Versatile and cooperative reactivity of a triruthenium polyhydride cluster. A computational study

The reaction of a trinuclear polyhydride complex Ru3H5(C5H5)3 with cyclopentadiene, C5H6, has been studied computationally. A mechanism for the experimentally observed selective C-C bond activation is proposed. All three Ru centers participate in various steps of the mechanism. The catalytic involvement of two cluster hydrides in the transformation of the C5Hn fragment is emphasized.     

Some remarks on the universal cover of an open K3 surface

 We shall give, in an optimal form, a sufficient numerical condition for the finiteness of the fundamental group of the smooth locus of a normal K3 surface. We shall moreover prove that, if the normal K3 surface is elliptic and the above fundamental group is not finite, then there is a finite covering which is a complex torus. Received: 13 April 2001 / Published online: 16 October 2002 RID="⋆" ID="⋆" Supported by Korea Research Foundation Grant(KRF-2001-041-D00025) Mathematics Subject Classification (2000): 14J28     

Nonadiabatic conditional geometric phase shift with NMR

A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance (NMR) under adiabatic conditions. However, in quantum computation, everything must be completed within the decoherence time. The adiabatic condition makes any fast conditional Berry phase (cyclic adiabatic geometric phase) shift gate impossible. Here we show that by using a newly designed sequence of simple operations with an additional vertical magnetic field, the conditional geometric phase shift gate can be run nonadiabatically. Therefore geometric quantum computation can be done at the same rate as usual quantum computation.     

Optimization of asymmetric hydrogenation of 3-phenyl-3-butenoic acid catalyzed by rhodium(I)-4,5-bis[(diphenylphosphino)methyl]-2,2-dimethyldioxolane (DIOP)

Enantioselective, homogeneous hydrogenation of 3-phenyl-3-butenoic acid (1) has extensively been examined in the presence of the rhodium(I)/4,5-bis[(diphenylphosphino)methyl]-2,2-dimethyldioxolane (DIOP) catalyst systems. Optimization of the reaction conditions was undertaken mainly by controlling effects of added tertiary amines as well as solvent polarities on the enantio-selectivity of the product. The best asymmetric yield (85.1% e.e.) was attained when the hydrogenation was carried out in the presence of triethylamine (5 mol%) in 75% aqueous methanol using a neutral rhodium-DIOP catalyst.     

Luminance and Chromaticity Conditions of a Bichromatic Cross Pattern for Chromatically-Uniform Transparency

We can perceive a surface through another surface. This perception is called transparency. It is known that transparency can be perceived even if the stimulus conditions are not consistent with physical conditions for a real transparent surface. In this study, we measured the ranges of luminance and chromaticity of the overlapping area of two crossed layers at which a surface was perceived as chromatically-uniform transparent. As the results, the luminance range of the overlapping area existed around or near the luminance of the inducing area. The upper and lower limits of the luminance range were higher for the dark background than for the light background. Moreover, the chromatic range existed around the additive colormixture line between two chromaticities of the inducing areas for both dark and light backgrounds. This indicates that the perceptual transparency mechanism would divide the color of an additive color mixture into the original colors that exist in the inducing areas. We noticed that the perceptual appearance of the stimulus changed greatly depending on the luminances of the overlapping area and the background. These differences in perceptual appearance would be a factor explaining individual difference and deciding the luminance conditions for transparency.     

Analysis of banding problem in multiple beam scanning system of laser printer

In the slant scanning method of multiple beams a misalignment of the slant angle causes a beam spacing error and pitch irregularities of scan lines called “banding”. This paper evaluates the pitch irregularities and tries to clarify the allowable beam spacing error. The following results are obtained: (1) The maximum spacing error of print lines is proportional to m/(dpi), where m is the number of multiple beams and dpi print dot density. (2) The noticeable limit of periodic variations of print density at low spatial frequency was presumed to be a visibility between 1 and 2% in experiments. (3) The allowable beam spacing error was calculated introducing the human eye spatial frequency response. (4) The banding simulation experiments by laser recording on the photographic paper on the XY stage showed good coincidence with the theoretical evaluations.     

Hankel-type operators on the space of bounded harmonic functions

We study Hankel-type operators on the space of bounded harmonic functions on the open unit disk. These operators are related to tight uniform algebras, the Dunford-Pettis property, and Bourgain algebras.