Current Trends in Analysis and Its Applications: Proceedings of the 9th ISAAC Congress, Kraków 2013

Description

This book is a collection of papers from the 9th International ISAAC Congress held in 2013 in Kraków, Poland. The papers are devoted to recent results in mathematics, focused on analysis and a wide range of its applications. These include up-to-date findings of the following topics: - Differential Equations: Complex and Functional Analytic Methods - Nonlinear PDE - Qualitative Properties of Evolution Models - Differential and Difference Equations - Toeplitz Operators - Wavelet Theory - Topological and Geometrical Methods of Analysis - Queueing Theory and Performance Evaluation of Computer Networks - Clifford and Quaternion Analysis - Fixed Point Theory - M-Frame Constructions - Spaces of Differentiable Functions of Several Real Variables Generalized Functions - Analytic Methods in Complex Geometry - Topological and Geometrical Methods of Analysis - Integral Transforms and Reproducing Kernels - Didactical Approaches to Mathematical Thinking Their wide applications in biomathematics, mechanics, queueing models, scattering, geomechanics etc. are presented in a concise, but comprehensible way, such that further ramifications and future directions can be immediately seen.  Front Matter....Pages I-XVI Front Matter....Pages 1-1 A Tribute to the 70th Birthday of Prof Saburou Saitoh....Pages 3-4 Sergei Rogosin: Achievements so Far and Further Plans....Pages 5-7 Front Matter....Pages 9-9 The Degenerate Second-Order Elliptic Oblique Derivative Problem in a Domain with a Conical Boundary Point....Pages 11-18 On Locally Differentiable Solutions of the Stationary Schrödinger Equation with Discontinuous Coefficients....Pages 19-22 Riemann Problems for Single-Periodic Polyanalytic Functions II....Pages 23-32 Riemann–Hilbert Problem for Multiply Connected Domains....Pages 33-40 The Schottky–Klein Prime Function....Pages 41-47 Green Function of the Dirichlet Problem for the Laplacian and Inhomogeneous Boundary Value Problems for the Poisson Equation in a Punctured Domain....Pages 49-57 Boundary Value Problems and Method of Reflection for Quarter Ring and Half Hexagon....Pages 59-66 Harmonic Dirichlet Problem in a Ring Sector....Pages 67-75 The Parqueting-Reflection Principle....Pages 77-84 On Existence of the Resolvent and Discreteness of the Spectrum of a Class of Differential Operators of Hyperbolic Type....Pages 85-91 On the Singularities of the Emden–Fowler Type Equations....Pages 93-99 Differential Equations with Degenerated Variable Operator at the Derivative....Pages 101-108 Cauchy Problem for a First Order Ordinary Differential System with Variable Coefficients....Pages 109-115 General Solution of an n -th Order Linear Ordinary Differential Equation with Variable Coefficients....Pages 117-122 About a Class of Two Dimensional Volterra Type Integral Equations with Singular Boundary Lines....Pages 123-131 Optimal Control Problem on Optimization of Resources Productivity....Pages 133-142 Front Matter....Pages 143-143 The Amalgam Spaces $W( L^{p( x) },\ell^{\{ p_{n}\} })$ and Boundedness of Hardy–Littlewood Maximal Operators....Pages 145-161 Spaces of Generalised Smoothness in Summability Problems for Φ -Means of Spectral Decomposition....Pages 163-169 Front Matter....Pages 143-143 Viewing the Steklov Eigenvalues of the Laplace Operator as Critical Neumann Eigenvalues....Pages 171-178 Generalized Fractional Integrals on Central Morrey Spaces and Generalized σ -Lipschitz Spaces....Pages 179-189 Front Matter....Pages 191-191 Well-Posedness for a Generalized Boussinesq Equation....Pages 193-202 Energy Solutions for Nonlinear Klein–Gordon Equations in de Sitter Spacetime....Pages 203-208 A Benefit from the L ∞ Smallness of Initial Data for the Semilinear Wave Equation with Structural Damping....Pages 209-216 A Regularity Criterion for the Schrödinger Map....Pages 217-223 Microlocal Analysis for Hyperbolic Equations in Einstein-de Sitter Spacetime....Pages 225-232 Nonlinear Evolution Equations with Strong Dissipation and Proliferation....Pages 233-241 A Note on Real Powers of Time Differentiation....Pages 243-251 A Stationary Approach to the Scattering on Noncompact Star Graphs Containing Finite Rays....Pages 253-262 Integral Transform Approach to the Cauchy Problem for the Evolution Equations....Pages 263-269 Front Matter....Pages 271-271 On Some Solutions of Certain Versions of “Sigma” Model and Some Skyrme-Like Models....Pages 273-280 Sharp Sobolev–Strichartz Estimates for the Free Schrödinger Propagator....Pages 281-288 Nonlinear PDE as Immersions....Pages 289-297 Blow-Up for Nonlinear Inequalities with Singularities on Unbounded Sets....Pages 299-305 Well-Posedness and Stability of a Mindlin–Timoshenko Plate Model with Damping and Sources....Pages 307-314 On Deterministic and Stochastic Linear Quadratic Control Problems....Pages 315-322 Front Matter....Pages 323-323 Ergodic Theory, Boole Type Transformations, Dynamical Systems Theory....Pages 325-333 Fixed Points Theorems for Multivalued Mappings....Pages 335-339 Parametric Continuity of Choquet and Sugeno Integrals....Pages 341-346 Front Matter....Pages 323-323 Nonlinear Operators, Fixed-Point Theorems, Nonlinear Equations....Pages 347-360 Some Remarks About Chow, Hilbert and K-stability of Ruled Threefolds....Pages 361-374 Atiyah Classes of Lie Algebroids....Pages 375-393 Kähler Metrics with Cone Singularities and Uniqueness Problem....Pages 395-408 Front Matter....Pages 409-409 Teaching of Mathematics in Vocational Schools Upon 1951 Reorganisation....Pages 411-415 Arithmetic in Polish Parish Schools in the Period of the Commission of National Education....Pages 417-424 Life as an Example. S.M. Nikolskij....Pages 425-432 The Area Method and Proving Plane Geometry Theorems....Pages 433-439 Front Matter....Pages 441-441 Redundant Multiscale Haar Wavelet Transforms....Pages 443-449 Gabor Transform of Analytic Functional on the Sphere....Pages 451-458 On the Interpolation of Orthonormal Wavelets with Compact Support....Pages 459-465 An Estimation Method of Shift Parameters in Image Separation Problem....Pages 467-473 Slice Functional Calculus in Quaternionic Hilbert Spaces....Pages 475-484 Recent Progress on Spheroidal Monogenic Functions....Pages 485-497 Clifford Algebras with Induced (Semi)-Riemannian Structures and Their Compactifications....Pages 499-504 Front Matter....Pages 505-505 Generalized Shift Operators Generated by Convolutions of Integral Transforms....Pages 507-514 An Approach for Developing Fourier Convolutions and Applications....Pages 515-521 Whittaker Differential Equation Associated to the Initial Heat Problem....Pages 523-530 Recovery of Holomorphic Functions and Taylor Coefficients by Sampling....Pages 531-543 On Approximation of Lebedev Type Transforms....Pages 545-552 Front Matter....Pages 505-505 Reproducing Kernels and Discretization....Pages 553-559 Dirichlet’s Problem by Using Computers with the Theory of Reproducing Kernels....Pages 561-568 Front Matter....Pages 569-569 C ∗ -Algebras of Two-Dimensional Singular Integral Operators with Shifts....Pages 571-581 Uncertainty and Analyticity....Pages 583-590 Toeplitz Operators on the Harmonic Bergman Space with Pseudodifferential Defining Symbols....Pages 591-603 Theorems of Paley–Wiener Type for Spaces of Polyanalytic Functions....Pages 605-613 Fredholm Theory of Pseudodifferential Operators Acting in Variable Exponent Spaces of Bessel Potentials on Smooth Manifolds....Pages 615-621 Front Matter....Pages 623-623 Boundary Value Problems for the Radiative Transfer Equation with Reflection and Refraction Conditions....Pages 625-635 Asymptotic Approximations of a Thin Elastic Beam with Auxiliary Coupled 1D System due to Robin Boundary Condition....Pages 637-648 Smooth Solution of an Initial Value Problem for a Mixed-Type Differential Difference Equation....Pages 649-653 On the Classical Lorenz System....Pages 655-661 Discrete Singular Integrals in a Half-Space....Pages 663-670 Geometrical Features of the Soliton Solution....Pages 671-677 Front Matter....Pages 679-679 Approximate Dual M-Frames Constructions: The Gabor Case....Pages 681-687 Matrices of Operators on Some Function Spaces....Pages 689-693 Rank-M Frame Multipliers and Optimality Criterions for Density Operators of Rank M....Pages 695-704 Audio Inpainting Using M-Frames....Pages 705-713 Wavelet Frames to Optimally Learn Functions on Diffusion Measure Spaces....Pages 715-720 Front Matter....Pages 721-721 A Study on Ateb Transform as a Generalization of Fourier Transform....Pages 723-731 Queue-Size Distribution in Energy-Saving Model Based on Multiple Vacation Policy....Pages 733-740 Front Matter....Pages 721-721 Automobile System Safety Based on the Model for Stochastic Networks with Dependent Service Times....Pages 741-750 Front Matter....Pages 751-751 Damage Prediction of the Femur with Postresection Defect....Pages 753-759 Representative Elements for Polydispersed Composites....Pages 761-767 Random Non-overlapping Walks of Disks on the Plane....Pages 769-775 Symbolic Computation of Conformal Mappings onto Slit Domains....Pages 777-783 On One Approach to the Simulation of the Periodontal Ligament Takes into Account Its Viscoelastic Properties....Pages 785-791 Biomechanical Effects of Maxillary Expansion in Cross-Bite Patients During Orthodontic Treatment with Hyrax Screw....Pages 793-799 Front Matter....Pages 801-801 On the Solvability of a Nonlinear Optimal Control Problem for the Thermal Processes Described by Fredholm Integro-Differential Equations....Pages 803-821 Exact Null-Controllability of Evolution Equations by Smooth Controls and Applications to Controllability of Interconnected Systems....Pages 823-829 On the Sum of Contractive Type of Mappings I: Maps on the Same Class....Pages 831-842 On ( α , ψ ) Contractions of Integral Type on Generalized Metric Spaces....Pages 843-854 Infinite Dimensional Stochastic Cauchy Problems in Ito and Differential Forms: Comparison of Solutions....Pages 855-863 Biomechanical Model of the Human Eye on the Base of Nonlinear Shell Theory....Pages 865-871 Back Matter....Pages 873-892