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61.
In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.
62.
63.
Suppose that attached to each site z ∈ ? is a coin with bias θ(z), and only finitely many of these coins have nonzero bias. Allow a simple random walker to generate observations by tossing, at each move, the coin attached to its current position. Then we can determine the biases {θ(z)}z∈?, using only the outcomes of these coin tosses and no information about the path of the random walker, up to a shift and reflection of ?. This generalizes a result of Harris and Keane. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
64.
Alvaro P. Raposo Hans J. Weber David E. Alvarez-Castillo Mariana Kirchbach 《Central European Journal of Physics》2007,5(3):253-284
We briefly review the five possible real polynomial solutions of hypergeometric differential equations. Three of them are
the well known classical orthogonal polynomials, but the other two are different with respect to their orthogonality properties.
We then focus on the family of polynomials which exhibits a finite orthogonality. This family, to be referred to as the Romanovski
polynomials, is required in exact solutions of several physics problems ranging from quantum mechanics and quark physics to
random matrix theory. It appears timely to draw attention to it by the present study. Our survey also includes several new
observations on the orthogonality properties of the Romanovski polynomials and new developments from their Rodrigues formula. 相似文献
65.
A. Truffert 《Annals of Operations Research》1991,30(1):115-156
The conditional expectation of integrands and random sets is the main tool of stochastic optimization. This work wishes to make up for the lack of real synthesis about this subject. We improve the existing hypothesis and simplify the corresponding proofs. In the convex case we especially study the problem of the exchange of conditional expectation and subdifferential operators. 相似文献
66.
Eugene Savov 《Complexity》2007,12(3):61-76
The solar wind makes the magnetosphere to expand and contract as indicated by the expansions and contractions of the auroral oval due to balancing of the dynamic pressure of the ambient space plasma at inner and outer magnetic lines. This self‐similar magnetospheric behavior elucidates the controversial magnetic storm‐substorm relationship and reveals the 3D‐spiral structure of magnetic interaction. The found self‐similarly evolving structure of one seen as fundamental interaction suggests dynamic fractal unifying interaction that builds a firework universe having 3D‐spiral code. The unifying interaction is described with equation drawn in new fundamental dynamic fractal framework. The equation of unifying interaction converges to the inverse square laws and the principle of uncertainty at laboratory scales. The dynamic fractal fundamental framework is made of one 3D‐spirally‐faster‐inward contracting and expanding, oscillating, basic matter. It simply accounts for observed constant speed of light and for the creation of bright and dark bands on a screen behind a tiny slit. The dynamic fractal framework is quantitatively confirmed with the orbital data for the Milky Way Galaxy, the Sun, the Earth, and the triple asteroid system 87 Sylvia. Many testable predictions are also made. The presented new fundamental dynamic fractal framework allows qualitative and quantitative modeling and simplification. © 2007 Wiley Periodicals, Inc. Complexity 12: 61–76, 2007 相似文献
67.
For one‐dimensional simple symmetric random walk, the Hausdorff and packing dimensions of sets of sample paths with prescribed rate of returns to the origin are determined. This gives a multifractal decomposition of the underlying sample space. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
68.
Ansgar Jüngel 《Mathematische Nachrichten》1997,185(1):85-110
A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions. 相似文献
69.
70.
Jesús M. Velásquez Bermúdez 《Annals of Operations Research》2002,117(1-4):21-31
This document presents theoretical considerations about the solution of dynamic optimization problems integrating the Benders Theory, the Dynamic Programming approach and the concepts of Control Theory. The so called Generalized Dual Dynamic Programming Theory (GDDP) can be considered as an extension of two previous approaches known as Dual Dynamic Programming (DDP): The first is the work developed by Pereira and Pinto [3–5], which was revised by Velásquez and others [8,9]. The second is the work developed by Read and others [2,6,7]. 相似文献