Stochastic signal analysis: Numerical representation and applications to system theory

Alternative procedures for representing a stochastic signal as a denumerable series with uncorrelated terms are developed. The study includes considerations about parametric rescaling and its repercussions on the orthogonal expansion, as well as numerical techniques for approaching such an expansion. In addition, applications to the Gaussian characterization of stochastic signals, filtering and stochastic modelling are treated.     

A note about the Gaussian property of the Brownian bridge

The Gaussian property of the Brownian bridge is characterized as an application of Ramachandran's theorem in terms of the independence of the random variables that appear in the Karhunen-Loéve expansion of the process. A reference about the construction of the Brownian bridge by means of functional transformations is also included.     

基于Karhunen-Loève变换和小波谱特征矢量量化的三维谱像数据压缩

提出了基于Karhunen Lo埁ｖｅ变换的小波谱特征矢量量化三维谱像数据压缩方法耍幔颍瑁酰睿澹?Lo埁ｖｅ变换 /小波变换 /小波谱特征矢量量化方法应用了Karhunen Lo埁ｖｅ变换的消除谱相关性优良性能 ,应用二维小波变换消除空间相关性 ,在小波变换域内应用二维集分割嵌入块编码和一维谱特征矢量量化对三维谱像数据压缩 ,获得较高的压缩性能。实验结果表明 :Karhunen Lo埁ｖｅ变换 /小波变换 /小波谱特征矢量量化编码比Karhunen Lo埁ｖｅ变换 /小波变换 /改进对块零树编码和Karhunen Lo埁ｖｅ变换 /小波变换 /快速矢量量化编码方法在同样压缩比条件下 ,峰值信噪比提高 2dB和 1dB以上 ,而速度提高了 1.5和 8倍 ,整体压缩性能有较大的提高     

Spectrophotometric and physicochemical investigations of Congo,alizarin red dyes and BSA interactions with Au,Ag and Au/Ag mix nanoparticles,and their antimicrobial activities

Individual and mix metal nanoparticles of Ag and Au have been prepared by the reducing method where citrate was used as reducing/stabilizing agent. The prepared NPs were characterized with UV/Visible and transmission electron microscopic (TEM) tools. The characteristic peak in UV/Visible at 525, 444 and 531 nm for Au, Ag and Ag/Au mix NPs respectively, gave primary confirmation of prepared NPs. TEM analysis showed the size of nanoparticles as 44.04, 19.78 and 30.93 nm for Ag, Au and Ag/Au mix NPs respectively. Congo and alizarin red dye interactions studies have been performed with prepared NPs to see the removal of the pollutants from water. Congo dye has shown weaker interaction as compared to alizarin due to structural symmetry. Amongst all, the AgNPs have shown maximum 67% and 75% interactions with Congo red and alizarin respectively due to high negative charges on the surface. The Au, Ag and Au/Ag mix NPs have shown stronger interaction with bovine serum albumin (BSA) protein up to 51, 59, 55% respectively, estimated through UV/Vis and physicochemical analysis. The biological evaluations of the prepared NPs have shown their antibacterial activity against Gram + ve and –ve species showing up to 9 cm zone of inhibition. The BSA interaction and antibacterial activity of NPs reveal the importance of NPs in medicinal field.     

Probabilistic models for stochastic elliptic partial differential equations

Mathematical requirements that the random coefficients of stochastic elliptical partial differential equations must satisfy such that they have unique solutions have been studied extensively. Yet, additional constraints that these coefficients must satisfy to provide realistic representations for physical quantities, referred to as physical requirements, have not been examined systematically.     

Approximation and Reconstruction of the Electrostatic Field in Wire–Plate Precipitators by a Low-Order Model

The numerical computation of the ionic space charge and electric field produced by corona discharge in a wire–plate electrostatic precipitator (ESP) is considered. The electrostatic problem is defined by a reduced set of the Maxwell equations. Since self-consistent conditions at the wire and at the plate cannot be specified a priori, a time-consuming iterative numerical procedure is required. The efficiency of all numerical solvers of the reduced Maxwell equations depends in particular on the accuracy of the initial guess solution. The objectives of this work are two: first, we propose a semianalytical technique based on the Karhunen–Loève (KL) decomposition of the current density field J, which can significantly improve the performance of a numerical solver; second, we devise a procedure to reconstruct the complete electric field from a given J. The approximate solution of the current density field is based on the derivation of an analytical approximation , which, added to a linear combination of few KL basis functions, constitutes an accurate approximation of J. In the first place, this result is useful for optimization procedures of the current density field, which involve the computation of many different configurations. Second, we show that from the current density field we can obtain an accurate estimate for the complete electrostatic field which can be used to speed up the convergence of the iterative procedure of standard numerical solvers.     

Curvature Estimates for the Level Sets of Solutions to the Monge-Amp`ere Equation detD2u = 1

For the Monge-Ampere equation det D2u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained.     

A priori reduction method for solving the two-dimensional Burgers’ equations

The two-dimensional Burgers’ equations are solved here using the A Priori Reduction method. This method is based on an iterative procedure which consists in building a basis for the solution where at each iteration the basis is improved. The method is called a priori because it does not need any prior knowledge of the solution, which is not the case if the standard Karhunen-Loéve decomposition is used. The accuracy of the APR method is compared with the standard Newton-Raphson scheme and with results from the literature. The APR basis is also compared with the Karhunen-Loéve basis.     

Extending local mixture models

Local mixture models have proved useful in many statistical applications. This paper looks at ways in which the local assumption, which is used in an asymptotic approximation, can be relaxed in order to generate a much larger class of models which still have the very attractive geometric and inferential properties of local mixture models. The tool used to develop this large class of models is the Karhunen–Loève decomposition. Computational issues associated with working with these models are also briefly considered.