N Harmonic Mappings Between Annuli

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N Harmonic Mappings Between Annuli

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Author : Tadeusz Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

N Harmonic Mappings Between Annuli 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 2012 with Mathematics categories.

Iwaniec and Onninen (both mathematics, Syracuse U., US) address concrete questions regarding energy minimal deformations of annuli in Rn. One novelty of their approach is that they allow the mappings to slip freely along the boundaries of the domains, where it is most difficult to establish the existence, uniqueness, and invertibility properties of the extremal mappings. At the core of the matter, they say, is the underlying concept of free Lagrangians. After an introduction, they cover in turn principal radial n-harmonics, and the n-harmonic energy. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).

An Introduction To The Theory Of Higher Dimensional Quasiconformal Mappings

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Author : Frederick W. Gehring
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-05-03

An Introduction To The Theory Of Higher Dimensional Quasiconformal Mappings written by Frederick W. Gehring 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 2017-05-03 with Conformal mapping categories.

This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background. This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.

Complex Analysis And Dynamical Systems Iii

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Author : Mark Lʹvovich Agranovskiĭ
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Complex Analysis And Dynamical Systems Iii written by Mark Lʹvovich Agranovskiĭ 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 papers in this volume cover a wide variety of topics in the geometric theory of functions of one and several complex variables, including univalent functions, conformal and quasiconformal mappings, minimal surfaces, and dynamics in infinite-dimensional spaces. In addition, there are several articles dealing with various aspects of approximation theory and partial differential equations. Taken together, the articles collected here provide the reader with a panorama of activity in complex analysis, drawn by a number of leading figures in the field.

Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N

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Author : Aleksandr Sergeevich Kleshchëv
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Modular Branching Rules For Projective Representations Of Symmetric Groups And Lowering Operators For The Supergroup Q N written by Aleksandr Sergeevich Kleshchëv 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 2012 with Mathematics categories.

There are two approaches to projective representation theory of symmetric and alternating groups, which are powerful enough to work for modular representations. One is based on Sergeev duality, which connects projective representation theory of the symmetric group and representation theory of the algebraic supergroup $Q(n)$ via appropriate Schur (super)algebras and Schur functors. The second approach follows the work of Grojnowski for classical affine and cyclotomic Hecke algebras and connects projective representation theory of symmetric groups in characteristic $p$ to the crystal graph of the basic module of the twisted affine Kac-Moody algebra of type $A_{p-1}^{(2)}$. The goal of this work is to connect the two approaches mentioned above and to obtain new branching results for projective representations of symmetric groups.

The Kohn Sham Equation For Deformed Crystals

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Author : Weinan E
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-25

The Kohn Sham Equation For Deformed Crystals written by Weinan E 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 2013-01-25 with Mathematics categories.

The solution to the Kohn-Sham equation in the density functional theory of the quantum many-body problem is studied in the context of the electronic structure of smoothly deformed macroscopic crystals. An analog of the classical Cauchy-Born rule for crystal lattices is established for the electronic structure of the deformed crystal under the following physical conditions: (1) the band structure of the undeformed crystal has a gap, i.e. the crystal is an insulator, (2) the charge density waves are stable, and (3) the macroscopic dielectric tensor is positive definite. The effective equation governing the piezoelectric effect of a material is rigorously derived. Along the way, the authors also establish a number of fundamental properties of the Kohn-Sham map.

Pseudo Differential Operators With Discontinuous Symbols Widom S Conjecture

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Author : Aleksandr Vladimirovich Sobolev
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26

Pseudo Differential Operators With Discontinuous Symbols Widom S Conjecture written by Aleksandr Vladimirovich Sobolev 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 2013-02-26 with Mathematics categories.

Relying on the known two-term quasiclassical asymptotic formula for the trace of the function $f(A)$ of a Wiener-Hopf type operator $A$ in dimension one, in 1982 H. Widom conjectured a multi-dimensional generalization of that formula for a pseudo-differential operator $A$ with a symbol $a(\mathbf{x}, \boldsymbol{\xi})$ having jump discontinuities in both variables. In 1990 he proved the conjecture for the special case when the jump in any of the two variables occurs on a hyperplane. The present paper provides a proof of Widom's Conjecture under the assumption that the symbol has jumps in both variables on arbitrary smooth bounded surfaces.

Potential Wadge Classes

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Author : Dominique Lecomte
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-01-25

Potential Wadge Classes written by Dominique Lecomte 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 2013-01-25 with Mathematics categories.

Let $\bf\Gamma$ be a Borel class, or a Wadge class of Borel sets, and $2\!\leq\! d\!\leq\!\omega$ be a cardinal. A Borel subset $B$ of ${\mathbb R}^d$ is potentially in $\bf\Gamma$ if there is a finer Polish topology on $\mathbb R$ such that $B$ is in $\bf\Gamma$ when ${\mathbb R}^d$ is equipped with the new product topology. The author provides a way to recognize the sets potentially in $\bf\Gamma$ and applies this to the classes of graphs (oriented or not), quasi-orders and partial orders.

Characterization And Topological Rigidity Of Nobeling Manifolds

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Author : Andrzej Nagórko
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-04-22

Characterization And Topological Rigidity Of Nobeling Manifolds written by Andrzej Nagórko 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 2013-04-22 with Mathematics categories.

The author develops a theory of Nobeling manifolds similar to the theory of Hilbert space manifolds. He shows that it reflects the theory of Menger manifolds developed by M. Bestvina and is its counterpart in the realm of complete spaces. In particular the author proves the Nobeling manifold characterization conjecture.

Character Identities In The Twisted Endoscopy Of Real Reductive Groups

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Author : Paul Mezo
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26

Character Identities In The Twisted Endoscopy Of Real Reductive Groups written by Paul Mezo 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 2013-02-26 with Mathematics categories.

Suppose $G$ is a real reductive algebraic group, $\theta$ is an automorphism of $G$, and $\omega$ is a quasicharacter of the group of real points $G(\mathbf{R})$. Under some additional assumptions, the theory of twisted endoscopy associates to this triple real reductive groups $H$. The Local Langlands Correspondence partitions the admissible representations of $H(\mathbf{R})$ and $G(\mathbf{R})$ into $L$-packets. The author proves twisted character identities between $L$-packets of $H(\mathbf{R})$ and $G(\mathbf{R})$ comprised of essential discrete series or limits of discrete series.

A Study Of Singularities On Rational Curves Via Syzygies

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Author : David A. Cox
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26

A Study Of Singularities On Rational Curves Via Syzygies written by David A. Cox 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 2013-02-26 with Mathematics categories.

Consider a rational projective curve $\mathcal{C}$ of degree $d$ over an algebraically closed field $\pmb k$. There are $n$ homogeneous forms $g_{1},\dots, g_{n}$ of degree $d$ in $B=\pmb k[x, y]$ which parameterize $\mathcal{C}$ in a birational, base point free, manner. The authors study the singularities of $\mathcal{C}$ by studying a Hilbert-Burch matrix $\varphi$ for the row vector $[g_{1},\dots, g_{n}]$. In the ``General Lemma'' the authors use the generalized row ideals of $\varphi$ to identify the singular points on $\mathcal{C}$, their multiplicities, the number of branches at each singular point, and the multiplicity of each branch. Let $p$ be a singular point on the parameterized planar curve $\mathcal{C}$ which corresponds to a generalized zero of $\varphi$. In the `'triple Lemma'' the authors give a matrix $\varphi'$ whose maximal minors parameterize the closure, in $\mathbb{P}^{2}$, of the blow-up at $p$ of $\mathcal{C}$ in a neighborhood of $p$. The authors apply the General Lemma to $\varphi'$ in order to learn about the singularities of $\mathcal{C}$ in the first neighborhood of $p$. If $\mathcal{C}$ has even degree $d=2c$ and the multiplicity of $\mathcal{C}$ at $p$ is equal to $c$, then he applies the Triple Lemma again to learn about the singularities of $\mathcal{C}$ in the second neighborhood of $p$. Consider rational plane curves $\mathcal{C}$ of even degree $d=2c$. The authors classify curves according to the configuration of multiplicity $c$ singularities on or infinitely near $\mathcal{C}$. There are $7$ possible configurations of such singularities. They classify the Hilbert-Burch matrix which corresponds to each configuration. The study of multiplicity $c$ singularities on, or infinitely near, a fixed rational plane curve $\mathcal{C}$ of degree $2c$ is equivalent to the study of the scheme of generalized zeros of the fixed balanced Hilbert-Burch matrix $\varphi$ for a parameterization of $\mathcal{C}$.