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141.
In many practical problems, one needs to compare variabilities of several multidimensional populations. The concept of standardized generalized variance (SGV) is introduced as an extension of the concept of GV. Considering multivariate normal populations of possibly different dimensions and general covariance matrices, LRTs are derived for SGVs. The criteria turn out to be elegant multivariate analogs to those for tests for variances in the univariate cases. The null and nonnull distributions of the test criteria are deducdd in computable forms in terms of Special Functions, e.g., Pincherle'sH-function, by exploiting the theory of calculus of residues (Mathai and Saxena,Ann. Math. Statist.40, 1439–1448). 相似文献
142.
A random vector (X1, …, Xn), with positive components, has a Liouville distribution if its joint probability density function is of the formf(x1 + … + xn)x1a1.1 … xnan.1 with theai all positive. Examples of these are the Dirichlet and inverted Dirichlet distributions. In this paper, a comprehensive treatment of the Liouville distributions is provided. The results pertain to stochastic representations, transformation properties, complete neutrality, marginal and conditional distributions, regression functions, and total positivity and reverse rule properties. Further, these topics are utilized in various characterizations of the Dirichlet and inverted Dirichlet distributions. Matrix analogs of the Liouville distributions are also treated, and many of the results obtained in the vector setting are extended appropriately. 相似文献
143.
The present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations. Existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems. If the noise data are random, the results may be seen as a pathwise approach to SPDE's. For typical examples, such as spatially one-dimensional stochastic heat equations with additive or multiplicative perturbations of fractional Brownian type, we recover and extend known results. In addition, we propose to consider partial noises of low order. 相似文献
144.
145.
In this paper, we study the Holder regularity of weak solutions to the Dirichlet problem associated with the regional fractional Laplacian (-△)αΩ on a bounded open set Ω ■R(N ≥ 2) with C(1,1) boundary ■Ω. We prove that when f ∈ Lp(Ω), and g ∈ C(Ω), the following problem (-△)αΩu = f in Ω, u = g on ■Ω, admits a unique weak solution u ∈ W(α,2)(Ω) ∩ C(Ω),where p >N/2-2α and 1/2< α < 1. To solve this problem, we consider it into two special cases, i.e.,g ≡ 0 on ■Ω and f ≡ 0 in Ω. Finally, taking into account the preceding two cases, the general conclusion is drawn. 相似文献
146.
147.
分数阶微分方程的比较定理 总被引:3,自引:0,他引:3
本文给出了非线性Riemann—Liouville分数阶微分方程和Caputo分数阶微分方程与相应的非线性Volterra积分方程的等价性,并在此基础上建立了分数阶微分方程的比较定理. 相似文献
148.
随着物理与技术的深入研究,分数阶非线性系统的动力性态及其分数阶混沌系统的同步成为研究的焦点.研究了分数阶Duffing系统的动力性态包括混沌性质,并且由分数阶非线性稳定性准则得到了分数阶非自治系统的混沌同步.特别地,研究了由单一主动控制的分数阶Duffing系统的同步.相应的数值结果演示了方法的有效性. 相似文献
149.
150.
Vladimir V. Kisil 《Acta Appl Math》1999,59(1):79-109
We describe a construction of wavelets (coherent states) in Banach spaces generated by admissible group representations. Our main targets are applications in pure mathematics while connections with quantum mechanics are mentioned. As an example, we consider operator-valued Segal–Bargmann-type spaces and the Weyl functional calculus. 相似文献