Prime ends for domains in metric spaces

In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Carathéodory and Näkki. Modulus ends and prime ends, defined by means of the p$p$-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.     

Permeation of a solvent mixture through an elastomeric membrane—The case of pervaporation

This article presents a model for the permeation of solvent mixtures through an elastomer in the particular case of pervaporation. An analytical expression for each solvent permeation rate is derived, in the limited case of a membrane that undergoes small swelling, without making any assumptions on the solvent diffusion coefficients and their dependence on solvent concentrations. Applying this analytical expression to different situations, we fitted most of the curves previously published on pervaporation experiments. In particular, we correlated the synergy developed by a mixture of two solvents in the permeation process with the sign of their Flory–Huggins interaction parameter χ_AB. This explains why, in most cases (χ_AB > 0), a molecule permeating easily through a membrane is mixed with a molecule permeating much less easily; the latter can see its permeation flux increase by a factor 10 or 100 because the swelling of the polymer induced by the more permeable molecule “opens the meshes of the network” allowing the less permeable molecule to pass through more easily. Within our analysis, the efficiency of the pervaporation process, expressed through the separation factor, is derived very simply as a function of the interaction coefficients and the viscosities of solvents and exhibits an exponential dependence on the volume fraction of either component as seen in most experiments. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 183–193, 2003     

Electronic structure of porphyrins. All-valence-electron SCF MO CI calculations of the spectra of dianion and free base porphin

All-valence-electron SCF MO CI calculations of the spectra of dianion and free base porphin were performed. Comparisons are made with other SCF MO CI calculations and with experiment. The results obtained are seen to be in reasonable agreement with experiment. Characteristics of the calculated band between the usual L and M bands are also discussed.     

Thermal curve interpretation by spectral resolution into a basic set of rectangular pulse curves

An improvement of the algorithm of the spectral resolution method for the determination of thermokinetics is presented. With the aid of the modified computer program and an experimental thermal curve, an analysis of the method has been performed.     

Polarisation control of light by light in a nonlinear polymer

Received: 11 December 1997/Revised version: 11 May 1998     

Noncommutative Circle Bundles and New Dirac Operators

We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and the Dirac operator on the total space and on the base space of the bundle. We analyze in details the example of the noncommutative three-torus viewed as a U(1) bundle over the noncommutative two-torus and find all connections compatible with an admissible Dirac operator. Conversely, we find a family of new Dirac operators on the noncommutative tori, which arise from the base-space Dirac operator and a suitable connection.     

Dirac Operators on Quantum Projective Spaces

We construct a family of self-adjoint operators D _N , ${N\in{\mathbb Z}}We construct a family of self-adjoint operators D _N , N ? \mathbb Z{N\in{\mathbb Z}} , which have compact resolvent and bounded commutators with the coordinate algebra of the quantum projective space \mathbb CP^l_q{{\mathbb C}{\rm P}^{\ell}_q} , for any ℓ ≥ 2 and 0 < q < 1. They provide 0⁺-dimensional equivariant even spectral triples. If ℓ is odd and N=\frac12(l+1){N=\frac{1}{2}(\ell+1)} , the spectral triple is real with KO-dimension 2ℓ mod 8.     

224 nm segmented hollow-cathode silver ion laser

The segmented hollow-cathode discharge arrangement is used the first time to excite the 224 nm Ag II laser transition. Quasi-continuous output power of 45 mW is obtained during the 300 s current pulses at optimal discharge conditions (10 hPa of He+4% Ar buffer gas) for discharge current of 3 A. No power saturation is observed up to this current value. An average output power of 0.75 mW is reached using pulse repetition frequency of 190 Hz. The longitudinal mode structure of the TEM₀₀ transversal mode is measured by means of a scanning confocal Fabry–Perot interferometer. Two-mode operation is found to be dominant at high current values. Attempts and suggestions are made to prolong the lifetime of the laser tube. PACS 42.55.Lt; 42.60.Lh; 52.80.-s     

Properties of an equilibrium hadron gas subjected to the adiabatic longitudinal expansion

We consider an ideal gas of massive hadrons in thermal and chemical equilibrium. The gas expands longitudinally in an adiabatic way. This evolution for a baryonless gas reduces to a hydrodynamic expansion. Cooling process is parametrized by the sound velocity. The sound velocity is temperature dependent and is strongly influenced by hadron mass spectrum.Work partially supported by the Polish Committee for Scientific Research under contract KBN-200579101