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791.
Given a principal value convolution on the Heisenberg group H
n
= ℂ
n
× ℝ, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on ℂ
n
. We also calculate the Dirichlet kernel for the Laguerre expansion on the group H
n
.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
792.
Shi-Hai Dong 《Foundations of Physics Letters》2002,15(4):385-395
In this letter, by applying a suitable ansatz to the wave functions, the solutions of the D-dimensional radial Schrödinger equation with some anharmonic potentials are obtained. 相似文献
793.
794.
Predrag M. Rajković Sladjana D. Marinković Miomir S. Stanković 《The Ramanujan Journal》2006,12(2):245-255
We construct the sequence of orthogonal polynomials with respect to an inner product which is defined by q-integrals over a collection of intervals in the complex plane. We prove that they are connected with little q-Jacobi polynomials. For such polynomials we discuss a few representations, a recurrence relation, a difference equation,
a Rodrigues-type formula and a generating function.
2000 Mathematics Subject Classification Primary—33D45, 42C05 相似文献
795.
利用表象变换方法,对含逆场算符的J-C模型,分别在相互作用表象中和薛定谔表象中求出了系统的演化波函数,并讨论了失谐量为零时的拉比振动. 相似文献
796.
Di Xin ZHANG 《数学学报(英文版)》2006,22(2):339-346
So far the study of exponential bounds of an empirical process has been restricted to a bounded index class of functions. The case of an unbounded index class of functions is now studied on the basis of a new symmetrization idea and a new method of truncating the original probability space; the exponential bounds of the tail probabilities for the supremum of the empirical process over an unbounded class of functions are obtained. The exponential bounds can be used to establish laws of the logarithm for the empirical processes over unbounded classes of functions. 相似文献
797.
Let be a bounded domain with C
2 boundary. And let H
k
be the set of all polyharmonic functions f with order k on Ω. For 0<p, q≤∞ and ϕ a normal weight, the mixed-norm space consists of all function f in H
k
for which the mixed-norm ||·||
p, q, ϕ
<∞. The main result of the paper is the norm equivalence:
where x
0 is a fixed point in Ω, m is a positive integer and is the jth gradient of f. A similar result for Bloch-type spaces is also obtained.
This research is partially supported by the National Natural Science Foundation of China (10471039), the MNZŽS Grant No. 144010
(Serbia), and the Natural Science Foundation of Zhejiang Province (M103104). 相似文献
798.
In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc. 相似文献
799.
Sandra S. Ferreira Dário Ferreira Célia Nunes João T. Mexia 《Mathematical Methods in the Applied Sciences》2023,46(1):356-367
Sub-models of mixed linear models are considered. The independence of these sub-models leads to sufficient statistics for the parameters relevant for their densities. Using pivot variables, confidence regions are obtained as well hypothesis testing for variance components, estimable functions, and estimable vectors. In addition, to compare the estimators and the models, we present the histograms with the empirical joint densities for positive and negative parts of the estimators. The figures, for the two-dimensional charts, contain the corresponding UMVUE and are all unimodal with the UMVUE near the mode. The nearness of the estimators and the modes validates the presented methodology and allows the safe use of induced densities. A numerical example applied to real data is presented. 相似文献
800.
This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method. 相似文献