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.     

Sub-critical crack growth rate of soda-lime-silicate glass and less brittle glass as a function of fictive temperature

Sub-critical crack growth rates of soda-lime-silicate glass and less brittle glass with different fictive temperatures were compared using the DCDC method under both dry and humid atmospheres in order to investigate the origin of the unique mechanical features of the less brittle glass developed by Ito and his collaborators. In both dry and humid atmospheres, the crack velocity of the soda-lime-silicate glass was slower than that of the less brittle glass. For both glasses, the glass sample with higher fictive temperature showed a slower crack growth rate under both dry and humid atmospheres. These observations can be explained by the tendency for the plastic flow at the crack tip; the soda-lime-silicate glass is expected to show easier plastic flow under tension than the less brittle glass, and also the samples with higher fictive temperatures are expected to show easier plastic flow, leading to greater fracture toughness, K_IC, and slower crack growth rate.     

Synthesis of self‐photosensitizing polyesters containing donor–acceptor norbornadiene moieties and benzophenone groups and their photochemical reactions

The ring‐opening copolymerization of a glycidyl ester derivative having a benzophenone group and the donor–acceptor norbornadiene (D‐A NBD) dicarboxylic acid, 5‐(4‐methoxyphenyl)‐1,4,6,7,7‐pentamethyl‐2,5‐norbornadiene‐2,3‐dicarboxylic acid, monoglycidyl ester derivatives with D‐A NBD dicarboxylic anhydride using tetraphenylphosphonium bromide as a catalyst proceeded smoothly to give novel self‐photosensitizing NBD polymers in good yields. The molecular weight of these polyesters was about 4,000, and lower than that of analogous NBD polymers having no benzophenone group. All the synthesized NBD polymers isomerized smoothly to the corresponding quadricyclane (QC) polymers upon UV irradiation in tetrahydrofuran (THF) solution and in the film state. The rate of the photoisomerization of the D‐A NBD moieties in these polymers was higher than that of the D‐A NBD moieties in the polymer having no photosensitizing group. Furthermore, the rate of the photoisomerization of the D‐A NBD moieties in these polymers was also higher than that of the NBD polymer with low molecular weight photosensitizer in dilute solution. The photo‐irradiated polymers having QC moieties released thermal energies of 146–180 J/g. The D‐A NBD moieties contained in these NBD polymers possessed fair to good fatigue resistance. The degradation of the NBD moieties in these polymers was 15–30% after 50 repeated cycles of interconversion. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2978–2988, 2007     

Two-body forces and amplitudes in the three-body model for the4He(\vec d,pα)n reaction withE d =12 and 17 MeV

The⁴He( ,p)n cross section, vector and tensor analyzing-power data with 12 and 17 MeV deuterons at kinematic conditions including proton-alpha quasifree scattering, neutron-alpha and proton-alpha final-state interactions, as well as collinearity, are compared with the predictions of the three-body model using different nucleon-alpha and neutron-proton forces. In general, better two-body potentials give a better fit to the data, except for the vector analyzing-power data. The roles of the impulse and multiple-scattering amplitudes are studied to understand the sensitivity to two-body potentials and to understand the reason for the successes and the failures of the model.     

Measurement ofD(\vec p,p)D elastic scattering at 10.0, 12.0, 14.1 and 16.5 MeV especially for small forward and extreme backward scattering angles

The elastic scattering was investigated especially in the Coulomb sensitive scattering regions. Angular distributions of the differential cross section and of the analyzing powerA _y, with emphasis on small scattering angles, were measured at 10.0 and 14.1 MeV. For extreme backward angles up toJ _c.m.=179° the differential cross section was measured at 12.0, 14.1 and 16.5 MeV. The data have been compared with recent Faddeev calculations based on the realistic meson-exchange Paris potential and including an approximate Coulomb correction. There are discrepancies between the data and the calculations especially for the analyzing power. This indicates that the approximate treatment of Coulomb effects and possibly also the purely nuclear part of the calculations need to be improved.     

Metal components analysis of metallothionein-III in the brain sections of metallothionein-I and metallothionein-II null mice exposed to mercury vapor with HPLC/ICP-MS

Mercury vapor is effectively absorbed via inhalation and easily passes through the blood–brain barrier; therefore, mercury poisoning with primarily central nervous system symptoms occurs. Metallothionein (MT) is a cysteine-rich metal-binding protein and plays a protective role in heavy-metal poisoning and it is associated with the metabolism of trace elements. Two MT isoforms, MT-I and MT-II, are expressed coordinately in all mammalian tissues, whereas MT-III is a brain-specific member of the MT family. MT-III binds zinc and copper physiologically and is seemed to have important neurophysiological and neuromodulatory functions. The MT functions and metal components of MTs in the brain after mercury vapor exposure are of much interest; however, until now they have not been fully examined. In this study, the influences of the lack of MT-I and MT-II on mercury accumulation in the brain and the changes of zinc and copper concentrations and metal components of MTs were examined after mercury vapor exposure by using MT-I, II null mice and 129/Sv (wild-type) mice as experimental animals. MT-I, II null mice and wild-type mice were exposed to mercury vapor or an air stream for 2 h and were killed 24 h later. The brain was dissected into the cerebral cortex, the cerebellum, and the hippocampus. The concentrations of mercury in each brain section were determined by cold vapor atomic absorption spectrometry. The concentrations of mercury, copper, and zinc in each brain section were determined by inductively coupled plasma mass spectrometry (ICP-MS). The mercury accumulated in brains after mercury vapor exposure for MT-I, II null mice and wild-type mice. The mercury levels of MT-I, II null mice in each brain section were significantly higher than those of wild-type mice after mercury vapor exposure. A significant change of zinc concentrations with the following mercury vapor exposure for MT-I, II null mice was observed only in the cerebellum analyzed by two-way analysis of variance. As for zinc, the copper concentrations only changed significantly in the cerebellum. Metal components of metal-binding proteins of soluble fractions in the brain sections were analyzed by size-exclusion high-performance liquid chromatography (HPLC) connected with ICP-MS. From the results of HPLC/ICP-MS analyses, it was concluded that the mercury components of MT-III and high molecular weight metal-binding proteins in the cerebellum of MT-I, II null mice were much higher than those of wild-type mice. It was suggested that MT-III is associated with the storage of mercury in conditions lacking MT-I, and MT-II. It was also suggested that the physiological role of MT-III and some kind of high molecular weight proteins might be impaired by exposure to mercury vapor and lack of MT-I and MT-II.     

Electron spin resonance studies on radiation graft copolymerization in polyethylene. II. Grafting initiated by allyl radicals trapped in irradiated polyethylene

The regions trapping allyl radicals in irradiated polyethylene and the reactivity of the radicals with various monomers have been studied by electron spin resonance. Most of the allyl radicals are trapped in defects or surfaces of the crystallite, and only 10% of the radicals are trapped inside the crystallites. Since the reactivity of the allyl radicals depends on whether they come in contact with reactive monomers, the rate of reaction is related to the concentration of the monomers. When grafting reactions are initiated by allyl radicals, the rate of initiation is rapid and the rate of termination at the initial stage is also very fast. Consequently the yield of grafting increases at the initial stage but soon levels off, which is in contrast to the grafting behavior with alkyl radicals.     

Site-to-site peptide transport on a molecular platform using a small-molecule robotic arm

Peptides attached to a cysteine hydrazide ‘transporter module’ are transported selectively in either direction between two chemically similar sites on a molecular platform, enabled by the discovery of new operating methods for a molecular transporter that functions through ratcheting. Substrate repositioning is achieved using a small-molecule robotic arm controlled by a protonation-mediated rotary switch and attachment/release dynamic covalent chemistry. A polar solvent mixtures were found to favour Z to E isomerization of the doubly-protonated switch, transporting cargo in one direction (arbitrarily defined as ‘forward’) in up to 85% yield, while polar solvent mixtures were unexpectedly found to favour E to Z isomerization enabling transport in the reverse (‘backward’) direction in >98% yield. Transport of the substrates proceeded in a matter of hours (compared to 6 days even for simple cargoes with the original system) without the peptides at any time dissociating from the machine nor exchanging with others in the bulk. Under the new operating conditions, key intermediates of the switch are sufficiently stabilized within the macrocycle formed between switch, arm, substrate and platform that they can be identified and structurally characterized by ¹H NMR. The size of the peptide cargo has no significant effect on the rate or efficiency of transport in either direction. The new operating conditions allow detailed physical organic chemistry of the ratcheted transport mechanism to be uncovered, improve efficiency, and enable the transport of more complex cargoes than was previously possible.

Peptides are transported in either direction between chemically similar sites on a molecular platform, substrate repositioning is achieved using a cysteine hydrazide transporter module and a small-molecule robotic arm controlled by a rotary switch.     

A new synthesis of indoloquinolizines by Pictet-Spengler reaction of tryptamine type 1,2-dihydropyridines utilizing sec-nitrodienamine

The Pictet-Spengler reaction of tryptamine type 1,2-dihydropyridine 5c derived from the cycloaddition of the sec-nitrodienamine 3c with acetaldehyde afforded the indoloquinolizine derivatives 6 and 7.