Search results for "Mathematic"

Commutative Partial O*-Algebras

2002

This chapter is devoted to the integrability of commutative partial O*-algebras. Three notions of weak commutativity, commutativity and strong commutativity of an O*-vector space are defined and investigated. In Section 3.1, we analyze the relation between the integrability of weakly commutative O*-vector space M and the commutativity of the von Neumann algebra (M w ′ )′. In Section 3.2, we study the integrable extensions of partial O*-algebras. In Section 3.3, we describe another explicit example, namely, the partial O*-algebra M[S, T] generated by two weakly commuting symmetric operators S and T defined on a common dense domain in a Hilbert space. In particular, we investigate in detail t…

Isometries between spaces of multiple Dirichlet series

2019

Abstract In this paper we study spaces of multiple Dirichlet series and their properties. We set the ground of the theory of multiple Dirichlet series and define the spaces H ∞ ( C + k ) , k ∈ N , of convergent and bounded multiple Dirichlet series on C + k . We give a representation for these Banach spaces and prove that they are all isometrically isomorphic, independently of the dimension. The analogous result for A ( C + k ) , k ∈ N , which are the spaces of multiple Dirichlet series that are convergent on C + k and define uniformly continuous functions, is obtained.

Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians

2015

Carleson's counterexample and a scale of Lorentz-BMO spaces on the bitorus

2005

We introduce a full scale of Lorentz-BMO spaces BMO L p,q on the bidisk, and show that these spaces do not coincide for different values ofp andq. Our main tool is a detailed analysis of Carleson's construction in [C].

1973

The direct and the inverse problem of the light scattering from dilute polymer solutions is solved for GAUssian coils at the theta point. Theoretical scattering functions and their derivatives are analytically calculated for the general gamma distribution of molecular weights as a function of the non-uniformity and the weight average molecular weight, and also for various ratios of the statistical segment length of the coil to the wave length of the scattered light. The asymptote and the tangent of P are obtained by analysing the operator in the ZIMM equation and their mutual position is compared in the angle range 150° to 180°. The scattering envelopes of microgel systems are analytically …

Stochastic linearization for the response of MDOF systems subjected to external and parametric Gaussian excitations

1991

The stochastic linearization approach is examined for the most general case of non zero-mean response of non-linear MDOF systems subjected to parametric and external Gaussian white excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. Moreover, an extension of the Atalik-Utku approach to non zero-mean response systems allows to obtain simple formulations for the linearized drift coefficients. Some applications show the good accuracy of the method.

Computing Difficulties for Deriving Poverty Indices from Some Functional Forms of Lorenz Curves

2014

We examine three families of classical one-parameter functional forms for estimating a Lorenz curve: the power form (Pareto, elementary form), the exponential form (Gupta, elementary form) and fractional form (Rohde). For the first time, we systematically study these functions not for their ability to be estimated but on the point of view of the possibility of deriving poverty indices, which implies first determining the headcount ratio (i.e., the percentage of poor). We show that computing difficulties have been largely underestimated. Two forms, the most simple ones, pose no problem: the elementary power and exponential forms. However, the Pareto functional form poses problem with a restr…

Quenched and annealed free energies

1984

This paper gives a simple exposition of the Nishimori method to solve certain quenched, random bond spin-glass models. It allows a transparent physical interpretation in terms of annealed systems. As an application a special solution of the Sherrington-Kirkpatrick model with a discrete probability distribution is obtained and shown to agree with the solution for the Gaussian case. This substantiates the claim that the averaged free energy does not depend on the details of the probability distribution Expose simple de la methode de Nishimori pour resoudre certains modeles de verres de spin avec interactions aleatoires. Interpretation transparente en termes de systemes recuits. Presentation d…

How to Improve the Reliability of Chord?

2008

In this paper we focus on Chord P2P protocol and we study the process of unexpected departures of nodes from this system. Each of such departures may effect in losing any information and in classical versions of this protocol the probability of losing some information is proportional to the quantity of information put into this system. This effect can be partially solved by gathering in the protocol multiple copies (replicas) of information. The replication mechanism was proposed by many authors. We present a detailed analysis of one variant of blind replication and show that this solution only partially solves the problem. Next we propose two less obvious modifications of the Chord protoco…

ChemInform Abstract: Magnetic Exchange Between Metal Ions with Unquenched Orbital Angular Momenta: Basic Concepts and Relevance to Molecular Magnetism

2010

This review article is a first attempt to give a systematic and comprehensive description (in the framework of the unified theoretical approach) of the exchange interactions in polynuclear systems based on orbitally degenerate metal ions in the context of their relevance to the modern molecular magnetism. Interest in these systems is related to the fundamental problems of magnetism and at the same time steered by a number of impressive potential applications of molecular magnets, like high-density memory storage units, nanoscale qubits, spintronics and photoswitchable devices. In the presence of orbital degeneracy, the conventional spin Hamiltonian (Heisenberg–Dirac–van Vleck model) becomes…