COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

Differential roles of galectin-1 and galectin-3 in regulating leukocyte viability and cytokine secretion

Galectin-1 (Gal-1) and galectin-3 (Gal-3) exhibit profound but unique immunomodulatory activities in animals but their molecular mechanisms are incompletely understood. Early studies suggested that Gal-1 inhibits leukocyte function by inducing apoptotic cell death and removal, but recent studies show that some galectins induce exposure of the common death signal phosphatidylserine (PS) independently of apoptosis. In tfhis study, we report that Gal-3, but not Gal-1, induces both PS exposure and apoptosis in primary activated human T cells, whereas both Gal-1 and Gal-3 induce PS exposure in neutrophils in the absence of cell death. Gal-1 and Gal-3 bind differently to the surfaces of T cells and only Gal-3 mobilizes intracellular Ca(2+) in these cells, although Gal-1 and Gal-3 bind their respective T cell ligands with similar affinities. Although Gal-1 does not alter T cell viability, it induces IL-10 production and attenuates IFN-gamma production in activated T cells, suggesting a mechanism for Gal-1-mediated immunosuppression in vivo. These studies demonstrate that Gal-1 and Gal-3 induce differential responses in T cells and neutrophils, and identify the first factor, Gal-3, capable of inducing PS exposure with or without accompanying apoptosis in different leukocytes, thus providing a possible mechanism for galectin-mediated immunomodulation in vivo.

Approximate controllability of second-order distributed implicit functional systems

In this paper we study the approximate controllability of control systems with states and controls in Hilbert spaces, and described by a second-order semilinear abstract functional differential equation with infinite delay. Initially we establish a characterization for the approximate controllability of a second-order abstract linear system and, in the last section, we compare the approximate controllability of a semilinear abstract functional system with the approximate controllability of the associated linear system. (C) 2008 Elsevier Ltd. All rights reserved.

Existence of solutions for a class of abstract differential equations with nonlocal conditions

We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. (C) 2010 Elsevier Ltd. All rights reserved.

The differential role of alcohol expectancies, drinking refusal self-efficacy and coping resources in predicting alcohol consumption in community and clinical samples

This study explored the relationship between coping, alcohol expectancies and drinking refusal self-efficacy in predicting drinking behaviour in both community and clinical samples. These variables were found to have differential effects in their association with frequency and volume of alcohol consumption across the two samples. Generally, drinking refusal self-efficacy was a more salient factor in relation to frequency and volume of community drinking, while coping and expectancies were more strongly associated with frequency of drinking sessions by problem drinkers. The interaction between expectancies and drinking refusal self-efficacy was related to volume of consumption in both groups, while coping and expectancies interacted in their association with frequency in the clinical group. The findings are discussed with regard to the different patterns of cognitive variables governing the decision to drink and the amount consumed in each drinking session, which may differentiate community and problem drinkers.

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators.

Approximating fractional derivatives in the perspective of system control

The theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.

Challenges in the creation and development of a mathematics MOOC

The fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOC or MOOCs) are indicators of a shift in the way in which digital teaching and learning are understood. MOOC are a new style of online classes that allow any person with web access, anywhere, usually free of charge, to participate through video lectures, computer graded tests and discussion forums. They have been capturing the attention of many higher education institutions around the world. This paper will give us an overview of the “Introduction to Differential Calculus” a MOOC Project, created by an engaged volunteer team of Mathematics lecturers from four schools of the Polytechnic Institute of Oporto (IPP). The MOOC theories and their popularity are presented and complemented by a discussion of some MOOC definitions and their inherent advantages and disadvantages. It will also explore what MOOC mean for Mathematics education. The Project development is revealed by focusing on used MOOC structure, as well as the quite a lot of types of course materials produced. It ends with a presentation of a short discussion about problems and challenges met throughout the development of the project. It is also our goal to contribute for a change in the way teaching and learning Mathematics is seen and practiced nowadays, trying to make education more accessible to as many people as possible and increase our institution (IPP) recognition.

Reconceptualising public spaces of (IN)equality: sensing and creating layers of visibility

Tese apresentada para cumprimento dos requisitos necessários à obtenção do grau de Doutor em Geografia e Planeamento Territorial - Especialidade: Geografia Humana

On the applicability of mathematics : philosophical and historical perspectives

The present thesis is a contribution to the debate on the applicability of mathematics; it examines the interplay between mathematics and the world, using historical case studies. The first part of the thesis consists of four small case studies. In chapter 1, I criticize "ante rem structuralism", proposed by Stewart Shapiro, by showing that his so-called "finite cardinal structures" are in conflict with mathematical practice. In chapter 2, I discuss Leonhard Euler's solution to the Königsberg bridges problem. I propose interpreting Euler's solution both as an explanation within mathematics and as a scientific explanation. I put the insights from the historical case to work against recent philosophical accounts of the Königsberg case. In chapter 3, I analyze the predator-prey model, proposed by Lotka and Volterra. I extract some interesting philosophical lessons from Volterra's original account of the model, such as: Volterra's remarks on mathematical methodology; the relation between mathematics and idealization in the construction of the model; some relevant details in the derivation of the Third Law, and; notions of intervention that are motivated by one of Volterra's main mathematical tools, phase spaces. In chapter 4, I discuss scientific and mathematical attempts to explain the structure of the bee's honeycomb. In the first part, I discuss a candidate explanation, based on the mathematical Honeycomb Conjecture, presented in Lyon and Colyvan (2008). I argue that this explanation is not scientifically adequate. In the second part, I discuss other mathematical, physical and biological studies that could contribute to an explanation of the bee's honeycomb. The upshot is that most of the relevant mathematics is not yet sufficiently understood, and there is also an ongoing debate as to the biological details of the construction of the bee's honeycomb. The second part of the thesis is a bigger case study from physics: the genesis of GR. Chapter 5 is a short introduction to the history, physics and mathematics that is relevant to the genesis of general relativity (GR). Chapter 6 discusses the historical question as to what Marcel Grossmann contributed to the genesis of GR. I will examine the so-called "Entwurf" paper, an important joint publication by Einstein and Grossmann, containing the first tensorial formulation of GR. By comparing Grossmann's part with the mathematical theories he used, we can gain a better understanding of what is involved in the first steps of assimilating a mathematical theory to a physical question. In chapter 7, I introduce, and discuss, a recent account of the applicability of mathematics to the world, the Inferential Conception (IC), proposed by Bueno and Colyvan (2011). I give a short exposition of the IC, offer some critical remarks on the account, discuss potential philosophical objections, and I propose some extensions of the IC. In chapter 8, I put the Inferential Conception (IC) to work in the historical case study: the genesis of GR. I analyze three historical episodes, using the conceptual apparatus provided by the IC. In episode one, I investigate how the starting point of the application process, the "assumed structure", is chosen. Then I analyze two small application cycles that led to revisions of the initial assumed structure. In episode two, I examine how the application of "new" mathematics - the application of the Absolute Differential Calculus (ADC) to gravitational theory - meshes with the IC. In episode three, I take a closer look at two of Einstein's failed attempts to find a suitable differential operator for the field equations, and apply the conceptual tools provided by the IC so as to better understand why he erroneously rejected both the Ricci tensor and the November tensor in the Zurich Notebook.

HERV-W polymorphism in chromosome X is associated with multiple sclerosis risk and with differential expression of MSRV.

BACKGROUND Multiple Sclerosis (MS) is an autoimmune demyelinating disease that occurs more frequently in women than in men. Multiple Sclerosis Associated Retrovirus (MSRV) is a member of HERV-W, a multicopy human endogenous retroviral family repeatedly implicated in MS pathogenesis. MSRV envelope protein is elevated in the serum of MS patients and induces inflammation and demyelination but, in spite of this pathogenic potential, its exact genomic origin and mechanism of generation are unknown. A possible link between the HERV-W copy on chromosome Xq22.3, that contains an almost complete open reading frame, and the gender differential prevalence in MS has been suggested. RESULTS MSRV transcription levels were higher in MS patients than in controls (U-Mann-Whitney; p = 0.004). Also, they were associated with the clinical forms (Spearman; p = 0.0003) and with the Multiple Sclerosis Severity Score (MSSS) (Spearman; p = 0.016). By mapping a 3 kb region in Xq22.3, including the HERV-W locus, we identified three polymorphisms: rs6622139 (T/C), rs6622140 (G/A) and rs1290413 (G/A). After genotyping 3127 individuals (1669 patients and 1458 controls) from two different Spanish cohorts, we found that in women rs6622139 T/C was associated with MS susceptibility: [χ2; p = 0.004; OR (95% CI) = 0.50 (0.31-0.81)] and severity, since CC women presented lower MSSS scores than CT (U-Mann-Whitney; p = 0.039) or TT patients (U-Mann-Whitney; p = 0.031). Concordantly with the susceptibility conferred in women, rs6622139*T was associated with higher MSRV expression (U-Mann-Whitney; p = 0.003). CONCLUSIONS Our present work supports the hypothesis of a direct involvement of HERV-W/MSRV in MS pathogenesis, identifying a genetic marker on chromosome X that could be one of the causes underlying the gender differences in MS.

Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

Differential Behavior of Young Eucalyptus Clones in Response to Nitrogen Supply

Eucalyptus requires large amounts of nitrogen (N); however, it responds in diverse manners to the application of this nutrient. The aim of this study was to evaluate the differential performance in growth, mineral nutrition, and gas exchanges of N-fertilized Eucalyptus clones. The treatments consisted of two Eucalyptus clones (VM-01 and I-144) and six N application rates (0, 0.74, 2.93, 4.39, 5.85, and 8 mmol L-1 NH4NO3) arranged in a randomized complete block design with five replications. VM-01 had greater plant height and greater height/collar diameter ratio, as well as higher leaf concentrations of all macronutrients and of Cu, Fe, Mo, and Zn. In terms of total and root dry matter production, root/shoot ratio, and collar diameter, as well as stomatal conductance and transpiration, I-144 performed better. The performance of the clones was clearly differentiated, and the growth of I-144, despite lower leaf N concentration, was in general better than VM-01.