4,551 research outputs found
On the extreme value statistics of normal random matrices and 2D Coulomb gases: Universality and finite N corrections
In this paper we extend the orthogonal polynomials approach for extreme value
calculations of Hermitian random matrices, developed by Nadal and Majumdar
[1102.0738], to normal random matrices and 2D Coulomb gases in general.
Firstly, we show that this approach provides an alternative derivation of
results in the literature. More precisely, we show convergence of the rescaled
eigenvalue with largest modulus of a normal Gaussian ensemble to a Gumbel
distribution, as well as universality for an arbitrary radially symmetric
potential. Secondly, it is shown that this approach can be generalised to
obtain convergence of the eigenvalue with smallest modulus and its universality
for ring distributions. Most interestingly, the here presented techniques are
used to compute all slowly varying finite N correction of the above
distributions, which is important for practical applications, given the slow
convergence. Another interesting aspect of this work is the fact that we can
use standard techniques from Hermitian random matrices to obtain the extreme
value statistics of non-Hermitian random matrices resembling the large N
expansion used in context of the double scaling limit of Hermitian matrix
models in string theory.Comment: 25 pages, 6 figures, revised and extended version, including new
finite N results, change in title to highlight new results, as to be
published in JSTA
The higher duals of certain class of Banach algebras
Given a Banach space and fix a non-zero with
. Then the product
turning into a Banach algebra which will be denoted by Some
of the main properties of such as Arens regularity, -weak
amenability and semi-simplicity are investigated.Comment: 6 page
Free Rota-Baxter algebras and rooted trees
A Rota-Baxter algebra, also known as a Baxter algebra, is an algebra with a
linear operator satisfying a relation, called the Rota-Baxter relation, that
generalizes the integration by parts formula. Most of the studies on
Rota-Baxter algebras have been for commutative algebras. Two constructions of
free commutative Rota-Baxter algebras were obtained by Rota and Cartier in the
1970s and a third one by Keigher and one of the authors in the 1990s in terms
of mixable shuffles. Recently, noncommutative Rota-Baxter algebras have
appeared both in physics in connection with the work of Connes and Kreimer on
renormalization in perturbative quantum field theory, and in mathematics
related to the work of Loday and Ronco on dendriform dialgebras and
trialgebras.
This paper uses rooted trees and forests to give explicit constructions of
free noncommutative Rota--Baxter algebras on modules and sets. This highlights
the combinatorial nature of Rota--Baxter algebras and facilitates their further
study. As an application, we obtain the unitarization of Rota-Baxter algebras.Comment: 23 page
Lifting derivations and weak amenability of the second dual of a Banach algebra
We show that for the weak amenability of the second dual
\A^{**} of a Banach algebra \A implies that of \A. We also provide a
positive answer for the case which sharpens some older results. Our
method of proof also provides a unified approach to give short proofs for some
known results in the case where .Comment: 8 page
Reiter's properties for the actions of locally compact quantum groups on von Neumann algebras
The notion of an action of a locally compact quantum group on a von Neumann
algebra is studied from the amenability point of view. Various Reiter's
conditions for such an action are discussed. Several applications to some
specific actions related to certain representations and corepresentaions are
presented.Comment: 13 pages, To appear in Bull. Iranian Math. So
More on Lie Derivations of Generalized Matrix Algebras
Motivated by the Cheung's elaborate work [Linear Multilinear Algebra, 51
(2003), 299-310], we investigate the construction of a Lie derivation on a
generalized matrix algebra and apply it to give a characterization for such a
Lie derivation to be proper. Our approach not only provides a direct proof for
some known results in the theory, but also it presents several sufficient
conditions assuring the properness of Lie derivations on certain generalized
matrix algebras.Comment: 11 page
Numerical Solution of Cylindrically Converging Shock Waves
The cylindrically converging shock wave was numerically simulated by solving
the Euler equations in cylindrical coordinates with TVD scheme and MUSCL
approach, using Roe's approximate Riemann solver and super-bee nonlinear
limiter. The present study used the in house code developed for this purpose.
The behavior of the solution in the vicinity of axis is investigated and the
results of the numerical solution are compared with the computed data given by
Payne, Lapidus, Abarbanel, and Goldberg, Sod, and Leutioff et al.Comment: International Conference on Fascinating Advancement in Mechanical
Engineering (FAME08), India, 200
Weighted semigroup measure algebra as a WAP-algebra
Banach algebra A for which the natural embedding x into x^ of A into WAP(A)*
is bounded below; that is, for some m in R with m > 0 we have ||x^|| > m ||x||,
is called a WAP-algebra. Through we mainly concern with weighted measure
algebra M_b(S;w); where w is a weight on a semi-topological semigroup S. We
study those con- ditions under which M_b(S;w) is a WAP-algebra (respectively
dual Banach algebra). In particular, M_b(S) is a WAP-algebra (respectively dual
Banach algebra) if and only if wap(S) separates the points of S (respectively S
is compactly cancellative semigroup). We apply our results for improving some
older results in the case where S is discrete
Sensitivity of Numerical Predictions to the Permeability Coefficient in Simulations of Melting and Solidification Using the Enthalpy-Porosity Method
The high degree of uncertainty and conflicting literature data on the value
of the permeability coefficient (also known as the mushy zone constant), which
aims to dampen fluid velocities in the mushy zone and suppress them in solid
regions, is a critical drawback when using the fixed-grid enthalpy-porosity
technique for modelling non-isothermal phase-change processes. In the present
study, the sensitivity of numerical predictions to the value of this
coefficient was scrutinised. Using finite-volume based numerical simulations of
isothermal and non-isothermal melting and solidification problems, the causes
of increased sensitivity were identified. It was found that depending on the
mushy-zone thickness and the velocity field, the solid-liquid interface
morphology and the rate of phase-change are sensitive to the permeability
coefficient. It is demonstrated that numerical predictions of an isothermal
phase-change problem are independent of the permeability coefficient for
sufficiently fine meshes. It is also shown that sensitivity to the choice of
permeability coefficient can be assessed by means of an appropriately defined
P\'eclet number.Comment: The influence of the mushy-zone constant in simulations of melting
and solidification (phase-change materials) using the enthalpy-porosity
metho
Arens regularity of certain weighted semigroup algebras and countability
It is known that every countable semigroup admits a weight w for which the
semigroup algebra l_1(S,w) is Arens regular and no uncountable group admits
such a weight; see [4]. In this paper, among other things, we show that for a
large class of semigroups, the Arens regularity of the weighted semigroup
algebra l_1(S,w) implies the countability of S
- β¦