Functionally Countable Spaces and Baire Functions

The concept of the distinguished sets is applied to the investigation of the functionally countable spaces. It is proved that every Baire function on a functionally countable space has a countable image. This is a positive answer to a question of R. Levy and W. D. Rice.

Selections, Paracompactness and Compactness

2000 Mathematics Subject Classification: 54C60, 54C65, 54D20, 54D30.

A Countable Economy: An Example

Weiss (1981) established core equivalence and the existence of competitive equilibria in finitely additive exchange economies. To underline the relevance of finitely additive economies we present in this note an example with a close connection to finite exchange economies.

An Elementary Core Equivalence Theorem in a Countable Economy

We consider an infinite exchange economy with countably many traders, which can be regarded as a natural extension of finite exchange economies to an infinite one. In our countable economy the core defined in the traditional manner would be empty. To avoid this unwanted situation we have to strengthen the notion of “improves upon”. We will achieve this based on the idea that forming coalitions involve costs.

Compactness in quasi-Banach function spaces and applications to compact embeddings of Besov-type spaces

There are two main aims of the paper. The first one is to extend the criterion for the precompactness of sets in Banach function spaces to the setting of quasi-Banach function spaces. The second one is to extend the criterion for the precompactness of sets in the Lebesgue spaces $L_p(\Rn)$, $1 \leq p < \infty$, to the so-called power quasi-Banach function spaces. These criteria are applied to establish compact embeddings of abstract Besov spaces into quasi-Banach function spaces. The results are illustrated on embeddings of Besov spaces $B^s_{p,q}(\Rn)$, $0

Remyelination in experimentally demyelinated connexin 32 KnockOut mice

The aim of this study was to evaluate the role of connexin 32 (Cx 32) during remyelination of the peripheral nervous system, through a local injection of either 0,1% ethidium bromide solution or saline in the sciatic nerve of Cx 32 knockout mice. Euthanasia was performed ranging from 1, 2, 3, 7, 15, 21 to 30 days after injection. Histochemical, immunohistochemical, immunofluorescence and transmission electron microscopical techniques were used to analyze the development of the lesions. Within the sciatic nerves, Schwann cells initially showed signs of intoxication and rejected their sheaths; after seven days, some thin newly formed myelin sheaths with uneven compactness and redundant loops (tomacula) were conspicuous. We concluded that the regeneration of lost myelin sheaths within the PNS followed the pattern already reported for this model in other laboratory species. Therefore, these results suggest that absence of Cx 32 did not interfere with the normal pattern of remyelination in this model in young mice.

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).

The 1000 brightest HIPASS galaxies: Newly cataloged galaxies

The H I Parkes All-Sky Survey (HIPASS) is a blind 21 cm survey for extragalactic neutral hydrogen, covering the whole southern sky. The HIPASS Bright Galaxy Catalog (BGC) is a subset of HIPASS and contains the 1000 H I brightest (peak flux density) galaxies. Here we present the 138 HIPASS BGC galaxies that had no redshift measured prior to the Parkes multibeam H I surveys. Of the 138 galaxies, 87 are newly cataloged. Newly cataloged is defined as having no optical ( or infrared) counterpart in the NASA/IPAC Extragalactic Database. Using the Digitized Sky Survey, we identify optical counterparts for almost half of the newly cataloged galaxies, which are typically of irregular or Magellanic morphological type. Several H I sources appear to be associated with compact groups or pairs of galaxies rather than an individual galaxy. The majority ( 57) of the newly cataloged galaxies lie within 10degrees of the Galactic plane and are missing from optical surveys as a result of confusion with stars or dust extinction. This sample also includes newly cataloged galaxies first discovered by Henning et al. in the H I shallow survey of the zone of avoidance. The other 30 newly cataloged galaxies escaped detection because of their low surface brightness or optical compactness. Only one of these, HIPASS J0546-68, has no obvious optical counterpart, as it is obscured by the Large Magellanic Cloud. We find that the newly cataloged galaxies with -b->10degrees are generally lower in H I mass and narrower in velocity width compared with the total HIPASS BGC. In contrast, newly cataloged galaxies behind the Milky Way are found to be statistically similar to the entire HIPASS BGC. In addition to these galaxies, the HIPASS BGC contains four previously unknown H I clouds.

Existence Results for Second Order Differential Equations with Nonlocal Conditions in Banach Spaces

This work is concerned with implicit second order abstract differential equations with nonlocal conditions. Assuming that the involved operators satisfy sonic compactness properties, we establish the existence of local mild solutions, the existence of global mild solutions and the existence of asymptotically almost periodic solutions.

Path integrals for continuous-time Markov chains

This note presents a method of evaluating the distribution of a path integral for Markov chains on a countable state space.

Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

Integrals for continuous-time Markov chains

This paper presents a method of evaluating the expected value of a path integral for a general Markov chain on a countable state space. We illustrate the method with reference to several models, including birth-death processes and the birth, death and catastrophe process. (C) 2002 Elsevier Science Inc. All rights reserved.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.