Mass transport in anharmonic potentials

We investigate the effect of nuclear shell structure on the mass transport in low-energy heavy-ion collisions. The shell-correction energy leads to anharmonic driving potentials and thus, to nonlinear drift coefficients in the Fokker-Planck equation. Results for²³⁸U (7.42 MeV/nucleon)+²³⁸U are presented. The drift towards the closed Pb-shell enhances the fluctuations in the mass transport and provides an explanation for the large variances found experimentally. Local maxima in the mass distribution at the shell minima disappear due to the temperature dependence of the driving potential.     

Thin-layer chromatography of radioactively labelled cholesterol and precursors from biological material

Summary The investigation methods of the action of xenobiotics on sterol biosynthesis from ¹⁴C-acetate in rat hepatocyte cultures can be developed, with regard to extraction using Extrelut and the separation of the sterol pattern by thin-layer chromatography, in such a way that they are suitable for wider application, e.g., screening. Good visualisation and recognition of changes in the sterol pattern are possible using autoradiography of the thin-layer chromatogram.

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Dünnschicht-Chromatographie von radioaktiv markiertem Cholesterin und Vorstufen aus biologischem Material. Eine einfache und empfindliche Methode zur Untersuchung einer Beeinflussung des Sterolbiosynthesewegs

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Dedicated to Dr. E. Roesch on occasion of his 65th birthday     

On the congruence lattice of a Scott-domain

We prove that the congruence lattice of a Scott-domain can be characterized as a complete lattice.Presented by V. Trnkova.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Quantum diffusion of positive muons

Recent studies of the diffusion of positive muons in metals, particularly aluminium, are reviewed. At low temperatures, quantum tunnelling is an important process for the mobility of the muons and experiments aimed at the study of tunnelling in the presence of phonons and conduction electrons are discussed. The concept of quantum diffusion is introduced and the conditions for quantum diffusion and quantum propagation (i.e. band-like motion) in normal and superconducting metals are compared.     

Convergence of dynamical zeta functions

I study poles and zeros of zeta functions in one-dimensional maps. Numerical and analytical arguments are given to show that the first pole of one such zeta function is given by the first zero ofanother zeta function: this describes convergence of the calculations of the first zero, which is generally the physically interesting quantity. Some remarks on how these results should generalize to zeta functions of dynamical systems with pruned symbolic dynamics and in higher dimensions follow.     

Some homological properties of commutative semitrivial ring extensions

LetR be a commutative ring with 1 andM anR-module. If:M _R MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR M; in particular, we are interested in some homological properties ofR M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM ^*, where the isomorphism is given by the adjoint of.     

On theR-order of coupled sequences arising in single-step type methods

Summary As shown in preceding papers of the authors, the verification of anR-convergence order for sequences coupled by a system (1.1) of basic inequalities can be reduced to the positive solvability of system (3.3) of linear inequalities. Further, the bestR-order implied by (1.1) is equal to the minimal spectral radius of certain matrices composed from the exponents occuring in (1.1). Now, these results are proven in a unified and essentially simpler way. Moreover, they are somewhat extended in order to facilitate applications to concrete methods.     

Analyticity properties of eigenfunctions and scattering matrix

For potentialsV=V(x)=O(|x|^–2–) for |x|,x³ we prove that if theS-matrix of (–, –+V) has an analytic extension to a regionO in the lower half-plane, then the family of generalized eigenfunctions of –+V has an analytic extension toO such that for |Imk|<b. Consequently, the resolvent (–+V–z ²)^–1 has an analytic continuation from ⁺ to {kOImk|<b} as an operator from _b ={f=e ^–b|x| g|gL ₂(³)} to _–b . Based on this, we define for potentialsW=o(e ^–2b|x|) resonances of (–+V, –+V+W) as poles of and identify these resonances with poles of the analytically continuedS-matrix of (–+V, –+V+W).The author would like to thank the Institute for Advanced Study for its hospitality and the National Science Foundation for financial support under Grant No. DMS-8610730(1)