A -series identity and the arithmetic of Hurwitz zeta functions

Using a single variable theta identity, which is similar to the Jacobi Triple Product identity, we produce the generating functions for values of certain expressions of Hurwitz zeta functions at non-positive integers.     

Re-entrant phase transitions of the Blume-Emery-Griffiths model

We have investigated the spin-1 Ising model on the simple cubic lattice with bilinear, biquadratic interaction and anisotropic energy (BEG model). We have been specially interested in the case of antiferro biquadratic interaction, because the interaction will cause the competition with bilinear interaction and anisotropy. A two-sublattice ordering, so called the staggered quadrupole (SQ) phase, occurs as long as biquadratic interaction is negative large enough. We have obtained a full phase diagram in the whole interaction parameter space (for the positive bilinear interaction) by the Bethe approximation, and found several kinds of phase transitions, such as successive, re-entrant and double re-entrant transitions. These transitions are also confirmed by Monte Carlo simulations on simple cubic lattices.     

Dicationic ((−)-sparteine)palladium-catalyzed enantioselective aldol reaction of aldehydes with 1-phenyl-1-trimethylsilyloxyethene, proceeding via a palladium enolate

A dicationic ((−)-sparteine)palladium complex underwent a superior catalytic enantioselective aldol reaction of aldehydes with 1-phenyl-1-trimethylsilyloxyethene performing satisfactorily, starting with ((−)-sparteine)PdCl₂ and AgSbF₆ as catalyst precursors (1 mol % loading) in the presence of 3 Å molecular sieves over the reaction.     

Synthesis and biological activities of analogs of a lipid A biosynthetic precursor: 1-O-phosphonooxyethyl-4'-O-phosphono-disaccharides with (R)-3-hydroxytetradecanoyl or tetradecanoyl groups at positions 2, 3, 2' and 3'.

Two novel analogs of a biosynthetic precursor of lipid A (2) were synthesized. The one analog (3) has acyl groups identical to those of 2, and the other (4) has tetradecanoyl groups in place of the (R)-3-hydroxytetradecanoyl groups of 2. Both 3 and 4 possess an alpha-glycosidically-bound phosphonooxyethyl group in place of the alpha-glycosyl phosphate group of 2. Compounds 3 and 4 exhibited definite antitumor activity against Meth A fibrosarcoma and low toxicity in rabbits, as the original compound 2 does. The replacement of the hydroxytetradecanoyl groups with tetradecanoyl groups barely affected the antitumor activity, but slightly enhanced the toxicity in rabbits.     

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     

Synthesis and orientation study of a magnetically aligned liquid‐crystalline chitin/poly(acrylic acid) composite

A high magnetic field of 5 T was used to fabricate a magnetically aligned, optically anisotropic, liquid‐crystalline chitin/poly(acrylic acid) composite. The aligned mesophase was fixed by photoinitiated free‐radical polymerization. From an examination of polarized optical micrographs and an X‐ray diffraction study, a high degree of orientation of 0.70 was observed for the composite with a higher liquid‐crystalline chitin concentration (10.70 wt %); the orientation was reduced with a decreased chitin concentration at a given acrylic acid concentration. The X‐ray data for the developed composite showed a uniplanar orientation for the chitin crystallites, with its molecular long axes perpendicular to the direction of the magnetic field. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 711–714, 2003