On the characteristic polynomial of the adjacency matrix of the subdivision graph of a graph

The characteristic polynomial of the adjacency matrix of the subdivision graph G is related to the characteristic polynomials of the adjacency matrices of g and its line graph.     

Modified Ariki-Koike algebras and cyclotomic <Emphasis Type="Italic">q</Emphasis>-Schur algebras

The modified Ariki-Koike algebra is a variation of the original Ariki-Koike algebra over an integral domain R. When R is a rational function field over the independent parameters, But for general R, is not isomorphic to , and has a simpler structure than . In this paper, we construct a cellular basis of which has a similar property as the cellular basis of introduced by Dipper-James-Mathas. By comparing these two cellular bases, we obtain some estimate on the decomposition numbers of in terms of the decomposition numbers of . We also prove the integral form of the Schur-Weyl reciprocity between a certain quantum algebra U_q and on the tensor space      

Direct laser writing defects in holographic lithography-created photonic lattices

As a well-established laser fabrication approach, holographic lithography, or multibeam interference patterning, is known for its capability to create long-range ordered large-volume photonic crystals (PhCs) rapidly. Its broad use is, however, hampered by difficulty in inducing artificially designed defects for device functions. We use pinpoint femtosecond laser ablation to remove and two-photon photopolymerization to add desired defective features to obtain photonic acceptors and photonic donors, respectively, in an otherwise complete PhC matrix produced by holographic lithography. The combined use of the two direct laser writing technologies would immediately make holographic lithography a promising industrial tool for PhC manufacture.     

Cysteine-derived organocatalyst in a highly enantioselective intramolecular Michael reaction

Asymmetric intramolecular Michael reaction catalyzed by an organocatalyst derived from cysteine has been developed for the synthesis of chiral bicyclo[4.3.0]nonene and cis-disubstituted cyclopentane skeletons with a creation of three or two contiguous chiral centers in good yield with high diastereo- and excellent enantioselectivities.     

Thermodynamic Study on Vesicle Formation and Adsorption of Decyltrimethylammonium Decyl Sulfate

The surface tension of an aqueous solution of decyltrimethylammonium decyl sulfate (DeTADeS) was measured as a function of temperature T at various molalities &mcirc; under atmospheric pressure. DeTADeS has been found to form equilibrium multilamellar vesicles (MLV) spontaneously. The surface density, the entropies of adsorption, and the entropy of vesicle formation are evaluated. The mechanism of formation of equilibrium vesicles is investigated from the standpoint of thermodynamics and from the comparison of the results with those of the micelle-forming systems. From the relatively small change of the surface density Gamma;(H) on T at a given &mcirc;, the adsorbed film is implied to be tightly packed due to the strong electrostatic attraction between the polar headgroups. The energy change associated with adsorption from the vesicular state per mole of surfactant Delta(V)(H)u is positive in the entire temperature range; thus, the curved bilayer in MLV is energetically more favorable than the planar adsorbed film. From the negative values of the entropy of vesicle formation Delta(W)(V)s, it is concluded that vesicle formation is driven by enthalpy whereas micelle formation is mostly entropy driven. Copyright 2001 Academic Press.     

Asymmetric Ni(II)/Cr(II)-mediated coupling reaction: catalytic process

[reaction: see text] The stable, crystalline Cr(III)/sulfonamide complex 1a is shown to be an effective catalyst for the Ni/Cr-mediated coupling reaction. A possible mechanism is suggested for the process. 1a is also effective for other Cr-mediated coupling reactions. With this catalyst, a concise and efficient synthesis of the C14-C26 segment of halichondrins has been developed.     

Miscibility of Hydrocarbon and Fluorocarbon Surfactants in Adsorbed Film and Micelle

We investigated the miscibility of nonionic hydrocarbon and fluorocarbon surfactants in the adsorbed film and the micelle by surface tension measurements of the aqueous solution. The combination of tetraethyleneglycol monodecyl ether (C10E4) and tetraethyleneglycol mono-1,1,7-trihydrododecafluoroheptyl ether (FC7E4) was chosen because they have the same hydrophilic groups and about the same surface activity. The extent of nonideal mixing was estimated quantitatively in terms of the excess Gibbs energy in the adsorbed film g(H,E) and that in the micelle g(M,E). The excess area per adsorbed molecule, A(H,E), was also evaluated and discussed. The ionic hydrocarbon and fluorocarbon mixed surfactant systems, lithium dodecyl sulfate (LiDS)/lithium perfluorooctane sulfonate (LiFOS) and lithium tetradecyl sulfate (LiTS)/LiFOS systems are also investigated from the standpoint of excess Gibbs energy and excess area. It is also clearly shown that the regular solution approach does not fit in the systems that contain ionic species. Copyright 2001 Academic Press.     

Spin-wave description of nuclear spin-lattice relaxation in Mn12O12 acetate

In response to recent nuclear-magnetic-resonance (NMR) measurements on the molecular cluster Mn12O12 acetate, we study the nuclear spin-lattice relaxation rate 1/T(1), developing a modified spin-wave theory. Our microscopic new approach, which is distinct from previous macroscopic treatments of the cluster as a rigid spin of S=10, not only excellently interprets the observed temperature and applied-field dependences of 1/T(1) for 55Mn nuclei but also strongly supports the 13C NMR evidence for spin delocalization over the entire molecule.