Spatial chaotic structure of attractors of reaction-diffusion systems

The dynamics described by a system of reaction-diffusion equations with a nonlinear potential exhibits complicated spatial patterns. These patterns emerge from preservation of homotopy classes of solutions with bounded energies. Chaotically arranged stable patterns exist because of realizability of all elements of a fundamental homotopy group of a fixed degree. This group corresponds to level sets of the potential. The estimates of homotopy complexity of attractors are obtained in terms of geometric characteristics of the potential and other data of the problem.

     

Asymptotic behavior of eigenvalues and random updating schemes

For a stochastic matrix (Q _ij ^T ) _i,j=1 ^M withQ _ij ^T exp(–U(ij)/T) at the off-diagonal positions, we develop an algorithm to evaluate the asymptotic convergence rate of all eigenvalues ofQ _ij ^T asT 0 using Ventcel's optimal graphs. As an application we can compare the convergence rates of some random updating schemes used in image processing.This research was partially supported by the National Science Council, Taiwan and Air Force Office of Scientific Research Contract No. F49620 S5C 0144, and was completed while Tzuu-Shuh Chiang was visiting the Center for Stochastic Processes, Department of Statistics, University of North Carolina, Chapel Hill, NC 27599-3260, USA.     

The separation of tellurium and selenium by polyurethane foam sorbents

Tellurium and selenium can be sorbed from hydrochloric acid and hydrobromic acid solution by both polyether and polyester-based polyurethane foam. Although some acid is needed, the substitution of sodium chloride or sodium bromide increases the extraction significantly. Tellurium is extracted rapidly with > 99% sorbed in 2 min from 1.0/5.0M and 2.0/4.0M hydrochloric acid/sodium bromide. Selenium can also be sorbed quantitatively but much more slowly so that a separation is possible based on the relative rates of extraction. The capacity of polyether foam is 3% by weight of tellurium.     

The Reaction of Triplet State Benzophenone with Acetylacetone

Irradiation of benzophenone in acetic acid containing acetylacetone resulted in regiospecific addition to form cis-2,2-dihpenyl-3-hydroxy-3-methyl-4-acetyloxetane and the rearrangement products therefrom. In the co-presence of copper ions, the regiospecificity is scrambled to give these products and a small amount of 1,1-diphenyl-1-buten-3-one, the secondary decomposition product of the other oxetane arising from the alternative orientation of the addition.     

Enzymatic fabrication of DNA nanostructures: extension of a self-assembled oligonucleotide monolayer on gold arrays

Nucleic acid nanostructures are useful as templates for bionanofabrication of composite molecular nanostructures in materials science, molecular electronics, and biosensing. Here, we demonstrate that terminal deoxynucleotidyl transferase, which repetitively adds mononucleotides to the 3' end of a short DNA initiator, can be used to rapidly fabricate DNA nanostructures up to 121 nm high with lateral dimensions from 0.1 to 4 mum in 2 h. These programmable scaffolds can potentially be employed to build more complex nanostructures consisting of natural or unnatural nucleotides with selective docking sites along the single-stranded DNA.     

Metal Oxide Thin Films Containing Au Nano-Particles Prepared with Gas Diffusion Method

Au particles dispersed thin metal oxide films were prepared from precursor films containing HAuCl₄ with H₂S gas diffusion method. HAuCl₄ was uniformly dissolved in the films as promoted by hydroxypropyl cellulose (HPC). The mechanism of the Au particle formation was studied. It was found that HAuCl₄ was converted directly to Au metal particles upon contacting with H₂S gas. Au particles generated by this method were characterized with small particle size, sharp size distribution and high volume fraction in the films. The surface plasma resonance absorption of Au particles shifted to longer wavelength when TiO₂ component was introduced in the matrix.     

A trinuclear heterobimetallic Ru(II)/Pt(II) complex as a chemodosimeter selective for sulfhydryl-containing amino acids and peptides

A trinuclear heterobimetallic Ru(II)/Pt(II) complex, cis-{Ru(phen)2[CN-Pt(DMSO)Cl2]2} (phen = 1,10-phenanthroline), is able to function as a "switch-on" luminescent chemodosimeter for sulfhydryl-containing amino acids and peptides via specific binding of the amino acids/peptides with the Pt(II) centers and the subsequent cleavage of the Ru(II)-Pt(II) cyano-bridge.