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.     

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.     

Two synthetic approaches to rebeccamycin

Two synthetic approaches to a new indolocarbazole antitumor antibiotic, rebeccamycin, were developed. The absolute configuration of rebeccamycin was determined by a total synthesis.     

Rapid ruthenium-catalyzed synthesis of pyranopyrandiones by reconstructive carbonylation of cyclopropenones involving C[bond]C bond cleavage

Pyranopyrandiones were prepared by a novel ruthenium-catalyzed carbonylative dimerization of cyclopropenones via C-C bond cleavage. For example, treatment of dipropylcyclopropenone with a catalytic amount of Ru3(CO)12 and NEt3 in THF under 15 atm of carbon monoxide at 140 degrees C for 20 h gave a novel functional monomer, 3,4,7,8-tetrapropylpyrano[6,5-e]pyran-2,6-dione, in an isolated yield of 81%. Unsymmetrically substituted pyranopyrandiones were also obtained by ruthenium-catalyzed carbonylative coupling of cyclopropenones with alkynes under similar reaction conditions.     

Basic evaluation of highly sensitive thyroid stimulating hormone immunoradiometric assay kits

Usefulness of three kinds of TSH kits by immunoradiometric assay (IRMA) was evaluated. They were able to measure low levels (less than 0.1 microIU/ml) in serum thyroid stimulating hormone (TSH) with incubation of short time (4 hours). In particular, RIABEAD II kit had a highly specific affinity for TSH and the normal range (+/- 2 S.D.) using it showed from 0.20 to 3.50 microIU/ml in 150 normal subjects. In patients with hyperthyroidism and in patients with hypothyroidism, the values of TSH were lower and higher than those of normal subjects, respectively. Another kits showed similar results. These results indicate that these TSH-IRMA kits are useful to evaluate serum TSH levels exactly.     

The relationship between the chemical structure of nematic liquid crystals and their pretilt angles

About 50 different additives in one or more of three different nematic mixtures have been investigated to clarify the relationship between the chemical structure of the liquid crystal and the pretilt angle on a polyimide surface. The pretilts found for cells have been explained within our recently proposed population distribution model. For compounds with cyano-groups at one end, we find that the in-plane order is governed both by the surface-mesogen interaction and by the relative strength of the intermolecular interactions in the nematic phase. This strength is nearly linear in alkyl chain length for the compounds investigated. Changes in the strength due to variations in the core of the molecules can be calculated easily by using group contributions from the known Parachors. The in-plane order can be treated as a simple product of the contributions from the liquid crystal and from the polyimide. Different polar end groups will give different angles between the surface and the optical axis of the individual mesogens in the first monolayer. The cyano-group gives the highest angle and alkyl groups the lowest. For nitro-compounds the dimers formed are so strongly bound that they do not break up at the surface. Nitro-compounds will thus act as dialkyl compounds. For dialkyl compounds the pretilt angles are dominated by the difference between the chain lengths at the two ends of the molecule.