DOCSLIB.ORG

The Mathematical Sciences at Clemson

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

BIOMATHEMATICS IS The Geometry of Biological Time m Arthur Winfree, Purdue University The Geometry of Biological Time explains periodic processes in living systems >< and their nonliving analogues in the abstract terms of systems theory. Emphasis is on phase singularities, waves, and mutual synchronization in -n tissues composed of many clocklike units. Also provided are detailed de- )5-._U scriptions of the most commonly used experimental systems, such as electrical oscillations and waves, circadian clocks, the cell division cycle, and the crystal-like regularities observed in the regeneration of severed limbs. z No theoretical background is assumed: required notions are introduced through an extensive collection of illustrations and easily understood o examples. 1979/approx. 576 pp./290 lllus./Cioth $32.00 _ (Biomathematics. Volume 8) ISBN 0-387-09373-7 z Mathematical Population Genetics G) Warren J. Ewens, University of Pennsylvania, Philadelphia Presents the mathematical theory of population genetics with emphasis on those aspects relevant to evolutionary studies. The opening chapter pro- vides an excellent general historical and biological background. Subsequent chapters treat deterministic and stochastic models, discrete and continuous time processes, theory concerning classical and molecular aspects, and one, two, and many loci in a concise and comprehensive manner, with ample references to additional literature. An essential working guide for population geneticists interested in the mathematical foundations of their field and mathematicians involved in genetic evolutionary processes. 1979/ approx. 330 pp./ 4111us/17 Tables/ Cloth $32.00 (Biomathematics. Volume 9) ISBN 0-387-09577-2 Diffusion and Ecological Problems: M~thematical Models Akira Okubo, State University of New York, Stony Brook The first comprehensive book on mathematical models of diffusion in an ecological context. It provides a wide variety of problems ranging from passive diffusion of substances in the environment to active dispersal of interacting animal populations. Topics covered include the basics of diffusion, diffusion of spores in the air, transmission of insect pheromones, random search models for homing animals, dynamics of organism swarming, animal movements in home range, plankton patchiness, traveling waves of dis­ persing populations, models for density-dependent dispersal, and diffusion­ induced instability. Knowledge of basic probability and differential equations is assumed. 1979/ approx. 300 pp./114111us./ Cloth $42.90 (Biomathematics, Volume 10) ISBN 0-387-09620-5 to order, write,~ Springer-Verlag New York Inc. Department S194G 44 Hartz Way, Secaucus, NJ 07094 prices subject to change without notice Notices of the American Mathematical Society EDITORIAL COMMITTEE Volume 26, Number 8, December 1979 Ed Dubinsky, Richard j. Griego, Robion C. Kirby, Arthur P. Mattuck, Susan Montgomery, Barbara L. Osofsky, Special Issue Everett Pitcher (Chairman) Assistantships and Fellowships MANAGING EDITOR in the Mathematical Sciences 1980-1981 Lincoln K. Durst ASSOCIATE EDITOR FOR QUERIES Hans Samelson SUBSCRIPTION ORDERS Notices is published eight times a year (January, February, April, June, August, October, November, and December). Subscription for Vol. 27 (1980), $22.00 list, $11.00 member. The subscription price for members is included in the annual dues. Sub­ scriptions and orders for AMS publi­ cations should be addressed to the American Mathematical Society, P. 0. Box 1571, Annex Station, 510 COMMITTEE ON EMPLOYMENT AND Providence, R.I. 02901. All orders must be prepaid. EDUCATIONAL POLICY ADVERTISING & INQUIRIES 511 CASE HISTORY The Notices publishes situations Experiences Getting a Job, Spring 1979 wanted and classified advertising, and display advertising for publishers and academic or scientific organiza­ 513 ASSISTANTSHIPS AND FELLOWSHIPS tions. Requests for information: in the Mathematical Sciences in 1980-1981 Advertising: Elaine Lauble Change of address or subscriptions: Virginia Biber 577 CRITICAL, HISTORICAL OR EXPOSITORY To avoid interruption in service please THESES send address changes four to six weeks in advance. It is essential to include the member code which 579 STIPENDS FOR STUDY AND TRAVEL appears on the address label with Graduate Support, 579 all correspondence regarding subscriptions. Address correspondence Postdoctoral Support, 582 to American Mathematical Society, Travel and Study Abroad, 590 P. 0. Box 6248, Providence, Rl 02940. Telephone 401-272-9500. Study in U. S. for Foreign Nationals, 593 Second class postage paid at Sources of Fellowship Information, 594 Providence, Rl, and additional mailing offices. U.S. Postal Service Publication No. 398520. Copyright © 1979 by the A-657 INDEX OF ABSTRACTS, Volume 26 American Mathematical Society, Printed in the United States of America. A-692 INDEX, Volume 26 STATEMENT BY AMS COMMITTEE ON EMPLOYMENT AND EDUCATIONAL POLICY Current and prospective graduate students in and there are indications that this trend will continue, mathematics and their advisors should be aware of particularly outside the academic world. employment prospects in the profession. Talented More information on employment in mathematics young people should not be discouraged from becom- can be found in the following articles: Future job ing mathematicians. Some academic positions will Prospects for Ph.D.'s in the Mathematical Sciences, become available every year. In addition, there are by Wendell H. Fleming, December 1975 Notices, varied career opportunities outside of the academic page 377; Report on the 1977 AMS Nonacademic environment, and an increasing number of Ph.D. Salary Survey, by Robert j. Thompson, August 1978 mathematicians are choosing such careers. Notices, page 307; 22nd Annual AMS Survey, First Continuing studies made under the auspices of Report, October 1978 Notices, page 390; 22nd the AMS Committee on Employment and Educa- Annual AMS Survey, Second Report, February 1979 tiona) Policy indicate that, for some years to come, Notices, page 106; 23rd Annual AMS Survey, First the number of openings for traditional academic Report, October 1979 Notices, page 382. The employment in mathematics will be smaller than the pamphlet Seeking Employment in the Mathematical rate at which Ph.D.'s in pure mathematics are cur- Sciences, published by the Mathematical Sciences rently entering the job market. However these same Employment Register, also contains useful informa- studies have shown that employment pro~pects in tion on employment in mathematics. mathematics improved somewhat in recent years, COMMITTEE ON EMPLOYMENT AND EDUCATIONAL POLICY (December 1979) Lida K. Barrett, chairman Hans Schneider Arthur P. Mattuck Robert j. Thompson Donald C. Rung William P. Ziemer Data Subcommittee Employment Concerns Subcommittee Donald j. Albers, Wendell H. Fleming, Hans Schneider Barnet M. Weinstock, consultant chairman Audrey Terras chairman Lida K. Barrett Arthur P. Mattuck Robert j. Thompson Lincoln K. Durst Donald C. Rung Short Course Subcommittee Discontinued Doctoral Programs Subcommittee Alan j. Goldman, Cathleen S. Morawetz Lida K. Barrett William P. Ziemer chairman Barbara L. Osofsky Arthur P. Mattuck Ronald L. Graham Robert W. McKelvey Seeking Employment in the Mathematical Sciences This booklet gives mathematicians just entering the Sources of information available to mathematicians professional field information on how to find are listed. The Mathematical Sciences Employment employment best suited to their abilities and train­ Register, which is sponsored by the American ing. The role of the mathematicians in teaching, Mathematical Society, the Mathematical Association academic and industrial research, computing, and of America, and the Society for Industrial and government is discussed, along with information on Applied Mathematics, has compiled this booklet. how to go about seeking and applying for a position. Revised edition, 1977, 20 pages. $.50 first copy, $.10 each additional copy Prepayment is required for all American Mathematical Society publications. Send for the book above to: AMS, P.O. Box 1571, Annex Station, Providence, Rl 02901 510 A CASE HISTORY Experiences Getting a Job, Spring 1979 by Peter j. Welcher In what follows I will recount some of my per­ only thing I could sell myself as was as a programmer sonal experiences in looking for employment this at a starting salary of $13K to $15K! spring. I will also offer some comments and sugges­ I was interviewed (March-May) by General Public tions stemming from these experiences. The thing I Utilities, ITT Defense Communications, Raytheon, would most like to emphasize is that good non­ Sperry Microwave, and Teledyne-Brown Engineering, academic jobs are there, even for "pure" mathemati­ all set up through industrial recruiters. I was also cians. My impression is that some of the jobs in put in touch with around ten companies with jobs academia, particularly those for new Ph.D.'s, verge which violated my gross constraints. These gross on exploitation of them based on the poor job constraints were: (a) work interesting and definitely market. Nonacademic positions are a more-than­ not just computer programming; (b) salary of at viable alternative! least $20K, so as to be better than an academic 1. Case History. Initial conditions: B.A., Wes­ salary. It turned out the latter should probably have leyan University, 1974, Phi Beta Kappa, etc.; Ph.D., been set a little higher. M.I.T., 1978, in Algebraic Topology. Computer 2. Results. G.P.U. was
Recommended publications
  • Table of Contents

    Table of Contents

    Table of contents Table of contents..............................................................................................................................1 A Word from the Director................................................................................................................3 Presenting the CRM.........................................................................................................................5 Personnel..........................................................................................................................................6 Scientific Personnel..........................................................................................................................7 Members......................................................................................................................................... 7 Postdoctoral Fellows........................................................................................................................ 8 Visitors ..........................................................................................................................................10 Management................................................................................................................................... 12 Bureau...........................................................................................................................................12 Advisory Committee.......................................................................................................................12
  • Global Existence for Quasilinear Diffusion Equations in Nondivergence Form

    Global Existence for Quasilinear Diffusion Equations in Nondivergence Form

    GLOBAL EXISTENCE FOR QUASILINEAR DIFFUSION EQUATIONS IN NONDIVERGENCE FORM WOLFGANG ARENDT AND RALPH CHILL A. We consider the quasilinear parabolic equation u β(t, x, u, u)∆u = f (t, x, u, u) t − ∇ ∇ in a cylindrical domain, together with initial-boundary conditions, where the quasilinearity operates on the diffusion coefficient of the Laplacian. Un- der suitable conditions we prove global existence of a solution in the energy space. Our proof depends on maximal regularity of a nonautonomous lin- ear parabolic equation which we use to provide us with compactness in order to apply Schaefer’s fixed point theorem. 1. I We prove global existence of a solution of the quasilinear diffusion prob- lem u β(t, x, u, u)∆u = f (t, x, u, u) in (0, ) Ω, t − ∇ ∇ ∞ × (1) u = 0 in (0, ) ∂Ω, ∞ × u(0, ) = u0( ) in Ω, · · where Ω Rd is an open set, u H1(Ω) and ⊂ 0 ∈ 0 1 β : (0, ) Ω R1+d [ε, ](ε (0, 1) is fixed) and ∞ × × → ε ∈ f : (0, ) Ω R1+d R ∞ × × → are measurable functions which are continuous with respect to the last vari- able, for every (t, x) (0, ) Ω. The function f satisfies in addition a linear growth condition with∈ respect∞ × to the last variable. We prove in fact existence of a solution in the space H1 ([0, ); L2(Ω)) L2 ([0, ); D(∆ )) C([0, ); H1(Ω)), loc ∞ ∩ loc ∞ D ∩ ∞ 0 2 where D(∆D) is the domain of the Dirichlet-Laplacian in L (Ω). Date: October 21, 2008. 2000 Mathematics Subject Classification. 35P05, 35J70, 35K65.
  • Functional Analysis TMA401/MMA400

    Functional Analysis TMA401/MMA400

    Functional analysis TMA401/MMA400 Peter Kumlin 2018-09-21 1 Course diary — What has happened? Week 1 Discussion of introductory example, see section 1. Definition of real/complex vector space, remark on existence of unique zero vector and inverse vectors, example of real vector spaces (sequence spaces and function spaces). Hölder and Minkowski inequal- ities. Introducing (the to all students very well-known concepts) linear combination, linear independence, span of a set, (vector space-) basis (= Hamel basis) with examples. All vector spaces have basis (using Axiom of choice/Zorn’s lemma; it was not proven but stated). Introducing norms on vector spaces with examples, equivalent norms, con- vergence of sequences in normed spaces, showed that C([0; 1]) can be equipped with norms that are not equivalent. Stated and proved that all norms on finite-dimensional vector spaces are equivalent. A proof of this is supplied below. Also mentioned that all infinte-dimensional vector spaces can be equipped with norms that are not equivalent (easy to prove once we have a Hamel basis). Theorem 0.1. Suppose E is a vector space with dim(E) < 1. Then all norms on E are equivalent. Proof: We observe that the relation that two norms are equivalent is transitive, so it is enough to show that an arbitrary norm k · k on E is equivalent to a fixed norm k · k∗ on E. Let x1; x2; : : : ; xn, where n = dim(E), be a basis for E. This means that for every x 2 E there are uniquely defined scalars αk(x), k = 1; 2; : : : ; n, such that x = α1(x)x1 + α2(x)x2 + ::: + αn(x)xn: Set kxk∗ = jα1(x)j + jα2(x)j + ::: jαn(x)j for x 2 E.
  • 1. Harmonic Functions 2. Perron's Method 3. Potential Theor

    1. Harmonic Functions 2. Perron's Method 3. Potential Theor

    Elliptic and Parabolic Equations by J. Hulshof Elliptic equations: 1. Harmonic functions 2. Perron’s method 3. Potential theory 4. Existence results; the method of sub- and supersolutions 5. Classical maximum principles for elliptic equations 6. More regularity, Schauder’s theory for general elliptic operators 7. The weak solution approach in one space dimension 8. Eigenfunctions for the Sturm-Liouville problem 9. Generalization to more dimensions Parabolic equations: 10. Maximum principles for parabolic equations 11. Potential theory and existence results 12. Asymptotic behaviour of solutions to the semilinear heat equation Functional Analysis: A. Banach spaces B. Hilbert spaces C. Continous semigroups and Liapounov functionals 1 1. Harmonic functions Throughout this section, Ω ⊂ Rn is a bounded domain. 1.1 Definition A function u ∈ C2(Ω) is called subharmonic if ∆u ≥ 0 in Ω, harmonic if ∆u ≡ 0 in Ω, and superharmonic if ∆u ≤ 0 in Ω. 1.2 Notation The measure of the unit ball in Rn is Z n/2 n 2 2 2π ωn = |B1| = |{x ∈ R : x1 + ... + xn ≤ 1}| = dx = . B1 nΓ(n/2) The (n − 1)-dimensional measure of the boundary ∂B1 of B1 is equal to nωn. 1.3 Mean Value Theorem Let u ∈ C2(Ω) be subharmonic, and n BR(y) = {x ∈ R : |x − y| ≤ R} ⊂ Ω. Then 1 Z u(y) ≤ n−1 u(x)dS(x), nωnR ∂BR(y) where dS is the (n − 1)-dimensional surface element on ∂BR(y). Also 1 Z u(y) ≤ n u(x)dx. ωnR BR(y) Equalities hold if u is harmonic. Proof We may assume y = 0.
  • Pseudoparabolic Partial Differential Equations

    Pseudoparabolic Partial Differential Equations

    SIAM J. MATH. ANAL. Vol. 1, No. 1, February 1970 PSEUDOPARABOLIC PARTIAL DIFFERENTIAL EQUATIONS* R. E. SHOWALTERt AND T. W. TING: 1. Introduction. Various physical phenomena have led to a study of a mixed boundary value problem for the partial differential equation (1.1) -diu- rlau kau, where A denotes the Laplacian differential operator. The initial and boundary conditions for this equation are the same as those posed for solutions of the parabolic equation (1.2) --u kAu which is obtained from (1.1) by setting r/= 0. The class of equations which are considered here will be called pseudoparabolic, not only because the problems which are well-posed for the parabolic equation are also well-posed for these equations, but because the generalized solution to the parabolic equation (1.2) satisfying mixed initial and boundary conditions can be obtained as the limit of a sequence of solutions to the corresponding problem for equation (1.1) corres- ponding to any null sequence for the coefficient q. That is, a solution of the parabolic equation can be approximated by a solution of (1.1). More statements on the comparison of these problems will appear in the following. A study ofnonsteady flow of second order fluids [36] leads to a mixed boundary value problem for the one-dimensional case of (1.1) for the velocity of the fluid. In [36 the role of the material constant r/was examined, for this constant dis- tinguishes this theory of second order fluids from earlier ones. This principal result of interest here is that the mixed boundary value problem is mathematically well-posed.
  • Arxiv:1706.03727V4 [Math.AP] 23 Jan 2018 Β Condition 1.1

    Arxiv:1706.03727V4 [Math.AP] 23 Jan 2018 Β Condition 1.1

    ELLIPTIC EQUATIONS WITH TRANSMISSION AND WENTZELL BOUNDARY CONDITIONS AND AN APPLICATION TO STEADY WATER WAVES IN THE PRESENCE OF WIND HUNG LE Abstract. In this paper, we present results about the existence and uniqueness of so- lutions of elliptic equations with transmission and Wentzell boundary conditions. We provide Schauder estimates and existence results in H¨older spaces. As an application, we develop an existence theory for small-amplitude two-dimensional traveling waves in an air-water system with surface tension. The water region is assumed to be irrotational and of finite depth, and we permit a general distribution of vorticity in the atmosphere. 1. Introduction 1.1. Elliptic theory. Let Ω Rn be a connected bounded C2,β domain for n > 1 and β (0, 1). Suppose that there⊂ exists a C2,β hypersurface Γ that divides Ω into two connected∈ regions such that Ω=Ω Γ Ω , Ω Ω = , ∂Ω ∂Ω =Γ, 1 ∪ ∪ 2 1 ∩ 2 ∅ 1 ∩ 2 and denote by S := ∂Ω. Let ν = (ν1,...,νn) be the normal vector field on the interface Γ pointing outward from Ω1. We define the co-normal derivative operator on Γ n ij ∂N := a νi∂xj , i,jX=1 and the tangential differential operator along Γ n := wst∂ , 1 s n, Ds xt ≤ ≤ t=1 X where w := In ν ν, and In is the n n identity matrix. Our main object− ⊗ of study is the following× transmission problem with a Wentzell boundary arXiv:1706.03727v4 [math.AP] 23 Jan 2018 condition Lu = f in Ω, u = 0 on S, (1.1) u = 0 onΓ, Bu = g on Γ, J K 2010 Mathematics Subject Classification.
  • Elementary Theory and Methods for Elliptic Partial Differential Equations

    Elementary Theory and Methods for Elliptic Partial Differential Equations

    Elementary Theory and Methods for Elliptic Partial Differential Equations John Villavert Contents 1 Introduction and Basic Theory 4 1.1 Harmonic Functions . 5 1.1.1 Mean Value Properties . 5 1.1.2 Sub-harmonic and Super-harmonic Functions . 8 1.1.3 Further Properties of Harmonic Functions . 11 1.1.4 Energy and Comparison Methods for Harmonic Functions . 14 1.2 Classical Maximum Principles . 17 1.2.1 The Weak Maximum Principle . 17 1.2.2 The Strong Maximum Principle . 18 1.3 Newtonian and Riesz Potentials . 21 1.3.1 The Newtonian Potential and Green's Formula . 21 1.3.2 Riesz Potentials and the Hardy-Littlewood-Sobolev Inequalitiy . 23 1.3.3 Green's Function and Representation Formulas of Solutions . 25 1.3.4 Green's Function for a Half-Space . 26 1.3.5 Green's Function for a Ball . 28 1.4 H¨olderRegularity for Poisson's Equation . 31 1.4.1 The Dirichlet Problem for Poisson's Equation . 33 1.4.2 Interior H¨olderEstimates for Second Derivatives . 36 1.4.3 Boundary H¨olderEstimates for Second Derivatives . 40 2 Existence Theory 43 2.1 The Lax-Milgram Theorem . 43 2.1.1 Existence of Weak Solutions . 44 2.2 The Fredholm Alternative . 47 2.2.1 Existence of Weak Solutions . 48 2.3 Eigenvalues and Eigenfunctions . 52 1 2.4 Topological Fixed Point Theorems . 53 2.4.1 Brouwer's Fixed Point Theorem . 54 2.4.2 Schauder's Fixed Point Theorem . 55 2.4.3 Schaefer's Fixed Point Theorem . 56 2.4.4 Application to Nonlinear Elliptic Boundary Value Problems .
  • © Copyright 2015

    © Copyright 2015

    Handbook of Mathematics Index © Copyright 2015. Index A-basis, 316 Adjoint functor, 302 A-module, 316 Adjoint functors, 595 Ab-category, 585 Adjoint functors (adjunction), 595 Ab-enriched (symmetric) monoidal category, 586 Adjoint map, 243 Abel lemma, 121, 453 Adjoint of a linear map, 243 Abel theorem, 129 Adjoint operator, 243, 375 Abel-Poisson, 487 Adjoint pair (of functors), 311 Abelian category, 584, 591 Adjointness, 589 Abelian group, 42, 43, 82, 84, 88, 89, 103, 474, 475, 516, 517, 521, 584, 590, Adjunction, 595 599 Adjunction isomorphism, 596 Abelian integral, 437 Adjunction of indeterminates, 120 Abelian semigroup, 43, 516 Admissible open set, 306 Abelian variety, 513 Admissible parameter, 393 Abelianization, 315 Admissible parameterization, 393 Abraham-Shaw, 748 Affine algebraic set, 513 Absolute complement, 8, 12 Affine bijection, 169 Absolute consistency, 5 Affine combination, 278 Absolute extrema, 45 Affine connection, 417, 418 Absolute frequency, 620 Affine coordinates system, 190 Absolute geometry, 149, 151, 152 Affine endomorphism, 191 Absolute gometry Affine form, 191 models 1,2,3,4, 151 Affine geometry, 155 Absolute homology groups , 291 Affine group, 168 Absolute Hurewicz theorem, 315 Affine independent, 278 Absolute maximum, 670 Affine independent set, 278 Absolute valuation, 79 Affine isometry, 187 Absolute value, 145 anti-displacement, 187 in the field of rationals, 145 displacement, 187 non-Archimedean, 145 Affine map, 168, 169 Absolute value of a rational number, 62 A ffi ne m ap in R3, 186 Absolutely convergent series, 324 Affine morphism, 564
  • The Development of Nonlinear Science£

    The Development of Nonlinear Science£

    The development of nonlinear science£ Alwyn Scott Department of Mathematics University of Arizona Tucson, Arizona USA August 11, 2005 Abstract Research activities in nonlinear science over the past three centuries are reviewed, paying particular attention to the explosive growth of interest in chaos, solitons, and reaction-diffusion phenomena that occurred during the 1970s and considering whether this explosion was an example of a “sci- entific revolution” or Gestalt-like “paradigm shift” as proposed by Thomas Kuhn in the 1962. The broad structure of modern nonlinear science is sketched and details of developments in several areas of nonlinear research are presented, including cosmology, theories of matter, quantum theory, chemistry and biochemistry, solid-state physics, electronics, optics, hydro- dynamics, geophysics, economics, biophysics and neuroscience. It is con- cluded that the emergence of modern nonlinear science as a collective in- terdisciplinary activity was a Kuhnian paradigm shift which has emerged from diverse areas of science in response to the steady growth of comput- ing power over the past four decades and the accumulation of knowledge about nonlinear methods, which eventually broke through the barriers of balkanization. Implications of these perspectives for twentyfirst-century research in biophysics and in neuroscience are discussed. PACS: 01.65.+g, 01.70.+w, 05.45.-a £ Copyright ­c 2005 by Alwyn C. Scott. All rights reserved. 1 Contents 1 Introduction 6 1.1 What is nonlinear science? ...................... 6 1.2 An explosion of activity . ...................... 10 1.3 What caused the changes? ...................... 12 1.4 Three trigger events .......................... 16 2 Fundamental phenomena of nonlinear science 18 2.1 Chaos theory .
  • Well-Posedness of a Pulsed Electric Field Model in Biological Media And

    Well-Posedness of a Pulsed Electric Field Model in Biological Media And

    Well-posedness of a Pulsed Electric Field Model in Biological Media and its Finite Element Approximation Habib Ammari∗ Dehan Chen† Jun Zou‡ Abstract This work aims at providing a mathematical and numerical framework for the analysis on the effects of pulsed electric fields on biological media. Biological tissues and cell suspensions are described as having a heterogeneous permittivity and a heterogeneous conductivity. Well-posedness of the model problem and the regularity of its solution are established. A fully discrete finite element scheme is proposed for the numerical approximation of the potential distribution as a function of time and space simultaneously for an arbitrary shaped pulse, and it is demonstrated to enjoy the optimal convergence order in both space and time. The presented results and numerical scheme have potential applications in the fields of medicine, food sciences, and biotechnology. Mathematics Subject Classification: 65M60, 78M30. Keywords: pulsed electric field, biological medium, well-posedness, numerical schemes, finite element, convergence. 1 Introduction The electrical properties of biological tissues and cell suspensions determine the pathways of current flow through the medium and, thus, are very important in the analysis of a wide range of biomedical applications and in food sciences and biotechnology [3, 16, 18]. A biological tissue is described as having a permittivity and a conductivity [17]. The conductivity can be regarded as a measure of the ability of its charge to be transported throughout its volume by an applied electric field while the permittivity is a measure of the ability of its dipoles to rotate or its charge to be stored by an applied external field.
  • Twenty-Eighth Annual Report of The

    Twenty-Eighth Annual Report of The

    National Science Foundation Twenty-Eighth Annual Report for Fiscal Year 1978 For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 - Price $3.25 Stock Number 038-000-00407-7 Letter of Transmittal Washington, D.C. DEAR MR. PRESIDENT: I have the honor to transmit herewith the Annual Report for Fiscal Year 1978 of the National Science Foundation for submission to the Congress as required by the National Science Foundation Act of 1950. Respectfully, Richard C. Atkinson Director, National Science foundation The Honorable The President of ihe United Slates Contents Page Director's Statement vii Mathematical and Physical Sciences, and Engineering 1 Physics 2 Chemistry 6 Mathematical and Computer Sciences 10 Engineering 16 Materials Research 21 Astronomical, Atmospheric, Earth, and Ocean Sciences 29 Astronomy 31 Atmospheric Sciences 39 Earth Sciences 45 Ocean Sciences 51 Polar Programs 56 Biological, Behavioral, and Social Sciences 61 Physiology, Cellular, and Molecular Biology 62 Behavioral and Neural Sciences 67 Environmental Biology 69 Social Sciences 73 Science Education '77 Science Education Resources Improvement 77 Science Education Development and Research 81 Scientific Personnel Improvement 86 Science and Society 91 Applied Science and Research Applications 97 Problem Analysis 98 Integrated Basic Research 98 Applied Research 99 Problem-Focused Research Applications 101 Intergovernmental Science and Public Technology 105 Scientific, Technological, and International Affairs 109 Policy Research and Analysis 110 Science Resources Studies 112 NSF Planning and Evaluation 115 Information Science and Technology 116 International Programs , 118 Appendices A. National Science Board, NSF Staff, Advisory Committees and Panels 121 B. Patents and Inventions Resulting from Activities Supported by the National Science Foundation 138 C.

  • The Role of Smoothing Effect in Some Dispersive Equations Ricardo

    The role of smoothing effect in some dispersive equations by Ricardo Grande Izquierdo Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2020 © Massachusetts Institute of Technology 2020. All rights reserved. Author............................................................................ Department of Mathematics May 1, 2020 Certified by........................................................................ Professor Gigliola Staffilani Abby Rockefeller Mauze Professor Thesis Supervisor Accepted by....................................................................... Davesh Maulik Chairman, Department Committee on Graduate Studies The role of smoothing effect in some dispersive equations by Ricardo Grande Izquierdo Submitted to the Department of Mathematics on May 1, 2020, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this thesis, we study the role of smoothing effect in the local well-posedness theory of dispersive partial differential equations in three different contexts. First, we use it to overcome a loss of derivatives in a family of nonlocal dispersive equations. Second, we exploit a discrete version of the smoothing effect to study a discrete system of particles and how to approximate it by a continuous dispersive equation. Third, we use an anisotropic version of the smoothing effect to establish the local well-posedness theory of the two-dimensional Dysthe equation, which is used to model oceanic rogue waves. Thesis Supervisor: Professor Gigliola Staffilani Title: Abby Rockefeller Mauze Professor Acknowledgements I would like to thank my advisor, Gigliola Staffilani, for her support, advice and encour- agement over the past five years. I also want to thank her for her generosity and wisdom, for creating a fantastic atmosphere to study mathematics at MIT, and for being the only one to help me out that one time at Sulmona.