Menus of kuratowski subgraphs

Motivated by heuristic embedding algorithms, this paper is concerned with the organization of potentially large lists of Kuratowski subgraphs of an arbitrary nonpianar graph. A graphical structure called a "nearly Hamiltonian" graph is defined. It is shown that lists of Kuralowski subgraphs can be lexicographically organized in such structures. It is shown that any nonpianar graph contains such structures and at least one such structure with a nonempty list of Kuratowski subgraphs can be located in linear time in ihe edges of the graph.     

Small angle X-ray scattering by spherical particles of Polystyrene and Polyvinyltoluene

The high intensity, high resolution multiple reflection diffractometer has been applied to make accurate measurements of the small angle X-ray scattering of eight different Dow Chemical latexes with stated diameters 2.051, 1.305, 0.814, 0.557, 0.365, 0.264, 0.126, and 0.088 μm. Using thin dry samples, the measured intensities of diffraction extrema with orders higher than the third were found to agree well with the simple Rayleigh-Gans theory which neglects multiple scattering as well as interparticle interference. Orders below the fourth showed a distinct effect of interparticle interference. This effect could be demonstrated to vanish when a liquid solution sample was used instead of a dry one. Scattering curves of thick dry samples had strongly decreased contrast between maxima and minima, an effect which is known to be due to multiple scattering. The following particle diameters were determined from the measured scattering curves: 2.102±0.013 μm, 1.313±0.008 μm, 0.823±0.004 μm, 0.552±0.002 μm, 0.352±0.002 μm, 0.254±0.002 μm, 0.119±0.001 μm and 0.078±0.001 μm. The discrepancies between these and the stated sizes are larger for the smaller particles. It is believed that the X-ray measurements are more accurate than the stated sizes which are based on measurements in the electron microscope. Therefore, as secondary standards, the diameter obtained from the X-ray measurements should be used.     

An X-ray interferometer with Bragg case beam splitting and beam recombination

A new type of X-ray interferometer which uses Bragg case transmission for beam splitting and for beam recombination is described. The principles and special problems of this interferometer are discussed and a strict plane-wave treatment of the interference phenomena is presented. The feasibility of such a device is demonstrated by some interference patterns, obtained with an instrument made from a silicon crystal for use with copperKα radiation and the 220 Bragg reflection. Since, for the operation of the Bragg case interferometer, strong absorption is not essential, such devices may also be more suitable than the previously reported Laue case interferometer^1,2 for use with neutrons.     

Hydrolysis of acetylcholinesterase inhibitors--organophosphorus acid anhydrolase enzyme immobilization on photoluminescent porous silicon platforms

We report on the immobilization of an OPAA enzyme on luminescent porous silicon devices, and on the utilization of this new platform to hydrolyze p-nitrophenyl-soman.     

Decay and growth for a nonlinear parabolic difference equation

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation when and a new growth result when 0$">.

     

An axiomatization of the consistent non-transferable utility value

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom.Previous versions: October 2003 (Center for the Study of Rationality DP-337), December 2004. Research partially supported by a grant of the Israel Academy of Sciences and Humanities. The author thanks Andreu Mas-Colell, Bezalel Peleg, Peter Sudhölter, the referees, and the editor for their comments and suggestions.     

Crystalline complexes of N,N'-ditritylurea (DTU) and N-tritylurea (NTU) hosts with molecular guests

This paper reports crystalline complexes of the new hosts N,N'-ditritylurea (DTU) and N-tritylurea (NTU) with various uncharged molecular guests. The crystal structures of the following complexes were elucidated by single crystal X-ray diffraction analysis at 115^oK: (I) 1:1 DTU-propanamide — space group C2/c, a=15.839Å, b=9.088Å, c=24.584Å, =111.05^o, Z=4; (II) 1:1 DTU-ethyl N-acetylglycinate — space group P1, a=9.010Å, b=10.800Å, c=19.810 Å, =105.29^o =94.33^o, =93.03^o, Z=2; (III) 2:1 NTU-N, N-dimethylformamide — space group Cc, a=29.614Å, b=8.906Å, c=16.127Å, =121.04^o, Z=4. The three crystal structures are stabilized mainly by a cooperative effect of hydrogen bonding between amide fragments displaced along the shortest axis of each crystal. This interaction occurs between host and guest in complexes I and II, and between host and host in complex III. The latter also represents a cage-type clathrate in which the guest molecules are accommodated in voids between the hydrophobic fragments of four neighboring NTU hosts. On the other hand, complexes of DTU are characterized by a more specific interaction between the two components, each guest molecule being inserted between two adjacent hosts (related by translation) and strongly bound to them via hydrogen bridges. These results illustrate a useful concept in the design of molecular species which can be potential hosts upon crystallization with neutral molecular guests. Supplementary Data relating to this article are deposited with the British Library as Supplementary Publication No. SUP 82022 (7 pages).