On Modular Forms Arising from a Differential Equation of Hypergeometric Type

Modular and quasimodular solutions of a specific second order differential equation in the upper-half plane, which originates from a study of supersingular j-invariants in the first author's work with Don Zagier, are given explicitly. Positivity of Fourier coefficients of some of the solutions as well as a characterization of the differential equation are also discussed.     

New Plasmon Waveguides Composed of Twin Metal Wedges with a Nano Gap

We have numerically shown the existence of coupled wedge plasmons (CWPs) which propagates along a nano gap of a twin metal wedge. The CWPs are formed by wedge plasmons which can interact with each other. The dispersion relations of the wavenumber, propagation distance, and beam area of CWPs, are described and show that the characteristics of CWPs are similar to those of wedge plasmons and of gap plasmons. We also propose a new plasmon waveguide composed of twin metal wedges with a nano gap.     

Measurement on Spot Size Dependence of Dense WDM Dielectric Multilayer Filters

We present the spot size dependence of dielectric multilayer filters for use in dense WDM systems. We found large dependences of filter performances on the spot size and the incident angle of input light, which should be important for miniaturizing multi-channel add/drop filters.     

Mesure invariante pour l’équation stochastique d’un modéle de compétition limitée entre des espéces avec une diffusion spatiale

On considére l’équation stochastique decrivant un systéme den espéces avec une perturbation stochastique du type environnemental et une diffusion dans un territoire de chaque espéce. On suppose la compétition avec un effet limité entre le espéces différentes, tandis que l’effet logistique pour chaque espéce est supposé quadratique. Sous une condition convenable pour les coefficients, on démontre l’existence d’une mesure invariante pour cette équation stochastique, oú la densité de population de chaque espéce est presque surement positive.      

Cytotoxic activity of marine algae and a cytotoxic principle of the brown alga Sargassum tortile.

Partition fractions of hexane, CCl4 and CHCl3 from methanolic extracts of marine algae were each examined for cytotoxic activities against cultured P-388 lymphocytic leukemia cells. Cytotoxic activities were found for partition fractions of 21 species of seaweed. Bioactivity-guided fractionation of the CCl4 partition fraction from Sargassum tortile, exhibiting the most prominent activity, afforded dihydroxysargaquinone (1) and sargatriol (2) previously isolated from this alga. The former was evaluated as a cytotoxic principle, and the latter, showing moderate activity, was suggested to be an artifact derived from 1 during the isolation procedure.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003     

Analysis of nonlinear sliding structures by modified stochastic linearization methods

Probabilistic characteristics of a sliding structure is investigated by using new versions of stochastic linearization technique. The structure is composed of base part and upper part, which are connected to each other in a spring-damping system. Coulomb friction between the base structure and earth ground is considered. Two alternative versions of stochastic linearization approach, suggested by X. Zhang and I. Elishakoff, respectively, are applied to such a sliding structure to evaluate its statistical properties. Compared with the results of Monte Carlo simulation, the two new approaches are performing much better than the conventional one in their applications to the sliding structure. Moreover, numerical results indicate that the criterion proposed by Elishakoff turns out to be superior to all other versions in the problem under study. Numerical results also suggest that the entire structure may be replaced by the rigid body in the sliding problem as long as the difference of velocity responses are considered less important than those of displacement responses.