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).

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Spaces of compact operators on C(2(m) circle plus [0, alpha]) spaces

We classify up to isomorphism the spaces of compact operators K(E, F), where E and F are Banach spaces of all continuous functions defined on the compact spaces 2(m) circle plus [0, alpha], the topological sum of Cantor cubes 2(m) and the intervals of ordinal numbers [0, alpha]. More precisely, we prove that if 2(m) and aleph(gamma) are not real-valued measurable cardinals and n >= aleph(0) is not sequential cardinal, then for every ordinals xi, eta, lambda and mu with xi >= omega(1), eta >= omega(1), lambda = mu < omega or lambda, mu is an element of [omega(gamma), omega(gamma+1)[, the following statements are equivalent: (a) K(C(2(m) circle plus [0, lambda]), C(2(n) circle plus [0, xi])) and K(C(2(m) circle plus [0, mu]), C(2(n) circle plus [0, eta]) are isomorphic. (b) Either C([0, xi]) is isomorphic to C([0, eta] or C([0, xi]) is isomorphic to C([0, alpha p]) and C([0, eta]) is isomorphic to C([0,alpha q]) for some regular cardinal alpha and finite ordinals p not equal q. Thus, it is relatively consistent with ZFC that this result furnishes a complete isomorphic classification of these spaces of compact operators. (C) 2010 Elsevier Inc. All rights reserved.

A inclusão da criança com Síndrome de Down na rede regular de ensino: desafios e possibilidades

O estudo teve como objetivo buscar evidências na literatura acerca da inclusão de crianças com Síndrome de Down na rede regular de ensino. Elaboraram-se revisão da literatura e busca dos artigos nas bases de dados PubMed e PsycINFO, utilizando as palavras-chave Down syndrome, schools, mainstreaming (education), education, infant, newborn, adolescent, child e preschool, no período de 1994 a 2007. Selecionaram-se oito artigos e sua análise permitiu a identificação do tema: experiências e recomendações para a inclusão. Os dados desta revisão, em sua maioria provenientes de relatos de experiências, indicaram que os fatores que colaboraram ou dificultaram o processo de inclusão da criança com síndrome de Down na rede regular de ensino relacionaram-se à escola, aos pais e ao professor. Os resultados deste estudo oferecem possibilidades para melhorar o processo de inclusão, apresentam os desafios e ainda apontam a necessidade do desenvolvimento de novas pesquisas, cujos resultados possam ser aplicados na prática.

Nonexistence of regular stationary solution in a metric nonsymmetric theory of gravitation

It is proven that the field equations of a previously studied metric nonsymmetric theory of gravitation do not admit any non-singular stationary solution which represents a field of non-vanishing total mass and non-vanishing total fermionic charge.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

Evaluation of Cadaveric Renal Vein Lengths and Their Extension Loss with Three Types of Ligature and Section

Background and Purpose: The right kidney has been less frequently used in live donor nephrectomy, because of the shorter length of the right renal vein (RRV) that is associated with technical difficulties and higher rates of venous thrombosis. In live open donor or deceased donor transplant nephrectomy, an additional cuff of the inferior vena cava is usually removed, but this is a more difficult and risky maneuver in laparoscopic nephrectomy. For this reason, laparoscopic right nephrectomy (LRN) for renal transplantation (RT) is not frequently performed in most medical institutions. We evaluate the difference between RRV and left renal vein (LRV) lengths in cadavers, as harvested for RT by three clamping methods. Our objective was to obtain information that could clarify when LRN for RT should be encouraged or avoided with regard to conventional surgery. Materials and Methods: Ninety adult fresh unfrozen cadavers were randomly divided into three groups of 30, according to the clamping device used: Satinsky, stapler, and Hem-o-lok clip. The abdominal viscera were removed through a median xyphopubic incision, and the veins were measured on the bench. Two lateral limits were used: The renal hilum and the tangential line of the renal poles. As for medial limits, the inferior vena cava or the laparoscopic clipping device on the RRV were used on the right side, while on the LRV, the medial border of the emergence of the adrenal vein was considered. After section of the renal vein, a slight traction of the extremity was applied for the measurement. All measurements were obtained three times using a metallic millimetric ruler, and the arithmetic mean was considered. The chi-square, one-way analysis of variance, and paired t tests were used for statistical analysis. Statistical significance was accepted at P <= 0.05. Results: The groups of cadavers were homogeneous in demographic characteristics. Regardless of the clamping method and considering the useful length of the LRV, the RRV was statistically smaller. The evaluation of the vein length did not depend on the lateral limit considered. Independent of the clamping method, on both sides, the lengths after the vein section were larger than before the section, a fact attributed to traction. Use of a stapler and a single Hem-o-lok presented the same waste of vein length on the right side. On average, the RRV was 13.7% shorter than the LRV. Conclusions: With the wide acceptance of laparoscopic live donor nephrectomy, the length difference between the veins of both kidneys is an important issue, and the right kidney is therefore used less than the left, compared with conventional surgery. This article represents the first step to quantify the anatomic length of renal veins in different situations. Certainly, more imagenologic or surgical studies should be carried out before decisions can be made for better selection of patients for LRN.

EVOLUTION OF DISPARITY BETWEEN THE REGULAR AND VARIANT PHLOEM IN BIGNONIEAE (BIGNONIACEAE)

Premise of the study: The phloem is a plant tissue with a critical role in plant nutrition and signaling. However, little is still known about the evolution of this tissue. In lianas of the Bignoniaceae, two distinct types of phloem coexist: a regular and a variant phloem. The cells associated with these two phloem types are known to be anatomically different; however, it is still unclear what steps were involved in the evolution of such differences. Methods: Here we studied the anatomical development of the regular and variant phloem in representatives of all 21 genera of Bignonieae and used a phylogenetic framework to investigate the timing of changes associated with the evolution of each phloem type. Key results: We found that the variant phloem always appears in a determinate location, between the leaf orthostichies. Furthermore, the variant phloem was mostly occupied by very wide sieve tubes and generally included a higher concentration of fibers, indicating an increase in conduction and mechanical support. On the other hand, the regular phloem included much more parenchyma, more and wider rays, and tiny sieve tubes that resembled terminal sieve tubes from plants with seasonal formation of vascular tissues; these findings suggest reduced conduction and higher storage capacity in the regular phloem. Conclusions: Overall, differences between the regular and variant phloem increased over time, leading to further specialization in conduction in the variant phloem and an increase in storage specialization in the regular phloem.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

Gravitational wave recoil in Robinson-Trautman spacetimes

We consider the gravitational recoil due to nonreflection-symmetric gravitational wave emission in the context of axisymmetric Robinson-Trautman spacetimes. We show that regular initial data evolve generically into a final configuration corresponding to a Schwarzschild black hole moving with constant speed. For the case of (reflection-)symmetric initial configurations, the mass of the remnant black hole and the total energy radiated away are completely determined by the initial data, allowing us to obtain analytical expressions for some recent numerical results that have appeared in the literature. Moreover, by using the Galerkin spectral method to analyze the nonlinear regime of the Robinson-Trautman equations, we show that the recoil velocity can be estimated with good accuracy from some asymmetry measures (namely the first odd moments) of the initial data. The extension for the nonaxisymmetric case and the implications of our results for realistic situations involving head-on collision of two black holes are also discussed.

A NEW PROOF OF OKAJI'S THEOREM FOR A CLASS OF SUM OF SQUARES OPERATORS

Let P be a linear partial differential operator with analytic coefficients. We assume that P is of the form ""sum of squares"", satisfying Hormander's bracket condition. Let q be a characteristic point; for P. We assume that q lies on a symplectic Poisson stratum of codimension two. General results of Okaji Show that P is analytic hypoelliptic at q. Hence Okaji has established the validity of Treves' conjecture in the codimension two case. Our goal here is to give a simple, self-contained proof of this fact.

DJKM ALGEBRAS I: THEIR UNIVERSAL CENTRAL EXTENSION

The purpose of this paper is to explicitly describe in terms of generators and relations the universal central extension of the infinite dimensional Lie algebra, g circle times C[t, t(-1), u vertical bar u(2) = (t(2) - b(2))(t(2) - c(2))], appearing in the work of Date, Jimbo, Kashiwara and Miwa in their study of integrable systems arising from the Landau-Lifshitz differential equation.

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.

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.