The discriminants associated to isotropy representations of symmetric spaces

We consider a generalized discriminant associated to a symmetric space which generalizes the discriminant of real symmetric matrices, and note that it can be written as a sum of squares of real polynomials. A method to estimate the minimum number of squares required to represent the discrimininant is developed and applied in examples.

BANACH SPACES WITHOUT MINIMAL SUBSPACES - EXAMPLES

We analyse several examples of separable Banach spaces, some of them new, and relate them to several dichotomies obtained in [11], by classifying them according to which side of the dichotomies they fall.

How far is C-0(Gamma, X) with Gamma discrete from C-0(K, X) spaces?

For a locally compact Hausdorff space K and a Banach space X we denote by C-0(K, X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Gamma an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C-0(Gamma, X) and C-0(K, X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C-0(N, X) and C([1, omega(n)k], X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Hypoellipticity in spaces of ultradistributions-Study of a model case

In this work we study C (a)-hypoellipticity in spaces of ultradistributions for analytic linear partial differential operators. Our main tool is a new a-priori inequality, which is stated in terms of the behaviour of holomorphic functions on appropriate wedges. In particular, for sum of squares operators satisfying Hormander's condition, we thus obtain a new method for studying analytic hypoellipticity for such a class. We also show how this method can be explicitly applied by studying a model operator, which is constructed as a perturbation of the so-called Baouendi-Goulaouic operator.

Numerical assessment of stability of interface discontinuous finite element pressure spaces

The stability of two recently developed pressure spaces has been assessed numerically: The space proposed by Ausas et al. [R.F. Ausas, F.S. Sousa, G.C. Buscaglia, An improved finite element space for discontinuous pressures, Comput. Methods Appl. Mech. Engrg. 199 (2010) 1019-1031], which is capable of representing discontinuous pressures, and the space proposed by Coppola-Owen and Codina [A.H. Coppola-Owen, R. Codina, Improving Eulerian two-phase flow finite element approximation with discontinuous gradient pressure shape functions, Int. J. Numer. Methods Fluids, 49 (2005) 1287-1304], which can represent discontinuities in pressure gradients. We assess the stability of these spaces by numerically computing the inf-sup constants of several meshes. The inf-sup constant results as the solution of a generalized eigenvalue problems. Both spaces are in this way confirmed to be stable in their original form. An application of the same numerical assessment tool to the stabilized equal-order P-1/P-1 formulation is then reported. An interesting finding is that the stabilization coefficient can be safely set to zero in an arbitrary band of elements without compromising the formulation's stability. An analogous result is also reported for the mini-element P-1(+)/P-1 when the velocity bubbles are removed in an arbitrary band of elements. (C) 2012 Elsevier B.V. All rights reserved.

Reproducing kernel Hilbert spaces associated with kernels on topological spaces

We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space X being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.

Antioxidant and inflammatory aspects of lipoprotein-associated phospholipase A2 (Lp-PLA2 ): a review

The association of cardiovascular events with Lp-PLA2 has been studied continuously today. The enzyme has been strongly associated with several cardiovascular risk markers and events. Its discovery was directly related to the hydrolysis of the platelet-activating factor and oxidized phospholipids, which are considered protective functions. However, the hydrolysis of bioactive lipids generates lysophospholipids, compounds that have a pro-inflammatory function. Therefore, the evaluation of the distribution of Lp-PLA2 in the lipid fractions emphasized the dual role of the enzyme in the inflammatory process, since the HDL-Lp-PLA2 enzyme contributes to the reduction of atherosclerosis, while LDL-Lp-PLA2 stimulates this process. Recently, it has been verified that diet components and drugs can influence the enzyme activity and concentration. Thus, the effects of these treatments on Lp-PLA2 may represent a new kind of prevention of cardiovascular disease. Therefore, the association of the enzyme with the traditional assessment of cardiovascular risk may help to predict more accurately these diseases.

Influence of obesity and cardiometabolic makers on lipoprotein-associated phospholipase A2 (Lp-PLA2) activity in adolescents: the healthy young cross-sectional study

Abstract Background Lipoprotein-associated phospholipase A2 activity (Lp-PLA2) is a good marker of cardiovascular risk in adults. It is strongly associated with stroke and many others cardiovascular events. Despite this, the impact of obesity on this enzyme activity and its relation to biomarkers of cardiovascular disease in adolescents is not very well investigated. The purpose of this article is to evaluate the influence of obesity and cardiometabolic markers on Lp-PLA2 activity in adolescents. Results This cross-sectional study included 242 adolescents (10–19 years) of both gender. These subjects were classified in Healthy Weight (n = 77), Overweight (n = 82) and Obese (n = 83) groups. Lipid profile, glucose, insulin, HDL size, LDL(−) and anti-LDL(−) antibodies were analyzed. The Lp-PLA2 activity was determined by a colorimetric commercial kit. Body mass index (BMI), waist circumference and body composition were monitored. Food intake was evaluated using three 24-hour diet recalls. The Lp-PLA2 activity changed in function to high BMI, waist circumference and fat mass percentage. It was also positively associated with HOMA-IR, glucose, insulin and almost all variables of lipid profile. Furthermore, it was negatively related to Apo AI (β = −0.137; P = 0.038) and strongly positively associated with Apo B (β = 0.293; P < 0.001) and with Apo B/Apo AI ratio (β = 0.343; P < 0.001). The better predictor model for enzyme activity, on multivariate analysis, included Apo B/Apo AI (β = 0.327; P < 0.001), HDL size (β = −0.326; P < 0.001), WC (β = 0.171; P = 0.006) and glucose (β = 0.119; P = 0.038). Logistic regression analysis demonstrated that changes in Apo B/Apo AI ratio were associated with a 73.5 times higher risk to elevated Lp-PLA2 activity. Conclusions Lp-PLA2 changes in function of obesity, and that it shows important associations with markers of cardiovascular risk, in particular with waist circumference, glucose, HDL size and Apo B/Apo AI ratio. These results suggest that Lp-PLA2 activity can be a cardiovascular biomarker in adolescence.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Pullback exponential attractors for evolution processes in Banach spaces: properties and applications

This article is a continuation of our previous work [5], where we formulated general existence theorems for pullback exponential attractors for asymptotically compact evolution processes in Banach spaces and discussed its implications in the autonomous case. We now study properties of the attractors and use our theoretical results to prove the existence of pullback exponential attractors in two examples, where previous results do not apply.

Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

A fixed point theorem for Meir-Keeler contractions in ordered metric spaces

[EN] The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.

Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations

[EN] The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

Fixed point theorems in partially ordered spaces and aplications

[ES]Recientemente, en la Teoría del punto fijo, han aparecido muchos resultados que obtienen condiciones suficientes para la existencia de un punto fijo si trabajamos con aplicaciones en un conjunto dotado de un orden parcial. Generalmente, estos resultados combinan dos teoremas del punto fijo fundamentales: el Teorema de la contracción de Banach y el Teorema de Knaster-Tarski.