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Abelian Groups, Module Theory, and Topology
  • Language: en
  • Pages: 472

Abelian Groups, Module Theory, and Topology

  • Type: Book
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  • Published: 2019-05-31
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  • Publisher: CRC Press

Features a stimulating selection of papers on abelian groups, commutative and noncommutative rings and their modules, and topological groups. Investigates currently popular topics such as Butler groups and almost completely decomposable groups.

Norms on Possibilities. I: Forcing with Trees and Creatures
  • Language: en
  • Pages: 186

Norms on Possibilities. I: Forcing with Trees and Creatures

This book is intended for graduate students and research mathematicians interested in mathematical logic and foundations.

Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
  • Language: en
  • Pages: 127

Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems

In this work, the author examines the following: When the Hamiltonian system $m i \ddot{q} i + (\partial V/\partial q i) (t,q) =0$ with periodicity condition $q(t+T) = q(t),\; \forall t \in \germ R$ (where $q {i} \in \germ R{\ell}$, $\ell \ge 3$, $1 \le i \le n$, $q = (q {1},...,q {n})$ and $V = \sum V {ij}(t,q {i}-q {j})$ with $V {ij}(t,\xi)$ $T$-periodic in $t$ and singular in $\xi$ at $\xi = 0$) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity. This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

Categories of Operator Modules (Morita Equivalence and Projective Modules)
  • Language: en
  • Pages: 109

Categories of Operator Modules (Morita Equivalence and Projective Modules)

We employ recent advances in the theory of operator spaces, also known as quantized functional analysis, to provide a context in which one can compare categories of modules over operator algebras that are not necessarily self-adjoint. We focus our attention on the category of Hilbert modules over an operator algebra and on the category of operator modules over an operator algebra. The module operations are assumed to be completely bounded - usually, completely contractive. Wedevelop the notion of a Morita context between two operator algebras A and B. This is a system (A,B,{} {A}X {B},{} {B} Y {A},(\cdot,\cdot),[\cdot,\cdot]) consisting of the algebras, two bimodules {A}X {B and {B}Y {A} and...

Limit Theorems for Functionals of Ergodic Markov Chains with General State Space
  • Language: en
  • Pages: 225

Limit Theorems for Functionals of Ergodic Markov Chains with General State Space

This book is intended for graduate students and research mathematicians working probability theory and statistics.

Measure Theory and Nonlinear Evolution Equations
  • Language: en
  • Pages: 456

Measure Theory and Nonlinear Evolution Equations

This text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity. A comprehensive discussion of applications to quasilinear parabolic and hyperbolic problems is provided.

Controllability, Stabilization, and the Regulator Problem for Random Differential Systems
  • Language: en
  • Pages: 63

Controllability, Stabilization, and the Regulator Problem for Random Differential Systems

This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.

Tensor Products and Independent Sums of $\mathcal L_p$-Spaces, $1
  • Language: en
  • Pages: 90

Tensor Products and Independent Sums of $\mathcal L_p$-Spaces, $1

Two methods of constructing infinitely many isomorphically distinct $\mathcal L_p$-spaces have been published. In this volume, the author shows that these constructions yield very different spaces and in the process develop methods for dealing with these spaces from the isomorphic viewpoint.

The Defect Relation of Meromorphic Maps on Parabolic Manifolds
  • Language: en
  • Pages: 95

The Defect Relation of Meromorphic Maps on Parabolic Manifolds

This book is intended for graduate students and research mathematicians working in several complex variables and analytic spaces.

Infinite Groups 1994
  • Language: en
  • Pages: 356

Infinite Groups 1994

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.