Approximation theorems for a general class of truncated operators

In this paper we give direct approximation theorems for a general family of truncated operators. We discuss the linear and nonlinear cases.     

Pinpointing the complexity of the interval min–max regret knapsack problem

We show that a natural robust optimization variant of the knapsack problem is complete for the second level of the polynomial hierarchy.     

On the Numerical Range of Rational Matrix Functions

In this paper we investigate bounds of the numerical range of the derivative of a rational matrix function. Moreover, some results on connectedness are presented.     

Quasi-Frobenius Functors. Applications

We investigate functors between abelian categories having a left adjoint and a right adjoint that are similar (these functors are called quasi-Frobenius functors). We introduce the notion of a quasi-Frobenius bimodule and give a characterization of these bimodules in terms of quasi-Frobenius functors. Some applications to corings and graded rings are presented. In particular, the concept of quasi-Frobenius homomorphism of corings is introduced. Finally, a version of the endomorphism ring Theorem for quasi-Frobenius extensions in terms of corings is obtained.     

Analysis of underwater mammal vocalisations using time-frequency-phase tracker

One of the most challenging applications of time-frequency representations deals with the analysis of the signal issued from natural environment. Recently, the interest for passive underwater context increased, basically due to the rich information carried out by the natural signals. Taken into account the non-linear multi-component time-frequency behaviour of such signals, their analysis is a challenging problem.In this context, the analysis of underwater mammal’s whistles is aimed to extract, accurately and adaptively, their main time-frequency components. In this paper, we define a time-frequency-phase tracker which is composed of three steps. The first one consists of modelling the short-time segments of the vocalization by a set of third order polynomial phase modulations. The second step consists in the fusion of local polynomial phase modulations according to a local phase continuity criterion. Finally, in the third step, the detected time-frequency track is used to design the time-frequency filter, in charge of extracting the samples corresponding to the detected track. This procedure is then iterated until all component of interest are extracted.Tests provided for realistic scenarios and real data taken in Bay of Biscay at September 2009 containing whistles of common dolphin Delphinus delphis illustrate the potential and the benefits of the proposed approach.     

The large sieve inequality for integer polynomial amplitudes

We obtain a close to optimal version of the large sieve inequality with amplitudes given by the values of a polynomial with integer coefficients of degree ?2.     

Chain Conditions for Skew Polynomial Modules

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Strong tractability of multivariate integration of arbitrary high order using digitally shifted polynomial lattice rules

In this paper we prove the existence of digitally shifted polynomial lattice rules which achieve strong tractability results for Sobolev spaces of arbitrary high smoothness. The convergence rate is shown to be the best possible up to a given degree of smoothness of the integrand. Indeed we even show the existence of polynomial lattice rules which automatically adjust themselves to the smoothness of the integrand up to a certain given degree.Further we show that strong tractability under certain conditions on the weights can be obtained and that polynomial lattice rules exist for which the worst-case error can be bounded independently of the dimension. These results hold independent of the smoothness.     

Polynomial Neural Network for Linear and Non-linear Model Selection in Quantitative-Structure Activity Relationship Studies on the Internet

Abstract

This article presents a self-organising multilayered iterative algorithm that provides linear and non-linear polynomial regression models thus allowing the user to control the number and the power of the terms in the models. The accuracy of the algorithm is compared to the partial least squares (PLS) algorithm using fourteen data sets in quantitative-structure activity relationship studies. The calculated data show that the proposed method is able to select simple models characterized by a high prediction ability and thus provides a considerable interest in quantitative-structure activity relationship studies. The software is developed using client-server protocol (Java and C++ languages) and is available for world-wide users on the Web site of the authors.     

Extensions of some polynomial inequalities to the polar derivative

Let p(z) be a polynomial of degree n and for any real or complex number α, let Dαp(z)=np(z)+(α−z)p^′(z) denote the polar derivative of the polynomial p(z) with respect to α. In this paper, we obtain inequalities for the polar derivative of a polynomial having all its zeros inside or outside a circle. Our results shall generalize and sharpen some well-known polynomial inequalities.