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Wandering Solutions of Delay Equations with Sine-Like Feedback
  • Language: en
  • Pages: 138

Wandering Solutions of Delay Equations with Sine-Like Feedback

This book is intended for graduate students and research mathematicians interested in mechanics of particle systems.

Quantum Linear Groups and Representations of $GL_n({\mathbb F}_q)$
  • Language: en
  • Pages: 127

Quantum Linear Groups and Representations of $GL_n({\mathbb F}_q)$

We give a self-contained account of the results originating in the work of James and the second author in the 1980s relating the representation theory of GL[n(F[q) over fields of characteristic coprime to q to the representation theory of "quantum GL[n" at roots of unity. The new treatment allows us to extend the theory in several directions. First, we prove a precise functorial connection between the operations of tensor product in quantum GL[n and Harish-Chandra induction in finite GL[n. This allows us to obtain a version of the recent Morita theorem of Cline, Parshall and Scott valid in addition for p-singular classes. From that we obtain simplified treatments of various basic known facts...

A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model
  • Language: en
  • Pages: 82

A Stability Index Analysis of 1-D Patterns of the Gray-Scott Model

This work is intended for graduate students and research mathematicians interested in partial differential equations.

Blowing Up of Non-Commutative Smooth Surfaces
  • Language: en
  • Pages: 157

Blowing Up of Non-Commutative Smooth Surfaces

This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.

Equivariant $E$-Theory for $C^*$-Algebras
  • Language: en
  • Pages: 101

Equivariant $E$-Theory for $C^*$-Algebras

This title examines the equivariant e-theory for c*-algebra, focusing on research carried out by Higson and Kasparov. Let A and B be C*-algebras which are equipped with continuous actions of a second countable, locally compact group G. We define a notion of equivariant asymptotic morphism, and use it to define equivariant E-theory groups EULG(A, B) which generalize the E-theory groups of Connes and Higson. We develop the basic properties of equivariant E-theory, including a composition product and six-term exact sequences in both variables, and apply our theory to the problem of calculating K-theory for group C*-algebras. Our main theorem gives a simple criterion for the assembly map of Baum and Connes to be an isomorphism. The result plays an important role in the work of Higson and Kasparov on the Bau m-Connes conjecture for groups which act isometrically and metrically properly on Hilbert space

Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra
  • Language: en
  • Pages: 456

Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra

This volume contains refereed papers on themes explored at the AMS-IMS-SIAM Summer Research Conference, Commutative Algebra: Syzygies, Multiplicities, and Birational Algebra, held at Mount Holyoke College in 1992. The conference featured a series of one-hour invited lectures on recent advances in commutative algebra and interactions with such areas as algebraic geometry, representation theory, and combinatorics. The major themes of the conference were tight closure Hilbert functions, birational algebra, free resolutions and the homological conjectures, Rees algebras, and local cohomology. With contributions by several leading experts in the field, this volume provides an excellent survey of current research in commutative algebra.

Frobenius Groups and Classical Maximal Orders
  • Language: en
  • Pages: 125

Frobenius Groups and Classical Maximal Orders

Introduction Lemmas on truncated group rings Groups of real quaternions Proof of the classification theorem Frobenius complements with core index 1 Frobenius complements with core index 4 Frobenius complements with core index 12 Frobenius complements with core index 24 Frobenius complements with core index 60 Frobenius complements with core index 120 Counting Frobenius complements Maximal orders Isomorphism classes of Frobenius groups with Abelian Frobenius kernel Concrete constructions of Frobenius groups Counting Frobenius groups with Abelian Frobenius kernel Isomorphism invariants for Frobenius complements Schur indices and finite subgroups of division rings Bibliography

Non-cooperative Equilibria of Fermi Systems with Long Range Interactions
  • Language: en
  • Pages: 173

Non-cooperative Equilibria of Fermi Systems with Long Range Interactions

The authors define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and make explicit the structure of (generalized) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, the authors give a first answer to an old open problem in mathematical physics--first addressed by Ginibre in 1968 within a different context--about the validity of the so-called Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, the authors' method provides a systematic way to study all its correlation functions at equilibrium and can thus be used to analyze the physics of long range interactions. Furthermore, the authors show that the thermodynamics of long range models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the non-cooperative equilibria of a zero-sum game, called here thermodynamic game.

Analytic Methods in Commutative Algebra
  • Language: en
  • Pages: 308

Analytic Methods in Commutative Algebra

  • Type: Book
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  • Published: 1982-04-28
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  • Publisher: CRC Press

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Weighted Bergman Spaces Induced by Rapidly Increasing Weights
  • Language: en
  • Pages: 136

Weighted Bergman Spaces Induced by Rapidly Increasing Weights

This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.