Julia Sets And Complex Singularities Of Free Energies

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Julia Sets and Complex Singularities of Free Energies

Jianyong Qiao
Julia Sets and Complex Singularities of Free Energies Book PDF

Author : Jianyong Qiao
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 51,5 Mb
Release : 2015-02-06
Category : Mathematics
ISBN : 9781470409821

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Julia Sets and Complex Singularities of Free Energies by Jianyong Qiao Pdf

The author studies a family of renormalization transformations of generalized diamond hierarchical Potts models through complex dynamical systems. He proves that the Julia set (unstable set) of a renormalization transformation, when it is treated as a complex dynamical system, is the set of complex singularities of the free energy in statistical mechanics. He gives a sufficient and necessary condition for the Julia sets to be disconnected. Furthermore, he proves that all Fatou components (components of the stable sets) of this family of renormalization transformations are Jordan domains with at most one exception which is completely invariant. In view of the problem in physics about the distribution of these complex singularities, the author proves here a new type of distribution: the set of these complex singularities in the real temperature domain could contain an interval. Finally, the author studies the boundary behavior of the first derivative and second derivative of the free energy on the Fatou component containing the infinity. He also gives an explicit value of the second order critical exponent of the free energy for almost every boundary point.

On the Singular Set of Harmonic Maps into DM-Complexes

Georgios Daskalopoulos,Chikako Mese
On the Singular Set of Harmonic Maps into DM Complexes Book PDF

Author : Georgios Daskalopoulos,Chikako Mese
Publisher : American Mathematical Soc.
Page : 89 pages
File Size : 55,6 Mb
Release : 2016-01-25
Category : Differentiable manifolds
ISBN : 9781470414603

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On the Singular Set of Harmonic Maps into DM-Complexes by Georgios Daskalopoulos,Chikako Mese Pdf

The authors prove that the singular set of a harmonic map from a smooth Riemammian domain to a Riemannian DM-complex is of Hausdorff codimension at least two. They also explore monotonicity formulas and an order gap theorem for approximately harmonic maps. These regularity results have applications to rigidity problems examined in subsequent articles.

Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem

Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Geometric Complexity Theory IV Nonstandard Quantum Group for the Kronecker Problem Book PDF

Author : Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni
Publisher : American Mathematical Soc.
Page : 160 pages
File Size : 55,8 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410117

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Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by Jonah Blasiak,Ketan D. Mulmuley,Milind Sohoni Pdf

The Kronecker coefficient is the multiplicity of the -irreducible in the restriction of the -irreducible via the natural map , where are -vector spaces and . A fundamental open problem in algebraic combinatorics is to find a positive combinatorial formula for these coefficients. The authors construct two quantum objects for this problem, which they call the nonstandard quantum group and nonstandard Hecke algebra. They show that the nonstandard quantum group has a compact real form and its representations are completely reducible, that the nonstandard Hecke algebra is semisimple, and that they satisfy an analog of quantum Schur-Weyl duality.

Higher Moments of Banach Space Valued Random Variables

Svante Janson,Sten Kaijser
Higher Moments of Banach Space Valued Random Variables Book PDF

Author : Svante Janson,Sten Kaijser
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 43,9 Mb
Release : 2015-10-27
Category : Banach spaces
ISBN : 9781470414658

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Higher Moments of Banach Space Valued Random Variables by Svante Janson,Sten Kaijser Pdf

The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.

On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System

Weiwei Ao,Chang-Shou Lin,Juncheng Wei
On Non Topological Solutions of the A 2 and B 2 Chern Simons System Book PDF

Author : Weiwei Ao,Chang-Shou Lin,Juncheng Wei
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 51,6 Mb
Release : 2016-01-25
Category : Lie groups
ISBN : 9781470415433

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On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System by Weiwei Ao,Chang-Shou Lin,Juncheng Wei Pdf

Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography

Global Carleman Estimates for Degenerate Parabolic Operators with Applications

P. Cannarsa,P. Martinez,J. Vancostenoble
Global Carleman Estimates for Degenerate Parabolic Operators with Applications Book PDF

Author : P. Cannarsa,P. Martinez,J. Vancostenoble
Publisher : American Mathematical Soc.
Page : 209 pages
File Size : 47,6 Mb
Release : 2016-01-25
Category : Carleman theorem
ISBN : 9781470414962

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Global Carleman Estimates for Degenerate Parabolic Operators with Applications by P. Cannarsa,P. Martinez,J. Vancostenoble Pdf

Degenerate parabolic operators have received increasing attention in recent years because they are associated with both important theoretical analysis, such as stochastic diffusion processes, and interesting applications to engineering, physics, biology, and economics. This manuscript has been conceived to introduce the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Irreducible Geometric Subgroups of Classical Algebraic Groups

Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman
Irreducible Geometric Subgroups of Classical Algebraic Groups Book PDF

Author : Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 47,7 Mb
Release : 2016-01-25
Category : Geometric group theory
ISBN : 9781470414948

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Irreducible Geometric Subgroups of Classical Algebraic Groups by Timothy C. Burness,,Soumaïa Ghandour,Donna M. Testerman Pdf

Let be a simple classical algebraic group over an algebraically closed field of characteristic with natural module . Let be a closed subgroup of and let be a non-trivial irreducible tensor-indecomposable -restricted rational -module such that the restriction of to is irreducible. In this paper the authors classify the triples of this form, where is a disconnected maximal positive-dimensional closed subgroup of preserving a natural geometric structure on .

Stability of Line Solitons for the KP-II Equation in $\mathbb{R}^2$

Tetsu Mizumachi
Stability of Line Solitons for the KP II Equation in mathbb R 2 Book PDF

Author : Tetsu Mizumachi
Publisher : American Mathematical Soc.
Page : 95 pages
File Size : 43,6 Mb
Release : 2015-10-27
Category : Representations of algebras
ISBN : 9781470414245

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Stability of Line Solitons for the KP-II Equation in $\mathbb{R}^2$ by Tetsu Mizumachi Pdf

The author proves nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as . He finds that the amplitude of the line soliton converges to that of the line soliton at initial time whereas jumps of the local phase shift of the crest propagate in a finite speed toward . The local amplitude and the phase shift of the crest of the line solitons are described by a system of 1D wave equations with diffraction terms.

Faithfully Quadratic Rings

M. Dickmann,F. Miraglia
Faithfully Quadratic Rings Book PDF

Author : M. Dickmann,F. Miraglia
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 46,5 Mb
Release : 2015-10-27
Category : Commutative rings
ISBN : 9781470414689

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Faithfully Quadratic Rings by M. Dickmann,F. Miraglia Pdf

In this monograph the authors extend the classical algebraic theory of quadratic forms over fields to diagonal quadratic forms with invertible entries over broad classes of commutative, unitary rings where is not a sum of squares and is invertible. They accomplish this by: (1) Extending the classical notion of matrix isometry of forms to a suitable notion of -isometry, where is a preorder of the given ring, , or . (2) Introducing in this context three axioms expressing simple properties of (value) representation of elements of the ring by quadratic forms, well-known to hold in the field case.

Stability of KAM Tori for Nonlinear Schrödinger Equation

Hongzi Cong,Jianjun Liu,Xiaoping Yuan
Stability of KAM Tori for Nonlinear Schr dinger Equation Book PDF

Author : Hongzi Cong,Jianjun Liu,Xiaoping Yuan
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 51,8 Mb
Release : 2016-01-25
Category : Gross-Pitaevskii equations
ISBN : 9781470416577

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Stability of KAM Tori for Nonlinear Schrödinger Equation by Hongzi Cong,Jianjun Liu,Xiaoping Yuan Pdf

The authors prove the long time stability of KAM tori (thus quasi-periodic solutions) for nonlinear Schrödinger equation subject to Dirichlet boundary conditions , where is a real Fourier multiplier. More precisely, they show that, for a typical Fourier multiplier , any solution with the initial datum in the -neighborhood of a KAM torus still stays in the -neighborhood of the KAM torus for a polynomial long time such as for any given with , where is a constant depending on and as .

Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4

Bob Oliver
Reduced Fusion Systems over 2 Groups of Sectional Rank at Most 4 Book PDF

Author : Bob Oliver
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 42,9 Mb
Release : 2016-01-25
Category : Algebraic topology
ISBN : 9781470415488

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Reduced Fusion Systems over 2-Groups of Sectional Rank at Most 4 by Bob Oliver Pdf

The author classifies all reduced, indecomposable fusion systems over finite -groups of sectional rank at most . The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional -rank at most . But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Symmetry Breaking for Representations of Rank One Orthogonal Groups

Toshiyuki Kobayashi,Birgit Speh
Symmetry Breaking for Representations of Rank One Orthogonal Groups Book PDF

Author : Toshiyuki Kobayashi,Birgit Speh
Publisher : American Mathematical Soc.
Page : 112 pages
File Size : 50,9 Mb
Release : 2015-10-27
Category : Banach spaces
ISBN : 9781470419226

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Symmetry Breaking for Representations of Rank One Orthogonal Groups by Toshiyuki Kobayashi,Birgit Speh Pdf

The authors give a complete classification of intertwining operators (symmetry breaking operators) between spherical principal series representations of and . They construct three meromorphic families of the symmetry breaking operators, and find their distribution kernels and their residues at all poles explicitly. Symmetry breaking operators at exceptional discrete parameters are thoroughly studied. The authors obtain closed formulae for the functional equations which the composition of the symmetry breaking operators with the Knapp-Stein intertwining operators of and satisfy, and use them to determine the symmetry breaking operators between irreducible composition factors of the spherical principal series representations of and . Some applications are included.

Deformation Theory and Local-Global Compatibility of Langlands Correspondences

Martin Luu
Deformation Theory and Local Global Compatibility of Langlands Correspondences Book PDF

Author : Martin Luu
Publisher : American Mathematical Soc.
Page : 101 pages
File Size : 52,5 Mb
Release : 2015-10-27
Category : Automorphic forms
ISBN : 9781470414221

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Deformation Theory and Local-Global Compatibility of Langlands Correspondences by Martin Luu Pdf

The deformation theory of automorphic representations is used to study local properties of Galois representations associated to automorphic representations of general linear groups and symplectic groups. In some cases this allows to identify the local Galois representations with representations predicted by a local Langlands correspondence.

On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation

M. Escobedo,J. J. L. Velázquez
On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation Book PDF

Author : M. Escobedo,J. J. L. Velázquez
Publisher : American Mathematical Soc.
Page : 107 pages
File Size : 44,8 Mb
Release : 2015-10-27
Category : SCIENCE
ISBN : 9781470414344

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On the Theory of Weak Turbulence for the Nonlinear Schrodinger Equation by M. Escobedo,J. J. L. Velázquez Pdf

The authors study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schrödinger equation. They define suitable concepts of weak and mild solutions and prove local and global well posedness results. Several qualitative properties of the solutions, including long time asymptotics, blow up results and condensation in finite time are obtained. The authors also prove the existence of a family of solutions that exhibit pulsating behavior.

Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk

A. Rod Gover,Emanuele Latini,Andrew Waldron
Poincare Einstein Holography for Forms via Conformal Geometry in the Bulk Book PDF

Author : A. Rod Gover,Emanuele Latini,Andrew Waldron
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 50,6 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410926

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Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk by A. Rod Gover,Emanuele Latini,Andrew Waldron Pdf

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.