记录值中的随机序与年龄性质

研究记录值中的随机序与年龄性质．证明了任何通过两个分布函数的行为所定义的随机序,均可以被它们相应的记录值所保持,而两个随机变量之间的剩余财富序,可以导致其相应记录值序列的平均连续增量的序关系．也讨论了K-记录值的连续增量的年龄性质．     

Rough singular integrals associated with surfaces of Van der Corput type简

In this paper,the authors establish the Lp-mapping properties for a class of singular integrals along surfaces in Rn of the form {φ(|u|)u : u ∈ Rn} as well as the related maximal operators provided that the function φ satisfies certain oscillatory integral estimates of Van der Corput type,and the integral kernels are given by the radial function h ∈Δγ(R+) for γ 1 and the sphere function Ω∈ Fβ(Sn.1) for some β 0,which is distinct from H1(Sn.1).     

An ultra-fast smoothing algorithm for time–frequency transforms based on Gabor functions

Gabor functions, Gaussian wave packets, are optimally localized in time and frequency, and thus in principle ideal as (frame) basis functions for a wavelet, windowed Fourier or wavelet-packet transform for the detection of events in noisy signals or for data compression. A major obstacle for their use is that a tailored efficient operator acting on the transform coefficients for altering the width of the wave packets does not exist. However, by virtue of a curious property of the Gabor functions it is possible to change the width of the wave packets using just one-dimensional convolutions with very short kernels. The cost of a wavelet-type transform based on the scheme presented below is similar to that of a low order wavelet transform for a compact kernel and significantly less than the algorithme à trous. The scheme can hence easily be employed for the processing of signals in real time.     

Optimized projections for compressed sensing via rank-constrained nearest correlation matrix

Optimizing the acquisition matrix is useful for compressed sensing of signals that are sparse in overcomplete dictionaries, because the acquisition matrix can be adapted to the particular correlations of the dictionary atoms. In this paper a novel formulation of the optimization problem is proposed, in the form of a rank-constrained nearest correlation matrix problem. Furthermore, improvements for three existing optimization algorithms are introduced, which are shown to be particular instances of the proposed formulation. Simulation results show notable improvements and superior robustness in sparse signal recovery.     

Dunkl’s theory and best approximation by entire functions of exponential type in L 2-metric with power weight

In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L2,κ(Rd) by a subspace E2κ(σ)(SE2κ(σ)), which is a subspace of entire functions of exponential type(spherical exponential type) at most σ. Here L2,κ(Rd) denotes the space of all d-variate functions f endowed with the L2-norm with the weight v2κ(x) =ξ∈R, which is defined by a positive+|(ξ, x)|κ(ξ)subsystem R+ of a finite root system RRdand a function κ(ξ) : R → R+ invariant under the reflection group G(R) generated by R. In the case G(R) = Zd2, we get some exact results. Moreover,the deviation of best approximation by the subspace E2κ(σ)(SE2κ(σ)) of some class of the smooth functions in the space L2,κ(Rd) is obtained.     

On spatial contagion and multivariate GARCH models

We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two‐step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula‐GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.     

Real Paley-Wiener theorems for the Clifford Fourier transform

Associated with the Dirac operator and partial derivatives, this paper establishes some real Paley-Wiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform (CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT, the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin.     

Numerical inversion of laplace transform via wavelet in partial differential equations

This article presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that P is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulae of listing table (Chen et al., Journal of The Franklin Institute 303 (1977), 267–284) to a minimum expression and obtain the optimal operation speed. The local property of Haar wavelet is fully applied to shorten the calculation process in the task. The operational method presented in this article owns the advantages of simpler computation as well as broad application. We still can obtain satisfying solution even under large matrix. Moreover, we do not have numerically unstable problems. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 536–549, 2014     

一种基于相关系数矩阵的TOPSIS决策方法

在多属性决策分析中,传统的TOPSIS法是基于欧氏距离来计算各方案到正负理想点的距离,但欧氏距离没有考虑各属性之间的相关性;从这一角度出发,将相关系数矩阵与欧式距离结合,从而弥补了欧氏距离的不足,最后进行了实例分析.