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34479 results in Mathematics (general)

Page 99 of 1724

  • 12 - Infinite Orbits and Quitting Games

  • Eilon Solan, Tel-Aviv University
  • Book:
    A Course in Stochastic Game Theory
    Published online:
    05 May 2022
    Print publication:
    26 May 2022, pp 211-235

  • Summary

    In this chapter, we define infinite orbits and show how to approximate such orbits. We prove that for every function that has no fixed point there is an approximate infinite orbit with unbounded variation, and we use this result to show that a certain class of quitting games admits undiscounted $\ep$-equilibria.

  • 5 - Two-Player Zero-Sum Discounted Games

  • Eilon Solan, Tel-Aviv University
  • Book:
    A Course in Stochastic Game Theory
    Published online:
    05 May 2022
    Print publication:
    26 May 2022, pp 62-81

  • Summary

    In this chapter, we extend the notion of discounted payoff to the model of stochastic games, and we define the concept of discounted equilibrium. We then prove that every two-player zero-sum stochastic game admits a discounted value, and that each player has a stationary discounted optimal strategy. The proof uses the same tools we employed in Chapter~\ref{section:mdp} to prove that in Markov decision problems the decision maker has a stationary discounted optimal strategy.

    We finally prove that the discounted value is continuous in the parameters of the game, namely the payoff function, the transition function, and the discount factor.

  • 14 - Well-Posed Input/State/Output Systems

  • Damir Z. Arov, Olof J. Staffans, Åbo Akademi University, Finland
  • Book:
    Linear State/Signal Systems
    Published online:
    05 May 2022
    Print publication:
    26 May 2022, pp 816-906

  • Summary

    This chapter is devoted to the study of well-posed i/s/o systems. These systems are assumed to be solvable and to satisfy a well-posedness condition that guarantees the existence of a unique future generalized trajectory for any given initial state and input function that belongs locally to L2. Although it is not obvious from the definition, every well-posed i/s/o system is internally well-posed, i.e., it has a nonempty resolvent set-and its main operator generates a C0 semigroup. Semi-bounded i/s/o systems are well-posed. The class of well-posed i/s/o systems is the largest class in this book for which can to prove connections between time and frequency domain results that are analogous to those established in Chapter 8 for the class of semi-bounded i/s/o systems. At the end of this chapter we define the notion of a scattering passive system, and show that scattering passive systems are well-posed. A scattering passive system is characterized by the fact that it is regular, and its system operator is maximally scattering dissipative. Well-posed s/s systems are discussed in Chapter 15.

Fourier Analysis
  • T. W. Körner
  • Foreword by Terence Tao
  • Published online:
    19 May 2022
    Print publication:
    09 June 2022
  • Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
Article has an altmetric score of 2
Article has an altmetric score of 2

Transcendental Number Theory
  • Alan Baker
  • Foreword by David Masser
  • Published online:
    19 May 2022
    Print publication:
    09 June 2022
  • First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue–Siegel–Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindžuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.

Attractors for Semigroups and Evolution Equations
  • Olga A. Ladyzhenskaya
  • Foreword by Gregory A. Seregin, Varga K. Kalantarov, Sergey V. Zelik
  • Published online:
    19 May 2022
    Print publication:
    09 June 2022
  • In this volume, Olga A. Ladyzhenskaya expands on her highly successful 1991 Accademia Nazionale dei Lincei lectures. The lectures were devoted to questions of the behaviour of trajectories for semigroups of nonlinear bounded continuous operators in a locally non-compact metric space and for solutions of abstract evolution equations. The latter contain many initial boundary value problems for dissipative partial differential equations. This work, for which Ladyzhenskaya was awarded the Russian Academy of Sciences' Kovalevskaya Prize, reflects the high calibre of her lectures; it is essential reading for anyone interested in her approach to partial differential equations and dynamical systems. This edition, reissued for her centenary, includes a new technical introduction, written by Gregory A. Seregin, Varga K. Kalantarov and Sergey V. Zelik, surveying Ladyzhenskaya's works in the field and subsequent developments influenced by her results.

Surveys in Combinatorics 2022
  • Edited by Anthony Nixon, Sean Prendiville
  • Published online:
    13 May 2022
    Print publication:
    09 June 2022
  • This volume contains eight survey articles by the invited speakers of the 29th British Combinatorial Conference, held at Lancaster University in July 2022. Each article provides an overview of recent developments in a current hot research topic in combinatorics. These topics span graphs and hypergraphs, Latin squares, linear programming, finite fields, extremal combinatorics, Ramsey theory, graph minors and tropical geometry. The authors are among the world's foremost researchers on their respective topics but their surveys are aimed at nonspecialist readers: they are written clearly with little prior knowledge assumed and with pointers to the wider literature. Taken together these surveys give a snapshot of the research frontier in contemporary combinatorics, making the latest developments accessible to researchers and graduate students in mathematics and theoretical computer science with an interest in combinatorics and helping them to keep abreast of the field.
Article has an altmetric score of 3
Article has an altmetric score of 3

Page 99 of 1724