QUASISTATIONARY DISTRIBUTIONS AND FLEMING-VIOT PROCESSES IN FINITE SPACES

Consider a continuous-time Markov process with transition rates matrix Q in the state space Lambda boolean OR {0}. In In the associated Fleming-Viot process N particles evolve independently in A with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Lambda is finite, we show that the empirical distribution of the particles at a fixed time converges as N -> infinity to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N -> infinity to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1/N.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

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.

On isomorphism classes of C(2(m) circle plus [0, alpha]) spaces

We provide a complete isomorphic classification of the Banach spaces of continuous functions on the compact spaces 2(m) circle plus [0, alpha], the topological sums of Cantor cubes 2(m), with m smaller than the first sequential cardinal, and intervals of ordinal numbers [0, alpha]. In particular, we prove that it is relatively consistent with ZFC that the only isomorphism classes of C(2(m) circle plus [0, alpha]) spaces with m >= N(0) and alpha >= omega(1) are the trivial ones. This result leads to some elementary questions on large cardinals.

Dually discrete spaces

A neighbourhood assignment in a space X is a family O = {O-x: x is an element of X} of open subsets of X such that X is an element of O-x for any x is an element of X. A set Y subset of X is a kernel of O if O(Y) = U{O-x: x is an element of Y} = X. We obtain some new results concerning dually discrete spaces, being those spaces for which every neighbourhood assignment has a discrete kernel. This is a strictly larger class than the class of D-spaces of [E.K. van Douwen, W.F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81 (2) (1979) 371-377]. (c) 2008 Elsevier B.V. All rights reserved.

Generalizations of Pelczynski`s decomposition method for Banach spaces containing a complemented copy of their squares

Suppose that X and Y are Banach spaces isomorphic to complemented subspaces of each other. In 1996, W. T. Gowers solved the Schroeder- Bernstein Problem for Banach spaces by showing that X is not necessarily isomorphic to Y. However, if X-2 is complemented in X with supplement A and Y-2 is complemented in Y with supplement B, that is, { X similar to X-2 circle plus A Y similar to Y-2 circle plus B, then the classical Pelczynski`s decomposition method for Banach spaces shows that X is isomorphic to Y whenever we can assume that A = B = {0}. But unfortunately, this is not always possible. In this paper, we show that it is possible to find all finite relations of isomorphism between A and B which guarantee that X is isomorphic to Y. In order to do this, we say that a quadruple (p, q, r, s) in N is a P-Quadruple for Banach spaces if X is isomorphic to Y whenever the supplements A and B satisfy A(p) circle plus B-q similar to A(r) circle plus B-s . Then we prove that (p, q, r, s) is a P-Quadruple for Banach spaces if and only if p - r = s - q = +/- 1.

On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

A family of Schroeder-Bernstein type theorems for Banach spaces

Motivated by a characterization of the complemented subspaces in Banach spaces X isomorphic to their squares X-2, we introduce the concept of P-complemented subspaces in Banach spaces. In this way, the well-known Pelczynski`s decomposition method can be seen as a Schroeder-Bernstein type theorem. Then, we give a complete description of the Schroeder-Bernstein type theorems for this new notion of complementability. By contrast, some very elementary questions on P-complementability are refinements of the Square-Cube Problem closely connected with some Banach spaces introduced by W.T. Gowers and B. Maurey in 1997. (C) 2007 Elsevier Inc. All rights reserved.

Some Schroeder-Bernstein type theorems for Banach spaces

We first introduce the notion of (p, q, r)-complemented subspaces in Banach spaces, where p, q, r is an element of N. Then, given a couple of triples {(p, q, r), (s, t, u)} in N and putting Lambda = (q + r - p)(t + u - s) - ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p, q, r)-complemented in Y and Y is (s, t, u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds: (a) Lambda not equal 0, Lambda divides p - q and s - t, p = 1 or q = 1 or s = 1 or t = 1. (b) p = q = s = t = 1 and gcd(r, u) = 1. The case {(2, 1, 1), (2, 1,1)} is the well-known Pelczynski`s decomposition method. Our result leads naturally to some generalizations of the Schroeder-B em stein problem for Banach spaces solved by W.T. Gowers in 1996. (C) 2007 Elsevier Inc. All rights reserved.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.

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.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

A BROADER CONTEXT FOR MONOTONICALLY MONOLITHIC SPACES

This is a sequel of the work done on (strongly) monotonically monolithic spaces and their generalizations. We introduce the notion of monotonically kappa-monolithic space for any infinite cardinal kappa and present the relevant results. We show, among other things, that any sigma-product of monotonically kappa-monolithic spaces is monotonically kappa-monolithic for any infinite cardinal kappa; besides, it is consistent that any strongly monotonically omega-monolithic space with caliber omega(1) is second countable. We also study (strong) monotone kappa-monolithicity in linearly ordered spaces and subspaces of ordinals.

Uso do teste ML-Flow como auxiliar na classificação e tratamento da hanseníase

FUNDAMENTOS: O tratamento da hanseníase é definido pela classificação de pacientes em paucibacilares (PB) e multibacilares (MB). A OMS (Organização Mundial de Saúde) classifica os doentes de acordo com o número de lesões, mas Ridley-Jopling (R&J) utiliza também exames complementares, porém é de difícil utilização fora dos serviços de referência. Em 2003 foi desenvolvido um teste denominado ML-Flow, uma alternativa à sorologia por ELISA para auxiliar na classificação de pacientes em PB e MB e auxiliar na decisão terapêutica. OBJETIVOS: Observar a concordância entre o teste de ML-Flow e baciloscopia de linfa, exame já consagrado para detecção de MB. Analisar a utilidade do teste de ML-Flow em campo. MATERIAL E MÉTODOS: Estudo retrospectivo avaliando prontuário de 55 pacientes virgens de tratamento, diagnosticados como PB ou MB por R&J. Submetidos à baciloscopia e ao teste de ML-Flow. RESULTADOS: Nos MB, a baciloscopia foi positiva em 80% dos casos, o ML-flow foi positivo em 82,5%. Entre os PB, o ML-Flow foi positivo em 37,5% e a baciloscopia do esfregaço foi negativa em 100% dos casos. A concordância entre os resultados da baciloscopia do esfregaço e ML-Flow foi de 87,5%, kappa=0,59, p<0,001. CONCLUSÃO: Nenhum teste laboratorial é 100% sensível e específico para a correta classificação de todas as formas de hanseníase. O ML-Flow é um teste rápido, de fácil manuseio em campo, menos invasivo que a baciloscopia podendo ser útil para auxiliar na decisão terapêutica em locais de difícil acesso a serviços de referência.

Effect of cement type and water storage time on the push-out bond strength of a glass fiber post

This study investigated the effects of the cement type and the water storage time on the push-out bond strength of a glass fiber post. Glass fiber posts (Fibrekor, Jeneric Pentron) were luted to post spaces using a self-cured resin cement (C&B Cement [CB]), a glass ionomer cement (Ketac Cem [KC]) or a resin-modified glass ionomer cement (GC FujiCEM [FC]) according to the manufacturers’ instructions. For each luting agent, the specimens were exposed to one of the following water storage times (n=5): 1 day (T1), 7 days (T7), 90 days (T90) and 180 days (T180). Push-out tests were performed after the storage times. Control specimens were not exposed to water storage, but subjected to the push-out test 10 min after post cementation. Data (in MPa) were analyzed by Kruskal-Wallis and Dunn`s test (α=0.05). Cement type and water storage time had a significant effect (p<0.05) on the push-out bond strength. CB showed significantly higher values of retention (p<0.05) than KC and FC, irrespective of the water storage time. Water storage increased significantly the push-out bond strength in T7 and T90, regardless of the cement type (p<0.05). The results showed that fiber posts luted to post spaces with the self-cured resin cement exhibited the best bonding performance throughout the 180-day water storage period. All cements exhibited a tendency to increase the bond strength after 7 and 90 days of water storage, decreasing thereafter.