We analyse the representation of positive polynomials in terms Sums Squares. provide a quantitative version Putinar’s Positivstellensatz over compact basic semialgebraic set S, with new polynomial bound on degree positivity certificates. This involves Łojasiewicz exponent associated to description S. show that if gradients active constraints are linearly independent S (Constraint Qualification ...

Chapter 1 Pseudo Generalized Least Squares Regression Estimation with Spatial Data Abstract It is hard to account for all pairwise correlations in the estimation of the mean parameters for a large sample of spatial data. In a linear regression model, a pseudo generalized least squares (PGLS) approach is proposed. Data could be divided into groups according to natural geographic areas, only corr...

This paper considers the electromagnetic scattering problem of periodically corrugated surface with local imperfection of structural periodicity, and presents a formulation based on the coordinate transformation method (C-method). The C-method is originally developed to analyze the plane-wave scattering from perfectly periodic structures, and uses the pseudo-periodic property of the fields. The...

inclined retaining walls with slopes less than perpendicular are appropriate candidates in several engineering problems. yet, to the knowledge of authors, only a few analytical solution for calculation of active earth pressure on such walls, which will be usually smaller than the same pressure on vertical ones, has been presented neither in research papers nor in design codes. considering limit...

Recently, the block-pulse functions (BPFs) are used in solving electromagnetic scattering problem, which are modeled as linear Fredholm integral equations (FIEs) of the second kind. But the theoretical aspect of this method has not fully investigated yet. In this article, in addition to presenting a new approach for solving FIE of the second kind, the theory of both methods is investigated as a...

Pseudo-repetitions are a natural generalisation of the classical notion of repetitions in sequences: they are the repeated concatenation of a word and its encoding under a certain morphism or antimorphism (anti-/morphism, for short). We approach the problem of deciding efficiently, for a word w and a literal anti-/morphism f , whether w contains an instance of a given pattern involving a variab...