Гармонические отображения и, в частности, гармонические полиномы находят приложения во многих задачах прикладной математики, математической физики, механики и электротехники. Это связано с ключевой ролью, которую функции играют краевых физики. используются при описании плоских гармонических векторных полей гидродинамике, теории жидких кристаллов, плоского потенциала. Оценки полиномов их произво...

Many works have been carried out to compare the efficiency of several goodness of fit procedures for identifying whether or not a particular distribution could adequately explain a data set. In this paper a study is conducted to investigate the power of several goodness of fit tests such as Kolmogorov Smirnov (KS), Anderson-Darling(AD), CramervonMises (CV) and a proposed modification of Kolmogo...

Our investigation aims at detecting network intrusions using decision tree algorithms. Large differences in prior class probabilities of intrusion data have been reported to hinder the performance of decision trees. We propose to replace the Shannon entropy used in tree induction algorithms with a Kolmogorov Smirnov splitting criterion which locates a Bayes optimal cutpoint of attributes. The K...

Let ~o denote an arbitrary non-parametric unbiased test for a Gaussian shift given by an infinite dimensional parameter space. Then it is shown that the curvature of its power function has a principal component decomposition based on a Hilbert Schmidt operator. Thus every test has reasonable curvature only for a finite number of orthogonal directions of alternatives. As application the two-side...

Accurate goodness-of-fit tests for the extreme tails of empirical distributions is a very important issue, relevant in many contexts, including geophysics, insurance, and finance. We have derived exact asymptotic results for a generalization of the large-sample Kolmogorov-Smirnov test, well suited to testing these extreme tails. In passing, we have rederived and made more precise the approximat...

A statistical application to Gene Set Enrichment Analysis implies calculating the distribution of themaximum of a certain Gaussian process, which is a modification of the standard Brownian bridge. Using the transformation into a boundary crossing problem for the Brownian motion and a piecewise linear boundary, it is proved that the desired distribution can be approximated by an n-dimensional Ga...