Right closure of martingale sequences in the sense of theA-integral

In this paper new sufficient (necessary and sufficient for martingales of special form) conditions for the martingale closure from the right in the sense of theA-integral are given. These results follow from the theorem about passing to the limit under theA-integral. The theorem is established using the criterion for transposing iterated limits with respect to the base. It is shown that the sufficient conditions thus obtained are stronger than those previously known. Translated fromMatematicheskie Zametki, Vol.68, No. 1, pp. 98–104, July, 2000.     

Measurability of automorphisms of topological groups

Relations between the measurability and continuity of algebraic automorphisms of topological groups depending on the types of groups are examined. Various cases are considered and theorems on the continuity of measurable automorphisms are proved; for instance, such theorems are proved for separable locally compact groups and automorphisms measurable with respect to nonnegative Haar measures. On the other hand, examples of nonmetrizable nonseparable compact groups with Haar measures and of non-locally-compact separable metrizable groups with measures μ quasi-invariant with respect to dense subgroups admittings μ-measurable discontinous automorphisms are given. Translated fromMatenmaticheskie Zametki, Vol. 68, No. 1, pp. 105–112, July, 2000. An erratum to this article can be found online at .     

"非汉字符号"-Haar子空间的性质

引进1个新的L-Haar子空间,证明了当L为单位算子时, L-Haar子空间与通常的Haar子空间等价,给出了L-Haar子空间的1个性质定理.     

Rationalized Haar functions method for solving Fredholm and Volterra integral equations

This paper presents a computational technique for Fredholm integral equation of the second kind and Volterra integral equation of the second kind. The method is based upon Haar functions approximation. Properties of Rationalized Haar functions are first presented, the operational matrix of integration together with product operational matrix and Newton–Cotes nodes are utilized to reduce the computation of integral equations into some algebraic equations. The method is computationally attractive and applications are demonstrated through illustrative examples.     

Bayes estimation of number of signals

Bayes estimation of the number of signals, q, based on a binomial prior distribution is studied. It is found that the Bayes estimate depends on the eigenvalues of the sample covariance matrix S for white-noise case and the eigenvalues of the matrix S ₂ (S ₁+A)^–1 for the colored-noise case, where S ₁ is the sample covariance matrix of observations consisting only noise, S ₂ the sample covariance matrix of observations consisting both noise and signals and A is some positive definite matrix. Posterior distributions for both the cases are derived by expanding zonal polynomial in terms of monomial symmetric functions and using some of the important formulae of James (1964, Ann. Math. Statist., 35, 475–501).     

Rearrangements of the Haar System that Preserve BMO

Let D denote the collection of dyadic intervals in the unitinterval. Let be a rearrangement of the dyadic intervals. Westudy the induced operator where h_I is the L normalized Haar function. We find geometricconditions on which are necessary and sufficient for T to bebounded on BMO. We also characterize the rearrangements of theL^p normalized Haar system in L^p. 1991 Mathematics Subject Classification:42C20, 43A17, 47B38.     

正交Haar变换的眉毛识别方法

【目的】提高现有眉毛识别方法的识别效率。【方法】采用快速正交Haar变换模板匹配算法(FOHT),设计一种基于正交Haar变换的眉毛识别方法;同时,使用最大标准子模板和自适应阈值解决了FOHT算法只能处理标准模板且需要手动设置阈值的缺陷。【结果】所构建的眉毛识别方法比原方法效率提高约32%。【结论】正交Haar变换的眉毛识别方法实时性强,具有一定的实用价值。     

A Haar wavelets based approximation for nonlinear inverse problems influenced by unknown heat source

In this discussion, a new numerical algorithm focused on the Haar wavelet is used to solve linear and nonlinear inverse problems with unknown heat source. The heat source is dependent on time and space variables. These types of inverse problems are ill-posed and are challenging to solve accurately. The linearization technique converted the nonlinear problem into simple nonhomogeneous partial differential equation. In this Haar wavelet collocation method (HWCM), the time part is discretized by using finite difference approximation, and space variables are handled by Haar series approximation. The main contribution of the proposed method is transforming this ill-posed problem into well-conditioned algebraic equation with the help of Haar functions, and hence, there is no need to implement any sort of regularization technique. The results of numerical method are efficient and stable for this ill-posed problems containing different noisy levels. We have utilized the proposed method on several numerical examples and have valuable efficiency and accuracy.