ENCYCLOPEDIA OF MATHEMATICS

By Y. DASIL

CONTENTS BRAIDS AND DIFFERENTIAL EQUATIONS 1 FROM COMBINATORICS TO ERGODIC THEORY AND BACK AGAIN 57 FROM BROUWER THEORY TO THE STUDY OF HOMEOMORPHISMS OF SURFACES 77 ALL, MOST, SOME DIFFERENTIABLE DYNAMICAL SYSTEMS 99 GEODESICS ON ?AT SURFACES ASYMPTOTIC BEHAVIOR OF SMOOTH SOLUTIONS FOR PARTIALLY DISSIPATIVE HYPERBOLIC SYSTEMS AND RELAXATION APPROXIMATION 147 NONLINEAR SCHRÖDINGER EQUATIONS IN INHOMOGENEOUS MEDIA: WELLPOSEDNESS AND ILLPOSEDNESS OF THE CAUCHY PROBLEM 157 THE PERIODIC LORENTZ GAS IN THE BOLTZMANN-GRAD LIMIT 183 CONFORMAL INVARIANTS AND NONLINEAR ELLIPTIC EQUATIONS ASYMPTOTIC SOLUTIONS FOR LARGE TIME OF HAMILTON–JACOBI EQUATIONS 213 THE WEAK-COUPLING LIMIT OF LARGE CLASSICAL AND QUANTUM SYSTEMS SYMMETRY OF ENTIRE SOLUTIONS FOR A CLASS OF SEMILINEAR ELLIPTIC EQUATIONS 257 VORTICES IN THE GINZBURG–LANDAU MODEL OF SUPERCONDUCTIVITY RECENT DEVELOPMENTS IN ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS OF MONGE–AMPÈRE TYPE 291 THE INITIAL VALUE PROBLEM FOR NONLINEAR SCHRÖDINGER EQUATIONS SINGULAR SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS MODELLING CHEMOTACTIC AGGREGATION 321 FROM TOPOLOGICAL ?ELD THEORY TO DEFORMATION QUANTIZATION AND REDUCTION MATRIX ANSATZ AND LARGE DEVIATIONS OF THE DENSITY IN EXCLUSION PROCESSES 367 CORRELATION FUNCTIONS OF THE XXZ HEISENBERG SPIN CHAIN: BETHE ANSATZ APPROACH GROMOV–WITTEN INVARIANTS AND TOPOLOGICAL STRINGS: A PROGRESS REPORT 409 THE CAUCHY PROBLEM IN GENERAL RELATIVITY 421 CHRISTOPH SCHWEIGERT*, JÜRGEN FUCHS, AND INGO RUNKEL CATEGORI?CATION AND CORRELATION FUNCTIONS IN CONFORMAL ?ELD THEORY 443 SOLITON DYNAMICS AND SCATTERING 459 HYPOCOERCIVE DIFFUSION OPERATORS METASTABILITY: A POTENTIAL THEORETIC APPROACH ON ISING DROPLETS 519 SIMPLE RANDOM COVERING, DISCONNECTION, LATE AND FAVORITE POINTS 535 MODELLING GENES: MATHEMATICAL AND STATISTICAL CHALLENGES IN GENOMICS 559 GEOMETRIC STOCHASTIC ANALYSIS ON PATH SPACES 575 STATISTICAL CHALLENGES WITH HIGH DIMENSIONALITY: FEATURE SELECTION IN KNOWLEDGE DISCOVERY RANDOM MATRICES AND ENUMERATION OF MAPS THE WEAK/STRONG SURVIVAL TRANSITION ON TREES AND NONAMENABLE GRAPHS 637 NEW DEVELOPMENTS IN STOCHASTIC DYNAMICS STOCHASTIC CLASSI?CATION MODELS 669 RANDOM PARTITIONS AND INSTANTON COUNTING 687 DOMINIQUE PICARD* AND GÉRARD KERKYACHARIAN ESTIMATION IN INVERSE PROBLEMS AND SECOND-GENERATION WAVELETS 713 CONFORMAL RESTRICTION PROPERTIES THE COMPLEXITY OF GENERATING FUNCTIONS FOR INTEGER POINTS IN POLYHEDRA AND BEYOND RATIONAL AND ALGEBRAIC SERIES IN COMBINATORIAL ENUMERATION TOWARDS A STRUCTURE THEORY FOR MATRICES AND MATROIDS 827 CHEREDNIK ALGEBRAS, MACDONALD POLYNOMIALS AND COMBINATORICS 843 POISSON CLONING MODEL FOR RANDOM GRAPHS 873 RANDOMNESS AND REGULARITY 899 ADDITIVE COMBINATORICS AND GEOMETRY OF NUMBERS 911 GEOMETRIC BISTELLAR ?IPS: THE SETTING, THE CONTEXT AND A CONSTRUCTION 931 A SURVEY OF PFAF?AN ORIENTATIONS OF GRAPHS DETERMINANT VERSUS PERMANENT 985 THE ADDITIVITY PROBLEM IN QUANTUM INFORMATION THEORY COMPLEX NETWORKS AND DECENTRALIZED SEARCH ALGORITHMS ON EXPANDER GRAPHS AND CONNECTIVITY IN SMALL SPACE POTENTIAL FUNCTIONS AND THE INEF?CIENCY OF EQUILIBRIA SUBLINEAR TIME ALGORITHMS PSEUDORANDOMNESS AND COMBINATORIAL CONSTRUCTIONS LEAST-SQUARES ?NITE ELEMENT METHODS A POSTERIORI ERROR ANALYSIS AND ADAPTIVE METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS ERROR ESTIMATES FOR ANISOTROPIC ?NITE ELEMENTS AND APPLICATIONS LINEAR SUBDIVISION SCHEMES FOR THE RE?NEMENT OF GEOMETRIC OBJECTS WAVE PROPAGATION SOFTWARE, COMPUTATIONAL SCIENCE, AND REPRODUCIBLE RESEARCH REDUCED BASIS METHOD FOR THE RAPID AND RELIABLE SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS FINITE ELEMENT ALGORITHMS FOR TRANSPORT-DIFFUSION PROBLEMS: STABILITY, ADAPTIVITY, TRACTABILITY ERGODIC CONTROL OF DIFFUSION PROCESSES CONVEX OPTIMIZATION OF GRAPH LAPLACIAN EIGENVALUES (IMANUVILOV) CONTROLLABILITY OF EVOLUTION EQUATIONS OF ?UID DYNAMICS PORT-HAMILTONIAN SYSTEMS: AN INTRODUCTORY SURVEY PASSIVE LINEAR DISCRETE TIME-INVARIANT SYSTEMS CONTROL AND NUMERICAL APPROXIMATION OF THE WAVE AND HEAT EQUATIONS MULTISCALE MODELING FOR EPITAXIAL GROWTH COMPRESSIVE SAMPLING TOTAL VARIATION BASED IMAGE DENOISING AND RESTORATION A WAVELET BASED SPARSE GRID METHOD FOR THE ELECTRONIC SCHRÖDINGER EQUATION MATHEMATICAL AND NUMERICAL ANALYSIS FOR MOLECULAR SIMULATION: ACCOMPLISHMENTS AND CHALLENGES EVOLUTIONARY DYNAMICS OF COOPERATION FRACTIONAL BROWNIAN MOTION: STOCHASTIC CALCULUS AND APPLICATIONS ATOMISTIC AND CONTINUUM MODELS FOR PHASE CHANGE DYNAMICS COMPETITIONS AND MATHEMATICS EDUCATION UNDERSTANDING AND MISUNDERSTANDING THE THIRD INTERNATIONAL MATHEMATICS AND SCIENCE STUDY: WHAT IS AT STAKE AND WHY K-12 EDUCATION STUDIES MATTER MATHEMATICS, THE MEDIA, AND THE PUBLIC PANEL A: CONTROVERSIAL ISSUES IN K-12 MATHEMATICAL EDUCATION PANEL B: WHAT ARE PISA AND TIMSS? WHAT DO THEY TELL US? PANEL C: THE ROLE OF MATHEMATICIANS IN K-12 MATHEMATICS EDUCATION ON THE ORIGINS OF HILBERT’S SIXTH PROBLEM: PHYSICS AND THE EMPIRICIST APPROACH TO AXIOMATIZATION