Search results for "Mathematica"
showing 10 items of 7971 documents
Algebraic dynamics in O*-algebras: a perturbative approach
2009
In this paper the problem of recovering an algebraic dynamics in a perturbative approach is discussed. The mathematical environment in which the physical problem is considered is that of algebras of unbounded operators endowed with the quasiuniform topology. After some remarks on the domain of the perturbation, conditions are given for the dynamics to exist as the limit of a net of regularized linear maps. © 2002 American Institute of Physics.
On the representation of integers by indefinite binary Hermitian forms
2011
Given an integral indefinite binary Hermitian form f over an imaginary quadratic number field, we give a precise asymptotic equivalent to the number of nonequivalent representations, satisfying some congruence properties, of the rational integers with absolute value at most s by f, as s tends to infinity.
On density and π-weight of Lp(βN,R, μ)
2012
In Integration Theory, it is important to establish the separability or not of Lebesgue spaces of the type Lp, with 1 ≤ p < +∞. In general, the usual proof of this type of results for certain Lebesgue spaces, is conducted through methods of Real Analysis. In this work, we use some concepts and methods of pure General Topology in proving the non-separability of a particular Lebesgue space. Further, we provide some estimates for density and π-weight of such a space.
Assouad dimension, Nagata dimension, and uniformly close metric tangents
2013
We study the Assouad dimension and the Nagata dimension of metric spaces. As a general result, we prove that the Nagata dimension of a metric space is always bounded from above by the Assouad dimension. Most of the paper is devoted to the study of when these metric dimensions of a metric space are locally given by the dimensions of its metric tangents. Having uniformly close tangents is not sufficient. What is needed in addition is either that the tangents have dimension with uniform constants independent from the point and the tangent, or that the tangents are unique. We will apply our results to equiregular subRiemannian manifolds and show that locally their Nagata dimension equals the to…
On the construction, comparison, and exchangeability of tuning systems
2015
The aim of this article is to describe mathematically different tuning systems, to study their mathematical properties, and to propose a construction allowing their comparison. In order to reach these goals, we introduce a concept of similarity between tuning systems and then we provide two sufficient conditions for the particular case in which a tuning system generated by an interval and a circulating temperament are compared. Finally, we show by means of an example that, for two tuning systems to be exchangeable, some well-known results determining the suitable number of notes per octave are not enough.
Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type
2021
The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.
Tripled Fixed Point Results for T-Contractions on Abstract Metric Spaces
2014
In this paper we introduce the notion of T-contraction for tripled fi xed points in abstract metric spaces and obtain some tripled fi xed point theorems which extend and generalize well-known comparable results in the literature. To support our results, we present an example and an application to integral equations.
Lévy flights and Lévy-Schrödinger semigroups
2010
We analyze two different confining mechanisms for L\'{e}vy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Levy-Schroedinger semigroups which induce so-called topological Levy processes (Levy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological L\'{e}vy process with the very same invariant pdf and in the reverse.
Scattering resonances and Pseudospectrum : stability and completeness aspects in optical and gravitational systems
2022
The general context of this thesis is an effort to establish a bridge between gravitational andoptical physics, specifically in the context of scattering problems using as a guideline concepts andtools taken from the theory of non-self-adjoint operators. Our focus is on Quasi-Normal Modes(QNMs), namely the natural resonant modes of open leaky structures under linear perturbationssubject to outgoing boundary conditions. They also are referred to as scattering resonances.In the conservative self-adjoint case the spectral theorem guarantees the completeness andspectral stability of the associated normal modes. In this sense, a natural question in the non-self-adjoint setting refers to the char…
Existence results for $L^1$ data of some quasi-linear parabolic problems with a quadratic gradient term and source
2002
In this paper we deal with a Cauchy–Dirichlet quasilinear parabolic problem containing a gradient lower order term; namely, ut - Δu + |u|2 γ-2u |∇u|2 = |u|p-2u. We prove that if p ≥ 1, γ ≥ ½ and p < 2 γ + 2, then there exists a global weak solution for all initial data in L1 (Ω). We also see that there exists a non-negative solution if the initial datum is non-negative.