Self-organized ZnAl2O4 nanostructures grown on -sapphire

Self-organized ZnAl₂O₄ nanostructures with the appearance (in SEM) of high aspect ratio horizontal nanowires are grown on uncatalysed c-sapphire by vapour phase transport. The nanostructures grow as three equivalent crystallographic variants on c-sapphire. Raman and cathodoluminescence spectroscopy confirm that the nanostructures are not ZnO and TEM shows that they are the cubic spinel, zinc aluminate, ZnAl₂O₄, formed by the reaction of Zn and O with the sapphire substrate.     

Separation in distributive congruence lattices

We define separable sets in algebraic lattices. For a finitely generated congruence distributive variety V \mathcal{V} , we show a close connection between non-separable sets in congruence lattices of algebras in V \mathcal{V} and the structure of subdirectly irreducible algebras in V \mathcal{V} . We apply the general results to some lattice varieties.     

Lower bounds of the Laplacian graph eigenvalues

In this paper we prove that all positive eigenvalues of the Laplacian of an arbitrary simple graph have some positive lower bounds. For a fixed integer k 1 we call a graph without isolated vertices k-minimal if its kth greatest Laplacian eigenvalue reaches this lower bound. We describe all 1-minimal and 2-minimal graphs and we prove that for every k 3 the path P_k+1 on k + 1 vertices is the unique k-minimal graph.     

Natural Operators Lifting Vector Fields to Bundles of Weil Contact Elements

Let A be a Weil algebra. The bijection between all natural operators lifting vector fields from m-manifolds to the bundle functor K ^A of Weil contact elements and the subalgebra of fixed elements SA of the Weil algebra A is determined and the bijection between all natural affinors on K ^A and SA is deduced. Furthermore, the rigidity of the functor K ^A is proved. Requisite results about the structure of SA are obtained by a purely algebraic approach, namely the existence of nontrivial SA is discussed.     

Working group report: Neutrino and astroparticle physics

This is the report of neutrino and astroparticle physics working group at WHEPP-7. Discussions and work on CP violation in long baseline neutrino experiments, ultra high energy neutrinos, supernova neutrinos and water Cerenkov detectors are discussed.     

Volume Chemistry of Nitrogen in Binary Metal Nitrides and Subnitrides

A comparison of the concept of volume increments created by W. Biltz with that based on quantum mechanical calculations by R.F.W. Bader was performed for crystal structures of binary metal nitrides and ‐subnitrides. The mutual comparison of both concepts permits insights into the bonding relationships of these compounds and reveals the considerable range of volume demand of a strongly polarisable bonding partner, such as the nitride ion. Finally it becomes clear that the Biltz volume increments show a quantum‐chemical relevance in the chemistry of solids.     

Model of free charge generation in polymers

A time solution of the excimer-ion pair system is presented here with a special attention to the time asymptote. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997. This work was supported by the grant No. C 1050601 of the Grant Agency of the Academy of Sciences of the Czech Republic.     

Spectral distributions in nuclei: General principles and applications

The subject of spectral distribution methods where one derives and applies the locally smoothed forms of observables in nuclei is briefly reviewed. It is well understood that the local forms (with respect to energy) of the level density function, expectation values and strength densities are Gaussian, linear (or ratio of Gaussians) and a bivariate Gaussian respectively. To accomodate symmetries in the above forms, one has to deal with multivariate distributions in general; for example the angular-momentum (J) decomposition leads to a bivariate Gaussian form for the level density. These results extend to indefinitely large spaces by method of partitioning and they generate convolution forms. The origin of these remarkable spectral properties is discussed and shell model examples are given to substantiate their applicability to nuclear systems. Spectral distribution theory is a practical, usable theory because the smoothed forms are defined in terms of traces of low particle-rank operators, and the trace information propagates. Finally we discuss the application of the spectral methods for a wide range of nuclear problems; these include binding energies, orbit occupancies, electromagnetic andβ-decay sum rule quantities, analysis of operators, symmetry breaking, numerical level densities, and determination of bounds on time-reversal non-invariant part of nucleon-nucleon interaction.