An ergodic study of Painlevé VI

An ergodic study of Painlevé VI is developed. The chaotic nature of its Poincaré return map is established for almost all loops. The exponential growth of the numbers of periodic solutions is also shown. Principal ingredients of the arguments are a moduli-theoretical formulation of Painlevé VI, a Riemann–Hilbert correspondence, the dynamical system of a birational map on a cubic surface, and the Lefschetz fixed point formula. Dedicated to Professor Masuo Hukuhara on his 100th birthday.     

Long-range structures on the dihydride Si(001) surface

From several large supercell MD simulations with an empirical tight-binding method, we have found the long-range structure on the dihydride Si(001) surface. This structure can be viewed as the well-known canted phase with domain walls. The formation energy of a single domain wall on the surface is estimated to be 1.3–1.5 eV.     

Expressed Sequence Tag Analysis of the Dinoflagellate Lingulodinium polyedrum During Dark Phase¶

To collect information on gene expression during the dark period in the luminous dinoflagellate Lingulodinium polyedrum, normalized complementary DNA (cDNA) libraries were constructed from cells collected during the first hour of night phase in a 12:12 h light‐dark cycle. A total of 4324 5′‐end sequence tags were isolated. The sequences were grouped into 2111 independent expressed sequence tags (EST) from which 433 groups were established by similarity searches of the public nonredundant protein database. Homology analysis of the total sequences indicated that the luminous dinoflagellate is more similar to land plants and animals (vertebrates and invertebrates) than to prokaryotes or algae. We also isolated three bioluminescence‐related (luciferase and two luciferinbinding proteins [LBP]) and 37 photosynthesis‐related genes. Interestingly, two kinds of LBP genes occur in multiple copies in the genome, in contrast to the single luciferase gene. These cDNA clones and EST sequence data should provide a powerful resource for future genome‐wide functional analyses for uncharacterized genes.     

A Tensor Product of Representations of Cuntz Algebras

We introduce a nonsymmetric and associative tensor product among representations of Cuntz algebras by using embeddings. Since the tensor product of permutative representations is also a permutative representation, the decomposition of such a tensor product is unique up to unitary equivalence. We show the decomposition formulae explicitly. As an application, we show properties of concrete endomorphisms.      

Chromatographic resolution of dipeptide enantiomers and diastereomers on chiral stationary phases from poly-( -leucine) or poly( -phenylalanine)

Two types of chiral stationary phase, polymer-bonded and non-bonded, containing poly( -leucine) and poly( -phenylalanine) were prepared. These stationary phases gave higher enantioselectivity for the optical resolution of various derivatives of leucylphenylalanine methyl ester by liquid chromatography than did poly( -alanine) and poly( -glutamate).     

Swelling and deswelling kinetics of poly(N-isopropylacrylamide) gels

Swelling and deswelling kinetics was investigated for three types of cylindrical poly(N-isopropylacrylamide) (PNIPA) gels differing in crosslink density. The temperature dependence curves of the volume of the gel specimens were different from one another. One of the gel specimens was considered as a critical gel showing the continuous volume phase transition. The volume change process of the specimens after a temperature jump was examined. In the deswelling processes with temperature jumps to temperatures higher than 35 degrees C, a phase separation was observed in the gel specimens and the volume change slowed down due to the homogenization after the phase separation. The value of the diffusion constant obtained without the phase separation decreased rapidly as temperature approaches the transition temperature. The rapid decrease for the critical gel indicates the emergence of the critical slowing-down. The value of the critical exponent for the correlation length suggests that the universality class for the volume phase transition of the critical PNIPA gel belongs to the class for the classical theory.     

Polymerization of aromatic aldehydes. IV. Cationic copolymerization of phthalaldehyde isomers and styrene

Copolymerizations of three phthalaldehyde isomers (M₂) with styrene (M₁) were carried out in methylene chloride or in toluene with BF₃OEt₂ catalyst. The monomer reactivity ratios were r₁ = 0.77, r₂ = 0 for the meta isomer and r₁ = 0.60, r₂ = 0 for the para isomer. The second aldehyde group of both isomers did not participate in polymerization and acted simply as the electron-withdrawing group, thus reducing the cationic reactivity of these monomers. Copolymerization behaviors of the ortho isomer (o-PhA) were quite different between 0°C and ?78°C. At ?78°C, o-PhA preferentially polymerized to yield “living” cyclopolymers, until an equilibrium concentration of o-PhA monomer was reached. Then, styrene propagated from the living terminal rather slowly. The block structure of the copolymer was confirmed by the chemical and spectroscopic means. In the copolymerization at 0°C, the o-PhA unit in copolymer consisted both of cyclized and uncyclized units. This copolymer seemed to contain short o-PhA sequences. The variation of the o-PhA-St copolymer structure with the polymerization temperature was explained on the basis of whether the polymerization was carried out above or below the ceiling temperature (?43°C) of the homopolymerization of o-PhA.     

Furopyridines. XXI. Synthesis of cyano derivatives of furo-[2,3-b]-, -[2,3-c]- and -[3,2-c]pyridine and their conversion to derivatives having another carbon-substituent

Cyanation of furo[2,3-b]-, -[2,3-c]- and -[3,2-c]pyridine N-oxides 1a, 1b and 1c by the Reissert-Henze method, reaction with benzoyl chloride and trimethylsilyl cyanide in dichloromethane and the reaction with trimethylsilyl cyanide and triethylamine in acetonitrile afforded 6-cyanofuro[2,3-b]- 2a , 7-cyanofuro[2,3-c]- 2b and 4-cyanofuro[3,2-c]pyridine 2c in moderate to excellent yield. The cyano group in 2a, 2b and 2c was converted to carboxamides 3a, 3b and 3c , ethyl imidates 5a, 5b and 5c and ethyl carboxylates 6a, 6b and 6c . Reaction of the N-oxides with trimethylsily bromide in acetonitrile gave the deoxygenated furopyridine 7a and 7d , bifuropyridyl 8b and 8c , and the N-oxide 9 of 8c .     

Preparation of polyimides from pyromellitic dithioanhydride and aromatic diamines

The reaction of phthalic thioanhydride and aniline yielded N-phenylphthalimide quite readily. The reaction was strongly dependent on solvent and temperature. Various additives tried as a reaction promoter were almost ineffective. By the extension of the model reaction, polyimides were prepared in a simple one-step synthesis from pyromellitic dithioanhydride and aromatic diamines in dimethylacetamide or other solvents. Polymers with inherent viscosity up to 0.3 in concentrated sulfuric acid were obtained in approximately quantitative yield.     

Synthesis of microtubes with a surface of "house of cards" structure via needlelike particles and control of their pore size

The conditions for synthesizing microtubes with a surface of "house of cards" structure via needlelike particles were examined in detail. Magnesium carbonate trihydrate was formed as a metastable phase in the reaction process using magnesium hydroxide and carbon dioxide as starting materials. Subsequently, in the formation of basic magnesium carbonate from magnesium carbonate trihydrate, microtubes with a surface of house of cards structure were obtained via needlelike particles of magnesium carbonate trihydrate under certain conditions where the temperature and added amount of sodium hydroxide were properly controlled. The pore size of the microtubes could be controlled within a range of 0.5-6 microm by adjusting the condition of needlelike particle formation. In addition, the sustainability of naphthalene release from the microtube was found to be about 6 times higher than that from naphthalene crystal.