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.     

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.      

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.     

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.     

Spintronic Transport through Polyphenoxyl Radical Molecules

The coherent quantum transport properties through the spin-polarized polyphenoxyl radical molecule have been investigated, using the density-functional-derived tight-binding model and the Green's functions method. The majority and minority spin components exhibit considerably different transmission spectra in the vicinity of the Fermi level. Namely, each spin component carries a different amount of current when the bias voltage is applied between the two electrodes that sandwich the polyradical molecule. Therefore, if the magnetization axis of the polyradical is fixed by the external magnetic field, and if the spin flip does not occur during the transmission, the assumed molecular bridge is expected to work as a spin filter or a spin valve. Furthermore, as long as the bias voltage is weak, the total spin current is observed to be larger than the current through its reduced molecular form. It indicates that the adsorption of some chemical species on the radical sites can be sensed by the change in conductance of the molecular bridge.     

Practical and Efficient Method for α-Sialylation with an Azide Sialyl Donor Using a Microreactor

Efficient α-sialylation with a C5 azide sialyl donor was investigated under microfluidic conditions using a microreactor composed of a Comet X-01 micromixer and a tube reactor. Precise temperature control realized excellent α-selectivity, and Siaα(2,6)Gal, Siaα(2,3)Gal, and Siaα(2,9)Sia disaccharides were obtained in moderate to good yields.     

Homo- and Heterogeneous Glycoconjugates on the Basis of N-Glycans and Human Serum Albumin: Synthesis and Biological Evaluation

Neoglycoconjugates mimicking natural compounds and possessing a variety of biological functions are very successful tools for researchers to understand the general mechanisms of many biological processes in living organisms. These substances are characterized by high biotolerance and specificity, with low toxicity. Due to the difficult isolation of individual glycoclusters from biological objects, special interest has been directed toward synthetic analogs. This review is mainly focused on the one-pot, double-click methodology (containing alkyne–azide click cycloaddition with the following 6π-azaelectrocyclization reactions) used in the synthesis of N-glycoconjugates. Homogeneous (including one type of biantennary N-glycan fragments) and heterogeneous (containing two to four types of biantennary N-glycan fragments) glycoclusters on albumin were synthesized via this strategy. A series of cell-, tissue- and animal-based experiments proved glycoclusters to be a very promising class of targeted delivery systems. Depending on the oligosaccharide units combined in the cluster, their amount, and arrangement relative to one another, conjugates can recognize various cells, including cancer cells, with high selectivity. These results open new perspectives for affected tissue visualization and treatment.     

Recent Progress in Polyhedral Harmonics

Polyhedral harmonics is a subject which deals with the problem of characterizing the continuous functions satisfying the mean value property with respect to a polytope. The main feature of it is the finite dimensionality of the space of polyhedral harmonic functions. The theory involves not only analysis but also algebra and combinatorics, and has a rather different flavor from classical harmonic analysis. This paper aims at providing a survey on the subject, focusing on the author's recent results.     

Highly permeable mesoporous silica membranes synthesized by vapor infiltration of tetraethoxysilane into non-ionic alkyl poly(oxyethylene) surfactant films

Mesoporous silica membranes were prepared on porous alumina substrates by a vapor infiltration of tetraethoxysilane (TEOS) into a non-ionic poly(oxyethylene) (Brij56) surfactant film. Periodic mesostructured silica membranes were formed on both α- and γ-alumina substrates pre-treated with polystyrene. The polystyrene polymer plugged the pores of the alumina substrates and inhibited the deposition of silica in the alumina pores, resulting in the formation of a very thin silica membrane without a silica/alumina composite layer at the interface between mesoporous silica and the alumina substrates. The calcined mesoporous silica membrane showed very high nitrogen permeance (>10⁻⁶ mol m⁻² s⁻¹ Pa⁻¹). The single gas permeation was governed by the Knudsen diffusion mechanism. The durability of the mesoporous silica membrane against moisture in air was improved by a silylation with trimethylethoxysiliane.