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).

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.

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.

Selection of compositions with high glass forming ability in the Ni-Nb-B alloy system

A combination of an extension of the topological instability "λ criterion" and the "average electronegativity" has been recently reported in the literature to predict compositions with high glass-forming ability (GFA). In the present work, both criteria have been applied to select the Ni61.0Nb36.0B3 alloy with a high glass-forming ability. Ingots were prepared by arc-melting and were used to produce ribbons processed by the melt-spinning technique further characterized by differential scanning calorimetry (DSC), X-ray diffraction (XRD) and scanning electron microscopy (SEM). The Ni61.0Nb36.0B3 alloy revealed a complete amorphization and supercooled liquid region ΔTx = 68 K. In addition, wedge-shaped samples were prepared using copper mold casting in order to determine the critical thickness for amorphous formation. Scanning electron microscopy (SEM) revealed that fully amorphous samples could be obtained, reaching up to ~800 µm in thickness.

Effects of selective bile duct ligation on liver parenchyma in young animals: histologic and molecular evaluations

Background/Purpose: The mechanisms of increased collagen production and liver parenchyma fibrosis are poorly understood. These phenomena are observed mainly in children with biliary obstruction (BO), and in a great number of patients, the evolution to biliary cirrhosis and hepatic failure leads to the need for liver transplantation before adolescence. However, pediatric liver transplantation presents with biliary complications in 20% to 30% of cases in the postoperative period. Intra-or extrahepatic stenosis of bile ducts is frequent and may lead to secondary biliary cirrhosis and the need for retransplantation. It is unknown whether biliary stenosis involving isolated segments or lobes may affect the adjacent nonobstructed lobes by paracrine or endocrine means, leading to fibrosis in this parenchyma. Therefore, the present study aimed to create an experimental model of selective biliary duct ligation in young animals with a subsequent evaluation of the histologic and molecular alterations in liver parenchyma of the obstructed and nonobstructed lobes. Methods: After a pilot study to standardize the surgical procedures, weaning rats underwent ligation of the bile ducts of the median, left lateral, and caudate liver lobes. The bile duct of the right lateral lobe was kept intact. To avoid intrahepatic biliary duct collaterals neoformation, the parenchymal connection between the right lateral and median lobes was clamped. The animals were divided into groups according to the time of death: 1, 2, 3, 4, and 8 weeks after surgical procedure. After death, the median and left lateral lobes (with BO) and the right lateral lobe (without BO [NBO]) were harvested separately. A group of 8 healthy nonoperated on animals served as controls. Liver tissues were subjected to histologic evaluation and quantification of the ductular proliferation and of the portal fibrosis. The expressions of smooth muscle alpha-actin (alpha-SMA), desmin, and transforming growth factor beta 1 genes were studied by molecular analyses (semiquantitative reverse transcriptase-polymerase chain reaction and real-time polymerase chain reaction, a quantitative method). Results: Histologic analyses revealed the occurrence of ductular proliferation and collagen formation in the portal spaces of both BO and NBO lobes. These phenomena were observed later in NBO than BO. Bile duct density significantly increased 1 week after duct ligation; it decreased after 2 and 3 weeks and then increased again after 4 and 8 weeks in both BO and NBO lobes. The portal space collagen area increased after 2 weeks in both BO and NBO lobes. After 3 weeks, collagen deposition in BO was even higher, and in NBO, the collagen area started decreasing after 2 weeks. Molecular analyses revealed increased expression of the alpha-SMA gene in both BO and NBO lobes. The semiquantitative and quantitative methods showed concordant results. Conclusions: The ligation of a duct responsible for biliary drainage of the liver lobe promoted alterations in the parenchyma and in the adjacent nonobstructed parenchyma by paracrine and/or endocrine means. This was supported by histologic findings and increased expression of alpha-SMA, a protein related to hepatic fibrogenesis. (C) 2012 Elsevier Inc. 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.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Do ciberespaço à iconomia: projeções metapóricas

Na sociedade contemporânea o ser humano se vê inserido – ou invadido – em ambientes cada vez mais configurados por complexos recursos tecnológicos. É o ciberespaço, onde as imagens inundam o cotidiano e se traduzem em valor, o corpo adquire novo status imaterial e as noções de lugar e tempo se transformam e quase se anulam. O cinema pensa e produz também uma desterritorialização da imagem em movimento desde os seus primeiros tempos de imagem-máquina. Este trabalho reflete sobre as transformações da ordem social que implicam a emergência de uma “iconomia” a partir dos espaços simbólicos, tomando três momentos críticos na história do cinema como índices de uma convergência entre material e imaterial que se consolida a partir da emergência do ciberespaço. O quase-método metapórico é mobilizado como ferramenta de reconstrução metodológica desses ícones da história do cinema relacionados à desconstrução do Homo faber. O “outro lado” do ciberespaço, abrindo continuamente novos espaços-tempos de criação de valor, identifica-se a uma iconomia em que as projeções narrativas tornam-se fontes paradigmáticas de valor e de “mais gozar”.

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.

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).

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.

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.

A holistic approach to model-based testing of Web service compositions

The behavior of composed Web services depends on the results of the invoked services; unexpected behavior of one of the invoked services can threat the correct execution of an entire composition. This paper proposes an event-based approach to black-box testing of Web service compositions based on event sequence graphs, which are extended by facilities to deal not only with service behavior under regular circumstances (i.e., where cooperating services are working as expected) but also with their behavior in undesirable situations (i.e., where cooperating services are not working as expected). Furthermore, the approach can be used independently of artifacts (e.g., Business Process Execution Language) or type of composition (orchestration/choreography). A large case study, based on a commercial Web application, demonstrates the feasibility of the approach and analyzes its characteristics. Test generation and execution are supported by dedicated tools. Especially, the use of an enterprise service bus for test execution is noteworthy and differs from other approaches. The results of the case study encourage to suggest that the new approach has the power to detect faults systematically, performing properly even with complex and large compositions. Copyright © 2012 John Wiley & Sons, Ltd.