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This book collects papers based on the XXXVI Białowieża Workshop on Geometric Methods in Physics, 2017. The Workshop, which attracts a community of experts active at the crossroads of mathematics and physics, represents a major annual event in the field. Based on presentations given at the Workshop, the papers gathered here are previously unpublished, at the cutting edge of current research, and primarily grounded in geometry and analysis, with applications to classical and quantum physics. In addition, a Special Session was dedicated to S. Twareque Ali, a distinguished mathematical physicist at Concordia University, Montreal, who passed away in January 2016. For the past six years, the Białowieża Workshops have been complemented by a School on Geometry and Physics, comprising a series of advanced lectures for graduate students and early-career researchers. The extended abstracts of this year’s lecture series are also included here. The unique character of the Workshop-and-School series is due in part to the venue: a famous historical, cultural and environmental site in the Białowieża forest, a UNESCO World Heritage Centre in eastern Poland. Lectures are given in the Nature and Forest Museum, and local traditions are interwoven with the scientific activities.

Geometric quantization --- Global analysis. --- Group theory. --- Functions, special. --- Geometry. --- Global Analysis and Analysis on Manifolds. --- Group Theory and Generalizations. --- Special Functions. --- Mathematics --- Euclid's Elements --- Special functions --- Mathematical analysis --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Global analysis (Mathematics). --- Manifolds (Mathematics). --- Special functions. --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic

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This book explores several important aspects of recent developments in the interdisciplinary applications of mathematical analysis (MA), and highlights how MA is now being employed in many areas of scientific research. Each of the 23 carefully reviewed chapters was written by experienced expert(s) in respective field, and will enrich readers’ understanding of the respective research problems, providing them with sufficient background to understand the theories, methods and applications discussed. The book’s main goal is to highlight the latest trends and advances, equipping interested readers to pursue further research of their own. Given its scope, the book will especially benefit graduate and PhD students, researchers in the applied sciences, educators, and engineers with an interest in recent developments in the interdisciplinary applications of mathematical analysis.

Mathematical analysis. --- Differential equations, partial. --- Integral equations. --- Differential Equations. --- Operator theory. --- Functional analysis. --- Functions, special. --- Partial Differential Equations. --- Integral Equations. --- Ordinary Differential Equations. --- Operator Theory. --- Functional Analysis. --- Special Functions. --- Functional analysis --- 517.91 Differential equations --- Differential equations --- Equations, Integral --- Functional equations --- Special functions --- Mathematical analysis --- Partial differential equations --- Functional calculus --- Calculus of variations --- Integral equations --- Partial differential equations. --- Differential equations. --- Special functions.

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This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks. One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

Sequences (Mathematics). --- Functions, special. --- Number theory. --- Mathematics. --- Mathematical physics. --- Engineering mathematics. --- Sequences, Series, Summability. --- Special Functions. --- Number Theory. --- Real Functions. --- Mathematical Methods in Physics. --- Engineering Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Math --- Science --- Number study --- Numbers, Theory of --- Algebra --- Special functions --- Mathematical sequences --- Numerical sequences --- Mathematics --- Integrals. --- Calculus, Integral --- Special functions. --- Functions of real variables. --- Physics. --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Real variables --- Functions of complex variables

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Fractional equations and models play an essential part in the description of anomalous dynamics in complex systems. Recent developments in the modeling of various physical, chemical and biological systems have clearly shown that fractional calculus is not just an exotic mathematical theory, as it might have once seemed. The present book seeks to demonstrate this using various examples of equations and models with fractional and generalized operators. Intended for students and researchers in mathematics, physics, chemistry, biology and engineering, it systematically offers a wealth of useful tools for fractional calculus.

Fractional differential equations. --- Extraordinary differential equations --- Differential equations --- Fractional calculus --- Mathematical physics. --- Physics. --- Probabilities. --- System theory. --- Partial differential equations. --- Special functions. --- Mathematical Physics. --- Mathematical Methods in Physics. --- Probability Theory and Stochastic Processes. --- Complex Systems. --- Partial Differential Equations. --- Special Functions. --- Special functions --- Mathematical analysis --- Partial differential equations --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Systems, Theory of --- Systems science --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Physical mathematics --- Physics --- Philosophy

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During the past four decades or so, various operators of fractional calculus, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdelyi–Kober, Liouville–Caputo, and so on, have been found to be remarkably popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integro-differential equations, together with the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.

applied mathematics --- fractional derivatives --- fractional derivatives associated with special functions of mathematical physics --- fractional integro-differential equations --- operators of fractional calculus --- identities and inequalities involving fractional integrals --- fractional differintegral equations --- chaos and fractional dynamics --- fractional differential --- fractional integrals