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.     

Some fatty acids having an O-heterocycle in their terminal positions. I. ω-(3-Chromonyl)alkanoic acids

Some ω-(3-chromonyl)alkanoic acid derivatives, 1a and 2a , n = 4, 5; 3a, 4a and 5a , n = 2-6, were synthesized by cyclization of corresponding methyl ω-(2-hydroxybenzoyl)alkanoates 7b or ethyl ω-(2,4-dihydroxybenzoyl)alkanoates 8b with N,N-dimethylformamide-dimethyl acetal or acetic anhydride-DBU followed by hydrolysis.     

4.6-dimethyl-7-hydroxy-nonan-3-one,a sex pheromone of the cigarette beetle (Lasioderma serricorne F.)

A structure of the sex pheromone produced by the female cigarette beetle (Lasioderma serricorne F.) is established as 4,6-dimethyl-7-hydroxy-nonan-3-one (Ia) by chemical and spectroscopic evidences.     

Molecular theory of the viscoelāstic properties of concentrated polymer solutions

The viscoelastic properties of concentrated polymer solutions are discussed on the basis of the fixed tube model proposed by de Gennes. It is shown that the steady flow viscosity is proportional to M³, where M is the molecular weight, and that the relaxation spectrum exhibits a hump in the relaxation time proportional to M³.     

Domain and surface structures of sodium tungsten bronzes,NaxWo3 (0.4 < x < 1)

Polarized-light microscopic observations have shown that the birefringent, twin-domain structure of metallic sodium tungsten bronze is exhibited by Na-deficient surface films and hence is not, as had been reported elsewhere, a bulk property. The film can be synthesized by anodic electrolysis in alkaline solution. It is chemically inert, translucent, and often laminates to a multiple layer. The domain structure of the film is hypersensitive to lateral stress and to thermal variation, exhibiting a marked change at the phase transition of the substrate through apparent epitaxial coherence. The domain-wall movement is often slow enough to be visible, and the thermally induced domain modulation is occasionally accompanied by audible high-pitched sound. The bulk structure of the substrate exhibits pseudoperiodic subboundaries that are probably caused by growth defects and the segregation of the sodium atoms. The near-surface of the substrate also shows the sodium segregation that tends to precipitate in periodic patterns. Optical and morphological properties of the substrate structures exhibited no detectable change due to thermal variation or external stress.     

An anomalous emission excited near the absorption edge of pyrene crystals

Emission spectra and decay times of the fluorescence excited at the absorption edge region in pyrene crystals were measured. At liquid nitrogen temperature, the fluorescence under the excitation at 390 nm is considered as the excimer emission and its band peak shifts a little to the short wavelength in comparison with that of the excimer emission under the excitation at 360 nm. The emission decay times under the excitation at the 390 nm and 360 nm are about 155 ns and 180 ns, respectively, at liquid nitrogen temperature. The former decay time changes its value abruptly near 127 K. This abrupt change of the decay time may be due to the phase transition in pyrene crystals.     

Doppler-limited dye laser excitation spectroscopy of the HSO radical

The cw dye laser excitation spectrum of the vibronic transition of the HSO radical was observed between 16 420 and 16 520 cm⁻¹ with Doppler-limited resolution, 0.03 cm⁻¹. The HSO radical was produced by reaction of discharged oxygen with H₂S or CH₃SH. The observed spectra were assigned to 751 transitions of the K′_a ← K″_a = 2 ← 3, 1 ← 2, 0 ← 1, 1 ← 0, 2 ← 1, and 3 ← 2 subbands, and were analyzed to determine rotational constants, centrifugal distortion constants, and spin-rotation interaction constants with good precision. The signs of the spin-rotation interaction constants were determined for both the upper and the lower state from the observed spectra. The band origin obtained is 16 483.0252 (2.5σ = 0.0013) cm⁻¹. The molecular constants which were determined reproduce the observed transitions with an average deviation of 0.0045 cm⁻¹.     

Observation of surface composition of copper-nickel alloy by auger spectra in the lower energy region (at around 100 eV)

The interaction of oxygen with a clean (110) molybdenum surface has been studied by LEED and RHEED. At room temperature two simple chemisorbed structures are found, at higher exposures a multiple order pattern is seen. At temperatures above 750 K a complex LEED pattern is observed. Initially a corresponding RHEED pattern is seen which has a different structure. Epitaxial oxide nucleation may be followed by RHEED but the initial process is not seen by LEED. More extensive epitaxial films are needed before oxide reflexions appear in the LEED pattern. The formation of an epitaxial oxide film is accompanied by the growth of {100} molybdenum facets. These may be seen after the film has been carefully evaporated away. The nuclei of oxide which form are shown by both RHEED and transmission microscopy of replicas to be characteristically shaped.     

Band shapes and moment analysis of the far-infrared absorptions of dipolar molecules in solutions

The moment analyses were performed on the far-infrared absorption bands of CH₃CN, CHCl₃, CH₂Cl₂, and their deuterated compounds dissolved in nonpolar solvents. The values of torque acting on the solute molecules were estimated from the fourth moments. The band profiles were simulated by means of the continued-fraction representation of the time correlation function by Mori, using the moment values obtained. The third order long-time approximation of the correlation function yields essentially good simulations. The effective rotation angles of molecules between collisions were estimated from the first positive-to-negative turning points of the memory functions. The solvent effects on the torque and the rotation angle were consistent with each other.     

Theory of diffusion-controlled reaction between non-simple molecules. II

A simplified version of the closure approximation, presented in the preceding paper, is applied to the reaction of rigid or flexible macromolecular systems. Two effects are found to be important for understanding the characteristic features of the reaction rates of these systems: (i) the orientation effect, which expresses the accessibility of the active sites, and (ii) the relaxation effect, which reflects the nature of the brownian motion of the active sites.