On the width of resonances

A method to get both upper and lower bounds on real and imaginary parts of resonance eigenvalues is extended to Schrödinger operators with exterior dilation analytic potential. We apply it to a simple model potential where the bound states and resonances are exactly known.     

High-Resolution X-ray Crystallography—An Experimental Method for the Description of Chemical Bonds

By increasing the accuracy of an X-ray analysis, results are obtained which allow one to beyond the location of hydrogen atoms and say something about the distribution of electrons in molecules. Using several examples from organic and organometallic chemistry, the methods, problems, and results of this approach are described.     

Nonlinear Connections and Nearly Autoparallel Maps in General Relativity

We apply the method of moving anholonomic frames with associated nonlinear connections to the (pseudo) Riemannian space geometry and examine the conditions when locally anisotropic structures (Finsler like and more general ones) could be modeled in the general relativity theory and/or Einstein–Cartan–Weyl extensions [1]. New classes of solutions of the Einstein equations with generic local anisotropy are constructed. We formulate the theory of nearly autoparallel (na) maps generalizing the conformal transforms and formulate the Einstein gravity theory on na–backgrounds provided with a set of na–map invariant conditions and local conservation laws. There are illustrated some examples when vacuum Einstein fields are generated by Finsler like metrics and chains of na–maps.     

Chiral and gluon condensates at finite temperature

We investigate the thermal behaviour of gluon and chiral condensates within an effective Lagrangian of pseudoscalar mesons coupled to a scalar glueball. This Lagrangian mimics the scale and chiral symmetries of QCD.     

Solid State Metathesis Reactions in Various Applications

Solid state metathesis reactions have been studied in fused silica tubes, by differential thermal analysis, and by X‐ray powder diffraction. A selection of reactions between metal (La, Nb, and Ni) chlorides and lithium nitride or lithium acetylide were investigated to get more insight into reaction pathways and intermediate reaction stages that may be adopted on course of the formation of metal nitrides or carbides. Intermediate compounds are considered to be important because they can control the reactivity of a system. Such compounds were traced by changing the molar ratios of reaction partners away from the salt‐balanced binary metal nitride or carbide target compositions. New preparative perspectives are discovered when metal chlorides were reacted with lithium nitridoborate or lithium cyanamide. Due to their reductive nature towards several d‐block metal chlorides, (BN₂)^3‐ and (CN₂)^2‐ react to form metals or metal nitrides plus X‐ray amorphous BN, and probably C₃N₄. With lanthanum chloride they can react to form nitridoborates and nitridocarbonates. The metathesis reaction between lithium cyanamide and cyanuric chloride (C₃N₃Cl₃) instead of metal chloride was studied for the synthesis of C₃N₄.     

A dynamic approach to ‘simple’ algebraic curves

Despite its low relevance for teaching in schools the desideratum “Algebraic Curves’ has always been an issue within mathematical didactics. This article aims to continue this tradition with respect to a project oriented mathematics instruction by applying current dynamic geometry software (Cabri II+).     

Accelerating the convergence of the method of alternating projections

The powerful von Neumann-Halperin method of alternating projections (MAP) is an algorithm for determining the best approximation to any given point in a Hilbert space from the intersection of a finite number of subspaces. It achieves this by reducing the problem to an iterative scheme which involves only computing best approximations from the individual subspaces which make up the intersection. The main practical drawback of this algorithm, at least for some applications, is that the method is slowly convergent. In this paper, we consider a general class of iterative methods which includes the MAP as a special case. For such methods, we study an ``accelerated' version of this algorithm that was considered earlier by Gubin, Polyak, and Raik (1967) and by Gearhart and Koshy (1989). We show that the accelerated algorithm converges faster than the MAP in the case of two subspaces, but is, in general, not faster than the MAP for more than two subspaces! However, for a ``symmetric' version of the MAP, the accelerated algorithm always converges faster for any number of subspaces. Our proof seems to require the use of the Spectral Theorem for selfadjoint mappings.