Generalized Brjuno functions associated to α-continued fractions

For $0\le \alpha \le 1$ given, we consider the one-parameter family of $\alpha$-continued fraction maps, which include the Gauss map ($\alpha =1$), the nearest integer ($\alpha =1/2$) and by-excess ($\alpha =0$) continued fraction maps. To each of these expansions and to each choice of a positive function $u$ on the interval ${\mathbb{I}}_{\alpha }$ we associate a generalized Brjuno function $B_{(\alpha ,u)}\left(x\right)$. When $\alpha =1/2$ or $\alpha =1$, and $u\left(x\right)=?log\left(x\right)$, these functions were introduced by Yoccoz in his work on linearization of holomorphic maps.We compare the functions obtained with different values of $\alpha$ and we prove that the set of $(\alpha ,u)$-Brjuno numbers does not depend on the choice of $\alpha$ provided that $\alpha \ne 0$. We then consider the case $\alpha =0$, $u\left(x\right)=?log\left(x\right)$ and we prove that $x$ is a Brjuno number (for $\alpha \ne 0$) if and only if both $x$ and $?x$ are Brjuno numbers for $\alpha =0$.     

High-yield sol-gel synthesis of well-dispersed, colorless ZrO(2) nanocrystals

A 93% high-yield synthesis of well-dispersed, colorless zirconium dioxide (ZrO(2)) nanocrystals is reported. In this synthesis, hydrolysis and condensation reactions of zirconium(IV) tert-butoxide in the presence of oleic acid (100 degrees C) formed ZrO(2) precursors. The ZrO(2) precursors were made of -Zr-O-Zr- networks surrounded by oleic acid molecules. Annealing (280 degrees C) the precursors dispersed in dioctyl ether caused crystallization of the -Zr-O-Zr- networks, thereby generating 4 nm ZrO(2) nanocrystals stabilized with oleic acid. The particles were highly crystalline and tetragonal phase. A dense ZrO(2) nanocrystal dispersion in toluene (280 mg/mL) showed a transmittance of about 90% (3 mm optical path length) in the whole visible region.     

Polymer microarrays for cellular adhesion

Microarray screening of polymer libraries for cellular adhesion was developed utilising a thin film of agarose to allow unsurpassed localisation of cell binding onto the array substrate and the discovery of cell specific polymers.     

"Beta-cis-SAr effect" on decarbonylation from alpha,beta-unsaturated acyl and aroyl complexes

Lone pair of heteroatom located at the beta-cis position in alpha,beta-unsaturated acyl and aroyl group 10 metal complexes dramatically facilitated the stoichiometric and catalytic decarbonylation reactions.     

Size sorting of biological micro-particles by Newton-ring nano-gap device

The size determination and the size sorting of micrometer-sized particles were carried out by using a piezo-controlled nano-gap. The nano-gap was built by combining a plano-convex lens and a flat glass plate. The fabricated gap had a gradient, while the center of the lens was narrow and the outer side was wide. When the sample solution was injected into the gap, a meniscus force carried the sample particles toward the center of the lens with solvent evaporation; then the individual particle was trapped at the specific position where the particle diameter was equal to the gap distance. The size determination ability of this new method was certified by using the standard polystyrene particles and the size measurements of DNA molecules and yeast cells were demonstrated.     

Electric polarizability of DNA in aqueous salt solution

Monte Carlo simulations are performed to determine the anisotropy of the electric polarizability of a model DNA fragment in aqueous salt solution. By taking into consideration the participation of coions in the electroneutrality condition, at every simulation step, we obtain a list of counterions constituting the net charge arranged in increasing order of their distance from the DNA and calculate the contribution to the dipole moment from the first n counterions in the list. We define a partial polarizability tensor due to these n counterions to understand the origin of the polarizability in close relation to the solution structure. The ionic distributions are described by the counterion condensation theory. Characteristic features of the electric properties of polyelectrolytes are reproduced. The anisotropy of the electric polarizability Deltaalpha of DNA decreases with the addition of salt, yielding values comparable to experiment. The effect of electrophoretic motion of the polyion is examined by estimating its upper limit.     

A pde approach to small stochastic perturbations of Hamiltonian flows

In this note we present a unified approach, based on pde methods, for the study of averaging principles for (small) stochastic perturbations of Hamiltonian flows in two space dimensions. Such problems were introduced by Freidlin and Wentzell and have been the subject of extensive study in the last few years using probabilistic arguments. When the Hamiltonian flow has critical points, it exhibits complicated behavior near the critical points under a small stochastic perturbation. Asymptotically the slow (averaged) motion takes place on a graph. The issues are to identify both the equations on the sides and the boundary conditions at the vertices of the graph. Our approach is very general and applies also to degenerate anisotropic elliptic operators which could not be considered using the previous methodology.     

In vitro self-assembly of bacteriochlorophyll c derivatives monoesterified with α,ω-diols isolated from the green sulfur photosynthetic bacterium Chlorobaculum tepidum

Esterifying chains of chlorophyllous pigments play important roles in the formation of photosynthetic supramolecules, but their effects have not thoroughly been unraveled yet. Substitution of the esterifying chains in these pigments will be one possible strategy to elucidate this enigma. Recently, unnatural bacteriochlorophylls (BChls) c possessing a hydroxy group at the terminus of the esterifying chains were successfully biosynthesised in the green sulfur bacterium Chlorobaculum (Cba.) tepidum grown by supplementation of α,ω-diols. In this paper, in vitro assembling behaviours of unnatural BChls c isolated from Cba. tepidum grown with 1,8-octanediol, 1,12-dodecanediol and 1,16-hexadecanediol were characterised in aqueous Triton X-100 micelles to investigate the effects of the terminal hydroxy group in the esterifying chains of BChls c on self-aggregates such as chlorosomes, major antenna complexes in green photosynthetic bacteria. The bacteriochlorophyll (BChl) c derivatives monoesterified with α,ω-diols formed chlorosomal self-aggregates, but their formations were much slower than those of natural BChl c. The Q_y absorption bands of the residual monomers of these BChl c derivatives were larger than those of natural BChl c. These suggest that the esterifying α,ω-diols in these unnatural BChls c somewhat interfered with formation of chlorosome-like aggregates compared with the natural esterifying farnesol.