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.

Distribution patterns of a marsh vegetation metacommunity in relation to habitat configuration

The identification of the factors behind the distribution of plant communities in patched habitats may prove useful towards better understanding how ecosystems function. Plant assemblages are especially important for wetland productivity and provide food and habitat to animals. The present study analyses the distribution of a metacommunity of helophytes and phreatophytes in a wetland complex in oder to identify the effects of habitat configuration on the colonisation process. Ponds with wide vegetated shores and a short distance to a big (> 10 ha) wetland, had higher species richness. The average percentage of surface covered by each species in all the wetlands correlated positively with the number of patches occupied by that species. Moreover, the community presented a nested pattern (species-poor patches were subsets of species-rich patches), and this pattern came about by selective extinction and colonisation processes. We also detected the presence of some idiosyncratic species that did not follow nestedness. Conservation managers should attempt to maximise the vegetated shore width and to reduce the degree of isolation to enhance species richness. Furthermore, a single large and poorly isolated reserve may have the highest level of biodiversity in emergent vegetation species in this wetland complex, however, the particular ecological requirements of idiosyncratic species should also be taken into account when managing this type of community.

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.

Effects of photobioreactor configuration, nitrogen source and light intensity on the fed-batch cultivation of Arthrospira (Spirulina) platensis. Bioenergetic aspects

Bioenergetic analysis may be applied in order to predict microbial growth yields, based on the Gibbs energy dissipation and mass conservation principles of the overall growth reaction. The bioenergetics of the photoautotrophic growth of the cyanobacterium Arthrospira (Spirulina) platensis was investigated in different bioreactor configurations (tubular photobioreactor and open ponds) using different nitrogen sources (nitrate and urea) and under different light intensity conditions to determine the best growing conditions in terms of Gibbs energy dissipation, number of photons to sustain cell growth and phototrophic energy yields distribution in relation to the ATP and NADPH formation, and release of heat. Although an increase in the light intensity increased the Gibbs energy dissipated for cell growth and maintenance with both nitrogen sources, it did not exert any appreciable influence on the moles of photons absorbed by the system to produce one C-mol biomass. On the other hand, both bioenergetic parameters were higher in cultures with nitrate than with urea, likely because of the higher energy requirements needed to reduce the former nitrogen source to ammonia. They appreciably increased also when open ponds were substituted by the tubular photobioreactor, where a more efficient light distribution ensured a remarkably higher cell mass concentration. The estimated percentages of the energy absorbed by the cell showed that, compared with nitrate, the use of urea as nitrogen source allowed the system to address higher energy fractions to ATP production and light fixation by the photosynthetic apparatus, as well as a lower fraction released as heat. The best energy yields values on Gibbs energy necessary for cell growth and maintenance were achieved in up to 4-5 days of cultivation, indicating that it would be the optimum range to maintain cell growth. Thanks to this better bioenergetic situation, urea appears to be a quite promising low-cost, alternative nitrogen source for Arthrospira platensis cultures in photobioreactors. (C) 2011 Elsevier Ltd. All rights reserved.

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.

VCD to determine absolute configuration of natural product molecules: secolignans from Peperomia blanda

The absolute configuration and solution-state conformers of three peperomin-type secolignans isolated from Peperomia blanda (Piperaceae) are unambiguously determined by using vibrational circular dichroism (VCD) spectroscopy associated with density functional theory (DFT) calculations. Advantages of VCD over the electronic form of CD for the analysis of diastereomers are also discussed. This work extends our growing knowledge about secondary metabolites within the Piperaceae family species while providing a definitive and straightforward method to assess the absolute stereochemistry of secolignans.

Further monoterpene chromane esters from Peperomia obtusifolia: VCD determination of the absolute configuration of a new diastereomeric mixture

A reinvestigation of the monoterpene chromane ester enriched fraction from Peperomia obtusifolia using chiral chromatography led to the identification of a minor peak, which was elucidated by NMR and HRMS as fenchyl-3,4-dihydro-5-hydroxy-2,7-dimethyl-8-(3 ''-methyl-2 ''-butenyl)-2-(4'-methyl-1',3'-pentadienyl)-2H-1-benzopyran-6-carboxylate, the same structure assigned to two other fenchyl esters described previously, pointing out a stereoisomeric relationship among them. Further NMR analysis revealed that it was actually a mixture of two compounds, whose absolute configurations were determined by VCD measurements. Although, almost no vibrational transitions could be assigned to the chiral chromane, the experimental VCD spectrum was largely opposite to that obtained for the average experimental VCD [(2S,1'''R,2'''R,4'''S + 2R,1'''R,2'''R,4'''S)/2] for fenchol derivatives. These results allowed us to assign the putative compounds as a racemic mixture of the chiral chromane esterified with the monoterpene (1S,2S,4R)fenchol, which had not been identified in our early work. (C) 2012 Elsevier Ltd. All rights reserved.

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.

Integral form of Yang-Mills equations and its gauge invariant conserved charges

Despite the fact that the integral form of the equations of classical electrodynamics is well known, the same is not true for non-Abelian gauge theories. The aim of the present paper is threefold. First, we present the integral form of the classical Yang-Mills equations in the presence of sources and then use it to solve the long-standing problem of constructing conserved charges, for any field configuration, which are invariant under general gauge transformations and not only under transformations that go to a constant at spatial infinity. The construction is based on concepts in loop spaces and on a generalization of the non-Abelian Stokes theorem for two-form connections. The third goal of the paper is to present the integral form of the self-dual Yang-Mills equations and calculate the conserved charges associated with them. The charges are explicitly evaluated for the cases of monopoles, dyons, instantons and merons, and we show that in many cases those charges must be quantized. Our results are important in the understanding of global properties of non-Abelian gauge theories.

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.