Voronoi diagrams and arrangements

We propose a uniform and general framework for defining and dealing with Voronoi diagrams. In this framework a Voronoi diagram is a partition of a domainD induced by a finite number of real valued functions onD. Valuable insight can be gained when one considers how these real valued functions partitionD ×R. With this view it turns out that the standard Euclidean Voronoi diagram of point sets inR ^d along with its order-k generalizations are intimately related to certain arrangements of hyperplanes. This fact can be used to obtain new Voronoi diagram algorithms. We also discuss how the formalism of arrangements can be used to solve certain intersection and union problems.     

Semi-rigid analogues of the calcium antagonist verapamil: A molecular modelling study

Summary In this work the rigid-analogue approach has been used to obtain information on the active conformation(s) of the calcium antagonist verapamil. A series of semi-rigid analogues of verapamil were synthesized and their biological activities evaluated on guinea-pig heart and aorta. These molecules were analysed by means of molecular modelling techniques.On the basis of the pharmacological profile and conformational analysis of these compounds, two different models for negative inotropic and negative chronotropic activity are proposed. The two actions seem to be due to conformations of the molecules which differ in the orientation of their phenylethylamino groups.     

Computing convolutions by reciprocal search

In this paper we show how certain geometric convolution operations can be computed efficiently. Here efficiently means that our algorithms have running time proportional to the input size plus the output size. Our convolution algorithms rely on new optimal solutions for certain reciprocal search problems, such as finding intersections between blue and green intervals, and overlaying convex planar subdivisions.This research was done while on leave from Cornell at DEC/SRC.     

Generalized statistical gelation theory

Gel points in random polymerizations of the general type Σ_iRA + Σ_jRB in which A-groups react with A- and B-groups, and B-groups react only with A-groups are considered. (The symbols Σ_i and Σ_i signify that the A- and B-bearing reactants RA and RB can be mixtures of monomers of different functionalities, denoted generally as f_ai and f_bj.) The usual case of A-groups reacting only with B-groups is a special case of the present theory. The effects of chemical kinetics, the competitive reaction of A- and B-groups, are separated from the generalized statistical condition for gelation. The former are used to define reaction curves and the latter, gelation curves. Both types of curve are represented as p_a as a function of p_b. For a given polymerization, gelation occurs when the reaction curve and the gelation curve intersect. When A-groups react only with B-groups, the gel points are those for the usual type of Σ_iRA + Σ_jRB polymerization, and, in the limit of A-groups only reacting with A-groups, the gel points are those for Σ_iRA self polymerizations.     

On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition

We study a zero-flux type initial-boundary value problem for scalar conservation laws with a genuinely nonlinear flux. We suggest a notion of entropy solution for this problem and prove its well-posedness. The asymptotic behavior of entropy solutions is also discussed.     

Nachweis und Bestimmung des Eisens, sowie seine Trennung von anderen Elementen

Ohne Zusammenfassung     

Darstellung von Trifluormethylhalogen-Iodaten(I) des Typs (CH3)4N+CF3IX− (X = F,Cl, Br) und Trifluormethyltrifluormethoxyiodat(I) (CH3)4N+CF3IOCF3−

Preparation of Trifluormethylhalogen Iodate(I) Salts (CH₃)₄N⁺CF₃IX^? (X = F, Cl, Br) and Trifluormethyltrifluormethoxy Iodate(I) (CH₃)₄N⁺CF₃IOCF₃^? We describe the preparation of new trifluormethyliodate(I) salts CF₃IX^? (X = F, Cl, Br, OCF₃). (CH₃)₄N⁺CF₃ICl^? and (CH₃)₄N⁺CF₃IBr^? are obtained via addition of CF₃I with the corresponded tetramethylammonium halogenide. (CH₃)₄N⁺CF₃IOCF₃^? is synthesized by comproportionation of (CH₃)₄N⁺CF₃ICl^? with CF₃OCl under formation of Cl₂ at ?78°C. (CH₃)₄N⁺CF₃IF^? is formed either, through thermolysis of (CH₃)₄N⁺ CF₃IOCF₃^? under separation of COF₂, or reaction of CF₃I with (CH₃)₄N⁺ OCF₃^?. The thermolabile compounds have been characterized by i.r., Raman, ¹⁹F-, ¹³C NMR spectroscopy.