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Quadratic integral equations in reflexive Banach space

Hussein A.H. Salem (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is devoted to proving the existence of weak solutions to some quadratic integral equations of fractional type in a reflexive Banach space relative to the weak topology. A special case will be considered.

Quadratic Mean Radius of a Polynomial in C(Z)

Ivanov, K., Sharma, A. (1996)

Serdica Mathematical Journal

* Dedicated to the memory of Prof. N. ObreshkoffA Schoenberg conjecture connecting quadratic mean radii of a polynomial and its derivative is verified for some kinds of polynomials, including fourth degree ones.

Quantifier elimination in quasianalytic structures via non-standard analysis

Krzysztof Jan Nowak (2015)

Annales Polonici Mathematici

The paper is a continuation of an earlier one where we developed a theory of active and non-active infinitesimals and intended to establish quantifier elimination in quasianalytic structures. That article, however, did not attain full generality, which refers to one of its results, namely the theorem on an active infinitesimal, playing an essential role in our non-standard analysis. The general case was covered in our subsequent preprint, which constitutes a basis for the approach presented here....

Quantifier elimination, valuation property and preparation theorem in quasianalytic geometry via transformation to normal crossings

Krzysztof Jan Nowak (2009)

Annales Polonici Mathematici

This paper investigates the geometry of the expansion Q of the real field ℝ by restricted quasianalytic functions. The main purpose is to establish quantifier elimination, description of definable functions by terms, the valuation property and preparation theorem (in the sense of Parusiński-Lion-Rolin). To this end, we study non-standard models of the universal diagram T of Q in the language ℒ augmented by the names of rational powers. Our approach makes no appeal to the Weierstrass preparation...

Quantitative Isoperimetric Inequalities on the Real Line

Yohann de Castro (2011)

Annales mathématiques Blaise Pascal

In a recent paper A. Cianchi, N. Fusco, F. Maggi, and A. Pratelli have shown that, in the Gauss space, a set of given measure and almost minimal Gauss boundary measure is necessarily close to be a half-space.Using only geometric tools, we extend their result to all symmetric log-concave measures on the real line. We give sharp quantitative isoperimetric inequalities and prove that among sets of given measure and given asymmetry (distance to half line, i.e. distance to sets of minimal perimeter),...

Quasi-concave copulas, asymmetry and transformations

Elisabetta Alvoni, Pier Luigi Papini (2007)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider a class of copulas, called quasi-concave; we compare them with other classes of copulas and we study conditions implying symmetry for them. Recently, a measure of asymmetry for copulas has been introduced and the maximum degree of asymmetry for them in this sense has been computed: see Nelsen R.B., Extremes of nonexchangeability, Statist. Papers 48 (2007), 329–336; Klement E.P., Mesiar R., How non-symmetric can a copula be?, Comment. Math. Univ. Carolin. 47 (2006), 141–148....

Quasicontinuity and related properties of functions and multivalued maps

Janina Ewert (1995)

Mathematica Bohemica

The main results presented in this paper concern multivalued maps. We consider the cliquishness, quasicontinuity, almost continuity and almost quasicontinuity; these properties of multivalued maps are characterized by the analogous properties of some real functions. The connections obtained are used to prove decomposition theorems for upper and lower quasicontinuity.

Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...

Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Marcus Wagner (2011)

ESAIM: Control, Optimisation and Calculus of Variations

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration...

Quasi-copulas with quadratic sections in one variable

José Antonio Rodríguez–Lallena, Manuel Úbeda-Flores (2008)

Kybernetika

We introduce and characterize the class of multivariate quasi-copulas with quadratic sections in one variable. We also present and analyze examples to illustrate our results.

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