Levy area for the free Brownian motion: existence and non-existence

This note extends the work of Capitaine (J. Funct. Anal. 179 (1) (2001) 153) on the Levy area process for the free Brownian motion in two directions. First, we reprove that a Levy area for the Free Brownian motion exists in the Von Neumann tensor product, by exhibiting a non-commutative Burkholder-Davis-Gundy type inequality. Then, we show that there does not exist a Levy area in the projective tensor product.     

FREE BOUNDARY PROBLEM ARISING FROM EVAPORATION FROM POROUS MEDIUM

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Effects of oxygen in gamma irradiated aromatic polyesters in film

The effect of gamma irradiation in air is investigated on four thermoplastic polyesters (PET, PBT, PEN, PCT-co-ET) in films containing aromatic rings, in order to evaluate the influence of aromatic density and the role of oxygen on radiation resistance. Physical-chemical-nuclear analyses were used to this purpose. EPR measurements were carried out to detect radical stability against oxygen permeation. Viscometric investigations reported a very similar trend for all the investigated polyesters: a chain break effect that decreases at the highest doses. FT-IR analyses focused on the formation of oxidized species. Positron annihilation spectra pointed out a decrease of the intensity of ortho-positronium formation, while its lifetime remains unchanged with radiation dose.     

A uniqueness theorem for a free boundary problem

In this paper, we prove a uniqueness theorem for a free boundary problem which is given in the form of a variational inequality. This free boundary problem arises as the limit of an equation that serves as a basic model in population biology. Apart from the interest in the problem itself, the techniques used in this paper, which are based on the regularity theory of variational inequalities and of harmonic functions, are of independent interest, and may have other applications.

     

On classical analogues of free entropy dimension

We define a classical probability analogue of Voiculescu's free entropy dimension that we shall call the classical probability entropy dimension of a probability measure on Rn. We show that the classical probability entropy dimension of a measure is related with diverse other notions of dimension. First, it can be viewed as a kind of fractal dimension. Second, if one extends Bochner's inequalities to a measure by requiring that microstates around this measure asymptotically satisfy the classical Bochner's inequalities, then we show that the classical probability entropy dimension controls the rate of increase of optimal constants in Bochner's inequality for a measure regularized by convolution with the Gaussian law as the regularization is removed. We introduce a free analogue of the Bochner inequality and study the related free entropy dimension quantity. We show that it is greater or equal to the non-microstates free entropy dimension.     

Well-posedness of a multidimensional free boundary problem modelling the growth of nonnecrotic tumors

In this paper we study a free boundary problem modelling the growth of nonnecrotic tumors. The main trait of this free boundary problem is that it is essentially multidimensional, so that its well-posedness is hard to establish by using the usual methods in the classical theory of free boundary problems. In this paper we use the functional analysis method based on the theory of analytic semigroups to prove that this problem has a unique local solution in suitable function spaces. Continuous dependence of the solution on the initial data and regularities of the solution can also be easily obtained by using the argument of this paper.     

Calculating Gibbs free energies of transfer from Gibbs ensemble Monte Carlo simulations

The partitioning of the ternary systems n-pentane/n-heptane/(helium or argon) at ambient conditions is investigated using configurational-bias Monte Carlo simulations in the Gibbs ensemble. The results demonstrate that this approach yields very precise partition constants and free energies of transfer. Simulations are carried out to study the dependence of the n-pentane partitioning with respect to the carrier gas, the system size, and the overall solute concentrations. None of the changes of variables, within the ranges used here, has a significant effect on the alkane partitioning. However, chemical potentials calculated via Widom's ghost particle insertions show a strong number dependence for phases containing relatively few molecules of a given type. This problem originates from the fact that the chemical potential is calculated for a concentration of real particles plus one ghost particle that is systematically larger than the equilibrium concentration. A simple correction term is suggested to account for this problem. Received: 13 May 1998 / Accepted: 18 June 1998 / Published online: 4 September 1998     

Homolytic Cyclizations of N-Chloroalkenylamines

Many N-chloroalkylamines with double bond(s) dissociate homolytically to give chlorine atoms and aminyl radicals which undergo intramolecular cyclization reactions. Here, the nature of the aminyl radicals (neutral, protonated, or complexed to metal salts) appears to be important. The reactivity varies strongly from one species to another, and their selectivities can be different towards addition, substitution, abstraction, or dimerization reactions. A good synthetic tool appears to be the “complexed radical”, which is generated under mild conditions. A variety of β-functionalized, substituted, fused, or bridged azaheterocycles with alkaloid part structures thus become easily accessible in high yields, in a regio- and, possibly, stereoselective manner. Many examples are discussed illustrating the synthetic possibilities, limitations, and mechanistic features of this cyclization process.     

Aluminium(III) as a promoter of cellular oxidation

Aluminium has been known as a neurotoxic agent to experimental animals since the last century (Arch. Exp. Pharmacol. 40 (1897) 98). However, great interest arose in it bioinorganic chemistry as well biology when it was demonstrated to be the causative agent in pathologies related to the long-term dialysis treatment of uremic subjects with renal failure (Life Chem. 11 (1994) 197), and as a potential etiopathogenic cofactor for several neurodegenerative diseases. The inorganic biochemistry of aluminium is still largely to be discovered. In this review the pro-oxidative property of aluminium toward biological membrane will be presented and its implications in involvement in human pathology will be discussed in an interdisciplinary frame from the bioinorganic point of view.     

Spin Density Distribution in 2,4,6-Triphenylphenoxyl

The distribution of the unpaired electron over the oxygen and the 24 carbon atoms in the free 2,4,6-triphenylphenoxy radical was determined by electron spin resonance spectroscopy and quantum-mechanical approximation methods. The hyperfine splitting was evaluated with the aid of the spectra of triphenylphenoxyls deuterated in some or all of the substituent phenyl groups. The results of the quantum-mechanical approximations were checked by recording the ESR spectra of triphenylphenoxyls labeled with ¹³C in positions 1,2,3, or 4 of the central ring. The spin density distribution permits a first discussion of the ¹⁷O-coupling constants of correspondingly labeled triphenylphenoxyl and other organic free radicals.