The cross ratio and Clifford algebras

Motivated by recent quaternionic approach of Bobenko and Pinkall to the complex cross ratio we presenta simple method to eva]uate the cross ratio in the Euclidean space? ⁿ identifying the space with vectors generating the Clifford algebraC(n). We apply the Clifford cross ratio to describe discrete analogues of orthogonal nets in? ⁿ .     

Volume of Polynomial Lemniscates in C n

Kiselman's method permitting one to estimate the volume of sublevel sets of a plurisubharmonic function f in C ⁿ with the aid of the Lelong number of f is applied to polynomial lemniscates in C ⁿ . In particular, it yields estimates from below of the volume of polynomial lemniscates which completes recent results of Cuyt, Driver and Lubinsky.     

Lie-Algebraic Discrete Approximation for Nonlinear Evolution Equations

An efficient procedure of Lie-algebraic discrete approximation for nonlinear evolution equations in a Banach space is developed. A convergent approximation is constructed, and the analysis of stability is carried out. For the Lie-algebraic discrete approximation of linear and nonlinear differential operators, an application of the multivariate form of Lagrangian interpolating schemes in star-shaped domains is suggested.     

Collective quadrupole dynamics and the band structure of the nucleus 127Cs

Excited states of ¹²⁷₅₅Cs were populated in the ¹²⁷I(α, 4n)¹²⁷Cs reaction. Singles, prompt and delayed γ-ray spectra, γγ coincidence spectra, angular distributions and excitation functions were measured, and negative and positive parity bands established. The h_{$\text{11}\text{2}$} families of excited levels in ^{127, 129}Cs and ¹³³La were reproduced by core-particle coupling calculations, regardless of whether the cores were taken to be rigid triaxial rotors or to have all five quadrupole degrees of freedom. The hamiltonians for the latter case were based on microscopic calculations which attribute an important role to the γ-dependence of the mass functions for collective quadrupole motion. From a core-quasiparticle analysis of the positive-parity levels in ¹²⁷Cs, indications of a “Coriolis attenuation” anomaly were inferred.     

Calculation of kinetic parameters from TG curve on the base of dehydration process of hydrous titanium dioxide

A direct method of evaluating of kinetic equation parameters based on TG curve is proposed. The method was applied to calculate kinetic parameters of the process of dehydration of hydrous titanium dioxide.

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Zusammenfassung Es wird ein direktes Verfahren zur Bestimmung der Parameter der kinetischen Gleichung auf der Basis von TG-Kurven gegeben. Das Verfahren wurde zur Berechnung der kinetischen Parameter des Dehydratationsprozesses von wasserhaltigem Titandioxid benutzt.

     

High-spin states in 232U investigated with the 232Th(α, 4nγ) reaction

The ground-state rotational band of ²³²U is established up to I^π = 16⁺ (tentatively 18⁺) through a study of the ²³²Th(α, 4nγ) reaction. Conversion electron spectroscopy is found to be especially useful in circumventing the difficulties caused by strong fission competition.     

Relaxation problem with a quadratic noise: Analysis

The properties of a linear differential equation with an additive quadratic noise are analyzed. The graphs of the probability distribution of the process are presented for various values of the noise strength and the damping constant. The time evolution of the distribution is also shown. An infinitesimal generator of the evolution operator of the process is constructed. A diffusion-type approximation is considered and a comparison of the exact solution with the approximate solution is carried out.This paper is dedicated to the memory of Prof. A. Pawlikowski.     

Sur les solutions d'une équation fonctionnelle,III

Sans résumé

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