646 research outputs found
Module homomorphisms and multipliers on locally compact quantum groups
For a Banach algebra with a bounded approximate identity, we investigate
the -module homomorphisms of certain introverted subspaces of , and
show that all -module homomorphisms of are normal if and only if
is an ideal of . We obtain some characterizations of compactness and
discreteness for a locally compact quantum group \G. Furthermore, in the
co-amenable case we prove that the multiplier algebra of \LL can be
identified with \MG. As a consequence, we prove that \G is compact if and
only if \LUC={\rm WAP}(\G) and \MG\cong\mathcal{Z}({\rm LUC}(\G)^*); which
partially answer a problem raised by Volker Runde.Comment: The detailed proof of Lemma 4.1 is added in addendum. 11 pages, To
appear in J. Math. Anal. App
POD‐identification reduced order model of linear transport equations for control purposes
Intrusive reduced order modeling techniques require access to the solver's discretization and solution algorithm, which are not available for most computational fluid dynamics codes. Therefore, a nonintrusive reduction method that identifies the system matrix of linear fluid dynamical problems with a least-squares technique is presented. The methodology is applied to the linear scalar transport convection-diffusion equation for a 2D square cavity problem with a heated lid. The (time-dependent) boundary conditions are enforced in the obtained reduced order model (ROM) with a penalty method. The results are compared and the accuracy of the ROMs is assessed against the full order solutions and it is shown that the ROM can be used for sensitivity analysis by controlling the nonhomogeneous Dirichlet boundary conditions
Solution and Asymptotic Behavior for a Nonlocal Coupled System of Reaction-Diffusion
This paper concerns with existence, uniqueness and asymptotic behavior of the
solutions for a nonlocal coupled system of reaction-diffusion. We prove the
existence and uniqueness of weak solutions by the Faedo-Galerkin method and
exponential decay of solutions by the classic energy method. We improve the
results obtained by Chipot-Lovato and Menezes for coupled systems. A numerical
scheme is presented
A global method for coupling transport with chemistry in heterogeneous porous media
Modeling reactive transport in porous media, using a local chemical
equilibrium assumption, leads to a system of advection-diffusion PDE's coupled
with algebraic equations. When solving this coupled system, the algebraic
equations have to be solved at each grid point for each chemical species and at
each time step. This leads to a coupled non-linear system. In this paper a
global solution approach that enables to keep the software codes for transport
and chemistry distinct is proposed. The method applies the Newton-Krylov
framework to the formulation for reactive transport used in operator splitting.
The method is formulated in terms of total mobile and total fixed
concentrations and uses the chemical solver as a black box, as it only requires
that on be able to solve chemical equilibrium problems (and compute
derivatives), without having to know the solution method. An additional
advantage of the Newton-Krylov method is that the Jacobian is only needed as an
operator in a Jacobian matrix times vector product. The proposed method is
tested on the MoMaS reactive transport benchmark.Comment: Computational Geosciences (2009)
http://www.springerlink.com/content/933p55085742m203/?p=db14bb8c399b49979ba8389a3cae1b0f&pi=1
Closed quantum subgroups of locally compact quantum groups
We investigate the fundamental concept of a closed quantum subgroup of a
locally compact quantum group. Two definitions - one due to S.Vaes and one due
to S.L.Woronowicz - are analyzed and relations between them discussed. Among
many reformulations we prove that the former definition can be phrased in terms
of quasi-equivalence of representations of quantum groups while the latter can
be related to an old definition of Podle\'s from the theory of compact quantum
groups. The cases of classical groups, duals of classical groups, compact and
discrete quantum groups are singled out and equivalence of the two definitions
is proved in the relevant context. A deep relationship with the quantum group
generalization of Herz restriction theorem from classical harmonic analysis is
also established, in particular, in the course of our analysis we give a new
proof of Herz restriction theorem.Comment: 24 pages, v3 adds another reference. The paper will appear in
Advances in Mathematic
A Comparison of Consistent Discretizations for Elliptic Problems on Polyhedral Grids
In this work, we review a set of consistent discretizations for second-order elliptic equations, and compare and contrast them with respect to accuracy, monotonicity, and factors affecting their computational cost (degrees of freedom, sparsity, and condition numbers). Our comparisons include the linear and nonlinear TPFA method, multipoint flux-approximation (MPFA-O), mimetic methods, and virtual element methods. We focus on incompressible flow and study the effects of deformed cell geometries and anisotropic permeability.acceptedVersio
Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models
We present a detailed study of quantized noncompact, nonlinear SO(1,N)
sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on
issues of spontaneous symmetry breaking of boost and rotation elements of the
symmetry group. The models are defined on a lattice both in terms of a transfer
matrix and by an appropriately gauge-fixed Euclidean functional integral. The
main results in all dimensions \geq 2 are: (i) On a finite lattice the systems
have infinitely many nonnormalizable ground states transforming irreducibly
under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is
spontaneously broken. For D =2 this shows that the systems evade the
Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the
Noether currents are derived to verify numerically the absence of explicit
symmetry breaking; (iv) numerical results are presented for the two-point
functions of the spin field and the Noether current as well as a new order
parameter; (v) in a large N saddle-point analysis the dynamically generated
squared mass is found to be negative and of order 1/(V \ln V) in the volume,
the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N)
invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and
spontaneous symmetry breaking extended to all dimension
On twisted Fourier analysis and convergence of Fourier series on discrete groups
We study norm convergence and summability of Fourier series in the setting of
reduced twisted group -algebras of discrete groups. For amenable groups,
F{\o}lner nets give the key to Fej\'er summation. We show that Abel-Poisson
summation holds for a large class of groups, including e.g. all Coxeter groups
and all Gromov hyperbolic groups. As a tool in our presentation, we introduce
notions of polynomial and subexponential H-growth for countable groups w.r.t.
proper scale functions, usually chosen as length functions. These coincide with
the classical notions of growth in the case of amenable groups.Comment: 35 pages; abridged, revised and update
A contribuição de Victor Valla ao pensamento da educação popular.
Em setembro de 2009, faleceu Victor Vicent Valla, educador e pesquisador norte-americano residente no Rio de Janeiro, que veio para o Brasil em 1964 e marcou o campo da educação popular com importantes contribuições teóricas e organizativas. Foi, antes de tudo, uma pessoa indignada com a pobreza latino-americana e fascinada com suas potências de criação, alegria, conhecimento e proposição política. Investiu grande parte de seu esforço na tentativa de compreensão dos diferentes caminhos da busca de ser mais das classes populares, com quem a cultura erudita costuma ter tanto desprezo. Participou ativamente do Grupo de Trabalho Educação Popular da Associação Nacional de Pós-Graduação e Pesquisa em Educação (ANPEd), durante duas décadas, marcando fortemente o seu modo de funcionamento e a sua identidade. Em 2007, esse grupo de trabalho colocou como prioridade de estudo a compreensão de sua contribuição para a educação popular, encomendando um trabalho para pesquisadores que conviveram mais de perto com suas atividades acadêmicas: Maria Tereza Goudart Tavares, Reinaldo Matias Fleuri, Eveline Bertino Algebaile e Eymard Mourão Vasconcelos. O próprio Victor Valla, depois de provocado, concordou em participar dessa avaliação crítica de sua obra. Essas reflexões, apresentadas na 30ª Reunião Anual da ANPEd, estão sendo publicadas nesse número em sua homenagem. Trata-se de um texto, com diferentes análises sobre a contribuição de Victor Valla ao pensamento da educação popular, que procurou responder a algumas questões: o que há na sua produção teórica e no seu modo de gerir as relações acadêmicas que possibilitou tão grande impacto de suas contribuições? Que impactos são esses? Além de sua competente atuação acadêmica e de seu posicionamento sempre contrário às injustiças sociais que ainda marcam nosso país, Valla será lembrado por ter sido sempre um homem generoso, íntegro e leal
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