The Vlasov-Poisson-Boltzmann system for non-cutof hard potentials

This paper is concerned with the construction of globally smooth solutions near a given global Maxwellian to the Cauchy problem of the Vlasov-Poisson-Boltzmann system for non-cutof hard potentials in three space dimensions without the neutral condition imposed on the initial perturbation.Our analysis is based on the time-weighted energy method and some delicate estimates.     

Singular Continuous Spectrum for a Class of Substitution Hamiltonians II

We consider discrete one-dimensional Schrödinger operators with aperiodic potentials generated by primitive substitutions. Using the three-block version of Gordon's criterion, we establish purely singular continuous spectrum with probability one provided that the potentials have index greater than three. It is also shown that one cannot use this criterion to prove uniform results.     

Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff

Abstract

For regularized hard potentials cross sections, the solution of the spatially homogeneous Boltzmann equation without angular cutoff lies in Schwartz's space 𝒮(? ^N ) for all (strictly positive) time. The proof is presented in full detail for the two-dimensional case, and for a moderate singularity of the cross section. Then we present those parts of the proof for the general case, where the dimension, or the strength of the singularity play an essential role.     

Radii of Redox Components from Absolute Redox Potentials Compared with Covalent and Aqueous Ionic Radii

Aqueous standard potentials, referred to that of the SHE as zero, were recently shown to vary linearly with gaseous ionization potentials, with the absolute potential of SHE as the intercept. This enabled arriving at the absolute redox potentials of elements. Here, the distances between the oxidized and reduced forms in aqueous solutions have been evaluated. From the linear dependence of these distances on the covalent radii of atoms, the radii of the redox components have been obtained. The latter also vary linearly with the aqueous ionic radii estimated earlier from ion‐water distances, and indicate the presence of aqueous molecular anions.     

Electrical resistivity of the alkaline earth metals Ca,Sr and Ba in the 50–300K temperature region

The computed values of the temperature dependent electrical resistivity is presented for the alkaline earth metals Ca, Sr and Ba. Numerical values of the mean free paths obtained using a finite mean free path approach is also reported. The structure factor has been evaluated using experimental values for the phonon spectra while local model potentials were used for the form factors. Our numerical results compare favourably with experiments.     

Quantum model for the price dynamics: The problem of smoothness of trajectories

We apply methods of quantum mechanics to mathematical modelling of price dynamics in a financial market. We propose to describe behavioral financial factors (e.g., expectations of traders) by using the pilot wave (Bohmian) model of quantum mechanics. Our model is a quantum-like model of the financial market, cf. with works of W. Segal, I.E. Segal, E. Haven. In this paper we study the problem of smoothness of price-trajectories in the Bohmian financial model. We show that even the smooth evolution of the financial pilot wave ψ(t,x) (representing expectations of traders) can induce jumps of prices of shares.     

Optimal Control of the Obstacle for an Elliptic Variational Inequality

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H ¹ ₀ (Ω) so that the state is close to the desired profile while the H ¹ (Ω) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established. Accepted 11 September 1996     

Free energy and some sample path properties of a random walk with random potential

We study the asymptotic behavior of the free energy for a model (defined by Sinai) of one-dimensional random walk with random potential. In particular, we obtain a central limit theorem and a strong law of large numbers for this free energy. We use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization. Some exponents describing the recurrence and localization are found.     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.