Lindelof spaces which are indestructible, productive, or D

We discuss relationships in Lindelof spaces among the properties "indestructible". "productive", "D", and related properties. (C) 2011 Elsevier B.V. All rights reserved.

Two extensions for the ALWABP: Parallel stations and collaborative approach

In this article, we introduce two new variants of the Assembly Line Worker Assignment and Balancing Problem (ALWABP) that allow parallelization of and collaboration between heterogeneous workers. These new approaches suppose an additional level of complexity in the Line Design and Assignment process, but also higher flexibility; which may be particularly useful in practical situations where the aim is to progressively integrate slow or limited workers in conventional assembly lines. We present linear models and heuristic procedures for these two new problems. Computational results show the efficiency of the proposed approaches and the efficacy of the studied layouts in different situations. (C) 2012 Elsevier B.V. All rights reserved.

Collaborative fuzzy clustering algorithms: some refinements and design guidelines

There are some variants of the widely used Fuzzy C-Means (FCM) algorithm that support clustering data distributed across different sites. Those methods have been studied under different names, like collaborative and parallel fuzzy clustering. In this study, we offer some augmentation of the two FCM-based clustering algorithms used to cluster distributed data by arriving at some constructive ways of determining essential parameters of the algorithms (including the number of clusters) and forming a set of systematically structured guidelines such as a selection of the specific algorithm depending on the nature of the data environment and the assumptions being made about the number of clusters. A thorough complexity analysis, including space, time, and communication aspects, is reported. A series of detailed numeric experiments is used to illustrate the main ideas discussed in the study.

International collaborative project to compare and monitor the nutritional composition of processed foods

Background: Chronic diseases are the leading cause of premature death and disability in the world with overnutrition a primary cause of diet-related ill health. Excess energy intake, saturated fat, sugar, and salt derived from processed foods are a major cause of disease burden. Our objective is to compare the nutritional composition of processed foods between countries, between food companies, and over time. Design: Surveys of processed foods will be done in each participating country using a standardized methodology. Information on the nutrient composition for each product will be sought either through direct chemical analysis, from the product label, or from the manufacturer. Foods will be categorized into 14 groups and 45 categories for the primary analyses which will compare mean levels of nutrients at baseline and over time. Initial commitments to collaboration have been obtained from 21 countries. Conclusions: This collaborative approach to the collation and sharing of data will enable objective and transparent tracking of processed food composition around the world. The information collected will support government and food industry efforts to improve the nutrient composition of processed foods around the world.

THE ASSOCIATION BETWEEN CHILDHOOD ADVERSITY AND COMPONENTS OF METABOLIC SYNDROME IN ADULTS WITH MOOD DISORDERS: RESULTS FROM THE INTERNATIONAL MOOD DISORDERS COLLABORATIVE PROJECT

Objective: We sought to determine whether a reported history of childhood adversity is associated with components of the National Cholesterol Education Program Adult Treatment Panel III (NCEP-ATP-III)-defined metabolic syndrome in adults with mood disorders. Method: This was a cross-sectional analysis of adult outpatients (N = 373; n = 230 female, n = 143 male; mean age [SD] = 42.86 [14.43]) from the International Mood Disorders Collaborative Project (University of Toronto and Cleveland Clinic) with DSM-IV-defined major depressive disorder and bipolar I/II disorder. Childhood adversity was measured with the Klein Trauma & Abuse-Neglect self-report scale. The groups with and without childhood adversity were compared to determine possible differences in the rates of metabolic syndrome and its components. Logistic and linear regressions adjusted for age, sex, education, employment status, and smoking were used to evaluate the association between childhood adversity and components of metabolic syndrome. Results: For the full sample, 83 subjects (22.25%) met criteria for metabolic syndrome. Individuals reporting a history of any childhood adversity had higher systolic and diastolic blood pressure (systolic: p = 0.040; diastolic: p = 0.038). Among subjects with a history of sexual abuse, a significant proportion met criteria for obesity (45.28% vs. 32.88%; p = 0.010); a trend toward overweight was found for subjects with a history of physical abuse (76.32% vs. 63.33%; p = 0.074), although this relationship did not remain significant after adjusting for potential confounders. There was no statistically significant difference in the overall rate of dyslipidemia and/or metabolic syndrome between subjects with and without childhood adversity. Conclusion: The results herein provide preliminary evidence suggesting that childhood adversity is associated with metabolic syndrome components in individuals with mood disorders. Int'l. J. Psychiatry in Medicine 2012;43:165-177)

On universal Banach spaces of density continuum

We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a""(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a""(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C([0, c]) into a""(a)/c (0).

MAXIMAL PSEUDOCOMPACT AND MAXIMAL R-CLOSED SPACES

In this paper a space X is pseudocompact if it is Tychonoff and every real-valued continuous function on X is bounded. We obtain conditions under which a Tychonoff space is maximal pseudocompact and study conditions under which a regular space is maximal R-closed.

GEOMETRIC RELATIONS BETWEEN SPACES OF NUCLEAR OPERATORS AND SPACES OF COMPACT OPERATORS

We extend and provide a vector-valued version of some results of C. Samuel about the geometric relations between the spaces of nuclear operators N(E, F) and spaces of compact operators K(E, F), where E and F are Banach spaces C(K) of all continuous functions defined on the countable compact metric spaces K equipped with the supremum norm. First we continue Samuel's work by proving that N(C(K-1), C(K-2)) contains no subspace isomorphic to K(C(K-3), C(K-4)) whenever K-1, K-2, K-3 and K-4 are arbitrary infinite countable compact metric spaces. Then we show that it is relatively consistent with ZFC that the above result and the main results of Samuel can be extended to C(K-1, X), C(K-2,Y), C(K-3, X) and C(K-4, Y) spaces, where K-1, K-2, K-3 and K-4 are arbitrary infinite totally ordered compact spaces; X comprises certain Banach spaces such that X* are isomorphic to subspaces of l(1); and Y comprises arbitrary subspaces of l(p), with 1 < p < infinity. Our results cover the cases of some non-classical Banach spaces X constructed by Alspach, by Alspach and Benyamini, by Benyamini and Lindenstrauss, by Bourgain and Delbaen and also by Argyros and Haydon.

Average control of Markov decision processes with Feller transition probabilities and general action spaces

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

New characterizations for hyperbolic cylinders in anti-de Sitter spaces

In this paper we study complete maximal spacelike hypersurfaces in anti-de Sitter space H-1(n+1) with either constant scalar curvature or constant non-zero Gauss-Kronecker curvature. We characterize the hyperbolic cylinders H-m(c(1)) x Hn-m(c(2)), 1 <= m <= n - 1, as the only such hypersurfaces with (n - 1) principal curvatures with the same sign everywhere. In particular we prove that a complete maximal spacelike hypersurface in H-1(5) with negative constant Gauss-Kronecker curvature is isometric to H-1(c(1)) x H-3(c(2)). (C) 2012 Elsevier Inc. All rights reserved.

COPIES OF c(0)(Gamma) IN C(K, X) SPACES

We extend some results of Rosenthal, Cembranos, Freniche, E. Saab-P. Saab and Ryan to study the geometry of copies and complemented copies of c(0)(Gamma) in the classical Banach spaces C(K, X) in terms of the carclinality of the set Gamma, of the density and caliber of K and of the geometry of X and its dual space X*. Here are two sample consequences of our results: (1) If C([0, 1], X) contains a copy of c(0)(N-1), then X contains a copy of c(0)(N-1). (2) C(beta N, X) contains a complemented copy of c(0)(N-1) if and only if X contains a copy of c(0)(N-1). Some of our results depend on set-theoretic assumptions. For example, we prove that it is relatively consistent with ZFC that if C(K) contains a copy of c(0)(N-1) and X has dimension NI, then C(K, X) contains a complemented copy of cc(0)(N-1).

Gauge and integrable theories in loop spaces

We propose an integral formulation of the equations of motion of a large class of field theories which leads in a quite natural and direct way to the construction of conservation laws. The approach is based on generalized non-abelian Stokes theorems for p-form connections, and its appropriate mathematical language is that of loop spaces. The equations of motion are written as the equality of a hyper-volume ordered integral to a hyper-surface ordered integral on the border of that hyper-volume. The approach applies to integrable field theories in (1 + 1) dimensions, Chern-Simons theories in (2 + 1) dimensions, and non-abelian gauge theories in (2 + 1) and (3 + 1) dimensions. The results presented in this paper are relevant for the understanding of global properties of those theories. As a special byproduct we solve a long standing problem in (3 + 1)-dimensional Yang-Mills theory, namely the construction of conserved charges, valid for any solution, which are invariant under arbitrary gauge transformations. (C) 2012 Elsevier B.V. All rights reserved.

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.