Degree Sums and Covering Cycles

It is shown that if in a simple graph G of order n the sum of degrees of any three pairwise non-adjacent vertices is at least n, then there are two cycles (or one cycle and an edge or a vertex) of GF that contain all the vertices. © 1995 John Wiley & Sons, Inc.     

A novel pre-shearing technique for measurement of the electrorheological effect of a side-chain liquid crystalline polysiloxane

A side-chain liquid crystalline polysiloxane derivative possessing mesogens was synthesized. The mesogens included a large dielectrically-anisotropic moiety. Phase transition behaviour was investigated and the electrorheological (ER) effect of the polymer considered. No ER effect was observed in non-sheared polysiloxane derivative because of its high inherent viscosity. However, a large ER effect was observed after pre-shearing. Pre-shearing, i.e. shearing with a high shear rate before the measurements, arranges the terminal mesogens in the shearing direction. Furthermore, a dilution of the sample led to a larger ER effect exceeding 10 000 Pa. We thus were able to demonstrate a new approach for the appearance of the ER effect.     

Thickness decrease of a grafted polyelectrolyte membrane exposed to shear flow

The effect of the shear flow on the thickness change of a polyelectrolyte membrane grafted onto a glass substrate was directly investigated with a flow cell combined with a confocal laser scanning microscope. The membrane thickness decreased proportionally to an increase in the shear stress of the flow when the shear rate exceeded a critical value of 1 s^?1. The higher the ionic strength was of the fluid, the greater the thinning effect was. The correlation between the critical shear rate and the relaxation of the polymer in the gel membrane was examined. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2808–2815, 2003     

Simple and rapid determination of hydrogen peroxide using phosphine-based fluorescent reagents with sodium tungstate dihydrate.

A simple batch method for the fluorometric determination of hydrogen peroxide using phosphine-based fluorescent reagents has been developed. A rapid, mild and selective derivatization reaction was achieved by adding sodium tungstate dihydrate to the reaction mixture of hydrogen peroxide and a phosphine-based fluorescent reagent. When 4-diphenylphosphino-7-methylthio-2,1,3-benzoxadiazole was used as a reagent, the derivatization reaction was completed after 2 min at room temperature. The calibration curve was linear between 12.5 and 500 ng hydrogen peroxide in a 10 microL sample solution. This method is accurate and has potential for on-line applications.     

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.     

Evolution of host-parasitoid network through homeochaotic dynamics

Host-parasitoid systems with evolving mutation rates are studied. By increasing the growth rate of hosts, the diversity of both species is maintained dynamically. For the lower growth rate, diversity is brought about by mere parasitism. The average mutation rate for parasites is elevated to a high value, while that for hosts is suppressed at a low level. For the higher growth rate, the mutation rates for both hosts and parasites are elevated to form a symbiotic cluster connected by on-going mutation. This symbiotic state is sustained through a chaotic oscillation keeping some coherency among species. For a flat landscape for hosts, dynamical clustering of oscillation is observed. Lyapunov spectra of such oscillations show that high dimensional chaos with small positive exponents underlies in the symbiotic state. This weak high dimensional chaos, termed "homeochaos," is essential to the maintenance of symbiosis in ecosystems.     

Study of γ d → π + π − d Reaction in an Energy Region of 0.67 ≤ E γ ≤ 1.08 GeV

Double charged pion photoproductions from the deuteron have been studied at Research Center for Electron Photon Science (ELPH), Tohoku University. Tagged photon beams in an energy range of 0.67 ≤ E _γ ≤ 1.08 GeV were impinged on the liquid deuteron target. Produced charged particles were observed with the Neutral Kaon Spectrometer2 (NKS2). The γ d → π ⁺ π ^? d process was clearly separated among the three charged tracks. We obtained the photon energy dependence of the normalized yields of this process.