Polarization Properties of the Enhanced Backscattering of Light from the Fractal Aggregate of Particles

The polarized intensity enhancement of the light backscattered multiply from a fractal aggregate of particles is numerically investigated using Monte Carlo simulations. It is confirmed only for the co-polarized intensity component that an effective mean free pathlength l_D defined for a fractal medium has the same physical meaning as a mean free pathlength l for a homogeneously random medium. Furthermore, co- and crosspolarized components of the backscattering intensity enhancement decrease in accordance with θ^2.16-1.03D and θ^4-1.8D in the far-field plane and with ζ^0.93D-3.94 and ζ^1.07D-3.98 in the boundary plane between the scattering medium and the air. Therefore, the two-dimensional Fourier transform relation is satisfied only between the co-polarized intensity distributions in the far-field and the boundary planes but not the cross-polarized ones with the accuracy of the numerical simulation. Finally, we notice the applicability of the enhanced backscattering light to estimating the dimension of the absorbent fractal medium on the basis of the result that the slope of the intensity decay of the intensity peak is directly proportional to the dimension of the medium but is independent of the absorption.     

The Diameters of Some Transition Graphs Constructed from Hamilton Cycles

 A complete undirected graph of order n has Hamilton cycles. We consider the diameter of a transition graph whose vertices correspond to those Hamilton cycles and any of two vertices are adjacent if and only if the corresponding Hamilton cycles can be transformed each other by exchanging two edges. Moreover, we consider several transition graphs related to it. Received: November 4, 1999 Final version received: August 28, 2000     

Polynomial invariants of graphs II

Negami and Kawagoe has already defined a polynomial associated with each graphG as what discriminates graphs more finely than the polynomialf(G) defined by Negami and the Tutte polynomial. In this paper, we shall show that the polynomial includes potentially the generating function counting the independent sets and the degree sequence of a graphG, which cannot be recognized fromf(G) in general, and discuss on of treesT with observations by computer experiments.     

Enantioselective catalysis of Claisen rearrangement by DABNTf-Pd(II) complex

Two types of palladium complexes, cationic and neutral (R)-DABNTf-Pd(CH₃CN)₂ were examined as chiral catalysts for enantioselective Claisen rearrangement. DABNTf-Pd(CH₃CN)₂ complex gave high enantio- and anti-diastereoselectivity, and good yield. This Claisen rearrangement should proceed via six-membered boat transition state through bi-dentate coordination to the Pd catalyst.     

Hydrogen-bond Networks Involving Protonated Bicapped-Keggin Tetradecavanadophosphate Anions

Tetraphenylphosphonium salts of protonated tetradecavanadophosphate (PV₁₄) anions, [(C₆H₅)₄P]₄H₅PV₁₄O₄₂·5H₂O (1) and [(C₆H₅)₄P]₂H₇PV₁₄O₄₂·6H₂O (2), have been synthesized and their crystal structures have been determined. Compound 1 crystallizes in triclinic, P1 with a=12.7866(1), b=15.5261(2), c=16.0730(3) ?, α=109.358(1), β=98.411(1), γ=110.040(1)°. Synchrotron radiation X-ray diffraction revealed that compound 2 crystallizes in monoclinic, P2₁/c with a=16.821(1), b=25.163(2), c=18.817(1) ?, β=109.992(2)°. In compound 1, the PV₁₄ anions are linked into a one-dimensional chain structure by water molecules of crystallization. In compound 2, hydrogen bonds directly link PV₁₄ anions into a zigzag chain, which are then woven into a three-dimensional network by hydrogen bonds bridged by water molecules.Dedicated to Professor Michael T. Pope on the occasion of his retirement, in recognition of his outstanding contributions to the polyoxometalate chemistry.     

Further studies on palytoxin. I.

The structures of two degradation products of N-(p-bromobenzoyl) palytoxin were elucidated, and then the sequences of those fragments were determined.     

Synthesis and properties of a bridged phenalenone incorported into bicyclo[3.2.2]nonane skeleton. 6,9-dihydro-6,9-ethenocyclohepta[gh]phenalen-1-one

6,9-Dihydro-6,9-ethenocyclohepta[gh]phenalen-1-one ($\text{1}$) has been synthesised starting from the Diels-Alder adduct ($\text{6}$) of acepleiadiene ($\text{5}$) and maleic anhydride through 10 steps with reasonable yields. Spectroscopic properties of $\text{1}$ suggestged the intramolecular electron supply from the remote ethylenes to the phenalenone π-systems in the ground-state of this molecule.     

STATIC QUENCHING OF EXCITED STATE OF TRIS(BIPYRIDINE)RUTHENIUM(II) COMPLEX-CONTAINING POLYMER BY SODIUM ANTHRAQUINONE-2-SULFONATE

Abstract— Quenching of excited state of Ru(bpy)₂(poly-4-methyl-4'-vinyl-2,2'-bipyridine)Cl₂ by sodium anthraquinone-2-sulfonate was found to be a static process. The quenching was interpreted by application of a modified Perrin model. Radius of the quenching sphere was estimated to correspond to 6.65 monomer units and was unchanged on varying the Ru²+ content of the polymer. Energy migration along the polymer chain was denied.