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CAIM 2016 Book of Abstracts THE 24th CONFERENCE ON APPLIED CAIM 2016 AND INDUSTRIAL MATHEMATICS CRAIOVA, SEPTEMBER 15{18, 2016 Book of Abstracts Organized by Romanian Society of Applied and Industrial Mathematics ROMAI \Gh. Mihoc - C. Iacob" Institute of Academy of Romanian Scientists Mathematical Statistics and Applied Mathematics of Romanian Academy University of Craiova Volume Editors: Carmen Roc¸soreanu, Mihaela Sterpu Printed in Romania: Editura SITECH Craiova Aleea Teatrului, nr. 2, Bloc T1, parter Tel/fax: 0251/414003 E-mail: [email protected]; offi[email protected] Editura SITECH face parte din lista editurilor rom^ane¸stide prestigiu, acreditate de fostul CNCSIS, actual CNCS, prin CNATDCU, pentru Panelul 4, care include domeniile: ¸stiint¸e juridice, sociologice, politice ¸siadministrative, ¸stiint¸e ale comunic˘arii,¸stiint¸e militare, informat¸ii ¸siordine public˘a,¸stiint¸e economice ¸siadministrarea afacerilor, ¸stiint¸e psihologice, ale educat¸iei, educat¸ie fizic˘a¸sisport. ISSN 2537 - 2688 Scientific Commitee Nuri AKSEL (Germany), Mihai ANASTASIEI (Ia¸si), Constantin BACUTA (U.S.A.), Vladimir BALAN (Bucure¸sti), Dumitru BOTNARU (Moldavia), Cornelia Livia BEJAN (Ia¸si), Tassos BOUNTIS (Greece), Wladimir-Georges BOSKOFF (Constant¸a), Sergiu CATARANCIUC (Moldavia), Vasile BRANZ^ ANESCU˘ (Bucure¸sti), Victor CHEPOI (France), Daniel BREAZ (Alba Iulia), Acad. Mitrofan CIOBANU (Moldavia), Ilie BURDUJAN (Ia¸si), Acad. Constantin CORDUNEANU ( U.S.A.), Adrian CARABINEANU (Bucure¸sti), Piergiulio CORSINI (Italy), Ovidiu CARJ^ A˘ (Ia¸si), Matthias DEHMER (Germany), Sanda CLEJA-T¸IGOIU (Bucure¸sti), Angelo FAVINI (Italy), Adrian CONSTANTINESCU (Bucure¸sti), Vladimir GERDT (Russia), Ion CRACIUN˘ (Ia¸si), Bogdan KAZMIERCZAK (Poland), Narcisa APREUTESEI DUMITRIU (Ia¸si), Victor LEPIN (Belarus), Gabriel DIMITRIU (Ia¸si), Boris LOGINOV (Russia), Ioan DZITAC (Oradea), Nenad MLADENOVICI (Great Britain), Constantin FETECAU˘ (Ia¸si), Andrei MOROIANU (France), Paul GEORGESCU (Ia¸si), Gheorghe MOROS¸ANU (Hungary), C˘alinIoan GHEORGHIU (Cluj), Lidia PALESE (Italy), Anca Veronica ION (Bucure¸sti), Mihail POPA (Moldavia), Stelian ION (Bucure¸sti), Maido RAHULA (Estonia), Acad. Marius IOSIFESCU (Bucure¸sti), Kumbakonam RAJAGOPAL (U.S.A.), Gabriela MARINOSCHI (Bucure¸sti), Liliana RESTUCCIA (Messina), Acad. Solomon MARCUS (Bucure¸sti), Ruggero Maria SANTILLI (U.S.A.), Ioan MAXIM (Suceava), Dana SCHLOMIUK (Canada), Acad. Radu MIRON (Ia¸si), Kiyoyuki TCHIZAWA (Japan), Ioana MOISIL (Sibiu), ˘ Ioan TODINCA (Moldavia), Sergiu MOROIANU (Bucure¸sti), C˘at˘alinTRENCHEA (U.S.A), Costic˘aMOROS¸ANU (Ia¸si), Nicolae VULPE (Moldavia), Titus PETRILA (Cluj-Napoca), Adrian-Lucia PLETEA (Ia¸si), Constantin POPA (Constant¸a), Vasile POSTOLICA˘ (Bac˘au), Carmen ROCS¸OREANU (Craiova), Bianca SATCO (Suceava), Ioan STANCU MINASIAN (Bucure¸sti), Mihaela STERPU (Craiova), Mirela S¸TEFANESCU˘ (Constant¸a), Dan TIBA (Bucure¸sti), Acad. Ioan TOMESCU (Bucure¸sti), Rodica TUDORACHE (Ia¸si), Mihai TURINICI (Ia¸si), Gheorghit¸˘aZBAGANU˘ (Bucure¸sti). Organizing Commitee President: Costic˘aMOROS¸OANU Anca Veronica ION Vice President: Carmen ROCS¸OREANU Stelian ION Mitrofan CHOBAN S¸erban VLAD C˘alinIoan GHEORGHIU Local Organizing Commitee: University of Craiova Carmen ROCS¸OREANU Mihaela STERPU Adela IONESCU Laura UNGUREANU Petre BAZAVAN 5 Contents Plenary talks 7 Section 1. Real, Complex, Functional and Numerical Analysis 13 Section 2. PDEs with Applications in Mechanics, Biology, etc. 23 Section 3. ODEs and Dynamical Systems 31 Section 4. Probability Theory, Mathematical Statistics, Operations Research 45 Section 5. Algebra, Logic, Geometry (with applications) 55 Section 6. Mathematical Modeling 73 Section 7. Computer Science 81 Section 8. Education 89 6 Plenary Talks 8 Plenary Talks Bloch-Iserles Hamiltonian system Vasile Br^ınz˘anescu Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Romania e-mail: [email protected] In a paper in 2009, Bloch, Br^ınz˘anescu,Iserles, Marsden and Ratiu studied the Hamiltonian system introduced by Bloch and Iserles in 2006 and showed that this system is completely in- tegrable. In 2015, Br^ınz˘anescuand Ratiu proved that this Hamiltonian system is algebraically complete integrable. We shall present the ideas of the proofs. General concept of multiplied fixed points of mappings Mitrofan M. Choban Tiraspol State University, Republic of Moldova e-mail: [email protected] In 1987, D. Guo and V. Lakshmikantham [5] introduced and initiated the study of the coupled fixed point. In 2010, Samet and Vetro presented one concept of a fixed point of m-order as an extension of the coupled fixed point. In 2004 A.C.M. Ran and M.C.B. Reurings and in 2006 T. Gnana Bhaskar and V. Lakshmikantham are proved interesting fixed point theorems in partially ordered metric spaces. Later, V. Berinde and M. Borcut introduced the concept of tripled fixed point and proved tripled fixed-point theorems using mixed monotone mappings. After that a substantial number of articles was dedicated on tripled fixed point and quadruple fixed point theory (see [3]). In [6, 7] were introduced a new concept of a fixed point of m-order. Our main aim is to introduced a general concept of a multidimensional fixed point in the ordered spaces with distance [4]. Fix m 2 N = f1; 2; :::g. Denote by λ = (λ1; :::; λm) a collection of mappings fλi : f1; 2; :::; mg −! f1; 2; :::; mg : i ≤ mg. Let X be a space and F : Xm −! X be an operator (mapping). The operator F and the m m mappings λ generate the operator λF : X −! X , where λF (x1; ::::; xm) = (y1; :::; ym) and yi m = F (xλi(1); :::; xλi(m)) for each point (x1; :::; xm) 2 X and any index i ≤ m. m A point a = (a1; :::; am) 2 X is a λ-multiplied point of the operator F if a = λF (a), i. e. ai = F (aλi(1); :::; aλi(m)) for any index i ≤ m. This concept of multiplied point is developed in context with methods from [1, 2, 4]. Let (X; d) be a distance space, m 2 N = f1; 2; :::g. On Xm consider the distance m { d ((x1; :::; xm); (y1; :::; ym)) = supfd(xi; yi): i ≤ mg, ¯m { d ((x1; :::; xm); (y1; :::; ym)) = Σfd(xi; yi): i ≤ mg. We say that the operator F : - is a λ-contraction if there exist a number k 2 [0; 1) such that d(F (x1; ::::; xm);F (y1; ::::; ym)) ≤ ksupfd(xi; yi): i ≤ mg m for all (x1; ::::; xm); (y1; ::::; ym) 2 X ; - is a λ¯-contraction if there exist a number k 2 [0; 1) such that d(F (x1; ::::; xm);F (y1; ::::; ym)) ≤ k=mΣfd(xi; yi): i ≤ mg CAIM 2016, Craiova, September 15-18, 2016 9 m for all (x1; ::::; xm); (y1; ::::; ym) 2 X . We analyze some results of the following kind: Theorem 1. Let (X; d) be a complete s-distance symmetric space. 1. If F is a λ-contraction, then any Picard sequence of the operator λF is a convergent Cauchy sequence and F has a unique multidimensional fixed point. ¯ 2. If F is a λ-contraction and for any i ≤ m the mapping λi is a surjection or, more general, −1 j [ fλi (j): j ≤ ngj = m for each i ≤ m, then any Picard sequence of the operator λF is a convergent Cauchy sequence and F has a unique multidimensional fixed point. References [1] Berinde, V. and Choban, M. M., Remarks on some completeness conditions involved in several common fixed point theorems, Creat. Math. Inform. 19 (2010), no. 1, 1{10. [2] Berinde, V. and Choban, M. M., Generalized distances and their associate metrics. Impact on fixed point theory, Creat. Math. Inform. 22 (2013), no. 1, 23{32. [3] Borcut, Puncte triple fixe pentru operatori definit¸i pe spat¸ii metrice part¸ial ordonate, Cluj- Napoca: Risoprint, 2016. [4] M. Choban, Fixed points of mappings defined on spaces with distance, Carpathian J. Math. 32 (2016), no. 2, 173{188. [5] D. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), 623{632. [6] A. Roldan, J. Martinez-Moreno, C. Roldan, Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl. 396 (2012), 536{545. [7] B. Samet, C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal. 1 (2010), 46{56. The inverse problem and the coalitional rationality for values of cooperative TU games Irinel Dragan University of Texas, Mathematics, Arlington, Texas, USA e-mail: [email protected] In this paper, we discuss two algorithmic procedures for solving what we call The Inverse problem, with coalitional rationality constraints, for cooperative TU games. First, for a TU game with the Shapley Value L find out a game, with the same Shapley value L, that belongs to the Core of the game. Second, for a TU game with the Semivalue M, defined by a weighted vector p subject to some normalization condition, find out a game, with the same Semivalue M, that belongs to its Power Core of the game. The main tools are the potential bases of the vector space of TU games, using the Hart/Mas-Colell potentials in the first case, and our potentials in the second case. A few examples illustrate the procedures. References [1] I. Dragan (1991), The potential basis and the weighted Shapley Value, Libertas Matematica, 11, 139-146. [2] I. Dragan (2005), On the Inverse Problem for Semivalues of Cooperative TU games, IJPAM, 4, 545-561. [3] S. Hart and A. Mas-Colell (1988), Potential, Value and Consistency, Econ., 57,3, 589-614. 10 Plenary Talks Approximation of the controls for the beam equation Sorin Micu Department of Mathematics, University of Craiova, Romania e-mail: sd [email protected] We consider the following equation u¨(x; t) + @4u(x; t) = 0; (x; t) 2 (0; 1) × (0;T ) x (1) u(x; 0) = u0(x); u_(x; 0) = u1(x); x 2 (0; 1); modelling the vibration of an elastic beam, whereu _ denotes the derivative of u with respect to time. To (1) we may attach different boundary conditions.
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