On Solutions of the q-Hypergeometric Equation with q N = 1

We consider the q-hypergeometric equation with q ^N = 1 and , , . We solve this equation on the space of functions given by a power series multiplied by a power of the logarithmic function. We prove that the subspace of solutions is two-dimensional over the field of quasi-constants. We get a basis for this space explicitly. In terms of this basis, we represent the q-hypergeometric function of the Barnes type constructed by Nishizawa and Ueno. Then we see that this function has logarithmic singularity at the origin. This is a difference between the q-hypergeometric functions with 0 < |q| < 1 and at |q| = 1.     

Hydrophobicity parameters determined by reversed-phase liquid chromatography. XV: optimal conditions for prediction of log P(oct) by using RP-HPLC procedures

The use of log k derived from reversed phase (RP)-HPLC retention times provides a convenient method for estimating log P(oct) values (P(oct): 1-octanol/water partition coefficient). In order to establish optimal HPLC conditions, the difference between chromatographic (C18 modified column and aqueous methanol eluents) and bulk solvent systems was examined by use of a batch-like equilibration with octane/aqueous methanol. Comparison of values for log P(O/M-W) (log P for the Octane/MeOH-Water partitioning system) and log k measured for monosubstituted pyrazines at different methanol concentrations, showed closest correlation (r, 0.94) with 50% aqueous methanol; and importantly, under these conditions, log k shows even better correlation (r, 0.99) with log P(oct). Effects of residual silanols on HPLC retention with C18 stationary phases were examined. The results show that, in the presence of a small quantity of accessible silanols, the use of 50% aqueous methanol (M50) as eluent yields values of log k directly proportional to log P(oct) in accord with our earlier proposal that use of log k(M50) provides a convenient means for rapid estimation and prediction of log P(oct).     

Nickel-catalyzed intermolecular coupling of 1,3-dienes and aldehydes via transmetalation of nickelacycles with diisobutylaluminum acetylacetonate

Intermolecular coupling reactions of 1,3-dienes and aldehydes via transmetalation of nickelacycle intermediate with (i)Bu(2)Al-acac were investigated. In the reactions, a linear adduct or a branched adduct was produced, depending upon the nature of 1,3-dienes and aldehydes, via two nickelacycles that were relatively stable among the four possible nickelacycles because of the equilibrium with pi-allynickel forms.     

First total synthesis of artepillin C established by o,o'-diprenylation of p-halophenols in water

We have demonstrated that prenylation of p-halophenols was dependent on the solvent effect and succeeded in o,o'-diprenylation of p-halophenols in water. Following the Mizoroki-Heck coupling of the diprenyl-p-iodophenol 3c with methyl acrylate and then hydrolysis, we first synthesized artepillin C [3-(4-hydroxy-3,5-di(3-methyl-2-butenyl)phenyl)-2(E)-propenoic acid] (1), which is a biologically active constituent of propolis. These reactions may be applicable to the synthesis of various useful natural products such as 2,4,6-trisubstituted phenol derivatives.     

Difference-frequency terahertz-wave generation from 4-dimethylamino-N-methyl-4-stilbazolium-tosylate by use of an electronically tuned Ti:sapphire laser

Among nonlinear materials, the organic ionic salt crystal 4-dimethylamino- N -methyl-4-stilbazolium-tosylate (DAST) is known for its large nonlinearity. We generated a coherent terahertz (THz) wave, using DAST, from the difference frequency between two oscillating wavelengths of an electronically tuned Ti:sapphire laser. In LiNbO(3), LiTaO(3), KTiOPO(4), and GaP crystals, THz-wave generation was not observed under the same experimental conditions. This result proves the high efficiency of DAST crystals for generation of difference-frequency THz waves.     

Sorption and diffusion of water vapor in polyimide films

Sorption and diffusion of water vapor are investigated gravimetrically for polyimide films. The activity dependence of the solubility and diffusion coefficients, S and D, respectively, is classified under four types: (1) constant S and D type, (2) dual-mode sorption and transport type, (3) dual-mode type followed by a deviation due to a plasticization effect at high vapor activity, and (4) constant S and D type followed by a deviation due to water cluster formation at high activity. For the dual-mode type, the Henry's law component is much larger than the Langmuir component except at low activity, and therefore deviation in behavior from the first type is small. S is larger for polyimides with higher content of polar groups such as carbonyl, carboxyl, and sulfonyl. D is larger for polyimides with a higher fraction of free space, with some exceptions. The polyimide from 3,3′,4,4′-biphenyltetracarboxylic dianhydride and dimethyl-3,7-diaminodibenzothiophene-5, 5-dioxide belongs to the third type and displays both large S and large D. The polyimide from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride and 4,4′-oxydianiline belongs to the fourth type, and has the largest D but rather small S because of the hydrophobic C(CF₃)₂ groups. © 1992 John Wiley & Sons, Inc.     

One-dimensional perturbations of the shift

The structure of isometries on a Hilbert space are well studied. In this paper we study contractions which are one-dimensional perturbations of isometries, in particular, perturbations of the shift operator onH ².