Search results for "Mathematica"
showing 10 items of 7971 documents
Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media
1981
SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.
Non Linear Systems Under Complex α-Stable Le´vy White Noise
2003
The problem of predicting the response of linear and nonlinear systems under Levy white noises is examined. A method of analysis is proposed based on the observation that these processes have impulsive character, so that the methods already used for Poisson white noise or normal white noise may be also recast for Levy white noises. Since both the input and output processes have no moments of order two and higher, the response is here evaluated in terms of characteristic function.Copyright © 2003 by ASME
Itô-Stratonovitch Formula for the Wave Equation on a Torus
2010
We give an Ito-Stratonovitch formula for the wave equation on a torus, where we have no stochastic process associated to this partial differential equation. This gives a generalization of the classical Ito-Stratonovitch equation for diffusion in semi-group theory established by ourself in [18], [20].
Random Walk and Diffusion
2014
The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.
Bounds for Bessel functions
1989
We establish lower and upper bounds for the Bessel functionJ v (x) and the modified Bessel functionI v(x) of the first kind. Our chief tool is the differential equation satisfied by these functions.
Noether’s International School in Modern Algebra
2020
Pavel Alexandrov and Heinz Hopf met for the first time in Gottingen in the spring of 1926, soon after Alexandrov departed from Blaricum. Hopf had recently taken his doctorate in Berlin under Ludwig Bieberbach and Erhard Schmidt, and his research interests differed sharply from Alexandrov’s work in general topology.
Erzwingt die Quantenmechanik eine drastische Änderung unseres Weltbilds? Gedanken und Experimente nach Einstein, Podolsky und Rosen
1989
Von den Anfangen der Quantenmechanik bis heute gibt es Versuche, sie als statistische Theorie uber Ensembles individueller ‚klassischer’ Systeme zu interpretieren. Die Bedingungen, unter denen Theorien verborgener Parameter zu deterministischen Beschreibungen dieser individuellen Systeme als ‚klassisch’ angesehen werden konnen, wurden von Einstein, Podolsky und Rosen 1935 formuliert: 1. Physikalische Systeme sind im Prinzip separierbar. 2. Zu jeder physikalischen Grose, deren Wert man ohne Storung des betrachteten Systems mit Sicherheit voraussagen kann, existiert ein ihr entsprechendes Element der physikalischen Realitat. Zusammen sind sie, wie Bell 1964 gezeigt hat, prinzipiell unvertragl…
COMPLEX CONVEXITY AND VECTOR-VALUED LITTLEWOOD–PALEY INEQUALITIES
2003
Let 2 p 0s uch thatfHp(X) (� f(0)� p + λ (1 −| z| 2 ) p−1 � f � (z)� p dA(z)) 1/p ,f or all f ∈ H p (X). Applications to embeddings between vector-valued BMOA spaces defined via Poisson integral or Carleson measures are provided.
Explicit expressions for Sturm-Liouville operator problems
1987
Throughout this paper H will denote a complex separable Hilbert space and L(H) denotes the algebra of all bounded linear operators on H. If T lies in L(H), its spectrum σ(T) is the set of all complex numbers z such zI–T is not invertible in L(H) and its compression spectrum σcomp(T) is the set of all complex numbers z such that the range (zI-T)(H) is not dense in H ([3, p. 240]). This paper is concerned with the Sturm–Liouville operator problemwhere λ is a complex parameter and X(t), Q, Ei, Fi for i = l,2, and t∈[0,a], are bounded operators in L(H). For the scalar case, the classical Sturm-Liouville theory yields a complete solution of the problem, see [4], and [7]. For the finite-dimension…
Mappings of finite distortion: Reverse inequalities for the Jacobian
2007
Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Holder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f.