Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Higher-order polarizations on the Virasoro group and anomalies
1991
In a previous paper the authors showed that the space of (first order) polarized functions on the Virasoro group is not, in general, irreducible. The full reduction was explicitly achieved by taking the orbit of the enveloping algebra through the vacuum. This additional step provided the proper quantization in the “strong-coupling” domain 0<c≦1. In this paper we introduce the concept of “higher order polarization” as a generalization of that of polarization. We prove that the imposing of the additional (higher-order) polarization conditions is equivalent to the taking of the above-mentioned orbit. This demonstrates that the generalized (higher-order) polarization conditions suffice to obtai…
On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem
2019
In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical approximation of similar problems we refer this approach as the global iterative method. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point argument, where the contractivity of the corresponding mapping is shown due to the continuous dependence of the weak solution on the given domain deformation. This estimate is obtain…
Statistic moments of the total energy of potential systems and application to equivalent non-linearization
2000
In this paper some properties of the total energy moments of potential systems, subjected to external white noise processes, are shown. Potential systems with a polynomial form of energy-dependent damping have been considered. It is shown that the analytical relations between the statistical moments of the energy associated with such systems can be obtained with the aid of the standard Ito calculus. Furthermore, it is shown that, for the stationary case, these analytical relations are very useful for the application of the equivalent non-linearization technique.
Some supplementary results on the 1+ $$\sqrt 2 $$ order method for the solution of nonlinear equations
1982
Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
Wavelet-like bases for thin-wire integral equations in electromagnetics
2005
AbstractIn this paper, wavelets are used in solving, by the method of moments, a modified version of the thin-wire electric field integral equation, in frequency domain. The time domain electromagnetic quantities, are obtained by using the inverse discrete fast Fourier transform. The retarded scalar electric and vector magnetic potentials are employed in order to obtain the integral formulation. The discretized model generated by applying the direct method of moments via point-matching procedure, results in a linear system with a dense matrix which have to be solved for each frequency of the Fourier spectrum of the time domain impressed source. Therefore, orthogonal wavelet-like basis trans…
Iterative closure method for non-linear systems driven by polynomials of Gaussian filtered processes
2008
This paper concerns the statistical characterization of the non-Gaussian response of non-linear systems excited by polynomial forms of filtered Gaussian processes. The non-Gaussianity requires the computation of moments of any order. The problem is solved profiting from both the stochastic equivalent linearization (EL), and the moment equation approach of Ito's stochastic differential calculus through a procedure divided into two parts. The first step requires the linearization of the system, while retaining the non-linear excitation; the response statistical moments are calculated exactly, and constitute a first estimate of the moments of the actual non-linear system. In the second step, t…
Programm des städtischen Realgymnasiums zu Riga
1867
Inhalt: 1. Hannibal und Scipio, eine historisch kritische Abhandlung / vom Gimnasial Lehrer W. Maczewski -- 2. Schulnachrichten / vom Director.
Breakdown of separability due to confinement
2017
A simple system of two particles in a bidimensional configurational space S is studied. The possibility of breaking in S the time-independent Schrodinger equation of the system into two separated one-dimensional one-body Schrodinger equations is assumed. In this paper, we focus on how the latter property is countered by imposing such boundary conditions as confinement to a limited region of S and/or restrictions on the joint coordinate probability density stemming from the sign-invariance condition of the relative coordinate (an impenetrability condition). Our investigation demonstrates the reducibility of the problem under scrutiny into that of a single particle living in a limited domain …
Number theory implications on the physical properties of elementary cubic networks of Josephson junctions
2003
Number theory concepts are used to investigate the periodicity properties of the voltage vs applied flux curves of elementary cubic networks of Josephson junctions. It is found that equatorial gaps appearing on the unitary sphere, on which points representing the directions in space for which these curves show periodicity are collected, can be understood by means of Gauss condition on the sum of the squares of three integers.
An Existence Result for Fractional Kirchhoff-Type Equations
2016
The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.