A singular Cauchy problem for the Euler–Poisson–Darboux equation

We consider a singular Cauchy problem for the Euler–Poisson–Darboux equation of Fuchsian type in the time variable with ramified Cauchy data. In this paper we establish an expansion of the solutions in a series of hypergeometric functions and then investigate the nature of the singularities of the solutions.     

Subexponential Densities of Infinitely Divisible Distributions on the Half-Line

Lithuanian Mathematical Journal - Abstract. We show that, under the long-tailedness of the densities of normalized Lévy measures, the densities of infinitely divisible distributions on the...     

Binding of Multivalent Anionic Porphyrins to V3 Loop Fragments of an HIV‐1 Envelope and Their Antiviral Activity

Interactions of multivalent anionic porphyrins and their iron(III) complexes with cationic peptides, V3_Ba‐L and V3_IIIB, which correspond to those of the V3 loop regions of the gp120 envelope proteins of the HIV‐1_Ba‐L and HIV‐1_IIIB strains, respectively, are studied by UV/Vis, circular dichroism, ¹H NMR, and EPR spectroscopy, a microcalorimetric titration method, and anti‐HIV assays. Tetrakis(3,5‐dicarboxylatophenyl)porphyrin (P1), tetrakis[4‐(3,5‐dicarboxylatophenylmethoxy)phenyl]porphyrin (P2), and their ferric complexes (Fe^IIIP1 and Fe^IIIP2) were used as the multivalent anionic porphyrins. P1 and Fe^IIIP1 formed stable complexes with both V3 peptides (binding constant K>10⁶ M ^?1) through combined electrostatic and van der Waals interactions. Coordination of the His residues in V3_Ba‐L to the iron center of Fe^IIIP1 also played an important role in the complex stabilization. As P2 and Fe^IIIP2 form self‐aggregates in aqueous solution even at low concentrations, detailed analysis of their interactions with the V3 peptides could not be performed. To ascertain whether the results obtained in the model system are applicable to a real biological system, anti‐HIV‐1_BA‐L and HIV‐1_IIIB activity of the porphyrins is examined by multiple nuclear activation of a galactosidase indicator (MAGI) and 3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyltetrazolium bromide (MTT) assays. There is little correlation between chemical analysis and actual anti‐HIV activity, and the size rather than the number of the anionic groups of the porphyrin is important for anti‐HIV activity. All the porphyrins show high selectivity, low cytotoxicity, and high viral activity. Fe^IIIP1 and Fe^IIIP2 are used for the pharmacokinetic study. Half‐lives of these iron porphyrins in serum of male Wistar rats are around 4 to 6 h owing to strong interaction of these porphyrins with serum albumin.     

Thermo-responsive extraction of cadmium(II) ion with TPEN-NIPA gel. Effect of the number of polymerizable double bond toward gel formation and the extracting behavior

N,N,N′,N′-(Tetrakis-2-pyridylmethyl)ethylenediamine (TPEN) derivatives bearing the different number (1-4) of a double bond moiety on the pyridine ring are synthesized and subjected to copolymerization with N-isopropylacrylamide in the presence of AIBN. The obtained poly(TPEN-NIPA) gels show thermo-responsive swelling/shrinking behaviors and are employed for the extraction of cadmium(II) ion from the aqueous solution to examine the relationship of the gel characteristics and the extraction performance. The polymer gels composed of the TPEN derivative bearing three or four double bonds exhibit temperature-dependent change of swelling and shrinking in water. These gels extract Cd^II ion efficiently from the aqueous solution in the swelling state at 5 °C, while little extraction was observed at 45 °C with shrinking.     

Thermal hysteresis and thickness dependence of the molecular orientation of poly(di-n-hexylsilane) in the film state

Molecular orientation of poly(di-n-hexylsilane) adsorbed on poly(vinyl alcohol) film has been studied by making use of the stretching technique. Dichroic ratio, Rd, strongly depended on the thickness of poly(di-n-hexylsilane) thin film and the highest value ca. 19 was observed at the film thickness of 110 +/- 30 nm. The thermal hysteresis of the molecular orientation was observed in the heating-cooling cycles. By studying the fluorescence spectrum it was confirmed that a portion of the poly(di-n-hexylsilane) molecules were in transoid conformation even at 320 K, although most of poly(di-n-hexylsilane) molecules were in disordered conformation (conformation D). This poly(di-n-hexylsilane) in transoid conformation is formed in the stretching process and may play a role of crystallization nucleus to induce the whole orientation of the poly(di-n-hexylsilane) in the film state.     

Coherent Array of White-Light Continuum Generated by Microlens Array

We generated a white-light continuum array by directing femtosecond laser pulses into a liquid with a microlens array. Experimental evidence demonstrates that the spatial coherence is high within a single light source in the array. We also confirmed that all the light sources in the white-light continuum array are mutually coherent. We found that the simple self-phase modulation model cannot explain this high coherence between the white continuum sources.     

Determination of light hydrocarbons dissolved in seawater

A practical method for the on board determination of light (C1-C4) hydrocarbons dissolved in seawater has been developed. The gaseous hydrocarbons in seawater were extracted quickly with a vacuum sparge tower and determined gas chromatographically. By using two cryogenic columns at dry ice-ethanol temperature (-80 degrees C) connected in series, it was possible to completely collect the hydrocarbons. The precision and sensitivity were comparable to that of previous methods. The analysis was completed within 45 min for one sample and the sample volume was 500 ml. The method was successfully applied to the northern North Pacific water collected in summer 1997. The concentrations of C2-C4 hydrocarbons in surface seawater ranged from several to several tens pmol l(-1), within the range of concentrations in previous studies.