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.

Color-space distortions following long-term occupational exposure to mercury vapor

Color vision was examined in subjects with long-term occupational exposure to mercury (Hg) vapor. The color vision impairment was assessed by employing a quantitative measure of distortion of individual and group perceptual color spaces. Hg subjects (n = 18; 42.1 +/- 6.5 years old; exposure time = 10.4 +/- 5.0 years; time away from the exposure source = 6.8 +/- 4.6 years) and controls (n = 18; 46.1 +/- 8.4 years old) were examined using two arrangement tests, D-15 and D-15d, in the traditional way, and also in a triadic procedure. From each subject`s `odd-one-out` choices, matrices of inter-cap subjective dissimilarities were derived and processed by non-metric multidimensional scaling (MDS). D-15d results differed significantly between the Hg-group and the control group (p < 0.05), with the impairment predominantly along the tritan axis. 2D perceptual color spaces, individual and group, were reconstructed, with the dimensions interpreted as the red-green (RG) and the blue-yellow (BY) systems. When color configurations from the Hg-group were compared to those of the controls, they presented more fluctuations along both chromatic dimensions, indicating a statistically significant difference along the BY axis. In conclusion, the present findings confirm that color vision impairments persist in subjects that have received long-term occupational exposure to Hg-vapor although, at the time of testing, they were presenting mean urinary concentration within the normal range for non-exposed individuals. Considering the advantages of the triadic procedure in clinical evaluation of acquired color vision deficiencies, further studies should attempt to verify and/or improve its efficacy.

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.

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).

Quality Metric to Assess Video Streaming Service over TCP considering Temporal Location of Pauses

There is a wide range of video services over complex transmission networks, and in some cases end users fail to receive an acceptable quality level. In this paper, the different factors that degrade users' quality of experience (QoE) in video streaming service that use TCP as transmission protocol are studied. In this specific service, impairment factors are: number of pauses, their duration and temporal location. In order to measure the effect that each temporal segment has in the overall video quality, subjective tests. Because current subjective test methodologies are not adequate to assess video streaming over TCP, some recommendations are provided here. At the application layer, a customized player is used to evaluate the behavior of player buffer, and consequently, the end user QoE. Video subjective test results demonstrate that there is a close correlation between application parameters and subjective scores. Based on this fact, a new metrics named VsQM is defined, which considers the importance of temporal location of pauses to assess the user QoE of video streaming service. A useful application scenario is also presented, in which the metrics proposed herein is used to improve video services(1).

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.

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.

Toward the optimal dose metric in continuous renal replacement therapy

Purpose: There is no consensus on the optimal method to measure delivered dialysis dose in patients with acute kidney injury (AKI). The use of direct dialysate-side quantification of dose in preference to the use of formal blood-based urea kinetic modeling and simplified blood urea nitrogen (BUN) methods has been recommended for dose assessment in critically-ill patients with AKI. We evaluate six different blood-side and dialysate-side methods for dose quantification. Methods: We examined data from 52 critically-ill patients with AKI requiring dialysis. All patients were treated with pre-dilution CWHDF and regional citrate anticoagulation. Delivered dose was calculated using blood-side and dialysis-side kinetics. Filter function was assessed during the entire course of therapy by calculating BUN to dialysis fluid urea nitrogen (FUN) ratios q/12 hours. Results: Median daily treatment time was 1,413 min (1,260-1,440). The median observed effluent volume per treatment was 2,355 mL/h (2,060-2,863) (p<0.001). Urea mass removal rate was 13.0 +/- 7.6 mg/min. Both EKR (r(2)=0.250; p<0.001) and K-D (r(2)=0.409; p<0.001) showed a good correlation with actual solute removal. EKR and K-D presented a decline in their values that was related to the decrease in filter function assessed by the FUN/BUN ratio. Conclusions: Effluent rate (ml/kg/h) can only empirically provide an estimated of dose in CRRT. For clinical practice, we recommend that the delivered dose should be measured and expressed as K-D. EKR also constitutes a good method for dose comparisons over time and across modalities.

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.

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

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.