Global Optimization of 0-1 Hyperbolic Programs

We develop eight different mixed-integer convex programming reformulations of 0-1 hyperbolic programs. We obtain analytical results on the relative tightness of these formulations and propose a branch and bound algorithm for 0-1 hyperbolic programs. The main feature of the algorithm is that it reformulates the problem at every node of the search tree. We demonstrate that this algorithm has a superior convergence behavior than directly solving the relaxation derived at the root node. The algorithm is used to solve a discrete p-choice facility location problem for locating ten restaurants in the city of Edmonton.The research was supported in part by NSF awards DMII 95-02722 and BES 98-73586 to NVS.     

On the realization of symmetries in quantum mechanics

The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general. It is Wigner’s theorem which allows the use of linear realizations of symmetries and therefore guarantees that, in the end, quantum theory stays a linear theory. In the present paper, we take a strictly geometrical point of view in order to prove this theorem. It becomes apparent that Wigner’s theorem is nothing else but a corollary of the fundamental theorem of projective geometry. In this sense, the proof presented here is simple, transparent and therefore accessible even to elementary treatments in quantum mechanics.     

Convergence theory of extrapolated iterative methods for a certain class of non-symmetric linear systems

Summary A variety of iterative methods considered in [3] are applied to linear algebraic systems of the formAu=b, where the matrixA is consistently ordered [12] and the iteration matrix of the Jacobi method is skew-symmetric. The related theory of convergence is developed and the optimum values of the involved parameters for each considered scheme are determined. It reveals that under the aforementioned assumptions the Extrapolated Successive Underrelaxation method attains a rate of convergence which is clearly superior over the Successive Underrelaxation method [5] when the Jacobi iteration matrix is non-singular.     

The effect of transverse shear onto the singular solutions of a complete spherical shell

Green's functions for the field variables of a complete sphere subjected to normal surface traction are obtained with “free space” properties. Further, self-equilibrated singular solutions of the variables associated with tangentially applied point loads and concentrated surface moments are constructed. The solution formulae are derived within the framework of the improved theory of thin shells and thus incorporate the effect of transverse shear in the equilibrium of the shell element. Despite the complex character of the solution, expressed in terms of complex Legendre functions, the closed form of it reveals the effects of the new assumptions (presence of shear strains) onto the singular behavior of the associated kernels. Numerical results for the field variables demonstrate the differences between the two theories, classical and improved.     

Neue Additionsverbindungen von Germaniumtetrajodid mit organischen Basen

Four new stable addition compounds have been prepared by reaction of germanium tetraiodide with various tertiary amines. It is a case of adducts of 1:4 composition, in contrast to the 1:5 addition compound with triethylamine, which we have also prepared and investigated for comparison. Formation, properties, analytical results, conductometric measurements and spectral data (IR and¹H-NMR) of these adducts are described and discussed in terms of possible structural types and the nature of the bonding.