COUNTABLE GROUPS OF ISOMETRIES ON BANACH SPACES

A group G is representable in a Banach space X if G is isomorphic to the group of isometrics on X in some equivalent norm. We prove that a countable group G is representable in a separable real Banach space X in several general cases, including when G similar or equal to {-1,1} x H, H finite and dim X >= vertical bar H vertical bar or when G contains a normal subgroup with two elements and X is of the form c(0)(Y) or l(p)(Y), 1 <= p < +infinity. This is a consequence of a result inspired by methods of S. Bellenot (1986) and stating that under rather general conditions on a separable real Banach space X and a countable bounded group G of isomorphisms on X containing -Id, there exists an equivalent norm on X for which G is equal to the group of isometrics on X. We also extend methods of K. Jarosz (1988) to prove that any complex Banach space of dimension at least 2 may be renormed with an equivalent complex norm to admit only trivial real isometries, and that any complexification of a Banach space may be renormed with an equivalent complex norm to admit only trivial and conjugation real isometrics. It follows that every real Banach space of dimension at least 4 and with a complex structure may be renormed to admit exactly two complex structures up to isometry, and that every real Cartesian square may be renormed to admit a unique complex structure up to isometry.

Controllability of Volterra-Fredholm type systems in Banach spaces

We show the results in Chalishajar [Controllability of mixed Volterra-Fredholm-type integro-differential systems in Banach space, J. Franklin Inst. 344(1) (2007) 12-21] and Chang and Chalishajar [Controllability of mixed Volterra-Fredholm type integro-differential systems in Banach space, J. Franklin Inst., doi:10.1016/j. jfranklin.2008.02.002] are only valid for ordinary differential control systems. As a result the examples provided cannot be recovered as applications of the abstract results. (C) 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Quantitative evaluation of altered hepatic spaces and membrane transport in fibrotic rat liver

Four animal models were used to quantitatively evaluate hepatic alterations in this study: (1) a carbon tetrachloride control group (phenobarbital treatment only), (2) a CCl4-treated group (phenobarbital with CCl4 treatment), (3) an alcohol-treated group (liquid diet with alcohol treatment), and (4) a pair-fed alcohol control group (liquid diet only). At the end of induction, single-pass perfused livers were used to conduct multiple indicator dilution (MID) studies. Hepatic spaces (vascular space, extravascular albumin space, extravascular sucrose space, and cellular distribution volume) and water hepatocyte permeability/surface area product were estimated from nonlinear regression of outflow concentration versus time profile data. The hepatic extraction ratio of H-3-taurocholate was determined by the nonparametric moments method. Livers were then dissected for histopathologic analyses (e.g., fibrosis index, number of fenestrae). In these 4 models, CCl4-treated rats were found to have the smallest vascular space, extravascular albumin space, H-3-taurocholate extraction, and water hepatocyte permeability/surface area product but the largest extravascular sucrose space and cellular distribution volume. In addition, a linear relationship was found to exist between histopathologic analyses (fibrosis index or number of fenestrae) and hepatic spaces. The hepatic extraction ratio of H-3-taurocholate and water hepatocyte permeability/surface area product also correlated to the severity of fibrosis as defined by the fibrosis index. In conclusion, the multiple indicator dilution data obtained from the in situ perfused rat liver can be directly related to histopathologic analyses.

Fixed point theorems of upper semicontinuous multivalued mappings with applications in hyperconvex metric spaces

In the present paper, we establish two fixed point theorems for upper semicontinuous multivalued mappings in hyperconvex metric spaces and apply these to study coincidence point problems and minimax problems. (C) 2002 Elsevier Science (USA). All rights reserved.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

"Vegeu el resum a l'inici del document del fitxer adjunt."

A cohort-based analysis of the evolution of lifetime prevalence of recourse to prostitution by men in the general population of Switzerland, 1987-2000

Background: Despite their relevance to the prevention of sexually transmitted infections, there are few data on the frequency of recourse to prostitution in the male population in Switzerland. Using data gathered for the evaluation of the Swiss AIDS prevention strategy, we analysed net aggregate change and cohort-based change in lifetime prevalence of recourse to prostitution. Methods: Seven repeated cross-sectional telephone surveys of the general population aged 17-45 years (17-30 years only for the 1987 and 1988 surveys) were undertaken from 1987 to 2000 providing information on sexual behaviour including men's recourse to prostitution (total n¼9318). Age categories were: 17-20, 21-25, 26-30, 31-35, 36-40 and 41-45 years. Prevalence at 17-30 years was available in all surveys and prevalence at 41-45 was available for 1989-2000, though not for the same cohorts. Intra-cohort increase in prevalence over 10 years was analysed using truncated information for cohorts aged 21-25 and 26-30 years in 1987 and 1990. Population estimates were computed with 95% confidence intervals (CI). Results: No net change occurred in the 17-45 years male population prevalence between 1989 (17.6%, CI ¼ 15.4; 20.0) and 2000 (17.7%, CI ¼ 15.6; 20.0). The median starting prevalence of recourse to prostitution at age 17-20 was 4.8% (in 1989, CI ¼ 2.0; 9.7) and the range was from 1.8 (in 1994) to 10.4% (in 1990). The median ending prevalence at age 41-45 was 21.9% (in 1994, CI 16.7; 27.9) and the range was from 17.9 (in 2000) to 26.1% (in 1992). No clear trend was observed in either starting or ending prevalence. Intra-cohort evolution of the 1997 and 1990 cohorts was very similar. Conclusions: Based on available data, there was no net (aggregate) change in the prevalence of recourse to prostitution by males in Switzerland between 1989 and 2000. Within the time frame available, intra-cohort evolution was also very similar.