Books in the Tutorials, Schools, and Workshops in the Mathematical Sciences series

This volume guides early-career researchers through recent breakthroughs in mathematics and physics as related to general relativity. Chapters are based on courses and lectures given at the July 2019 Domoschool, International Alpine School in Mathematics and Physics, held in Domodossola, Italy, which was titled ¿Einstein Equations: Physical and Mathematical Aspects of General Relativity¿. Structured in two parts, the first features four courses from prominent experts on topics such as local energy in general relativity, geometry and analysis in black hole spacetimes, and antimatter gravity. The second part features a variety of papers based on talks given at the summer school, including topics like:Quantum ergosphereGeneral relativistic Poynting-Robertson effect modellingNumerical relativityLength-contraction in curved spacetimeClassicality from an inhomogeneous universeEinstein Equations: Local Energy, Self-Force, and Fields in General Relativity will be a valuable resource for students and researchers in mathematics and physicists interested in exploring how their disciplines connect to general relativity.

This book presents four survey articles on various aspects of open quantum systems, specifically addressing quantum Markovian processes, Feller semigroups and nonequilibrium dynamics.

Part I: Introduction to Orthogonal Polynomials.- An Introduction to Orthogonal Polynomials.- Classical Continuous Orthogonal Polynomials.- Generating Functions and Hypergeometric Representations of Classical Continuous Orthogonal Polynomials.- Properties and Applications of the Zeros of Classical Continuous Orthogonal Polynomials.- Inversion, Multiplication and Connection Formulae of Classical Continuous Orthogonal Polynomials.- Classical Orthogonal Polynomials of a Discrete and a q-Discrete Variable.- Computer Algebra, Power Series and Summation.- On the Solutions of Holonomic Third-Order Linear Irreducible Differential Equations in Terms of Hypergeometric Functions.- The Gamma Function.- Part II: Recent Research Topics in Orthogonal Polynomials and Applications.- Hypergeometric Multivariate Orthogonal Polynomials.- Signal Processing, Orthogonal Polynomials, and Heun Equations.- Some Characterization Problems Related to Sheffer Polynomial Sets.- From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals.- Two Variable Orthogonal Polynomials and Fej├⌐r-Riesz Factorization.- Exceptional Orthogonal Polynomials and Rational Solutions to Painlev├⌐ Equations.- (R, p, q)-Rogers-Szeg├╢ and Hermite Polynomials, and Induced Deformed Quantum Algebras.- Zeros of Orthogonal Polynomials.- Properties of Certain Classes of Semiclassical Orthogonal Polynomials.- Orthogonal Polynomials and Computer Algebra.- Spin Chains, Graphs and State Revival.- An Introduction to Special Functions with Some Applications to Quantum Mechanics.- Orthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlev├⌐ Equations.