Contemporary computational mathematics - a celebration of the 80th birthday of Ian Sloan

This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life. Content: Intro Preface Family Perspectives Jan Sloan (Wife) Jenni Johnson (Daughter) Tony Sloan (Son) Sam Johnson (Grandson) Gus Sloan (Grandson) Mack Sloan (Grandson) Corrie Sloan (Grandson, Aged 12) Kiara (Button) Sloan (Granddaughter, Aged 9) Family A Fortunate Scientific Life Publications of Professor Sloan Books Edited Books, Special Issues, and Conference Proceedings Journal Articles, Book Chapters, and Conference Proceedings Papers Contents About the Editors On Quasi-Energy-Spectra, Pair Correlations of Sequences and Additive Combinatorics 1 Introduction 2 New Results. 3 Auxiliary Results4 Proof of Theorem 3 References Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains 1 Introduction 2 The Integral Fractional Laplacian and Its Weak Formulation 3 Finite Element Approximation of the Fractional Poisson Equation 4 Computation of Entries of the Stiffness Matrix 4.1 Reduction to Smooth Integrals 4.2 Determining the Order of the Quadrature Rules 5 Solving the Linear Systems 6 Sparse Approximation of the Matrix 7 Applications 7.1 Fractional Poisson Equation 7.2 Fractional Heat Equation. 7.3 Fractional Reaction-Diffusion Systems8 Conclusion Appendix 1: Derivation of Expressions for Singular Contributions Appendix 2: Proof of Consistency Error Due to Quadrature References Irregularities of Distributions and Extremal Sets in Combinatorial Complexity Theory 1 Introduction and Statement of Results 2 The ``Cheap Proof'' of Theorem 1 in the Case n e" d2 3 The ``Cheap Proof'' of Theorem 1 in the General Case 4 Point Sets Which Prohibit the ``Cheap Argument'', and Combinatorial Complexity Theory Appendix: Proof of Inequality (8) References. Importance Sampling and Stratification for Copula Models1 Introduction 2 Motivation and Background 2.1 Archimedean Copulas and Sampling Methods 2.1.1 Conditional Distribution Method 2.1.2 Marshall-Olkin Algorithm 2.2 Quasi-Monte Carlo and Copula Models 3 Importance Sampling for Copula Models 4 Importance Sampling Algorithm for Archimedean Copulas 4.1 Stratified Sampling Alternative to Importance Sampling 5 Variance Analysis and Calibration Method 6 Numerical Examples Appendix References A Spectral Method for the Biharmonic Equation 1 Introduction 2 Preliminaries. 2.1 Approximation Space3 The Numerical Method 3.1 Evaluating the Integrals 4 Numerical Examples 4.1 Planar Examples 4.2 A Three Dimensional Example 5 Nonhomogeneous Boundary Conditions References Quasi-Monte Carlo for an Integrand with a Singularity Along a Diagonal in the Square 1 Introduction 2 Background 3 Error Bounds 4 Extension Based Approaches 5 Transformation 6 Discussion References There Is No Strongly Regular Graph with Parameters(460, 153,32,60) 1 Introduction 2 Proof of Theorem 1 3 Conclusion References.