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The problem of enumerating maps (a map is a set of polygonal "countries" on a world of a certain topology, not necessarily the plane or the sphere) is an important problem in mathematics and physics, and it has many applications ranging from statistical physics,...
The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as:1) existence, uniqueness and...
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in...
This book is dedicated to study the inverse problem of ordinary differential equations, that is it focuses in finding all ordinary differential equations that satisfy a given set of properties. The Nambu bracket is the central tool in developing this approach. The...
This book presents a consistent development of the Kohn-Nirenberg type global quantization theory in the setting of graded nilpotent Lie groups in terms of their representations. It contains a detailed exposition of related background topics on homogeneous Lie groups,...
This book presents four survey articles on different topics in mathematical analysis that are closely linked to concepts and applications in physics. Specifically, it discusses global aspects of elliptic PDEs, Berezin-Toeplitz quantization, the stability of solitary...
This book presents, in his own words, the life of Hugo Steinhaus (1887–1972), noted Polish mathematician of Jewish background, educator, and mathematical popularizer. A student of Hilbert, a pioneer of the foundations of probability and game theory, and a contributor to...
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated. Three contributions give an insight on particular aspects of moduli problems. In the first of them,...
This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz (1646-1716) and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore...
This book provides an overview of the confluence of ideas in Turing’s era and work and examines the impact of his work on mathematical logic and theoretical computer science. It combines contributions by well-known scientists on the history and philosophy of...
This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper...
In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace...
In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the...
Over the last forty years, David Vogan has left an indelible imprint on the representation theory of reductive groups. His groundbreaking ideas have lead to deep advances in the theory of real and p-adic groups, and have forged lasting connections with other subjects,...
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical...
Reconstructing or approximating objects from seemingly incomplete information is a frequent challenge in mathematics, science, and engineering. A multitude of tools designed to recover hidden information are based on Shannon’s classical sampling theorem, a central...
This book features a series of lectures that explores three different fields in which functor homology (short for homological algebra in functor categories) has recently played a significant role. For each of these applications, the functor viewpoint provides both...
This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their...
The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump...
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