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.

Three new species of Lebiasina (Characiformes: Lebiasinidae) from the Brazilian Shield border at Serra do Cachimbo, Para, Brazil

Lebiasina marilynae n. sp., L. melanoguttata n. sp., and L. minuta n. sp. are described from the headwaters of the rio Curua in Serra do Cachimbo, Para, Brazil, and represent the only members of the Lebiasininae in the Brazilian Shied, so far. A close relationship among these species is proposed based on: I) the presence of a pair of foramina through which the rain us palatinus of the facial nerve passes, a modification unique in Lebiasinidae and apparently in the Characiformes, 2) the enlargement of the extrascapular bone, 3) the absence of the secondary stripe, and 4) the nearly equal length of caudal-fin lobes. Lebiasina marilynae additionally differs from all congeners in having the primary stripe extending from the tip of the snout to the distal border of the caudal-fin peduncle, the possession of two series of dark blotches parallel to the primary stripe, and a rounded dorsal surface of the mesethmoid. Lebiasina melanoguttata and Lebiasina minuta additionally differ from all congeners in the absence of the primary stripe and the caudal blotch, and the presence of three longitudinal series of dark blotches at the base of the scales of series 3-5. Lebiasina melanoguttata differs from Lebiasina minuta in the absence of a dark blotch at the base of the median rays of the dorsal fin, second infrapharyngobranchial bearing conical teeth, the reddish overall coloration of the eye and fins, and the dark blotches never coalescing (vs. dark dorsal-fin blotch present; the second infrapharyngobranchial being edentulous; dark, olive green eyes, and the yellowish overall color of body and fins; and the dark blotches of longitudinal series 3 and 4 coalescing where scales of adjacent longitudinal series overlap). The occurrence of species of the Lebiasininae on the Brazilian Shield is discussed, and the distribution pattern of the species described herein is compared to that of other endemic species of the Serra do Cachimbo, a highly biodiverse area isolated from the rest of the Amazon basin.

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).

Delays in the diagnosis of tuberculosis in a town at the triple border of Brazil, Paraguay, and Argentina

Objective. To identify the factors linked to patients and health services in delays in the diagnosis of tuberculosis. Methods. Epidemiological study in Foz do Iguacu, Parana, Brazil, 2009. The Primary Care Assessment Tool, adapted for appraising tuberculosis treatment, was the instrument used. Descriptive statistics techniques were used, such as frequency distributions, central tendency and dispersion measurements (median and interquartile intervals), and odds ratios. Results. There were greater delays in seeking health services for those in the age group 60 years and older, for females, for patients with low levels of education, and for patients with poor knowledge of the disease. Clinical variables (being a new case and HIV infection) and behavioral variables (use of tobacco and alcohol consumption) were not linked with delays in diagnosis. The median time delays before diagnosis attributable to patients and to the health services were 30 days and 10 days, respectively. Emergency 24-hour medical services and primary health care services were not effective in identifying suspicious cases of tuberculosis and requesting tests to confirm the diagnosis, with a high percentage of referrals to the Tuberculosis Control Program clinic. Conclusions. Going to primary health care services for diagnosis increased the time before diagnosis of the disease was reached. The Tuberculosis Control Program clinic was more effective in diagnosis of tuberculosis, due to the training of the staff and to an organized process for receiving patients, including the availability of tests to support the diagnosis.

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.

Three new species of Lebiasina (Characiformes: Lebiasinidae) from the Brazilian shield border at Serra do Cachimbo, Pará, Brazil

Lebiasina marilynae n. sp., L. melanoguttata n. sp., and L. minuta n. sp. are described from the headwaters of the rio Curuá, in Serra do Cachimbo, Pará, Brazil, and represent the only members of the Lebiasininae in the Brazilian Shied, so far. A close relationship among these species is proposed based on: 1) the presence of a pair of foramina through which the ramus palatinus of the facial nerve passes, a modification unique in Lebiasinidae and apparently in the Characiformes, 2) the enlargement of the extrascapular bone, 3) the absence of the secondary stripe, and 4) the nearly equal length of caudal-fin lobes. Lebiasina marilynae additionally differs from all congeners in having the primary stripe extending from the tip of the snout to the distal border of the caudal-fin peduncle, the possession of two series of dark blotches parallel to the primary stripe, and a rounded dorsal surface of the mesethmoid. Lebiasina melanoguttata and Lebiasina minuta additionally differ from all congeners in the absence of the primary stripe and the caudal blotch, and the presence of three longitudinal series of dark blotches at the base of the scales of series 3-5. Lebiasina melanoguttata differs from Lebiasina minuta in the absence of a dark blotch at the base of the median rays of the dorsal fin, second infrapharyngobranchial bearing conical teeth, the reddish overall coloration of the eye and fins, and the dark blotches never coalescing (vs. dark dorsal-fin blotch present; the second infrapharyngobranchial being edentulous; dark, olive green eyes, and the yellowish overall color of body and fins; and the dark blotches of longitudinal series 3 and 4 coalescing where scales of adjacent longitudinal series overlap). The occurrence of species of the Lebiasininae on the Brazilian Shield is discussed, and the distribution pattern of the species described herein is compared to that of other endemic species of the Serra do Cachimbo, a highly biodiverse area isolated from the rest of the Amazon basin.