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Julia Sets and Complex Singularities of Free Energies

2015-02-06 Mathematics
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Release : 2015-02-06
Genre : Mathematics
Kind : eBook
Book Rating : 828/5 ( reviews)

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Book Synopsis Julia Sets and Complex Singularities of Free Energies by : Jianyong Qiao

Download or read book Julia Sets and Complex Singularities of Free Energies written by Jianyong Qiao. This book was released on 2015-02-06. Available in PDF, EPUB and Kindle. Book excerpt: 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

2016-01-25 Mathematics
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Release : 2016-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 600/5 ( reviews)

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Book Synopsis On the Singular Set of Harmonic Maps into DM-Complexes by : Georgios Daskalopoulos

Download or read book On the Singular Set of Harmonic Maps into DM-Complexes written by Georgios Daskalopoulos. This book was released on 2016-01-25. Available in PDF, EPUB and Kindle. Book excerpt: 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

2015-04-09 Mathematics
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Release : 2015-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 117/5 ( reviews)

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Book Synopsis Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem by : Jonah Blasiak

Download or read book Geometric Complexity Theory IV: Nonstandard Quantum Group for the Kronecker Problem written by Jonah Blasiak. This book was released on 2015-04-09. Available in PDF, EPUB and Kindle. Book excerpt: 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

2015-10-27 Mathematics
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Release : 2015-10-27
Genre : Mathematics
Kind : eBook
Book Rating : 651/5 ( reviews)

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Book Synopsis Higher Moments of Banach Space Valued Random Variables by : Svante Janson

Download or read book Higher Moments of Banach Space Valued Random Variables written by Svante Janson. This book was released on 2015-10-27. Available in PDF, EPUB and Kindle. Book excerpt: 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

2016-01-25 Mathematics
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Release : 2016-01-25
Genre : Mathematics
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Book Rating : 437/5 ( reviews)

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Book Synopsis On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System by : Weiwei Ao

Download or read book On Non-Topological Solutions of the $A_{2}$ and $B_{2}$ Chern-Simons System written by Weiwei Ao. This book was released on 2016-01-25. Available in PDF, EPUB and Kindle. Book excerpt: Click here to view the abstract. IntroductionProof of Theorem 1.1 in the caseProof of Theorem 1.1 in the caseAppendixBibliography

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