Combinatorics on words in symbolic dynamics: the antisymmetric cubic map

This paper is contributed to the combinatorial properties of the periodic kneading words of antisymmetric cubic maps defined on a interval. The least words of given lengths, the adjacency relations on the words of given lengths and the parity-alternative property in some sets of such words are established.     

FeCl_3·6H_2O Catalyzed Reaction of Aromatic Aldehydes with 5, 5-Dimethyl-1, 3-cyclohexandione in Ionic Liquids

Room temperature ionic liquids with low melting point (<100℃) salts represent a new class of non-molecular, ionic solvents. Especially those based on the 1-N-alkyl-3- methylimidazolium cations, have shown great promise as an attractive alternative to conventional solvents for catalytic reactions1. On the other hand, FeCl3·6H2O was considered to be an environmentally benign Lewis acid and has been used successfully in several kinds of organic reactions2. Recently we have focused our interes…     

Investigation of sol-gel derived HfO2 on 4H-SiC

Deposition of HfO₂ films on n-type 4H-SiC substrates by sol-gel spin-on coating technique has been performed and the physical and electrical characteristics of this film as a function of annealing temperature (550, 750, and 850 °C for 30 min) have been reported. The physical properties of the film have been characterized using a Filmetrics and X-ray diffractometer, while conduction atomic force microscope and semiconductor parameter analyzer were used for electrical characterization. Phase transformation has been revealed in the oxide as the annealing temperature changed. Refractive index, relative density, dielectric constant of the film, and oxide-semiconductor interface trap density have been extracted and related to the leakage current through the oxide. It has been recorded that, oxide annealed at 700 °C has demonstrated the lowest leakage current and the best oxide reliability. The reasons of these observations have been explained.     

Dimension Gaps between Representability and Collapsibility

A simplicial complex K\mathsf{K} is called d -representable if it is the nerve of a collection of convex sets in ℝ ^d ; K\mathsf{K} is d -collapsible if it can be reduced to an empty complex by repeatedly removing a face of dimension at most d−1 that is contained in a unique maximal face; and K\mathsf{K} is d -Leray if every induced subcomplex of K\mathsf{K} has vanishing homology of dimension d and larger. It is known that d-representable implies d-collapsible implies d-Leray, and no two of these notions coincide for d≥2. The famous Helly theorem and other important results in discrete geometry can be regarded as results about d-representable complexes, and in many of these results, “d-representable” in the assumption can be replaced by “d-collapsible” or even “d-Leray.”     

Obituary for Professor Mikhail F. Zhukov

Plasma Chemistry and Plasma Processing -