Basic Global Relative Invariants For Nonlinear Differential Equations
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Basic Global Relative Invariants For Nonlinear Differential Equations
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Author : Roger Chalkley
language : en
Publisher:
Release Date : 2007
Basic Global Relative Invariants For Nonlinear Differential Equations written by Roger Chalkley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Differential equations, Nonlinear categories.
Invariant Differential Operators For Quantum Symmetric Spaces
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Author : Gail Letzter
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Invariant Differential Operators For Quantum Symmetric Spaces written by Gail Letzter and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces
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Author : Volkmar Liebscher
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-04-10
Random Sets And Invariants For Type Ii Continuous Tensor Product Systems Of Hilbert Spaces written by Volkmar Liebscher and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-10 with Mathematics categories.
In a series of papers Tsirelson constructed from measure types of random sets or (generalised) random processes a new range of examples for continuous tensor product systems of Hilbert spaces introduced by Arveson for classifying $E_0$-semigroups upto cocycle conjugacy. This paper starts from establishing the converse. So the author connects each continuous tensor product system of Hilbert spaces with measure types of distributions of random (closed) sets in $[0,1]$ or $\mathbb R_+$. These measure types are stationary and factorise over disjoint intervals. In a special case of this construction, the corresponding measure type is an invariant of the product system. This shows, completing in a more systematic way the Tsirelson examples, that the classification scheme for product systems into types $\mathrm{I}_n$, $\mathrm{II}_n$ and $\mathrm{III}$ is not complete. Moreover, based on a detailed study of this kind of measure types, the author constructs for each stationary factorising measure type a continuous tensor product system of Hilbert spaces such that this measure type arises as the before mentioned invariant.
Index Theory Eta Forms And Deligne Cohomology
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Author : Ulrich Bunke
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-03-06
Index Theory Eta Forms And Deligne Cohomology written by Ulrich Bunke and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-06 with Mathematics categories.
This paper sets up a language to deal with Dirac operators on manifolds with corners of arbitrary codimension. In particular the author develops a precise theory of boundary reductions. The author introduces the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator. Given a Dirac operator on a manifold with boundary faces the author uses the tamings of its boundary reductions in order to turn the operator into a Fredholm operator. Its index is an obstruction against extending the taming from the boundary to the interior. In this way he develops an inductive procedure to associate Fredholm operators to Dirac operators on manifolds with corners and develops the associated obstruction theory.
A Proof Of Alon S Second Eigenvalue Conjecture And Related Problems
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Author : Joel Friedman
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
A Proof Of Alon S Second Eigenvalue Conjecture And Related Problems written by Joel Friedman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A $d$-regular graph has largest or first (adjacency matrix) eigenvalue $\lambda_1=d$. Consider for an even $d\ge 4$, a random $d$-regular graph model formed from $d/2$ uniform, independent permutations on $\{1,\ldots,n\}$. The author shows that for any $\epsilon>0$ all eigenvalues aside from $\lambda_1=d$ are bounded by $2\sqrt{d-1}\;+\epsilon$ with probability $1-O(n^{-\tau})$, where $\tau=\lceil \bigl(\sqrt{d-1}\;+1\bigr)/2 \rceil-1$. He also shows that this probability is at most $1-c/n^{\tau'}$, for a constant $c$ and a $\tau'$ that is either $\tau$ or $\tau+1$ (``more often'' $\tau$ than $\tau+1$). He proves related theorems for other models of random graphs, including models with $d$ odd.
Spinor Genera In Characteristic 2
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Author : Yuanhua Wang
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Spinor Genera In Characteristic 2 written by Yuanhua Wang and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The purpose of this paper is to establish the spinor genus theory of quadratic forms over global function fields in characteristic 2. The first part of the paper computes the integral spinor norms and relative spinor norms. The second part of the paper gives a complete answer to the integral representations of one quadratic form by another with more than four variables over a global function field in characteristic 2.
Brownian Brownian Motion I
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Author : Nikolai Chernov
language : en
Publisher: American Mathematical Soc.
Release Date : 2009-03-06
Brownian Brownian Motion I written by Nikolai Chernov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-06 with Science categories.
A classical model of Brownian motion consists of a heavy molecule submerged into a gas of light atoms in a closed container. In this work the authors study a 2D version of this model, where the molecule is a heavy disk of mass $M \gg 1$ and the gas is represented by just one point particle of mass $m=1$, which interacts with the disk and the walls of the container via elastic collisions. Chaotic behavior of the particles is ensured by convex (scattering) walls of the container. The authors prove that the position and velocity of the disk, in an appropriate time scale, converge, as $M\to\infty$, to a Brownian motion (possibly, inhomogeneous); the scaling regime and the structure of the limit process depend on the initial conditions. The proofs are based on strong hyperbolicity of the underlying dynamics, fast decay of correlations in systems with elastic collisions (billiards), and methods of averaging theory.
Minimal Resolutions Via Algebraic Discrete Morse Theory
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Author : Michael Jöllenbeck
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Minimal Resolutions Via Algebraic Discrete Morse Theory written by Michael Jöllenbeck and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Language Arts & Disciplines categories.
"January 2009, volume 197, number 923 (end of volume)."
The Beltrami Equation
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Author : Tadeusz Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
The Beltrami Equation written by Tadeusz Iwaniec and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The measurable Riemann Mapping Theorem (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the state of the art as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.
Differential Geometry Lie Groups And Symmetric Spaces Over General Base Fields And Rings
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Author : Wolfgang Bertram
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Differential Geometry Lie Groups And Symmetric Spaces Over General Base Fields And Rings written by Wolfgang Bertram and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.