A transference theorem for hermite expansions

A transference theorem for multipliers of Hermite expansions is proved. The result allows to transfer weightedL ²(ℝ ⁿ ) estimates from lower to higher dimensions. Research of the author supported by grant BFM2003-06335-603-03 of the D.G.I..     

Hierarchical visual data mining for large-scale data

Summary  An increasingly important problem in exploratory data analysis and visualization is that of scale; more and more data sets are much too large to analyze using traditional techniques, either in terms of the number of variables or the number of records. One approach to addressing this problem is the development and use of multiresolution strategies, where we represent the data at different levels of abstraction or detail through aggregation and summarization. In this paper we present an overview of our recent and current activities in the development of a multiresolution exploratory visualization environment for large-scale multivariate data. We have developed visualization, interaction, and data management techniques for effectively dealing with data sets that contain millions of records and/or hundreds of dimensions, and propose methods for applying similar approaches to extend the system to handle nominal as well as ordinal data.     

Visualizing parameters from loglinear models

Summary  This paper presents a graphical display for the parameters resulting from loglinear models. Loglinear models provide a method for analyzing associations between two or several categorical variables and have become widely accepted as a tool for researchers during the last two decades. An important part of the output of any computer program focused on loglinear models is that devoted to estimation of parameters in the model. Traditionally, this output has been presented using tables that indicate the values of the coefficients, the associated standard errors and other related information. Evaluation of these tables can be rather tedious because of the number of values shown as well as their rather complicated structure, mainly when the analyst needs to consider several models before reaching a model with a good fit. Therefore, a graphical display summarizing tables of parameters could be of great help in this situation. In this paper we put forward an interactive dynamic graphical display that could be used in such fashion.     

A note on a generalization of Diliberto’s Theorem for certain differential equations of higher dimension

In the theory of autonomous perturbations of periodic solutions of ordinary differential equations the method of the Poincaré mapping has been widely used. For the analysis of properties of this mapping in the case of two-dimensional systems, a result first obtained probably by Diliberto in 1950 is sometimes used. In the paper, this result is (partially) extended to a certain class of autonomous ordinary differential equations of higher dimension.This research was supported by Grant No. 201/99/0295 of the Grant Agency of the Czech Republic.This revised version was published online in April 2005 with a corrected missing date string.     

Counting Singular Matrices with Primitive Row Vectors

We solve an asymptotic problem in the geometry of numbers, where we count the number of singular n×n matrices where row vectors are primitive and of length at most T. Without the constraint of primitivity, the problem was solved by Y. Katznelson. We show that as T, the number is asymptotic to for n3. The 3-dimensional case is the most problematic and we need to invoke an equidistribution theorem due to W. M. Schmidt.     

Anisotropic<Emphasis Type="Italic">s</Emphasis>-wave or<Emphasis Type="Italic">d</Emphasis>-wave pairing? Analysis of experiments on ion irradiation of YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-x</Subscript> films

The effect of ion irradiation on the superconducting transition temperatureT _c and resistivityρ _ab (T) of YBa₂Cu₃O_7-x films with different oxygen content (initial temperatureT _c0≈90 K and 60 K) is studied experimentally. The dependenciesT _c /T _c0 on residual resistivityρ _o are obtained in very wide range 0.2<T _c /T _c0 <1 andρ _o μΩ·cm. The critical values ofρ _o , corresponding to the vanishing of superconductivity, are found to be an order of magnitude larger then those predicted by theory ford-wave pairing. At 0.5÷0.6<T _c /T _c0<1 the experimental data are in close agreement with theoretical dependencies, obtained for the anisotropics-wave superconductor within the BCS-framework.     

Linear programming solutions and distance functions under α-returns to scale

This note generalizes analytical relationships among activity variables of Dataenvelopment analysis models previously derived in a previous article by theauthors of this note. We relax the assumption of constant returns to scale byshowing that the key results hold under a weaker assumption of homogeneity. Weuse the notion of α-returns to scale to extend the analysis tostrictly increasing and decreasing returns, covering now the whole range ofreturns to scale for multi-output homogenous technologies.     

Univalent Functions, <Emphasis Type="Italic">VMOA</Emphasis> and Related Spaces

This paper is concerned mainly with the logarithmic Bloch space ℬ_log which consists of those functions f which are analytic in the unit disc \mathbbD{\mathbb{D}} and satisfy sup_{|z| < 1}(1-|z|)log\frac11-|z||f^￠(z)| < ￥\sup_{\vert z\vert <1}(1-\vert z\vert )\log\frac{1}{1-\vert z\vert}\vert f^{\prime}(z)\vert <\infty , and the analytic Besov spaces B ^p , 1≤p<∞. They are all subspaces of the space VMOA. We study the relation between these spaces, paying special attention to the membership of univalent functions in them. We give explicit examples of:

A biased random-key genetic algorithm with forward-backward improvement for the resource constrained project scheduling problem

This paper presents a biased random-key genetic algorithm for the resource constrained project scheduling problem. The chromosome representation of the problem is based on random keys. Active schedules are constructed using a priority-rule heuristic in which the priorities of the activities are defined by the genetic algorithm. A forward-backward improvement procedure is applied to all solutions. The chromosomes supplied by the genetic algorithm are adjusted to reflect the solutions obtained by the improvement procedure. The heuristic is tested on a set of standard problems taken from the literature and compared with other approaches. The computational results validate the effectiveness of the proposed algorithm.