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On the Shape of a Pure $O$-Sequence

2012 Mathematics
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Release : 2012
Genre : Mathematics
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Book Rating : 108/5 ( reviews)

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Book Synopsis On the Shape of a Pure $O$-Sequence by : Mats Boij

Download or read book On the Shape of a Pure $O$-Sequence written by Mats Boij. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: A monomial order ideal is a finite collection X of (monic) monomials such that, whenever M∈X and N divides M, then N∈X. Hence X is a poset, where the partial order is given by divisibility. If all, say t t, maximal monomials of X have the same degree, then X is pure (of type t). A pure O-sequence is the vector, h_=(h0=1,h1,...,he), counting the monomials of X in each degree. Equivalently, pure O-sequences can be characterized as the f-vectors of pure multicomplexes, or, in the language of commutative algebra, as the h h-vectors of monomial Artinian level algebras. Pure O-sequences had their origin in one of the early works of Stanley's in this area, and have since played a significant role in at least three different disciplines: the study of simplicial complexes and their f f-vectors, the theory of level algebras, and the theory of matroids. This monograph is intended to be the first systematic study of the theory of pure O-sequences.

Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture

2013-02-26 Mathematics
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Release : 2013-02-26
Genre : Mathematics
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Book Rating : 875/5 ( reviews)

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Book Synopsis Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture by : Aleksandr Vladimirovich Sobolev

Download or read book Pseudo-Differential Operators with Discontinuous Symbols: Widom's Conjecture written by Aleksandr Vladimirovich Sobolev. This book was released on 2013-02-26. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013-01-25 Mathematics
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Release : 2013-01-25
Genre : Mathematics
Kind : eBook
Book Rating : 574/5 ( reviews)

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Book Synopsis Potential Wadge Classes by : Dominique Lecomte

Download or read book Potential Wadge Classes written by Dominique Lecomte. This book was released on 2013-01-25. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013-04-22 Mathematics
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Release : 2013-04-22
Genre : Mathematics
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Book Rating : 66X/5 ( reviews)

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Book Synopsis Characterization and Topological Rigidity of Nobeling Manifolds by : Andrzej Nagórko

Download or read book Characterization and Topological Rigidity of Nobeling Manifolds written by Andrzej Nagórko. This book was released on 2013-04-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013-02-26 Mathematics
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Release : 2013-02-26
Genre : Mathematics
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Book Rating : 655/5 ( reviews)

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Book Synopsis Character Identities in the Twisted Endoscopy of Real Reductive Groups by : Paul Mezo

Download or read book Character Identities in the Twisted Endoscopy of Real Reductive Groups written by Paul Mezo. This book was released on 2013-02-26. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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