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On the Steady Motion of a Coupled System Solid-Liquid

2013-10-23 Mathematics
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Release : 2013-10-23
Genre : Mathematics
Kind : eBook
Book Rating : 734/5 ( reviews)

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Book Synopsis On the Steady Motion of a Coupled System Solid-Liquid by : Josef Bemelmans

Download or read book On the Steady Motion of a Coupled System Solid-Liquid written by Josef Bemelmans. This book was released on 2013-10-23. Available in PDF, EPUB and Kindle. Book excerpt: We study the unconstrained (free) motion of an elastic solid B in a Navier-Stokes liquid L occupying the whole space outside B, under the assumption that a constant body force b is acting on B. More specifically, we are interested in the steady motion of the coupled system {B,L}, which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. We prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of B satisfies suitable geometric properties.

Effective Hamiltonians for Constrained Quantum Systems

2014-06-05 Mathematics
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Release : 2014-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 897/5 ( reviews)

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Book Synopsis Effective Hamiltonians for Constrained Quantum Systems by : Jakob Wachsmuth

Download or read book Effective Hamiltonians for Constrained Quantum Systems written by Jakob Wachsmuth. This book was released on 2014-06-05. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.

Generalized Descriptive Set Theory and Classification Theory

2014-06-05 Mathematics
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Release : 2014-06-05
Genre : Mathematics
Kind : eBook
Book Rating : 757/5 ( reviews)

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Book Synopsis Generalized Descriptive Set Theory and Classification Theory by : Sy-David Friedman

Download or read book Generalized Descriptive Set Theory and Classification Theory written by Sy-David Friedman. This book was released on 2014-06-05. Available in PDF, EPUB and Kindle. Book excerpt: Descriptive set theory is mainly concerned with studying subsets of the space of all countable binary sequences. In this paper the authors study the generalization where countable is replaced by uncountable. They explore properties of generalized Baire and Cantor spaces, equivalence relations and their Borel reducibility. The study shows that the descriptive set theory looks very different in this generalized setting compared to the classical, countable case. They also draw the connection between the stability theoretic complexity of first-order theories and the descriptive set theoretic complexity of their isomorphism relations. The authors' results suggest that Borel reducibility on uncountable structures is a model theoretically natural way to compare the complexity of isomorphism relations.

Cohomology for Quantum Groups via the Geometry of the Nullcone

2014-04-07 Mathematics
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Release : 2014-04-07
Genre : Mathematics
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Book Rating : 758/5 ( reviews)

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Book Synopsis Cohomology for Quantum Groups via the Geometry of the Nullcone by : Christopher P. Bendel

Download or read book Cohomology for Quantum Groups via the Geometry of the Nullcone written by Christopher P. Bendel. This book was released on 2014-04-07. Available in PDF, EPUB and Kindle. Book excerpt: In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when l (resp., p ) is smaller than the Coxeter number h of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible G -modules stipulates that p=h. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra H (u ? ,C) of the small quantum group.

Automorphisms of Manifolds and Algebraic $K$-Theory: Part III

2014-08-12 Mathematics
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Release : 2014-08-12
Genre : Mathematics
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Book Rating : 81X/5 ( reviews)

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Book Synopsis Automorphisms of Manifolds and Algebraic $K$-Theory: Part III by : Michael S. Weiss

Download or read book Automorphisms of Manifolds and Algebraic $K$-Theory: Part III written by Michael S. Weiss. This book was released on 2014-08-12. Available in PDF, EPUB and Kindle. Book excerpt: The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . The authors construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

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