Mathematical analysis and applications. Selected topics

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Content: Cover Title Page Copyright Contents Preface About the Editors List of Contributors Chapter 1 Spaces of Asymptotically Developable Functions and Applications 1.1 Introduction and Some Notations 1.2 Strong Asymptotic Expansions 1.3 Monomial Asymptotic Expansions 1.4 Monomial Summability for Singularly Perturbed Differential Equations 1.5 Pfaffian Systems References Chapter 2 Duality for Gaussian Processes from Random Signed Measures 2.1 Introduction 2.2 Reproducing Kernel Hilbert Spaces (RKHSs) in the Measurable Category 2.3 Applications to Gaussian Processes. 2.4 Choice of Probability Space2.5 A Duality 2.A Stochastic Processes 2.B Overview of Applications of RKHSs Acknowledgments References Chapter 3 Many-Body Wave Scattering Problems for Small Scatterers and Creating Materials with a Desired Refraction Coefficient 3.1 Introduction 3.2 Derivation of the Formulas for One-Body Wave Scattering Problems 3.3 Many-Body Scattering Problem 3.3.1 The Case of Acoustically Soft Particles 3.3.2 Wave Scattering by Many Impedance Particles 3.4 Creating Materials with a Desired Refraction Coefficient. 3.5 Scattering by Small Particles Embedded in an Inhomogeneous Medium3.6 Conclusions References Chapter 4 Generalized Convex Functions and their Applications 4.1 Brief Introduction 4.2 Generalized E-Convex Functions 4.3 Ea- Epigraph 4.4 Generalized s-Convex Functions 4.5 Applications to Special Means References Chapter 5 Some Properties and Generalizations of the Catalan, Fuss, and Fuss-Catalan Numbers 5.1 The Catalan Numbers 5.1.1 A Definition of the Catalan Numbers 5.1.2 The History of the Catalan Numbers 5.1.3 A Generating Function of the Catalan Numbers. 5.1.4 Some Expressions of the Catalan Numbers5.1.5 Integral Representations of the Catalan Numbers 5.1.6 Asymptotic Expansions of the Catalan Function 5.1.7 Complete Monotonicity of the Catalan Numbers 5.1.8 Inequalities of the Catalan Numbers and Function 5.1.9 The Bell Polynomials of the Second Kind and the Bessel Polynomials 5.2 The Catalan-Qi Function 5.2.1 The Fuss Numbers 5.2.2 A Definition of the Catalan-Qi Function 5.2.3 Some Identities of the Catalan-Qi Function 5.2.4 Integral Representations of the Catalan-Qi Function 5.2.5 Asymptotic Expansions of the Catalan-Qi Function. 5.2.6 Complete Monotonicity of the Catalan-Qi Function5.2.7 Schur-Convexity of the Catalan-Qi Function 5.2.8 Generating Functions of the Catalan-Qi Numbers 5.2.9 A Double Inequality of the Catalan-Qi Function 5.2.10 The q-Catalan-Qi Numbers and Properties 5.2.11 The Catalan Numbers and the k-Gamma and k-Beta Functions 5.2.12 Series Identities Involving the Catalan Numbers 5.3 The Fuss-Catalan Numbers 5.3.1 A Definition of the Fuss-Catalan Numbers 5.3.2 A Product-Ratio Expression of the Fuss-Catalan Numbers 5.3.3 Complete Monotonicity of the Fuss-Catalan Numbers.