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991.
陈振龙 《数学物理学报(B辑英文版)》2014,(1):141-161
Let X(1)= {X(1)(s), s ∈ R+ } and X(2)= {X(2)(t), t ∈ R+ } be two independent nondegenerate diusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X(1)and X(2)are studied. More generally, let E1, E2 ■(0, ∞) and F Rd be Borel sets. A necessary condition and a suffcient condition for P{X(1)(E1) ∩ X(2)(E2) ∩ F = φ} 0 are proved in terms of the Bessel-Riesz type capacity and Hausdor measure of E1 ×E2 ×F in the metric space(R+ ×R+ ×Rd, ρ), where ρ is an unsymmetric metric defined in R+ × R+ × Rd. Under reasonable conditions, results resembling those of Browian motion are obtained. 相似文献
992.
Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy. 相似文献
993.
Mano j K.YADAV 《数学物理学报(B辑英文版)》2014,(5):1461-1472
In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function |x|n-1eβ|x|2/2,β≥ 0, x ∈ Rn. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation. 相似文献
994.
By studying the spectral properties of the underlying operator corresponding to the M/G/1 queueing model with optional second service we obtain that the time-dependent solution of the model strongly converges to its steady-state solution. We also show that the time-dependent queueing size at the departure point converges to the corresponding steady-state queueing size at the departure point. 相似文献
995.
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf(xkv(y)k-1)dwK(k)= Φ g(x)h(y), x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d'Alembert's and Wilson's equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc. 相似文献
996.
In this article, we obtain explicit solutions of a linear PDE subject to a class of radial square integrable functions with a monotonically increasing weight function
|x|n−1eβ|x|2/2,,
β≥0, x ∈?n. This linear PDE is obtained from a system of forced Burgers equation via the Cole-Hopf transformation. For any spatial dimension n > 1, the solution is expressed in terms of a family of weighted generalized Laguerre polynomials. We also discuss the large time behaviour of the solution of the system of forced Burgers equation. 相似文献
997.
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1000.
本文研究了一类可数点集的盒维数的计算问题.通过构造双Lipschitz映射,把原可数点集的盒维数的求解问题转化为求解一类相对简单的可数点集的盒维数.获得了两个单调的可数点集在具有同阶间隔时具有相同的上盒维数和下盒维数的结论.该结论为计算一类可数点集的盒维数提供了方便. 相似文献