Berezinians,Exterior Powers and Recurrent Sequences

We study power expansions of the characteristic function of a linear operator A in a p|q-dimensional superspace V. We show that traces of exterior powers of A satisfy universal recurrence relations of period q. ‘Underlying’ recurrence relations hold in the Grothendieck ring of representations of GL(V). They are expressed by vanishing of certain Hankel determinants of order q+1 in this ring, which generalizes the vanishing of sufficiently high exterior powers of an ordinary vector space. In particular, this allows to express the Berezinian of an operator as a ratio of two polynomial invariants. We analyze the Cayley–Hamilton identity in a superspace. Using the geometric meaning of the Berezinian we also give a simple formulation of the analog of Cramer’s rule Mathematics Subject Classification (2000): 15A15, 58A50, 81R99 To the memory of Felix Alexandrovich Berezin     

Dynamic ℤ d -Random Walks in a Random Scenery: A Strong Law of Large Numbers

In this paper, we study a _d -random walk on nearest neighbours with transition probabilities generated by a dynamical system . We prove, at first, that under some hypotheses, verifies a local limit theorem. Then, we study these walks in a random scenery , a sequence of independent, identically distributed and centred random variables and show that for certain dynamic random walks, satisfies a strong law of large numbers.     

Statistical Dynamics of Clustering in the Genome Structure

Clustering and long-range correlations in the nucleotide sequences of different categories of organisms are discussed. Clustering, mostly observed in higher eucaryotes, can be found at different length scales in DNA and Central Limit Theorems are used as links between these length scales. Several dynamical, statistical, mean-field models are proposed based on biologically motivated dynamical mechanisms and they successfully reproduce both the short range behavior observed in coding DNA and the long range, out-of-equilibrium features of non-coding DNA. Such dynamical mechanisms include aggregation of oligonucleotides, influx and DNA length reduction schemes, transpositions, and fusions of large DNA macromolecules. Fractality can be inferred from the short and long range correlations observed in the sequence structure of higher eucaryotes, where the non-coding part is relatively extended. In these organisms the DNA coding/non-coding alternation has the characteristics of finite size, fractal, random sets.     

Minimizing and Stationary Sequences of Convex Constrained Minimization Problems

In the asymptotic analysis of the minimization problem for a nonsmooth convex function on a closed convex set X in ⁿ, one can consider the corresponding problem of minimizing a smooth convex function F on ⁿ, where F denotes the Moreau–Yosida regularization of f. We study the interrelationship between the minimizing/stationary sequence for f and that for F. An algorithm is given to generate iteratively a possibly unbounded sequence, which is shown to be a minimizing sequence of f under certain regularity and uniform continuity assumptions.     

Fast convergence of quasi-Monte Carlo for a class of isotropic integrals

We consider the approximation of -dimensional weighted integrals of certain isotropic functions. We are mainly interested in cases where is large. We show that the convergence rate of quasi-Monte Carlo for the approximation of these integrals is . Since this is a worst case result, compared to the expected convergence rate of Monte Carlo, it shows the superiority of quasi-Monte Carlo for this type of integral. This is much faster than the worst case convergence, , of quasi-Monte Carlo.

     

基于极坐标的相向运动图像模糊的递归模型

成像过程中,被摄像目标和摄像机之间的相向运动会造成图像的辐射状模糊,辐射状模糊将减小有效视场,影响成像质量.本文在扇形网格采样的基础上,利用状态空间模型模拟了退化过程,用递归方法解决了空变问题,并利用对状态空间系统求逆的方法对退化图像进行了复原.计算机模拟显示,算法简单,复原图像清晰,取得了较满意的结果.     

Meeting the Welch and Karystinos-Pados Bounds on DS-CDMA Binary Signature Sets

The Welch lower bound on the total-squared-correlation (TSC) of binary signature sets is loose for binary signature sets whose length L is not a multiple of 4. Recently Karystinos and Pados [6,7] developed new bounds that are better than the Welch bound in those cases, and showed how to achieve the bounds with modified Hadamard matrices except in a couple of cases. In this paper, we study the open cases.     

On multivariate Gaussian tails

Let {X _{n, n} ≥1} be a sequence of standard Gaussian random vectors in ℝ _d ,d ≥ 2. In this paper we derive lower and upper bounds for the tail probabilityP{X _n >t _n } witht _n ∈ ℝ _d some threshold. We improve for instance bounds on Mills ratio obtained by Savage (1962,J. Res. Nat. Bur. Standards Sect. B,66, 93–96). Furthermore, we prove exact asymptotics under fairly general conditions on bothX _n andt _n , as ‖t _n ‖→∞ where the correlation matrix Σ _n ofX _n may also depend onn.     

Nonparametric estimation of a regression function by delta sequences

A somewhat more general class of nonparametric estimators for estimating an unknown regression functiong from noisy data is proposed. The regressor is assumed to be defined on the closed interval [0, 1]. This class of estimators is shown to be pointwisely consistent in the mean square sense and with probability one. Further, it turns out that these estimators can be applied to a wide class of noises.     

Sharp estimates for Jacobi matrices and chain sequences, II

Chain sequences are positive sequences {c_n} of the form c_n=g_n(1−g_n−1) for a nonnegative sequence {g_n}. They are very useful in estimating the norms of Jacobi matrices and for localizing the interval of orthogonality for orthogonal polynomials. We give optimal estimates for the chain sequences which are more precise than the ones obtained in the paper (Constructive Approx. 6 (1990) 363) and in our earlier paper (J. Approx. Theory 118 (2002) 94).