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The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nashâ€™s legendary mathematical achievements.

The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer science, and more. Extensive discussions surrounding the progress made for each problem are designed to reach a wide community of readers, from graduate students and established research mathematicians to physicists, computer scientists, economists, and research scientists who are looking to develop essential and modern new methods and theories to solve a variety of open problems.- Author:
**John Forbes Nash, Jr., Michael Th. Rassias (eds.)** - Year:
**2016** - Publisher:
**Springer International Publishing** - Language:
**English** - ISBN:
**978-3-319-32160-8,978-3-319-32162-2**

- File size:
**8 398 707** - Format:
**pdf**

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Throughout this book, we discuss some open problems in various branches of science, including mathematics, theoretical physics, astrophysics, geophysics etc. It is of our hope that some of the problems discussed in this book will find their place either i...

Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures investigates third order rational difference equations by detailing the behavior of 225 special cases including boundedness, periodic nature, the global asymptotic st...

This is the first in a series of volumes, which provide an extensive overview of conjectures and open problems in graph theory. The readership of each volume is geared toward graduate students who may be searching for research ideas. However, the well-est...

One of the most challenging topics in applied mathematics is the development of the theory of nonlinear partial different equations. Many problems in mechanics, geometry, and probability lead to such equations when formulated in mathematical terms. Yet de...

This book constitutes the thoroughly refereed post-conference proceedings of the IFIP WG 11.4 International Workshop on Open Problems in Network Security, iNetSec 2015, held in Zurich, Switzerland, in October 2015. iNetSec is the main workshop of the IFIP...

This is an collection of some easily-formulated problems that remain open in the study of the geometry and analysis of Banach spaces. Assuming the reader has a working familiarity with the basic results of Banach space theory, the authors focus on concept...

Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically ri...

People delight in working on problems "because they are there," for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss...

People delight in working on problems "because they are there," for the sheer pleasure of meeting a challenge. This is a book full of such delights. In it, Murray S. Klamkin brings together 75 original USA Mathematical Olympiad (USAMO) problems for yearss...

Some in the social sciences argue that the same logic applies to both qualitative and quantitative methods. In A Tale of Two Cultures, Gary Goertz and James Mahoney demonstrate that these two paradigms constitute different cultures, each internally cohere...

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Today, more than 50% of the worldâ€™s population lives in cities and is subject to particular environmental and economic impacts against the backdrop of an evolving planetary crisis. This book explores the intimate relationship between the quality of life o...

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Automate Windows administration tasks with ease by learning the fundamentals of Windows PowerShell 3.0. Led by a Windows PowerShell expert, you'll learn must-know concepts and techniques through easy-to-follow explanations, examples, and exercises. Once y...