Singular cauchy problems for a class of weakly hyperbolic differential operators

In this paper singular Cauchy problems of Hamada's type are studied in the category of holomorphic functions and hyperfunctions for a class of hyperbolic differential operators with non-involutive multiple characteristics. Integral representations of their solutions are obtained.     

Nonabelian KP hierarchy with Moyal algebraic coefficients

A higher dimensional analogue of the KP hierarchy is presented. Fundamental constituents of the theory are pseudo-differential operators with Moyal algebraic coefficients. The new hierarchy can be interpreted as large-N limit of multi-component (gl (N) symmetric) KP hierarchies. Actually, two different hierarchies are constructed. The first hierarchy consists of commuting flows and may be thought of as a straightforward extension of the ordinary and multi-component KP hierarchies. The second one is a hierarchy of noncommuting flows, and related to Moyal algebraic deformations of selfdual gravity. Both hierarchies turn out to possess quasi-classical limit, replacing Moyal algebraic structures by Poisson algebraic structures. The language of W-infinity algebras provides a unified point of view to these results.     

Systematic analysis of enzyme-catalyzed reaction patterns and prediction of microbial biodegradation pathways

The roles of chemical compounds in biological systems are now systematically analyzed by high-throughput experimental technologies. To automate the processing and interpretation of large-scale data it is necessary to develop bioinformatics methods to extract information from the chemical structures of these small molecules by considering the interactions and reactions involving proteins and other biological macromolecules. Here we focus on metabolic compounds and present a knowledge-based approach for understanding reactivity and metabolic fate in enzyme-catalyzed reactions in a given organism or group. We first constructed the KEGG RPAIR database containing chemical structure alignments and structure transformation patterns, called RDM patterns, for 7091 reactant pairs (substrate-product pairs) in 5734 known enzyme-catalyzed reactions. A total of 2205 RDM patterns were then categorized based on the KEGG PATHWAY database. The majority of RDM patterns were uniquely or preferentially found in specific classes of pathways, although some RDM patterns, such as those involving phosphorylation, were ubiquitous. The xenobiotics biodegradation pathways contained the most distinct RDM patterns, and we developed a scheme for predicting bacterial biodegradation pathways given chemical structures of, for example, environmental compounds.     

Enhanced lasing properties of dissymmetric Eu(III) complex with bidentate phosphine ligands

The luminescent and lasing properties of Eu(III) complexes were enhanced by using an dissymmetric Eu(III) complex. The photophysical properties (the emission spectral shapes, the emission lifetimes, the emission quantum yields, and the stimulated emission cross section (SEC)) were found to be dependent on the geometrical structures of Eu(III) complexes. The geometrical structures of Eu(III) complexes were determined by X-ray single crystal analyses. The symmetrical group of Eu(hfa)3(BIPHEPO) (tris(hexafluoroacetylacetonato)europium(III) 1,1'-biphenyl-2,2'-diylbis(diphenylphosphine oxide)) was found to be C1, which was more dissymmetric than Eu(hfa)3(TPPO)2 (tris(hexafluoroacetylacetonato)europium(III) 1,2-phenylenebis(diphenylphosphine oxide): C2 symmetry) and Eu(hfa)3(OPPO)2 (tris(hexafluoroacetylacetonato)europium(III) 1,2-phenylenebis(diphenylphosphine oxide): C2 symmetry). The analytical data were supported by Judd-Ofelt analysis. The most dissymmetrical Eu(III) complex, Eu(hfa)3(BIPHEPO), showed large electron transition probability and large SEC (4.64 x 10(-20) cm2). The SEC of Eu(hfa)3(BIPHEPO) was superior to even the values of Nd-glass laser for practical use (1.6-4.5 x 10(-20) cm2). The lasing properties of Eu(III) complexes in polymer thin film were measured by photopumping of a Nd:YAG laser (355 nm). The threshold energy of lasing oscillation was found to be 0.05 mJ. The increasing rate of the lasing intensity of Eu(hfa)3(BIPHEPO) as a function of the excitation energy was much larger than that of Eu(hfa)3(TPPO)2 and Eu(hfa)3(OPPO)2. The dissymmetrical structure of Eu(hfa)3(BIPHEPO) promoted the enhancement of the lasing property.     

Synthesis of a tripalladium cluster containing an η:η:η-bridging butadienyl ligand stabilized by a zwitterionic structure

An η¹-butadienyl complex [trans-η¹-CH₂=C(Me)C=CH₂Pd(PPh₃)₂Cl] (1) reacted with [(μ-η²:η²-1,3-butadiene)Pd₂(PPh₃)(μCl)Cl] (2) to result in displacement of the diene ligand of 2 accompanied by exchange of PPh₃ of 1 with Cl anion of 2 producing a butadienyl tripalladium cluster [(μ-CH₂=C(Me)C=CH₂)Pd(PPh₃)Cl₂ · Pd₂(PPh₃)₂(μ-Cl)] (3) stabilized by the zwitterionic structure in moderate yield. The X-ray structure analysis of 3 revealed rigid binding of [Pd₂(PPh₃)₂(μ-Cl)]⁺ and [CH₂ =C(Me)C=CH₂Pd(PPh₃)Cl₂]⁻ through the π-bond coordination of the butadienyl group to the dipalladium cation.