On Systems of Equations Over Free Partially Commutative Groups
Author: Montserrat Casals-Ruiz
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 168
ISBN-13: 0821852582
DOWNLOAD EBOOK →"Volume 212, number 999 (end of volume)."
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Vector Bundles on Degenerations of Elliptic Curves and Yang-Baxter Equations
Author: Igor Burban
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 144
ISBN-13: 0821872923
DOWNLOAD EBOOK →"November 2012, volume 220, number 1035 (third of 4 numbers)."
The Schrodinger Model for the Minimal Representation of the Indefinite Orthogonal Group $O(p,q)$
Author: Toshiyuki Kobayashi
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 145
ISBN-13: 0821847570
DOWNLOAD EBOOK →The authors introduce a generalization of the Fourier transform, denoted by $\mathcal{F}_C$, on the isotropic cone $C$ associated to an indefinite quadratic form of signature $(n_1,n_2)$ on $\mathbb{R}^n$ ($n=n_1+n_2$: even). This transform is in some sense the unique and natural unitary operator on $L^2(C)$, as is the case with the Euclidean Fourier transform $\mathcal{F}_{\mathbb{R}^n}$ on $L^2(\mathbb{R}^n)$. Inspired by recent developments of algebraic representation theory of reductive groups, the authors shed new light on classical analysis on the one hand, and give the global formulas for the $L^2$-model of the minimal representation of the simple Lie group $G=O(n_1+1,n_2+1)$ on the other hand.
On First and Second Order Planar Elliptic Equations with Degeneracies
Author: Abdelhamid Meziani
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 90
ISBN-13: 0821853120
DOWNLOAD EBOOK →This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
Infinite-Dimensional Representations of 2-Groups
Author: John C. Baez
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 133
ISBN-13: 0821872842
DOWNLOAD EBOOK →Just as groups can have representations on vector spaces, 2-groups have representations on 2-vector spaces, but Lie 2-groups typically have few representations on the finite-dimensional 2-vector spaces introduced by Kapranov and Voevodsky. Therefore, Crane, Sheppeard, and Yetter introduced certain infinite-dimensional 2-vector spaces, called measurable categories, to study infinite-dimensional representations of certain Lie 2-groups, and German and North American mathematicians continue that work here. After introductory matters, they cover representations of 2-groups, and measurable categories, representations on measurable categories. There is no index. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
Elliptic Integrable Systems
Author: Idrisse Khemar
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 234
ISBN-13: 0821869256
DOWNLOAD EBOOK →In this paper, the author studies all the elliptic integrable systems, in the sense of C, that is to say, the family of all the $m$-th elliptic integrable systems associated to a $k^\prime$-symmetric space $N=G/G_0$. The author describes the geometry behind this family of integrable systems for which we know how to construct (at least locally) all the solutions. The introduction gives an overview of all the main results, as well as some related subjects and works, and some additional motivations.
Iterated Function Systems, Moments, and Transformations of Infinite Matrices
Author: Palle E. T. Jørgensen
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 122
ISBN-13: 0821852485
DOWNLOAD EBOOK →The authors study the moments of equilibrium measures for iterated function systems (IFSs) and draw connections to operator theory. Their main object of study is the infinite matrix which encodes all the moment data of a Borel measure on $\mathbb{R}^d$ or $\mathbb{C}$. To encode the salient features of a given IFS into precise moment data, they establish an interdependence between IFS equilibrium measures, the encoding of the sequence of moments of these measures into operators, and a new correspondence between the IFS moments and this family of operators in Hilbert space. For a given IFS, the authors' aim is to establish a functorial correspondence in such a way that the geometric transformations of the IFS turn into transformations of moment matrices, or rather transformations of the operators that are associated with them.
Parabolic Systems with Polynomial Growth and Regularity
Author: Frank Duzaar
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 135
ISBN-13: 0821849670
DOWNLOAD EBOOK →The authors establish a series of optimal regularity results for solutions to general non-linear parabolic systems $ u_t- \mathrm{div} \ a(x,t,u,Du)+H=0,$ under the main assumption of polynomial growth at rate $p$ i.e. $ a(x,t,u,Du) \leq L(1+ Du ^{p-1}), p \geq 2.$ They give a unified treatment of various interconnected aspects of the regularity theory: optimal partial regularity results for the spatial gradient of solutions, the first estimates on the (parabolic) Hausdorff dimension of the related singular set, and the first Calderon-Zygmund estimates for non-homogeneous problems are achieved here.
Axes in Outer Space
Author: Michael Handel
Publisher: American Mathematical Soc.
Published: 2011
Total Pages: 117
ISBN-13: 0821869272
DOWNLOAD EBOOK →"September 2011, volume 213, number 1004 (end of volume)."
Finite Order Automorphisms and Real Forms of Affine Kac-Moody Algebras in the Smooth and Algebraic Category
Author: Ernst Heintze
Publisher: American Mathematical Soc.
Published: 2012
Total Pages: 81
ISBN-13: 0821869183
DOWNLOAD EBOOK →Heintze and Gross discuss isomorphisms between smooth loop algebras and of smooth affine Kac-Moody algebras in particular, and automorphisms of the first and second kinds of finite order. Then they consider involutions of the first and second kind, and make the algebraic case. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com).
