On the Lipschitz classification of normed spaces, unit balls, and spheres

For every normed space , we note its closed unit ball and unit sphere by and , respectively. Let and be normed spaces such that is Lipschitz homeomorphic to , and is Lipschitz homeomorphic to .

We prove that the following are equivalent:

1. is Lipschitz homeomorphic to .

2. is Lipschitz homeomorphic to .

3. is Lipschitz homeomorphic to .

This result holds also in the uniform category, except (2 or 3) 1 which is known to be false.

     

Theoretical Study of the Electronic Structure of the KRb Molecule

Upon request of experimentalists now engaged in high-resolution spectroscopic investigations of the molecule KRb, we have determined the potential energy of electronic states (2S+1)Lambda((+)) correlating up to the limit K(5p) + Rb(5s) and of electronic states Omega((+/-)) correlating up to the limit K(4s) + Rb(4d(2)D(3/2)) in a large range of internuclear distance R. For the five states so far observed, the agreement between calculated and experimental molecular constants is good with DeltaR(e) < 0.08 ?, Deltaomega(e) < 6 cm(-1), and DeltaT(e) < 140 cm(-1). Extensive numerical data for energies versus R have been listed in a data base available at http://www.idealibrary.com. Copyright 2000 Academic Press.     

Ab initio simulation of phase transitions and dissociation of H2S at high pressure

By ab initio constant pressure molecular dynamics, we have identified the structure of phase V and phase VI of H2S at 35 and 65 GPa, respectively. The theoretical IR spectra of both phases are consistent with experimental findings and support our proposed structural models. We find that phase V is characterized by the presence of charged SH+3 and SH- species which are created and destroyed dynamically, whereas phase VI is no longer a molecular phase but consists of sheets of S with the majority of H intercalated between the layers. The stability of the two phases with respect to dissociation into elemental crystalline hydrogen and sulfur is discussed.     

Structural principles and amorphouslike thermal conductivity of Na-doped Si clathrates

The postulated low thermal conductivity and the possibility of altering the electronic conductivity of metal-doped clathrates with semiconducting host elements have stimulated great interest in exploring these compounds as promising thermoelectric materials. The electronic and thermal properties of the prototypical Na xSi (46) system are studied in detail here. It is shown that, despite the fact that the Na/Si clathrate is metallic, its thermal conductivity resembles that of an amorphous solid. A theoretical model is developed to rationalize the structural stability of the peculiar structural topology, and a general scheme for rational design of high efficiency thermoelectric materials is presented.     

Synthesis and functional pharmacological effects on human bronchi of 20-hydroxyeicosatetraenoic acid

We have synthesized 20-hydroxyeicosatetraenoic acid (20-HETE) following a new route and delineated its functional effects in human bronchi. Isometric tension measurements were performed, and they demonstrated that synthetic 20-HETE induced a concentration-dependent relaxant effect in ASM on resting tone and on bronchi pre-contracted with methacholine.     

The 3D Primitive Equations in the absence of viscosity: Boundary conditions and well-posedness in the linearized case

In this article we consider the 3D Primitive Equations (PEs) of the ocean, without viscosity and linearized around a stratified flow. As recalled in the Introduction, the PEs without viscosity ought to be supplemented with boundary conditions of a totally new type which must be nonlocal. In this article a set of boundary conditions is proposed for which we show that the linearized PEs are well-posed. The proposed boundary conditions are based on a suitable spectral decomposition of the unknown functions. Noteworthy is the rich structure of the Primitive Equations without viscosity. Our study is based on a modal decomposition in the vertical direction; in this decomposition, the first mode is essentially a (linearized) Euler flow, then a few modes correspond to a stationary problem partly elliptic and partly hyperbolic; finally all the other modes correspond to a stationary problem fully hyperbolic.     

Biological activities of phthalocyanines. XII: Synthesis tumor uptake and biodistribution of 14C-labeled disulfonated and trisulfonated gallium phthalocyanine in C3H mice

The biodistribution and metabolism of 14C-labeled disulfonated and trisulfonated gallium phthalocyanine (Ga-PcS) was studied in radiation-induced fibrosarcoma tumor-bearing C3H mice. The [14C]Ga-PcS compounds were prepared via the condensation of [14C]phthalic acid and sulfophthalic acid in the presence of gallium chloride and characterized by their spectroscopic and chromatographic properties. The tissue concentrations of the dyes was measured by scintillation counting of the 14C and by extraction and fluorescence measurements. Elevated dye levels were found in the liver, lungs, kidneys and spleen as well as in the tumor. Lower sulfonation of Ga-PcS favored liver and spleen uptake whereas higher dye sulfonation resulted in greater kidney uptake. Both dyes showed high tumor uptake with peak concentrations exceeding those of most tissues except for the liver in the case of Ga-PcS2. The highest tumor uptake was observed with Ga-PcS3. Both dyes were slowly excreted from the body. The liver-feces pathway was favored in the case of Ga-PcS2 with high activities persisting in the liver, even after 21 days. The Ga-PcS3 was preferentially excreted via the kidney-urine pathway. High performance liquid chromatography analysis of the liver and tumor extracts of [14C]Ga-PcS3-treated animals did not reveal desulfonation of the dye. However, urine analysis showed the presence of radioactive metabolites lacking the characteristic phthalocyanine absorption.     

A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

A generalization of Wegschcider's condition concerning equilibrium constants in chemically reacting systems is formulated, which is then proved to be a necessary and sufficient condition for detailed balancing. In order to include a large multitude of rate laws, a generalized mass action kinetics is considered which comprises usual mass action kinetics and all reversible enzyme kinetics and which is consistent with basic postulates of irreversible thermodynamics for ideal mixtures. Reaction systems of arbitrary stoichiometry are considered. They may contain reactants with fixed concentrations, as is characteristic for models of biochemical reaction networks. Existence, uniqueness, and global asymptotic stability of equilibrium states for reaction systems endowed with generalized man action kinetics are proved. Using these results, he generalized Wegscheider condition is shown to be a sufficient criterion for the applicability of the quasi-steady-state approximation.