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

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

Author: Bob Oliver

Publisher: American Mathematical Soc.

Published: 2016-01-25

Total Pages: 112

ISBN-13: 1470415488

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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.

Descent Construction for GSpin Groups

Descent Construction for GSpin Groups PDF

Author: Joseph Hundley

Publisher: American Mathematical Soc.

Published: 2016-09-06

Total Pages: 138

ISBN-13: 1470416670

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In this paper the authors provide an extension of the theory of descent of Ginzburg-Rallis-Soudry to the context of essentially self-dual representations, that is, representations which are isomorphic to the twist of their own contragredient by some Hecke character. The authors' theory supplements the recent work of Asgari-Shahidi on the functorial lift from (split and quasisplit forms of) GSpin2n to GL2n.

The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup

The Local Structure Theorem for Finite Groups With a Large $p$-Subgroup PDF

Author: U. Meierfrankenfeld

Publisher: American Mathematical Soc.

Published: 2016-06-21

Total Pages: 356

ISBN-13: 1470418770

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Let p be a prime, G a finite Kp-group S a Sylow p-subgroup of G and Q a large subgroup of G in S (i.e., CG(Q)≤Q and NG(U)≤NG(Q) for 1≠U≤CG(Q)). Let L be any subgroup of G with S≤L, Op(L)≠1 and Q⋬L. In this paper the authors determine the action of L on the largest elementary abelian normal p-reduced p-subgroup YL of L.

The $abc$-Problem for Gabor Systems

The $abc$-Problem for Gabor Systems PDF

Author: Xin-Rong Dai

Publisher: American Mathematical Soc.

Published: 2016-10-05

Total Pages: 116

ISBN-13: 1470420155

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A longstanding problem in Gabor theory is to identify time-frequency shifting lattices aZ×bZ and ideal window functions χI on intervals I of length c such that {e−2πinbtχI(t−ma): (m,n)∈Z×Z} are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above abc-problem for Gabor systems.

Nil Bohr-Sets and Almost Automorphy of Higher Order

Nil Bohr-Sets and Almost Automorphy of Higher Order PDF

Author: Wen Huang

Publisher: American Mathematical Soc.

Published: 2016-04-26

Total Pages: 98

ISBN-13: 147041872X

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Two closely related topics, higher order Bohr sets and higher order almost automorphy, are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any d∈N does the collection of {n∈Z:S∩(S−n)∩…∩(S−dn)≠∅} with S syndetic coincide with that of Nild Bohr0 -sets? In the second part, the notion of d -step almost automorphic systems with d∈N∪{∞} is introduced and investigated, which is the generalization of the classical almost automorphic ones.

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology

Monoidal Categories and the Gerstenhaber Bracket in Hochschild Cohomology PDF

Author: Reiner Hermann:

Publisher: American Mathematical Soc.

Published: 2016-09-06

Total Pages: 158

ISBN-13: 1470419955

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In this monograph, the author extends S. Schwede's exact sequence interpretation of the Gerstenhaber bracket in Hochschild cohomology to certain exact and monoidal categories. Therefore the author establishes an explicit description of an isomorphism by A. Neeman and V. Retakh, which links Ext-groups with fundamental groups of categories of extensions and relies on expressing the fundamental group of a (small) category by means of the associated Quillen groupoid. As a main result, the author shows that his construction behaves well with respect to structure preserving functors between exact monoidal categories. The author uses his main result to conclude, that the graded Lie bracket in Hochschild cohomology is an invariant under Morita equivalence. For quasi-triangular bialgebras, he further determines a significant part of the Lie bracket's kernel, and thereby proves a conjecture by L. Menichi. Along the way, the author introduces n-extension closed and entirely extension closed subcategories of abelian categories, and studies some of their properties.

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations

Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations PDF

Author: Genni Fragnelli

Publisher: American Mathematical Soc.

Published: 2016-06-21

Total Pages: 96

ISBN-13: 1470419548

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The authors consider a parabolic problem with degeneracy in the interior of the spatial domain, and they focus on observability results through Carleman estimates for the associated adjoint problem. The novelties of the present paper are two. First, the coefficient of the leading operator only belongs to a Sobolev space. Second, the degeneracy point is allowed to lie even in the interior of the control region, so that no previous result can be adapted to this situation; however, different cases can be handled, and new controllability results are established as a consequence.

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