterized in terms of two threshold quantities, being observed that the “richer” equilibrium (with more mosquitoes in the aquatic phase) has better chances to be stable, while a longer duration of the aquatic phase has the potential to destabilize both equilibria. It is also found that the stability of the trivial equilibrium appears to be mostly determined by the value of the maturation rate from the aquatic phase to the adult phase. A nonstandard finite difference (NSFD) scheme is devised to preserve the positivity of the approximating solutions and to keep consistency with the continuous model. The resulting discrete model is transformed into a delay-free model by using the method of 131 augmented states, a necessary condition for the existence of optimal controls then determined. The particularities of different control regimes under varying environmental temperature are investigated by means of numerical simulations. It is observed that a combination of all three controls has the highest impact upon the size of the aquatic population. At higher environmental temperatures, the oviposition rate is seen to possess the most prominent influence upon the outcome of the control measures.

From separation of variables to multiparameter eigenvalue problems. Numerical aspects

GHEORGHIU Calin - Ioan

Romanian Academy, T. Popoviciu Institute of Numerical Analysis, Cluj-Napoca, Romania

The main aim of this talk is to show that the Jacobi-Davidson type (space) methods are fairly accurate and robust methods for solving algebraic multiparameter eigenvalue problems that are provided by separation of variables applied to various boundary value problems attached to some classical partial differential equations (Helmholtz, Laplace, Schroedinger, Mathieu, Lam, etc.). The differential systems are discretized by spectral collocation method based on Chebyshev, Laguerre or Hermite functions. These methods also solve generalized algebraic eigenvalue problems with a singular second matrix. The first matrix in the pencil is nonsymmetric, full rank and ill-conditioned. Despite of these difficulties, and the large dimensions of the multiparameter problems, a specified region of the spectrum is computed accurately, as it is shown for matrices arising in some hydrodynamic stability problems. The methods also overcome the potentially severe problems associated with spurious unstable eigenvalues. A lot of numerical experiments are carried out and some pseudospectra and eigenfunctions are displayed for various aspect ratios of the geometrical domains.

A model for describing the structure and growth of epidermis

IANNELLI Mimmo

Universit`a di Trento, Italy Coauthors: Alberto Gandolﬁ, Gabriela Marinoschi

We consider a model with age and space structure designed to describe the evolution of the supra-basal epidermis. The model, presented and analyzed in [1, 2], includes different types of cells (proliferating cells, differentiated cells, corneous cells, and apoptotic cells) that move with the same velocity so that the local volume fraction, occupied by the cells is constant in space and time. We investigate the well-posedness of the problem determining conditions for the existence of a moving boundary representing the surface of the skin. We also consider the stationary case of the problem, that takes the form of a quasi-linear evolution problem of first order. This case corresponds to the normal status of the skin. A numerical scheme to compute the solution of the model is proposed and analyzed. Simulations are provided for realistic values of the parameters. References 1. Gandolfi A., Iannelli M., Marinoschi G.: An age-structured model of epidermis growth., J. Math. Biol. 62, 111-141 (2011) 2. Gandolfi A., Iannelli M., Marinoschi G.: Time evolution for a model of epidermis growth, J. Evol. Equat. 13, 509-533 (2013)

Qualitative and numerical study of a system of delay diﬀerential equations modeling leukemia

ION Anca Veronica

“Gh. Mihoc - C. Iacob” Institute of Mathematical Statistics and Applied Mathematics, Bucharest, Romania

This talk is a review of some previous works of ours concerning the investigation of a system of two delay diﬀerential equations, system that models the periodic chronic myelogenous leukemia. The system consists of two equations, one for the proliferating cells and 132 one for the so-called resting cells, and depends on ﬁve parameters. The equation for resting cells is independent of the other one. For this equation we study the stability of the two equillibria, the Hopf bifurcation, and the Bautin bifurcation. Then we study the behavior of the proliferating cells (that is determined by that of the resting cells).

Water ﬂow on vegetated hill. Shallow water equations model

ION Stelian

Institute of Statistical Mathematics and Applied Mathematics of Romanian Academy, Romania Coauthors: Dorin Marinescu, Stefan-Gicu Cruceanu

The plant presence on hills creates a resistance force to the water flow and influences the process of water accumulation on the soil surface. The large diversity of the growing plants on a hill makes the elaboration of an unitary model of water flow over a soil covered by plants very difficult. At a hydrographic basin scale, there are variations in the geometrical properties of the terrain (curvature, orientation, slope) and vegetation density or vegetation type etc. A mathematical model for the water flow on a hill covered by variable distributed vegetation is proposed in this article. The space averaging method is used to define an unique continuous model associated to a heterogeneous fluid-soil-plant mechanical system. Some mathematical properties of the model are presented and the behavior of a simplified model is illustrated by numerical results. References 1. G.I. Marchuk – Mathematical modeling in problem to protection the environment, Nauka, Moscow, 1982 (in Russian). 2. I. Secrieru, V. Ticau – Weighted approximate scheme for fractional order diffusion equation, Buletinul Institutul Politehnic din Iasi, tomul LVII(LXI), fasc.1, sectia MATEMATICA, MECANICA TEORETICA,FIZICA, Ed. POLITEHNIUM, Iasi, Romania, 2011 3. I. Secrieru – Application of the decomposition principle for plane fractional diffusion equation, Proceedings of the Conf. ”Modelare matematica, Optimizare si Tehnologii Informationale”, ATIC, Chisinau, Evrica, 2014, Republica Moldova, 201-205.

Dynamical analysis of a fractional-order Hindmarsh-Rose model

KASLIK Eva

Universitatea de Vest din Timisoara, Romania

This talk is dedicated to the stability and bifurcation analysis of a model of neuronal activity of Hindmarsh-Rose type and of fractional order. First, a two-dimensional model is considered, with respect to the membrane potential in the axon and the transport rate of sodium and potassium ions through fast ion channels. This model is later complemented by the addition of a third-order fractional diﬀerential equation that takes into account a slow adaptation current. The main purpose of this paper is to demonstrate that existing mathematical models of neuronal activity can be improved by using fractional derivatives instead of classical integer-order derivatives and that these new models reﬂect a better understanding of the biological reality, as suggested by the experimental results. Results of numerical simulations are also presented to validate the theoretical results.

Boundary value problems of transmission type for the Navier-Stokes and Darcy-Forchheimer-Brinkman systems in weighted Sobolev spaces

KOHR Mirela

Faculty of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania Coauthors: M. Lanza de Cristoforis, S.E. Mikhailov, W.L. Wendland

The purpose of this talk is to present existence and uniqueness results in L2-weighted Sobolev spaces for transmission problems 3 for the nonlinear Darcy-Forchheimer-Brinkman and Navier-Stokes systems in two complementary Lipschitz domains in mathbbR .We exploit layer potential theoretic methods for the Stokes and Brinkman systems combined with fixed point theorems in order to show the 133 desired existence and uniqueness results. Note that the Brinkman-Forchheimer-extended Darcy equation is a nonlinear equation that describes saturated porous media fluid flows. This talk is based on joint work with Massimo Lanza de Cristoforis (Padova), Sergey E. Mikhailov (London) and Wolfgang L. Wendland (Stuttgart).

About patterns driven by chemotaxis

LITCANU Gabriela

Institute of Mathematics “O. Mayer”, Romania

The pattern formation is a key process in the development of living systems. It describes the interplays between members of species at the intercellular or intracellular levels. We consider a coupled chemotaxis-haptotaxis system which describes a large variety of biological or medical phenomena. We investigate how both the change of parameters of the system and the singularities of the chemosensitivity term can generate pattern formation.

On the separation property between stable and unstable zones of the dynamical systems and it implications

MIGDALOVICI Marcel

Institute of Solid Mechanics of the Romanian Academy, Romania

Any definitely dynamical system with numerically specification of its parameters can be substituted by the corresponding dynamical system that depends on parameters, without parameters numerical particularization. We mention, as possible parameters of the dynamical systems, geometrical, physical (in particular mechanical), economical, chemical, biological parameters and other. We notice firstly the property of separation between stable and unstable zones, in the dynamical system free parameters domain, as important property of all definitely dynamical systems that depend on parameters met in the specialized literature so that we can emphasize this property as property that can contribute to environment mathematical modelling. The stability analysis of each dynamical system that depend on parameters is realized using the stable zones of the selected free parameters domain and some theorems concerning the linear dynamical system stable evolution through the matrix associated to the dynamical system definition or the dependence of the nonlinearly dynamical system stable evolution by the “first approximation” linear dynamical system stable evolution. The mathematical conditions that assure the continuity property transmissibility from the functions that define the dynamical system on parameters to the corresponding matrix eigenvalues functions of the linear dynamical system are analysed in the literature first time. These conditions assure and the separation between stable and unstable zones in the domain of dynamical system free parameters justified by us. The possibilities of stable evolution optimisation in the stable zones, assured by separation, on the specified dynamical system that depends on parameters are described.

Some generalizations of the Cahn-Hilliard equation

MIRANVILLE Alain

University of Poitiers, France

Our aim in this talk is to discuss some variants of the Cahn-Hilliard equation. Such models have, in particular, applications in biology and image inpainting. 134 Analysis of an iterative scheme of fractional steps type associated to the reaction-diﬀusion equation endowed with a regular potential and a general class of nonlinear and non-homogeneous dynamic boundary conditions

MOROSANU Costica

“Alexandru Ioan Cuza” University of Ia¸si, Romania

The convergence and error estimate results for an iterative scheme of fractional steps type, associated to the reaction-diﬀusion equation supplied with regular potential and a general class of nonlinear and non-homogeneous dynamic boundary conditions, are established.

On the raindrop motion

MUNTEAN Angela

Retired from Naval Academy “Mircea cel Batran” Constanta, Romania, Romania

The present talk deals with the way in which it has been studied the motion of raindrops in the case of collecting mass. Some aspects of raindrop motion has been studied, the velocity of the raindrop has been calculated. Provided in relation to the size of the raindrop to keep a spherical shape, it tries to estimate the height from which you must take in order for it to be spherical.

Hopf bifurcation analysis for the model of the hypothalamic-pituitary-adrenal axis with distributed time delay

NEAMTU Mihaela

West University of Timisoara, Romania Coauthors: Eva Kaslik, Dana Stoian, Dan B. Navolan

In the present talk we analyze the mathematical model of the hypothalamus-pituitary-adrenal axis. Since there is a spatial separation between the brain, where the hypothalamus and pituitary are situated, and the kidney, where the adrenal glands are situated, time is needed for transportation of the hormones between the glands. Thus, the distributed time delays are considered as both weak and Dirac kernels. The model, described by a nonlinear differential system with distributed time delay, is analyzed regarding the stability and bifurcation behavior. The last part contains some numerical simulations to illustrate the effectiveness of our results. Moreover, the behavior of the fractional differential time delay model is simulated.

The J5:2 mean motion resonance as a new source of H-chondrites

NEDELCU Dan Alin

Astronomical Institute of the Romanian Academy, Romania Coauthors: M. Birlan, M. Popescu, O. Badescu, D. Pricopi

The dynamical evolution of (214869) 2007 PA8, one of the largest Potentially Hazardous Asteroids was analyzed using a population of 1275 clones that was integrated backward in time for 200000 years using a realistic model of the Solar System modiﬁed to use an 80-bit extended precision data type. The numerical integration results shows that 2007 PA8 evolved rapidly on a time scale of 105 years toward higher eccentricities, via the 5:2 mean motion resonance with Jupiter by eccentricity pumping. 135 Some considerations on Reynolds’ equation for the lubricant thin ﬁlms

NICOLESCU Bogdan

University of Pitesti, Romania Coauthors: Tudor C. Petrescu

The aim of our talk is to present some addictions of Reynolds’ equation form depending on the flow domain geometry of lubricated fluid film. This aspect is very important especially in the case of the bio-tribological systems (human joints), because their geometries are very complex and so difficult to analytically approximated. Moreover, in these cases the simplifying assumptions of the Reynolds model must be applied according to each this geometry. One of our obtained results is related to a new form of the Reynolds equation for such a particular geometry.

Spatiotemporal compex dynamics in anisotropic ﬂuids

OPREA Iuliana

Colorado State University, USA

Spatially extended systems driven far from equilibrium may exhibit spatiotemporal complex dynamics manifested through spatiotemporal chaos, intermittency, defects, phase turbulence, etc. We present a comprehensive theoretical framework for the classiﬁcation and characterization of the spatiotemporal complex dynamics in one of the most challenging pattern forming anisotropic systems, the electroconvection of nematic liquid crystals, based on Ginzburg Landau type amplitude equations.

Saﬀman-Taylor instability for a non-Newtonian ﬂuid

PASA Gelu

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

We study the linear stability of a steady displacement of an Oldroyd-B fluid by air in a Hele-Shaw cell. We perform a depth-average procedure, across the Hele-Shaw gap, in the dynamic boundary condition at the interface. The new element is an exact formula of the growth rate of perturbations, obtained for small Deborah numbers. When the Deborah numbers are equal, our growth rate is quite similar to the Saffman-Taylor formula for a Newtonian liquid displaced by air. We prove the non-Newtonian destabilizing effects.

Elastoplastic models with continuously distributed defects: dislocations and disclinations, for ﬁnite and small strains

PASCAN Raisa

University Politehnica of Bucharest, Romania Coauthors: Cleja-Tigoiu Sanda, Tigoiu Victor

The models describe the behaviour of crystalline materials with microstructural defects. The mathematical measures of defects are defined in terms of the incompatible tensor fields and are based on anholonomic configurations. The non-local, diffusion-like evolution equations describe the coupling between dislocations and disclinations. The numerical results emphasize the effects induced by the initial heterogeneity in distribution of disclinations and by the two diffusion like parameters, involved in the evolution equations. 136 Parallel matrix function evaluation via initial value ODE modelling

PETCU Madalina

University of Poitiers, France Coauthors: Jean-Paul Chehab

The purpose of this talk is to propose ODE based approaches for the numerical evaluation of matrix functions f(A), a question of major interest in the numerical linear algebra. To this end, we model f(A) as the solution at a ﬁnite time T of a time dependent equation. We use parallel algorithms, such as the parareal method, on the time interval [0; T] in order to solve the evolution equation obtained.

The ﬂow through fractured porous media along Beavers-Joseph interfaces

POLISEVSCHI Dan

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania Coauthors: Isabelle Gruais

We study the flow through a porous medium fractured in blocks by an ε-periodic distribution of fissures filled with a Stokes fluid. We assume that the filtration fluid through the blocks is obeying the Darcy’s law and that it is coupled with the Stokes fluid from the fissures by a Beavers-Joseph type interface condition. We prove the existence and uniqueness of this coupled flow when it is confined by an impermeable boundary. The measure of the interface being of order 1/ε as ε → 0, we study the asymptotic behavior of the flow in the case when the permeability is of unity order and the Beavers-Joseph transfer coefficient is of ε-order. We prove that the two-scale limits of the velocities and of the pressures verify a well-posed problem, from which the so-called local problems can be decoupled and, therefore, the macroscopic(homogenized) behavior is explicit.

Quasistatic contact problems for viscoelastic bodies

POP Nicolae

Technical University of Cluj-Napoca and Institute of Solid Mechanics of the Romanian Academy, Romania

We describe some of our recent results concerning the modeling and analysis quasistatic contact problems with Coulomb friction. The frictional contact, when slip takes place, must takes thermal eﬀects into account and the wear of the contacting surfaces. For this we need to study thermoviscoelastic contact.

On single projection Kaczmarz extended-type algorithms

POPA Constantin

Ovidius University of Constanta, Romania

The Kaczmarz Extended (KE) algorithm has been proposed by the author in [2,3], as an extension of the Kaczmarz-Tanabe algorithm from [4], to inconsistent linear least squares problems. It uses in each iteration orthogonal projections onto the hyperplanes determined by all the rows and all the columns of the system matrix. Recently, in the paper [5], the authors proposed a single projection KE type algorithm, which in each iteration uses orthogonal projections onto the hyperplanes determined by only one row and one column. If the projection row and column indices i and j are selected it at random with probability proportional with a certain quotient of the norm of the i-th row, and j-th column, respectively, they prove that the sequence of approximations so generated converges in Expectation to a least square solution of the problem. 137

We propose two single projection KE type algorithms, in which the projection indices are selected in an it almost cyclic, and it remote control manner, respectively (see e.g. Y. Censor, A.Z. Stavros). We prove that the sequence of approximations generated in each case converges in norm to a least square solution of the problem. Numerical experiments and comparisons are also presented.

References

1. Y. Censor, A.Z. Stavros – Parallel optimization: theory, algorithms and applications. ”Numer. Math. and Sci. Comp.” Series, Oxford Univ. Press, New York, 1997. 2. C. Popa – Least-squares solution of overdetermined inconsistent linear systems using Kaczmarz’s relaxation. Intern. J. Comp. Math., 55 (1995), pages 79-89. 3. C. Popa – Extensions of block-projections methods with relaxation parameters to inconsistent and rank-deﬃcient least-squares problems. it B I T, 38 (1998), pages 151-176. 4. K. Tanabe – Projection Method for Solving a Singular System of Linear Equations and its Applications, Numer. Math., 17 (1971), pages 203-214. 5. A. Zouzias A., N.M. Freris – Randomized Extended Kaczmarz for Solving Least Squares, arXiv:1205.5770v3 (5.01.2013).

Two-body problem associated to Buckingham potential

POPESCU Emil

Astronomical Institute of the Romanian Academy, Romania Coauthors: Dumitru Pricopi

We study the two-body problem associated to Buckingham potential. Regularized equations of motion are obtained using McGehee- type transformations. In this framework, we describe two limit situations of motion, collision and escape, and provide the symmetries and the equilibrium points that characterize the problem.

Fractional kinetic equations as a model of intermittent bursts in solar wind turbulence

POPESCU Nedelia Antonia

Astronomical Institute of the Romanian Academy, Romania Coauthors: Emil Popescu

The statistics of several quantities in space plasma are in agreement with some models based on space-time fractional derivative equations. In this paper we underline that the fractional calculus is a good approach to modeling the typical “anomalous” features that are observed in solar wind turbulence, which has both solar and interplanetary sources. In the case of solar wind velocity and interplanetary magnetic ﬁeld data obtained by Ulysses mission, solutions of space-time fractional equations are used to analyze the presence or absence of heavy tails typically associated with multiscale behaviour.

Border-collision bifurcations in a piece-wise smooth planar dynamical system associated with cardiac potential

POPOVICI Irina

United States Naval Academy, USA and Romania

The talk addresses the bifurcations of a two-dimensional non-linear dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation. The dynamical behavior of this continuous (but only piece-wise smooth) model 138 transitions from simple (a unique attracting cycle) to complicated (co-existence of stable cycles) as the stimulus period is decreased from large towards zero. The ﬁrst bifurcation, of discontinuous period-doubling type, results from the collision of two cycles with a switching manifold. For stimuli periods just shorter than collision time, of the two cycles about to collide, the 2:1 escalator is stable and the alternate solution is unstable; with those co-exists a stable 1-escalator whose orbit lays away from the switching manifold. The principal results show that the dynamical system associated with the collision exhibits two distinct types of domains of attraction, some impossible in smooth dynamics.

Mathematical models of stem cell transplantation

PRECUP Radu

Babes-Bolyai University of Cluj-Napoca, Romania

We present simple mathematical models expressed as three-dimensional ordinary diﬀerential systems for describing the dynamics of three cell lines after allogeneic and autologous stem cell transplantation [1], [3]. The evolution ultimately leads either to the normal hematopoietic state achieved by the expansion of normal cells and the elimination of the cancer cells, or to the leukemic hematopoietic state characterized by the proliferation of the cancer line and the suppression of the normal cells. A theoretical basis for the control of post-transplant evolution is provided for the allogeneic transplant [4]. Thus, we describe several scenarios of change of system parameters by which a bad post-transplant evolution can be corrected and turned into a good one, and we propose therapy planning algorithms for guiding the correction treatment [2]. We also conclude about the eﬀectiveness of the autologous transplantation as therapeutic procedure for AML [3]. References 1. R. Precup et al. – Mathematical modeling of cell dynamics after allogeneic bone marrow transplantation, Int. J. Biomath. 5 (2012), 1250026, 1–18. 2. R. Precup et al. – A planning algorithm for correction therapies after allogeneic stem cell transplantation, J. Math. Model. Algor. 11 (2012), 309–323. 3. R. Precup – Mathematical understanding of the autologous stem cell transplantation, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity 10 (2012), 155–167. 4. R. Precup, M.-A. Serban, D. Trif – Asymptotic stability for a model of cell dynamics after allogeneic bone marrow transplantation, Nonlinear Dyn. Syst. Theory 13 (2013), 79–92.

Modelling of pulsations of giant stars

PRICOPI Dumitru

Astronomical Institute of the Romanian Academy, Romania Coauthors: Marian Doru Suran

We tackle the problem of interaction between convection and pulsations in giant stars. We present the results of numerical computations of oscillation properties of a model of the G9.5 giant Oph, based on a new treatment of convection. The eﬀects on modes stability and modes inertia are pointed out.

Dynamic networks: from connectivity to temporal behavior

RADULESCU Anca

State University of New York at New Paltz, United States

Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time- dependent fashion. We illustrate how the hardwired structure (adjacency graph) can affect dynamics (temporal behavior) for two 139 particular types of networks: one with discrete and one with continuous temporal updates. The nodes are coupled according to a connectivity scheme that obeys certain constrains, but also incorporates random aspects. We develop new measures (such as probabilistic bifurcations and extensions of Julia sets) to compare the effects of different ways of increasing connectivity: by altering edge weights versus edge density versus edge configuration. We determine that the adjacency spectrum is a poor predictor of dynamics, that increasing the number of connections is not equivalent to strengthening them, and that there is no single factor among those we tested that governs the stability of the system. We discuss the potential applications of our results towards increasing our understanding of neural dynamics and genetic replication processes.

Optimal control of Imatinib treatment in a competition model of Chronic Myelogenous Leukemia with immune response

RADULESCU Rodica

University Politehnica of Bucharest, Romania Coauthors: Doina Candea, Andrei Halanay

We present an optimal control strategy for a delay differential system with application to the drug therapy of Chronic Myelogenous Leukemia. The mathematical model is represented by a nonlinear system of five equations from population dynamics which is based on the competition between normal cells and leukemic cells (stem-like and mature). The effect of the immune system through anti- leukemia T-cells is also included in the model. The effect of Imatinib therapy is introduced in the form of several factors controlling cell multiplication and mortality for leukemia cell populations and the evolution of immune cell population. The optimal control method is applied to eliminate the leukemic cells whilst minimizing the amount of drug. In order to derive necessary optimality conditions in the form of Pontryagins minimum principle, discretization methods are applied and the delayed control problem is augmented to a nondelayed problem to which Pontryagins minimum principle is applicable. The obtained results are illustrated by numerical simulations and discussed in view of the optimal treatment approach.

Computational scheme for drift-diﬀusion equations in multiply connected domain

RIBACOVA Galina

Moldova State University, Republic of Moldova Coauthors: Vladimir Patiuc

The computational scheme for solving partial differential equations of convection-diffusion type, i.e. for equations that can be parabolic or hyperbolic depending on the values of the coefficients, is elaborated. Using as a framework the idea of the finite volume method, we create the algorithm and corresponding software to solve the nonlinear problem for semiconductor diode based on drift-diusion equations in multiply connected domain. We construct the nonuniform grid for domain discretization. The refinement of the grid is carried out in areas where the impurity profile function has large gradients and in the vicinity of the point where the type of boundary condition is changed. There are presented some results of numerical simulation.

Algorithms for accelerating convergence of power series by means of Euler type operators

SADIKU Murat

South East European University, FYR of Macedonia

We examine the acceleration convergence of alternative and non-alternative power series by means of an Euler type operator that is defined earlier by G.A. Sorokin [1984] and I.Z. Milovanovic [1989]. Through this type of linear operator of generalized difference of 140 sequence is achieved that alternative and non-alternative power series to be transformed into series with higher speed of convergence than the initial series. The main contribution of this paper is findings and implementation of algorithms on accelerating convergence of power series.

The stable approximate schemes for the evolution equation of the plane fractional diﬀusion process

SECRIERU Ivan

State University of Moldova, Republic of Moldova

The mathematical modeling of the problems that appear in physique, ecologies, hydrogeology, finance and other depend of the domain where this process is studied. For example, in the problem to transport any substance in atmosphere the main factors are the diffusion process, absorbtion of substance and advection- convection process. The classical model of this evolution problem with one space variable use the usual partial derivatives of first and second order (cf.[1]). In recent years many authors use the fractional space derivative to modeling such process. The class of approximate schemes for such models has been constructed in [2] for the case of one space variable. In this article is considered the same problem with two space variables of the form α α α α ∂ϕ − ∂ ϕ − ∂ ϕ − ∂ ϕ − ∂ ϕ d+(x) α d−(x) α d+(y) α d−(y) α = f(x, y, t), ∂t ∂+x ∂−x ∂+y ∂−y ϕ(x, y, 0) = s(x, y), (1) ϕ(x, y, t)=0 on the ∂D, in the domain D =[0,a] × [0,b] with the boundary ∂D and the time interval [0,T]. Using the decomposition principle it is proved the stability of the class of approximate schemes, constructed in [3] for the problem (1).

Direct-approximate methods in solving some classes of singular integral equations deﬁned on arbitrary smooth closed contours

SEICIUC Vladislav

Trade Cooperative University of Moldova, Republic of Moldova

The talk includes algorithms and substantiation theory, in some Banach space, of direct-approximate methods in solving the following class of singular integral equations (SIE) defined on arbitrary smooth closed contour Γ in the complex plane: 1) nonlinear singular integral equations(NSIE); 2) systems of NSIE; 3) linear singular integral equations (LSIE) with Carleman moved argument; 4) LSIE containing conjugated of unknown function; 5) LSIE with Carleman moved argument and conjugated of unknown function; 6) NSIE with Carleman moved argument; 7) NSIE with conjugated of unknown function. The direct-approximate methods in solving of SIE defined on a contour Γ begin to be studied and resolved in the 80s of last century due to the works of V.Zoltarevschi and his disciples. Further results on approximation for functions defined on a contour Γ with Lagrange polynomials built on Fejer nodes were established in Hölder Hβ (Γ ), 0 <β<1, generalized Hölder Hω(Γ ) and Lebesgue Lp(Γ ), 1

STRUGARU Magdalena

BCAM, Spain

Necking is a kind of deformation that typically undergo polymers and ductile metals when subjected to extreme tensile extension. It is a plastic deformation (which still can be modelled by elasticity theory) consisting of the decrease of cross-sectional area in a small region (typically, the center) of the material. Not all materials present necking, and in fact, it is at first glance counter-intuitive that necking needs less energy than the homogeneous deformation satisfying the same boundary conditions. Most of the available literature deals with general sufficient conditions for which necking does not occur or with one-dimensional models for which necking does occur. The goal of this work is to show analytically and numerically that necking is possible in some materials whose energy density is compatible with the existence theorems in nonlinear three-dimensional elasticity. We aim at finding an isotropic polyconvex function for which the homogeneous deformation (which is always a stationary point) is not a minimizer of the energy. This is not an easy task because polyconvexity implies at once that the homogeneous deformation satisfies all usual necessary conditions for local miminizers. Then, for that instance of energy density, we compute numerically the global minimizer of the energy. We present two classes of experiments: one that computes the minimizer using a trust-region Newton method and one that solves the minimization problem using an augmented Lagrangian algorithm.

Exploring the Space of Stellar Parameters for PLATO2 Space Mission Targets Using CESAM2k and LNAWENR/ROMOSC Codes

SURAN Marian Doru

Astronomical Institute of the Romanian Academy, Romania

In order to extract the basic stellar parameters we use the asteroseismic inversion method where the observed oscillation frequencies are used to estimate the stellar parameters. The inversion shall be understood such that the best estimated parameters for a given star correspond to the model input parameters for the model that shows frequencies most similar to the observed ones. We have computed a wide grid of stellar models and their associated oscillation frequencies and we have designed a tool to evaluate the value of χ2 on that grid for diﬀerent possible sets of observational data. Preliminary results were been obtained for some observed CoRoT and Kepler missions targets.

A hybrid mathematical model for cell motility in angiogenesis

TARFULEA Nicoleta

Purdue University Calumet, USA

The process of angiogenesis is regulated by the interactions between various cell types such as endothelial cells and macrophages, and by biochemical factors. In this talk, we present a hybrid mathematical model in which cells are treated as discrete units in a continuum field of a chemoattractant that evolves according to a system of reaction-diffusion equations, whereas the discrete cells serve as sources/sinks in this continuum field. It incorporates a realistic model for signal transduction and VEGF production and release, and gives insights into the aggregation patterns and the factors that influence stream formation. The model allows us to explore how changes in the microscopic rules by which cells determine their direction and duration of movement affect macroscopic formations. In particular, it serves as a tool for investigating tumor-vessel signaling and the role of mechano-chemical interactions of the cells with the substratum. 142 Asynchronous flows: the technical condition of proper operation and its generalization

VLAD Serban E.

Oradea City Hall, Romania

n n The asynchronous flows are given by Boolean functions Φ : {0, 1} −→ { 0, 1} that iterate their coordinates Φ1, ..., Φn independently on each other. In the study of the asynchronous sequential circuits, the situation when multiple coordinates of the state can change at the same time in called a race. When the outcome of the race affects critically the run of the circuit, for example its final state, the race is called critical. To avoid the critical races that could occur, Φ is specified in general so that only one coordinate of the state can change; such a circuit is called race-free and we also say that Φ fulfills the technical condition of proper operation. We formalize in this framework the technical condition of proper operation and give its generalization, consisting in the situation when races exist, but they are not critical. Section 8 Theoretical Computer Science, Operations Research and Mathematical Programming

Mobility types for cloud computing

AMAN Bogdan

Romanian Academy, Institute of Computer Science, Romania Coauthors: Gabriel Ciobanu

We propose a mobility type system for description and veriﬁcation of distributed systems in which processes are asked to move between locations where important local interactions are required. We use a simple version of distributed pi-calculus to deﬁne mobility types. The novelty of this approach is that we point out sequences of migrations as global types, and investigate scenarios in which processes are required to follow such a sequence of migrations along several locations. The typing system ensures certain properties including type soundness. (Joint work with Gabriel Ciobanu)

Language independent symbolic execution

ARUSOAIE Andrei

INRIA Lille-Nord Europe, France

The modern world is shifting from the traditional workmanship to a more automated work environment, where software systems are increasingly used for automating, controlling and monitoring human activities. In many cases, software systems appear in critical places which may immediately affect our lives or the environment. Therefore, the software that runs on such systems has to be safe. This requirement has led to the development of various techniques to ensure software safety. In this work, we introduce a language-independent framework for symbolic execution, which is a particular technique for testing, debugging, and verifying programs. The main feature of this framework is that it is parametric in the formal definition of a programming language. We formally define programming languages and symbolic execution, and then we prove that the feasible symbolic executions of a program and the concrete executions of the same program mutually simulate each other. This relationship between concrete and symbolic executions allow us to perform analyses on symbolic programs, and to transfer the results of those analyses to concrete instances of the symbolic programs in question. As applications of symbolic execution we focussed on verification using both Hoare Logic and Reachability Logic. A prototype implementation of our symbolic execution framework has been developed within the K framework (version 3.4). We use this prototype for verifying some nontrivial programs belonging to different programming languages in order to emphasise its genericity.

Phylogenetic networks: mathematical models and algorithms

BARONI Mihaela Carmen

“Dun˘area de Jos” University of Galat¸i, Romania

143 144

In the last ﬁfteen years there has been considerable interest in using phylogenetic networks to represent non-tree-like evolution. Several mathematical models and algorithms for constructing and analysing these networks will be presented.

Most vital elements of graphs

BAZGAN Cristina

Universit´e Paris Dauphine, France

We study the identiﬁcation of critical entities which can be determined with respect to a measure of performance or a cost associated to the system. By critical infrastructure we mean a set of points/links whose damage causes the largest increase in the cost within the network. Modeling this network by a weighted graph, identifying a vulnerable infrastructure amounts to ﬁnding a subset of nodes/edges whose removal from the graph causes the largest inconvenience to a particular property of a graph. In the literature this problem is referred to as the k most vital nodes/edges problem and its complementary version as the min node/edge blocker problem. We present results we obtained on complexity and approximation of the k most vital nodes (edges) and min node (edge) blocker for several classical problems like assignment, minimum spanning tree, p-median, p-center, vertex cover, independent set.

Order locatedness and strong extensionality in constructive mathematics

BARONI Marian Alexandru

“Dun˘area de Jos” University of Galat¸i, Romania

Several conditions of order locatedness are examined within the framework of Bishop’s constructive mathematics. Although order locatedness is vacuously true in classical mathematics, its signiﬁcance is revealed under constructive scrutiny. For example, upper locatedness is a necessary condition for the existence of the constructive supremum. Order locatedness is also related to order convergence and to strong extensionality. Every function is classically strongly extensional but not constructively. However, it turns out that each function that maps convergent sequences to order located sequences is strongly extensional.

Proving program equivalence

CIOBACˆ AS˘ ¸tefan

“Alexandru Ioan Cuza” University of Ia¸si, Romania Coauthors: Dorel Lucanu, Vlad Rusu, Grigore Rosu

Two programs are equivalent when they have the same behaviour. Depending on what is understood by behaviour, several deﬁnitions of program equivalence exist. We introduce some possible deﬁnitions of equivalence and we show how to prove that two programs are equivalent in a language-independent matter. Our proof system for program equivalence is parameterized by the semantics of the languages in which the two programs are written. (Joint work with Dorel Lucanu, Vlad Rusu, Grigore Ro¸su)

Probabilistic logic for timed migration

CIOBANU Gabriel

Romanian Academy, Ia¸si branch, Romania 145

When modelling distributed systems it is useful to have an explicit notion of location, local clocks, timed migration and interaction. After introducing the timed distributed pi-calculus, we introduced and studied a process algebra called TiMo having exactly these features. A probabilistic extension of TiMo assigns probabilities to the transitions that describe the behaviour of TiMo networks by solving the nondeterminism involved in the movement and in the communication of processes, as well as in the selection of active locations. The main reason for creating a probabilistic extension of TiMo is to gain the ability to verify quantitative properties of TiMo distributed systems networks, such as the probability that a certain transient or steady-state behaviour occurs. It is natural to have a probabilistic temporal logic for expressing such properties over networks of located processes. Unfortunately, quantitative logics as PCTL or aPCTL are not immediately compatible with all or most of the distinguishing features of TiMo. As a result, we define a novel logic called PLTM (Probabilistic Logic for Timed Mobility). The new probabilistic temporal logic PLTM is able to describe certain aspects that are not commonly found in other logics, such as the ability to check properties which make explicit reference to specific locations and processes, to impose temporal constraints over local clocks (finite or infinite upper bounds, for each location independently), to define complex action guards over multisets of actions and properties for transient and steady-state behaviours. Finally, we present a verification algorithm for PLTM, and determine its time complexity. Given that PLTM operates at the level of discrete-time Markov chains, it can also be applied to other process algebras which involve locations, timers, process movements and communications.

Automata, logic and Stone duality

DIACONESCU Denisa

University of Bern, Switzerland and University of Bucharest, Romania

The aim of this talk is to explain the role of Stone duality for defining a dictionary capable of translating finite automata (considered as set-theoretical objects) into the language of classical propositional logic. According to this translation, finite automata correspond to objects in classical propositional logic, called classical fortresses, which have the same power as finite automata: they accept regular languages. Furthermore, classical fortresses allow easy generalizations of finite automata in the context of non-classical logics. We explain our method for Gödel logic.

The automata-logic duality for temporal epistemic frameworks

DIMA C˘at˘alin

LACL, Universit´e Paris-Est, France

We present a number of recent results on expressiveness and decidability of temporal epistemic logics in which automata theory plays an important role.

On humans, plants and disease: algorithmic strategies for haplotype assembly problems

ISTRAIL Sorin

Brown University, USA

This talk is about a set of computational problems about haplotypes reconstruction from genome sequencing data for diploid organisms, such as humans, and for ployploid organisms, such as plants. Polyploidy is a fundamental area of molecular biology with powerful methods of Nobel prize recognition: polyploidy inducement for cell reprogramming, mosaicism for aneuploid chromosome content as the constitutional make-up of the mammalian brain, and the polyploidy design for highly thoughtafter agricultural crops and animal products. On the medical side, polyploidy refers to changes in the number of whole sets of chromosomes of an organism, and aneuploidy refers to changes in number of specific chromosomes or of parts of them. We will present an algorithmic framework, HapCOMPASS, for these problems that is based on graph theory. The software tools implementing our algorithms (available from the Istrail Lab) are already in use, by many users, and recognized as among the leading tools in the areas of human genome haplotype assembly, plant 146 polyploidy haplotype assembly, and tumor haplotype assembly. We will also present a number of unresolved computational problems whose solutions would advance our understanding of human biology, plant biology and human disease. To introduce the application areas, and a hint at the type of combinatorial problems of that biological import, a short primer follows. Humans, like most species whose cells have nuclei, are diploid, meaning they have two sets of chromosomes - one set inherited from each parent. In the genome era, the genome sequencing technologies are generating big data-bases of empirical patterns of genetic variation within and across species. A SNP (single nucleotide polymorphism) is a DNA sequence variation occuring commonly (e.g. 3%) at a fixed site on the genome within a population in which a single nucleotide A, C, G or T differs between individuals of a species, or between the mother-father chromosomes of a single individual. The different nucleotide bases at the SNP site are called alleles. SNPs account for large majority of genetic variation of species. For humans, there are about 10 million SNPs, so conceptually the SNPs variation of any individual is captured by two allele vectors (each with 10 million components), one inherited from mother and one from the father. Our approach to haplotype assembly is based on graph theoretical modeling of sequencing reads linking SNPs and assembling whole haplotypes based on such basic read-SNPs linkings. Polyploid organisms have more than two sets of chromosomes. Although this phenomenon is particularly common in plants (e.g., seedless watermelon is 3x, wheat 6x, strawberries 10x), it is also present in animals (e.g. fish could have 12x and up to 400 haplotypes), and in humans (e.g., some mammalian liver cells or heart cells or bone marrow cells are polyploid). While polyploidy refers to numerical change in the whole set of chromosomes, aneuploidy refers to organisms in which a part of the set of chromosomes (e.g. a particular chromosome or a segment of a chromosome) is under- or over- represented. Polyploidy and aneuploidy phenomena are recognized as disease mechanisms. Examples for polyploidy: triploidy birth conceptions end in misscariages, although mixoploidy, when both diploid and triploid cells are present, could lead to survival; triploidy, as a result of either digyny (the extra haploid set is from the mother by failure of one meiotic division during oogenesis) or diandry (mostly caused by reduplication of paternal haploid set from a single sperm or dispermic fertilization of the egg) could have parent-of-origin (genomic imprinting) medical consequences: diandry predominate among preterm labor misscariages while digyny predominates into survival into fetal period, although with a poor grown fetus and very small palcenta). Examples for aneuploidy: trisomy in the Down syndrome, cells with one chromosome missing while others with an extra copy of the chromosome, cells with unpredictably many chromosomes of a given type; mosaicism (when two or more populations of cells with different genotypes derived from a single individual) aneuploidy occurs in virtually all cancer cells. Work in collaboration with Derek Aguiar (Brown University) and Wendy Wong (INOVA Translational Medicine Institute).

Proving reachability properties by circular coinduction

LUCANU Dorel

“Alexandru Ioan Cuza” University of Ia¸si, Romania

Circular coinduction is a generic name associated to a series of algorithmic techniques to prove behavioral equivalence mechanically. In this talk we discuss how the circular coinduction can be used for proving reachability properties.

The independence polynomial of a well-covered graph at −1

MANDRESCU Eugen

Holon Institute of Technology, Israel Coauthors: Vadim E. Levit

α If a graph G has sk independent sets of size k, then I(G; x)=s0 + s1x + ...+ sαx is the independence polynomial of G, where α is the size of a maximum independent set (Gutman and Harary, 1983). It is known that |I(G; −1)|≤2d(G) ≤ 2c(G), where d(G)isthe decycling number and c(G) is the cyclomatic number (Engstrom, 2009; Levit, Mandrescu, 2011, 2013). Recall that G is a well-covered graph if all its maximal independent sets are of the same size (Plummer, 1970). In this talk we show that I(G; −1) ∈{−1, 0, 1} for every unicycle well-covered graph G = C3, while I(G; −1) = 0 for every connected c(G) c(G) well-covered graph G of girth ≥ 6,C7 = G = K2. We demonstrate that the bounds −2 , 2 are sharp for I(G; −1) and discuss other possible values of I(G; −1) belonging to [−2d(G), 2d(G)] (Cutler, Kahl, 2014). (Joint work with Vadim E. Levit) 147 Stone dualities for Markov processes

MARDARE Radu

Aalborg University, Denmark Coauthors: Dexter Kozen, Kim G. Larsen, Prakash Panangaden

We present a series of duality results involving Markov processes (MPs) and a special class of Boolean algebras with operators corresponding to (the non-compact) Markovian logics. The ﬁrst duality extends the classical Stone duality. The second duality takes into account a richer universe where between MPs we do not consider only behavioural equivalences (bisimulations) but also pseudometrics that measure their similarities. On the Boolean algebra side we will involve, correspondingly, a concept of norm. The talk summarizes a series of results obtained in collaboration with Dexter Kozen (Cornell University, USA), Kim G. Larsen (Aalborg University, Denmark) and Prakash Panangaden (McGill University, Canada) and presented at LICS2013 and MFPS2014.

Modeling and veriﬁcation of security for web applications and services

MINEA Marius

Politehnica University of Timi¸soara, Romania

In this talk we will first present how protocols and services with security properties can be modeled by a combination of symbolic transition systems for their workflow, together with Horn clauses for policies. Then we will comparatively describe different approaches for verifying them by model checking. Finally, we will present how to automatically infer state models of web applications by crawling and use SAT checking to detect security vulnerabilities due to unintended workflows.

Modeling with exploration systems

PETRE Ion

Turku Centre for Computer Science and Abo˚ Akademi University, Finland

Reaction systems were introduced in [4] as a new modelling framework inspired by the functioning/bio-energetics of the living cell. A reaction r in reaction systems can facilitate a reaction s by providing some of the reactants needed by s,orr can inhibit s by producing an inhibitor of s. The formal notion of a reaction system is an abstract set-theoretical notion A =(S, A); it allows any set S as the background set, and the set of reactions A specifies state transitions in the state space of A, i.e., the set of all subsets of S. Reaction systems capture two important features of biology: the non-permanency of its entities, and the open system aspect of the living cells. Zoom structures were introduced in [5] to capture another important feature of biological systems: their hierarchical organization. The notion of zoom structures is based on well-founded partial orders; a zoom (formally a walk against/along the edges of the partial order) allows the investigation of a system in increasing/decreasing level of detail, thus integrating multi-level knowledge about the system. Zoom structures and reaction systems together form the framework of exploration systems for modeling biological (and other types of) systems. Zoom structures represent the static, multi-level knowledge about the system and reaction systems capture the dynamic processes in the system as state transitions between zooms. We give a brief introduction to reaction systems, zoom structures and exploration systems. We illustrate these notions with examples from biology (heat shock response and intermediate filament assembly) and from particle physics. The talk is based on recent results from [1], [2], and [3]. References 1. S. Azimi, B. Iancu, I. Petre – Reaction system models for the heat shock response, Fundamenta Informaticae, 131(3):299-312, 2014. 2. S. Azimi, C. Panchal, E. Czeizler, I. Petre – Reaction systems models for the self-assembly of intermediate filaments, Annals of University of Bucharest, 2015. 3. A. Ehrenfeucht, I. Petre, G. Rozenberg – An application of exploration systems: a scenario from particle physics, In preparation. 4. A. Ehrenfeucht, G. Rozenberg – Reaction Systems. Fundamenta Informaticae, 75(1):263-280, January 2007. 5. A. Ehrenfeucht, G. Rozenberg – Zoom structures and reaction systems, International Journal of Foundations of Computer Science, 25:275-305, 2014. 148 A theory of service composition

PETRE Luigia

Abo˚ Akademi University, Finland

Service composition has become commonplace nowadays, in large part due to the increased complexity of software and supporting networks. Composition can be of many types, for instance sequential, prioritizing, non-deterministic. However, a fundamental feature of the services to be composed consists in their dependencies with respect to each other. Dependency can also be of several types, for instance we can think of type and format dependencies between data producers and data consumers or of signature and semantic dependencies between service providers and service users. In this paper we propose a theory of service dependency, modelled around a dependency operator in the Action Systems formalism. We analyze its properties, composition behaviour, and reﬁnement conditions with accompanying illustrative examples. We also set the stage for proposing a dependency theory in the related theory plugin of the Rodin Platform.

A conference management system with veriﬁed document conﬁdentiality

POPESCU Andrei

Middlesex University, London, United Kingdom Coauthors: Peter Lammich, Sergey Grebenshchikov, Sudeep Kanav

Conference management systems in current use occasionally exhibit embarrassing integrity and confidentiality flaws: authors learning about confidential comments by the PC members, authors receiving bogus acceptance notifications, etc. In general, a multi-user web- based system (such as a conference system) is a complex input-output automaton where even stating, let alone verifying, the correct behavior w.r.t. information flow is a daunting task. I describe our experience with implementing, fully verifying, and using CoCon, a conference system that comes with confidentiality guarantees. The formal specification and verification have been performed using the proof assistant Isabelle. (Joint work with Peter Lammich, Sergey Grebenshchikov, Sudeep Kanav)

Semantic variants of (truely) perfect recall in Alternating-Time Temporal Logic

POPOVICI Matei

Politehnica University of Bucharest, Romania Coauthors: Nils Bulling, Wojciech Jamroga

Alternating-Time Temporal Logic extends traditional temporal logics for program verification with means for expressing abilities of agents. Different assumptions regarding their (perfect/imperfect) recall and information render different semantics for ATL. However, when perfect recall is assumed, agents may still forget past observations when nested coalitional operators are used. We briefly introduce ATL with perfect recall, illustrate the no-forgetting phenomenon and put forward a semantics of truely perfect recall. (Joint work with Nils Bulling, Wojciech Jamroga)

Recurrent many-dimensional sequences over ﬁnite alphabets

PRUNESCU Mihai

Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania 149

Recurrent many-dimensional sequences over ﬁnite alphabets are considered. Aspects of symmetry, automaticity, generability by context-free substitutions and power of expressions are discussed. Many aspects maybe also of interest for the section Algebra and Number Theory.

Matching logic

ROS¸U Grigore

University of Illinois at Urbana-Champaign, USA

Matching logic, is a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives and quantifiers, but no difference is made between function and predicate symbols. In models, a pattern evaluates into a power-set domain (the set of values that match it), in contrast to FOL where functions and predicates map into a domain. Matching logic uniformly generalizes several logical frameworks important for program analysis, such as: propositional logic, algebraic specification, FOL with equality, and separation logic. Patterns can specify separation requirements at any level in any program configuration, not only in the heaps or stores, without any special logical constructs for that: the very nature of pattern matching is that if two structures are matched as part of a pattern, then they can only be spatially separated. Like FOL, matching logic can also be translated into pure predicate logic with equality, but it also admits its own sound and complete proof system. A practical aspect of matching logic is that FOL reasoning remains sound, so off-the-shelf provers and SMT solvers can be used for matching logic reasoning. Matching logic is particularly well-suited for reasoning about programs in programming languages which have a rewrite-based operational semantics.

Towards the synthesis of helper formulas in reachability logic-based program veriﬁcation

RUSU Vlad

INRIA Lille-Nord Europe, France

One major difficulty one faces when formally verifying programs with respect to Hoare-style logics is finding adequate helper formulas (e.g., inductive invariants for loops). In this talk I will describe progress in this direction for Reachability Logic, a recently introduced, language-independent logic of programs. I will show that reachability-logic formula verification can be reduced to standard abstraction- based verification techniques, and that reachability-logic formula synthesis can be reduced to Counter Example Guided Abstraction Refinement (CEGAR). Hence, the ongoing steady progress in abstraction-based verification and in CEGAR translates to progress in reachability-logic formula verification and synthesis.

Statistical tests in cryptographic evaluation

SIMION Emil

Politehnica University of Bucharest, Romania

Statistical tests are an efficient tool for establishing the ownership of a set of independent observations to a specific population or probability distribution; they are used in the field of cryptography, specifically in randomness testing. Statistics can be useful in showing a proposed system is weak. Thus, one criterion in validating ciphers is that there is no efficient method for breaking it that brute force. That is, if we have a collection of cipher texts (and eventually the corresponding plain texts) all the keys have the same probability to be the correct key, thus we have uniformity in the key space. If we are analyzing the output of the cipher and find non-uniform patterns, then it can be possible to break it. But if we cannot find these non-uniform patterns no one can guarantee that there are no analytical methods in breaking it. This talk is about requirements for validating the security of cryptographic primitives by statistical methods, construction of statistical tests and sample requirements for testing cryptographic functions. 150

Pushdown model checking in the K framework

S¸ERBANUT˘ ¸ ATraian˘

University of Bucharest, Romania Coauthors: Dorel Lucanu

We brieﬂy recall the pushdown model checking method developed by Javier Esparza and Stefan Schwoon and discuss its integration within the K semantic framework with emphasis on current development and challenges posed by its implementation in a non-language speciﬁc framework. (Joint work with Dorel Lucanu)

Codensity and Stone spaces

SIPOS¸ Andrei

“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Romania

Codensity monads are a standard construction in category theory and/or functional programming that has been used to reduce the asymptotic performance of functional code, but also to provide a natural description of concepts like ultrafilters or ultraproducts. This talk has as its goal to lay bare similar ”inevitability” results for Stone spaces and sober spaces. The category of Stone spaces will be characterized as the essential image of the codensity monad of the inclusion of the category of finite sets into the category of topological spaces. To obtain sober spaces, the category of finite sets will be replaces by another category for which we will provide the motivation.

Extremal cacti graphs for general sum-connectivity index and Narumi-Katayama index

TACHE Rozica-Maria

University of Bucharest, Romania

Topological indices are molecular structure descriptors that play a fundamental role in QSAR, QSPR modeling. Denoting d(u)the α degree of a vertex u ∈ V (G), we deﬁne the general sum-connectivity index of a graph G as χα(G)= d(u)+d(v) with uv∈E(G) α a real number and Narumi-Katayama index as NK(G)= u∈V (G) d(u). In this paper we determine the extremal cacti graphs for general sum-connectivity index and Narumi-Katayama index, with given girth or number of pendant vertices.

Symbolic and computational models for security policies and protocols

T¸ IPLEA Ferucio Laurent¸iu

“Alexandru Ioan Cuza” University of Ia¸si, Romania

Security policies and protocols are central to security and pervasive in computer systems. They can be found in many applications such as operating systems, firewalls, or protocols to secure network traffic. Although security policies and protocols may appear as conceptually straightforward, they are both very complex and error-prone in practice. Over the years, many efforts have been dedicated 151 to a better understanding (specification and verification) of them. This talk is an (partial) informal survey and discussion of the logical and computational models developed so far to reason about security policies and protocols.

Tolerance distances on minimal coverings

ZARA C˘at˘alin

UMass Boston, USA Coauthors: Dan Simovici

We define distances on the space of minimal coverings of a finite set that generalize entropy distances on partitions, and establish connections between these spaces. The metric space of minimal coverings has multiple applications in machine learning and data mining, in areas such as multilabel classifications and determination of frequent item sets. (Joint work with Dan Simovici)

Section 9 History and Philosophy of Mathematics

Axiom of choice in ﬁnitely supported mathematics

CIOBANU Gabriel

Romanian Academy, Ia¸si branch, Romania Coauthor: ALEXANDRU Andrei

Finitely Supported Mathematics (FSM) is consistent with the axioms of the Fraenkel-Mostowski (FM) set theory representing an “axiomatization” of the FM permutation model of the Zermelo-Fraenkel set theory with atoms. The axioms of the FM set theory are those of Zermelo-Fraenkel with atoms (over an infinite set of atoms), together with the special property of finite support which claims that for each element x in an arbitrary set we can find a finite set supporting x. The finite support axiom is motivated by the fact that usually a syntax can only involve finitely many names/variables. Therefore, in the FM set theory only finitely supported objects are allowed. The FM set theory was constructed initially in 1930s, in order to prove independence of the axiom of choice and other axioms in the classical ZF set theory. In 2000s, the FM set theory found some applications in computer science. However, the consistence of the various weaker forms of choice (which were proved to be independent from the axioms of ZF) remained an open problem. We present our results regarding the consistency of various choice principles in FSM. It is known (from 1930s) that the full axiom of choice is inconsistent in ZF and FSM. We prove that the choice principles denoted generally by AC, DC, CC, PCC, AC(fin), Fin, PIT, UFT, OP, KW, RKW, OEP rephrased in terms of finitely supported objects are all inconsistent in FSM. Moreover, if the set of atoms is countable, the choice principle generally denoted by CC(fin) is also inconsistent in FSM. It is worth noting that such results are not easy to prove in FSM, even if various related results regarding these choice principles hold in the ZF framework. This is because nobody guarantees that ZF results remain valid in FSM. Therefore, all the possible relationship results between various choice principles in FSM have to be independently proved in terms of finitely supported object.

Mathematics: current state and future direction

BARBOSU˘ Mihai

RIT (Rochester Institute of Technology), USA

The current state of mathematics will be a chapter of tomorrows History of Mathematics. There are various opinions and conversations on the future of the discipline and many questions on what and who determines the mathematics of tomorrow. It is also important to understand how and why the economic environment, academic leaders, faculty and researchers inﬂuence the direction of this ﬁeld. This presentation will address these questions and will entertain a debate on this topic. Moreover, case studies including experiences from Romanian universities will also be presented and discussed.

153 154 The 1874 controversy between Camille Jordan and Leopold Kronecker

BRECHENMACHER Fr´ed´eric

Ecole´ Polytechnique, France

During the whole of 1874, Camille Jordan and Leopold Kronecker quarrelled vigorously over the organisation of the theory of bilinear forms. That theory promised a general and homogeneous treatment of numerous questions arising in various 19th-century theoretical contexts, and it hinged on two theorems, stated independently by Jordan and Weierstrass, that would today be considered equivalent. It was, however, the perceived difference between those two theorems that sparked the 1874 controversy. Focusing on this quarrel allows us to explore the algebraic identity of the polynomial practices of the manipulations of forms in use before the advent of structural approaches to linear algebra. The latter approaches identified these practices with methods for the classification of similar matrices. We show that the practices - Jordan’s canonical reduction and Kronecker’s invariant computation - reflect identities inseparable from the social context of the time. Moreover, these practices reveal not only tacit knowledge, local ways of thinking, but also - in light of a long history tracing back to the work of Lagrange, Laplace, Cauchy, and Hermite - two internal philosophies regarding the significance of generality which are inseparable from two disciplinary ideals opposing algebra and arithmetic. By interrogating the cultural identities of such practices, this study aims at a deeper understanding of the history of linear algebra without focusing on issues related to the origins of theories or structures.

The correspondence between Hermann Weyl and Erich Hecke

ECKES Christophe

Archives Henri Poincar´e Universit´e de Lorraine, France

The mathematician and mathematical physicist Hermann Weyl carries on a regular correspondence with the number theorist Erich Hecke until the death of the latter in 1947. Their letters, which are currently preserved at the Hermann Weyl Archives (ETH Zrich) and at the Erich Hecke Archives (University of Gttingen) have not been studied systematically until now. However, their correspondence appears to be a central element in order to describe their career and to get an overview of their scientific productions. Moreover, a careful study of these letters also reveals that Hecke and Weyl share the same conception of mathematical knowledge and that they belong to very close intellectual circles. In the first part of our talk, we will try to explain why this correspondence has been neglected by many historians of mathematics until now and we will underline its importance in order to avoid some biases in the description of Heckes and Weyls institutional trajectories. In the second part, we will describe anew Weyls exil after the nazis came to power. We must recall here that Weyl becomes permanent professor at the Institute for Advanced Study (IAS, Princeton) during the Winter semester 1933 and he remains there until his retirement in 1951. We will refer in particular to his correspondence with Hecke and Abraham Flexner (Founding director of the IAS). At that time, Hecke worries about the academic future of his colleague and friend Erwin Panofsky, who has just been dismissed from the university of Hamburg in April 1933. Panofsky will finally get a permanent professorship in art history at the IAS in October 1935. In the last part of our talk, we will describe Heckes situation in Hamburg from 1933 to 1945: his participation to the international congress of mathematicians in Oslo in 1936, his six month stay at the IAS in 1938 (he is invited by Weyl), his strong friendship with the danish mathematicians Harald Bohr and Jakob Nielsen, etc.

Mathematical archaeology: Art Nouveau

DEACONESCU Marian

Dept. Mathematics, Kuwait University Around 1880, R. Dedekind considered, for a group G and for elements x, y ∈ G, the unique element f of G satisfying the equality xy = yxf and thus invented what today is called the commutator of the ordered pair (x, y). Both Dedekind and G.F. Frobenius considered the set C of all of the commutators in a group G and asked themselves whether C is always a subgroup of G. Interestingly, finding examples of groups G such that C is not a subgroup of G is a nontrivial exercise, for the smallest order groups where this happens have order 96. Examples showing that C need not be a subgroup of G appeared soon after and people considered the subgroup G of G generated by the set C, calling G the derived subgroup (or, commutator subgroup)ofG. Results ensuring that under suitable hypotheses G = C or G = C started to appear and, for the last one hundred years or so, people tried to find necessary and sufficient conditions for the equality G = C to hold. 155

My talk will tell the story of the long way towards the general solution of this problem for a ﬁnite group G. The solution was obtain jointly with G. L. Walls and is based on classic results and on ideas originating in the Art Nouveau period (circa 1890-1910): the Cauchy-Frobenius Lemma, Frobenius’ theory of complex characters, simple counting techniques and a measure on the set G deﬁned by using commutators. These combine to give a formula for the number |H \ C| of those elements of a normal subgroup H of G that are not commutators in G. Many new and somewhat surprising results follow as consequences. For example, it is well-known that every normal subgroup of G is the intersection of kernels of irreducible complex characters of G; but what becomes now transparent is that if the normal subgroup is the intersection of the kernels of more than half of the irreducible characters of G, then every element of that normal subgroup must be a commutator in G.

Aspects of parameter estimation

GIURGESCU Patricia

Bra¸sov, Romania

Adaptive and optimization aspects of the density estimation inference for the probability distribution generating a set of observable values.

The Concept of a Real Deﬁnition and that of Real Numbers

IONIT¸ AC˘˘ at˘alin

University “Politehnica” of Bucharest and CRIFST/DLMFS

The problem we approach has three main features. One is pure mathematical, the other belongs to philosophy, and the later concerns history of mathematics. Despite the difficulties each of them posses, all three are emerging into a whole. By the real definition of something we mean the aggregate of all our modalities which are answering to “how do we have to proceed to distinguish that something in things themselves”. In this setting, a real definition is unique. A real definition is part of any other definition of the same definiendum. It corresponds to what was called, long time ago, the real part of a definition (in contradistinction to the nominal part). A real definition does not say that other definitions would be wrong. On the contrary, the real definition has to be found, has to be formulated, and has to be proven that what was found is indeed the maximal real part of any other definition of the same definiendum. How do we have to prove that? It would mean to avoid the reduction of the definiendum to its pure nominal part. The problem is of an intrinsic philosophical interest only after the formal approach to a subject-matter is completely and exhaustively accomplished. That is the case of Euclidean geometry and of the system of real numbers. The unreasonable effectiveness and usefulness of contemporary mathematics cannot have another support than the real part they comprise from things themselves together with the real part of our actions upon things. Concerning the case of real numbers, we shall prove that the real part of the axiomatic/categorical definition of real numbers (the later is standing, we sustain, as the best of the best of what can be said) consists of definitions 3,4,5,7 (Euclid, Book 5, ratios of quantities [magnitudes]) attributed to Eudoxus. We have to show two facts. (A) Those definitions are contained in any other definition of real numbers. (B) Those definitions comprise the maximal real part of any other definition of real numbers. The new point is that we have to refer not to geometry but to quantities, magnitudes and their relationships. The problem necessarily involves both history and philosophy of mathematics in their foundational aspects. The problem of the relationships between Eudoxus definition and that of Dedekind cuts was raised by Lipschitz (Dedekind-Lipschitz correspondence). Dedekind answer concerns the essence of continuity. Five years later, Cantor’s discussion on the reality of infinite sets and transfinite numbers foundationally completed the turning point of mathematics to its present state of the art. In that setting, the problem we have raised was somewhat obscured by the productiveness of the new points of view. The problem was inspired to us by Gregory Chaitin’s How real are the real numbers? (arXiv:math/0411418v3, 2004), while the historical viewpoint we follow was inspired by Solomon Marcus’ claim: a critical research passing over the merely notation of facts in what concerns history of mathematics (Solomon Marcus: Mathematics in Romania, Report to CRM-Piteti 2003, CUB PRESS 22, 2004). 156 Arrow and Conway in spectacle: the impossibility theorem and the cosmological theorem

MARCUS Solomon

Romanian Academy and Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania

The impossibility theorem proved by Kenneth Arrow in 1951 refers to the aggregation of some individual preferences into a global one and shows that under reasonable requirements the existence of a dictator imposing his personal preference cannot be avoided. J. H. Conways cosmological theorem stated in 1986 refers to a specific discrete dynamical system as a sequence starting with a positive integer and so that to generate a term from the previous one have to read off the digits of the previous term, counting the number of digits in groups of the same digit: 1 is read off as one 1 or 11; 11 is read off as twice 1s or 21; 21 is read off as “one 2, then one 1” or 1211. Roughly speaking, he Cosmological theorem asserts, among other things, that starting with any positive integer different from 22 the above discrete dynamical system will have no attractor and its asymptotic behavior will simulate the Mendeleev periodic table. The recent presence in Romania of Arrow and of Conway gave the opportunity of a debate of these results with huge scientific and philosophical impact, in conjunction with some results I have obtained, some of them in joint work with Gheorghe Paun.

Tiberiu Popoviciu and his contribution to convex functions theory

NICULESCU Constantin

University of Craiova, Romania

Fifty years ago Tiberiu Popoviciu published in Analele Univ. Iasi one of the most striking characterization of convex functions of one real variable. Our talk is aimed to discuss the importance of this result as well as the main role played by Popoviciu in promoting the study of convex functions in Romania.

Petre Sergescu and the rebirthing of Bret’s theorems

STEFANESCU Doru

University of Bucharest, Romania

In 1815 Jean-Jacques Bret published a paper on the bounding of the positive roots of univariate polynomials over R . His results were less known than a bound obtained by J.-L. Lagrange and his proofs were not completely understood by his contemporaries. The results of Bret were reconsidered by Petre Sergescu (1893–1954) in several papers on the upper bounds for positive roots. He explained Bret’s proofs and obtained generalizations of his results. We discuss the historical context of the ﬁrst results on the upper bounds for positive roots and we present the contributions of Petre Sergescu on the reconsideration of the theorems of Bret.

Dan Barbilian at the 120 years anniversary. The contribution of Dan Barbilian in the history and philosophy of mathematics

VAIDA Dragos

Facultatea de Matematica si Informatica, Universitatea Bucuresti, Romania

The contributions of Dan Barbilian from various sources mathematical articles (Euclid’s argument on the inﬁnity of primes), courses (Theory of Galois) or conferences (Gauss and Hilbert) provide a basis for the history and philosophy of mathematics in our country 157 and a motivation for viewing mathematics as a part of culture. One presents an unknown essay of Barbilian on the experimental component in the mathematical investigation, a trend emphasized in the contemporary research. This essay indicates a mathematical realization of the Apollon-Dyonisos antinomy: concepts and ideas vs examples and concrete representations as an ur-phenomenon of the knowledge. The conventional image concerning Barbilian exclusively related to algebraic structures is thus corrected. An appendix on the symbolism of mirror suggests the existence of links between the mathematician (Dan Barbilian) and the poet (Ion Barbu). References to R. Gu´enon are relevant for the promoted theory of knowledge. The main case study of this paper deals with the Hilbert Theorem on the commutativity of the Archimedean po-division rings (D. Vaida: [2014] On partially ordered semiring-like systems A Tribute to Alexandru Mateescu. Gh. Paun, G. Rozenberg, A. Salomaa, eds., Discrete Mathematics and Computer Science. In Memoriam Alexandru Mateescu (1952-2005), Editura Academiei, Bucure¸sti).

Some aspects in the history of mathematics in Romania

VERNESCU Andrei

Valahia University of Targoviste, Romania

We emphasize some facts about several Romanian mathematicians.

Index

S1. Algebra and Number Theory, 37 TODEA Constantin - Cosmin, 52 AGORE Ana, 37 URSU Vasile, 52 ANTON Marian, 37 VELICHE Oana, 52 BALAN Adriana, 37 VLADOIU Marius, 53 BONCIOCAT Nicolae Ciprian, 38 VRACIU Adela, 53 BOTNARU Dumitru, 38 WELKER Volkmar, 53 BREAZ Simion, 38 YARAHMADI Zahra, 53 BULACU Daniel, 39 ZAROJANU Andrei, 54 BURCIU Sebastian, 39 S2. Algebraic, Complex and Diﬀerential Geometry and Topology, CAENEPEEL Stefaan, 39 55 CERBU Olga, 40 ANASTASIEI Mihai, 55 CHINDRIS Calin, 40 BEJAN Cornelia-Livia, 55 CHIS Mihai, 40 BERCEANU Barbu Rudolf, 55 CIMPOEAS Mircea, 41 BUCATARU Ioan, 56 CIPU Mihai, 41 BURGHELEA Dan, 56 COBELI Cristian, 41 CALDARARU Andrei, 57 COCONET Tiberiu, 41 CIOBAN Mitrofan, 57 COJOCARU Alina Carmen, 42 CONSTANTINESCU Oana, 57 COJUHARI Elena, 42 COSTINESCU Cristian, 58 CONSTANTINESCU Adrian, 42 CUZUB Stefan Andrei, 58 CONSTANTINESCU Alexandru, 43 DAMIAN Florin, 58 DEACONESCU Marian, 43 MACINIC Anca, 58 DIACONU Adrian, 43 MASCA Ioana Monica, 59 ENE Viviana, 44 MAXIM Laurentiu, 59 ENESCU Florian, 44 MIRON Radu, 59 GROZA Ghiocel, 44 MOSCOVICI Henri, 60 IACOB Alina, 44 MUNTEANU Marius, 60 ICHIM Bogdan, 45 MUNTEANU Ovidiu, 60 JONES Nathan, 45 NICOLAESCU Liviu, 60 LENART Cristian, 45 PAUNESCU Laurentiu, 61 MILITARU Gigel, 46 PEYGHAN Esmaeil, 61 NASTASESCU Constantin, 46 POPA Alexandru, 61 NICHITA Florin, 46 POPESCU Clement Radu, 61 OLTEANU Anda - Georgiana, 47 POPOVICI Elena, 62 PANAITE Florin, 47 RASDEACONU Rares, 62 PASOL Vicentiu, 47 SABAU Sorin, 62 POP Horia, 47 SECELEANU Alexandra, 62 POPA Alexandru Anton, 48 SUCIU Alexandru, 63 POPESCU Dorin, 48 SUVAINA Ioana, 63 POPESCU Sever-Angel, 48 TIBAR Mihai, 63 POPOVICI Florin, 48 TIMOFEEVA Nadezhda, 63 RAIANU Serban, 49 VAISMAN Izu, 64 RAICU Claudiu, 49 VILCU Costin, 64 RUDEANU Sergiu, 49 S3. Real and Complex Analysis, Potential Theory, 65 SECELEANU Alexandra, 49 AGORA Elona, 65 SMITH-TONE Daniel, 50 ANDREI Anca, 65 STAIC Mihai, 50 APREUTESEI Gabriela, 66 STAMATE Dumitru, 50 ATANASIU Dragu, 66 STANCU Radu, 50 BAYINDIR Hilal, 66 STEFANESCU Doru, 51 BENFRIHA Habib, 66 SZOLLOSI Istvan, 51 BERISHA Faton, 67

159 160 Index

BRACCI Filippo, 67 OMAR Benniche, 88 BREAZ Daniel, 67 OZCUBUKCU Zerrin, 89 BREAZ Nicoleta, 68 PERJAN Andrei, 89 BUCUR Gheorghe, 68 RADU Petronela, 89 BUCUR Ileana, 68 RUSU Galina, 90 CAZACU Cristian, 68 SATCO Bianca, 90 CIRSTEA Florica, 69 SERBAN Calin - Constantin, 90 CRISTEA Mihai, 69 SEREA Oana, 91 DEGER Ugur, 69 SHIRIKYAN Armen, 91 DEMETER Ciprian, 70 STANCU - DUMITRU Denisa, 91 FLORESCU Liviu, 70 TARFULEA Nicolae, 91 GHISA Dorin, 70 TATARU Daniel, 92 IANCU Mihai, 70 TKACENKO Alexandra, 92 IONITA George - Ionut, 71 TURINICI Gabriel, 93 IORDAN Andrei, 71 UNGUREANU Valeriu, 93 JOITA Cezar, 71 VARGA Csaba, 93 KOHR Gabriela, 72 VARVARUCA Eugen, 94 LIE Victor, 72 VICOL Vlad, 94 MARCOCI Anca Nicoleta, 72 VOISEI Mircea, 94 MARCOCI Liviu Gabriel, 73 ZARNESCU Arghir, 94 MINCULETE Nicusor, 73 S5. Functional Analysis, Operator Theory and Operator Algebras, MITROI-SYMEONIDIS Flavia-Corina, 73 Mathematical Physics, 97 MOCANU Marcelina, 73 ANGHEL Nicolae, 97 MUSCALU Camil, 74 BADEA Gabriela, 97 NEAGU Vasile, 74 BOCA Florin-Petre, 97 NISHIO Masaharu, 74 CATANA˘ Viorel, 98 OPRINA Andrei-George, 75 CORNEAN Horia, 98 OROS Georgia Irina, 75 COSTARA Constantin, 98 PASCU Nicolae, 75 CROITORU Anca, 99 PREDA Ovidiu, 75 DANET˘ ¸ Nicolae, 99 SALAGEAN Grigore Stefan, 76 DANET˘ ¸ Rodica-Mihaela, 100 SYMEONIDIS Eleutherius, 76 DADARLAT Marius, 99 VLADOIU Speranta, 76 DEACONU Valentin, 100 YASEMIN GOLBOL Sibel, 76 DUMITRASCU Constantin Dorin, 100 S4. Ordinary and Partial Diﬀerential Equations, Variational DUTKAY Dorin, 101 Methods, Optimal Control, 79 DZHUNUSHALIEV Vladimir, 101 ARAMA Bianca-Elena, 79 EXNER Pavel, 101 BAKSI Ozlem, 79 FALK Kurt, 101 BEREANU Cristian, 79 FURUICHI Shigeru, 102 BOT¸ Radu Ioan, 80 GHEONDEA Aurelian, 102 BOCEA Marian, 80 GOK Omer, 102 BOCIU Lorena, 80 JOIT¸ A Maria, 102 CASTRO Carlos, 80 MIHAILESCU Eugen, 103 CERNEA Aurelian, 81 MORADI Sirous, 103 CIUBOTARU Stanislav, 81 MUNTEANU Radu, 103 CSETNEK Ern¨o Robert, 82 NENCIU Irina, 103 DRAGAN Vasile, 82 NISTOR Victor, 104 FARCASEANU Maria, 82 NOMURA Takaaki, 104 FAVINI Angelo, 83 OLTEANU Cristian Octav, 104 GAL Ciprian G, 83 PALT˘ ANEA˘ Radu, 105 GAUDIELLO Antonio, 83 PAUNESCU Liviu, 105 GUIDETTI Davide, 84 PILLET Claude-Alain, 105 GUTU Valeriu, 84 POPA Ioan-Lucian, 105 IGNAT Liviu, 85 POPA Nicolae, 106 IGNAT Radu, 85 POPESCU Marian-Valentin, 106 ISAIA Florin, 85 POSTOLICA˘ Vasile, 107 KIRR Eduard-Wilhelm, 85 RADU Remus, 107 KIZILBUDAK CALISKAN Seda, 86 RASMUSSEN Morten Grud, 107 KRISTALY Alexandru, 86 SAH Ashok Kumar, 108 LOZOVANU Dmitrii, 86 SAVOIE Baptiste, 108 LUCA TUDORACHE Rodica, 86 SEZER Yonca, 108 MARICA Aurora, 87 SHARMA Preeti, 109 MARIS Mihai, 87 SPARBER Christof, 110 MAWHIN Jean, 87 STAMATE Elena-Cristina, 110 MIHAILESCU Mihai, 87 STRATIL˘ AS˘ ¸erban, 110 MOSCO Umberto, 88 TALPAU DIMITRIU Maria, 110 MUNTEANU Laura, 88 TANASE Raluca, 111 NEGRESCU Alexandru, 88 TEUFEL Stefan, 111 Index 161

VALUS¸ESCU Ilie, 111 MOROSANU Costica, 134 VASILESCU Florian-Horia, 112 MUNTEAN Angela, 134 ZSIDOL´´ aszló, 112 NEAMTU Mihaela, 134 S6. Probability, Stochastic Analysis, and Mathematical Statistics, NEDELCU Dan Alin, 134 113 NICOLESCU Bogdan, 135 ANTON Cristina, 113 OPREA Iuliana, 135 BALLY Vlad, 113 PASA Gelu, 135 BARBU Vlad-Stefan, 113 PASCAN Raisa, 135 CANEPA Elena, 114 PETCU Madalina, 136 CIMPEAN Iulian, 114 POLISEVSCHI Dan, 136 CIUIU Daniel, 114 POP Nicolae, 136 CLIMESCU-HAULICA Adriana, 115 POPA Constantin, 136 DE LA CRUZ CABRERA Omar, 115 POPESCU Emil, 137 DEACONU Madalina, 115 POPESCU Nedelia Antonia, 137 GOREAC Dan, 116 POPOVICI Irina, 137 GRADINARU Mihai, 116 PRECUP Radu, 138 HSU Elton P, 116 PRICOPI Dumitru, 138 HUCKEMANN Stephan, 116 RADULESCU Anca, 138 LOCHERBACH¨ Eva, 117 RADULESCU Rodica, 139 LAZARI Alexandru, 117 RIBACOVA Galina, 139 LUPAS¸CU Oana, 117 SADIKU Murat, 139 MARRON J. S., 118 SECRIERU Ivan, 140 MATICIUC Lucian, 118 SEICIUC Vladislav, 140 MATZINGER Henry, 118 STRUGARU Magdalena, 141 MOCIOALCA Oana, 118 SURAN Marian Doru, 141 NOVAC Ludmila, 119 TARFULEA Nicoleta, 141 PASCU Mihai N., 119 VLAD Serban E., 142 PATRANGENARU Vic, 120 S8. Theoretical Computer Science, Operations Research and PIRVU Traian, 120 Mathematical Programming, 143 ROCKNER¨ Michael, 120 AMAN Bogdan, 143 ROBE-VOINEA Elena-Gratiela, 120 ARUSOAIE Andrei, 143 ROTENSTEIN Eduard, 121 BARONI Marian Alexandru, 144 SOOS Anna, 121 BARONI Mihaela Carmen, 143 TONE Cristina, 121 BAZGAN Cristina, 144 TRUTNAU Gerald, 122 CIOBACˆ AS˘ ¸tefan, 144 UNGUREANU Viorica, 122 CIOBANU Gabriel, 144 VON DAVIER Alina A., 123 DIACONESCU Denisa, 145 S7. Mechanics, Numerical Analysis, Mathematical Models in DIMA C˘at˘alin, 145 Sciences, 125 ISTRAIL Sorin, 145 BADRALEXI Irina, 125 LUCANU Dorel, 146 BALAN Vladimir, 125 MANDRESCU Eugen, 146 BARBOSU Mihai, 125 MARDARE Radu, 147 BIRSAN Mircea, 126 MINEA Marius, 147 BUCUR Andreea-Valentina, 126 PETRE Ion, 147 CAPATINA Anca, 127 PETRE Luigia, 148 CARABINEANU Adrian, 127 POPESCU Andrei, 148 CASCAVAL Radu, 127 POPOVICI Matei, 148 CAVATERRA Cecilia, 127 PRUNESCU Mihai, 148 CHIRUTA Ciprian, 128 ROS¸U Grigore, 149 COLLI Pierluigi, 128 RUSU Vlad, 149 CONSTANTIN Diana Rodica, 128 SERBANUT˘ ¸ A˘ Traian, 150 CRACIUN Eduard - Marius, 129 SIMION Emil, 149 DELVARE Franck, 129 SIPOS¸ Andrei, 150 DIMITRIU Gabriel, 129 TACHE Rozica-Maria, 150 DMITRIEVA Irina, 129 TIPLEA Ferucio Laurent¸iu, 150 DRAGANESCU Andrei, 130 ZARA C˘at˘alin, 151 GALES Catalin Bogdan, 130 S9. History and Philosophy of Mathematics, 153 GEORGESCU Paul, 130 ALEXANDRU Andrei and CIOBANU Gabriel, 153 GHEORGHIU Calin - Ioan, 131 BARBOSU˘ Mihai, 153 GILARDI Gianni, 84 BRECHENMACHER Frédéric, 154 GRASSELLI Maurizio, 84 DEACONESCU Marian, 154 IANNELLI Mimmo, 131 ECKES Christophe, 154 ION Anca Veronica, 131 GIURGESCU Patricia, 155 ION Stelian, 132 IONIT¸ AC˘˘ at˘alin, 155 KASLIK Eva, 132 MARCUS Solomon, 156 KOHR Mirela, 132 NICULESCU Constantin, 156 LITCANU Gabriela, 133 STEFANESCU Doru, 156 MIGDALOVICI Marcel, 133 VAIDA Dragos, 156 MIRANVILLE Alain, 133 VERNESCU Andrei, 157