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.     

模糊控制技术中一种特殊的高维插值法

本文介绍一种在模糊控制技术中高维插值方法的应用。这种方法可以由有限数据或经验规则，通过高维插获完整的全值表，从而克服了过去去多因素，多目标，非线性的复杂被控系统由于经验规则远远不足，无法得到完整的控制规则表听困难。为进一步设计模糊模糊控制器提供了可行的基础。     

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…     

Laser Process Proximity Correction for Improvement of Critical Dimension Linearity on a Photomask

We report on the improvement of critical dimension (CD) linearity on a photomask by applying the concept of process proximity correction to a laser lithographic process used for the fabrication of photomasks. Rule‐based laser process proximity correction (LPC) was performed using an automated optical proximity correction tool and we obtained dramatic improvement of CD linearity on a photomask. A study on model‐based LPC was executed using a two‐Gaussian kernel function and we extracted model parameters for the laser lithographic process by fitting the model‐predicted CD linearity data with measured ones. Model‐predicted bias values of isolated space (I/S), arrayed contact (A/C) and isolated contact (I/C) were in good agreement with those obtained by the nonlinear curve‐fitting method used for the rule‐based LPC.     

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.”     

Monadic <Emphasis Type="Italic">GMV</Emphasis>-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed. The first author was supported by the Council of Czech Government, MSM 6198959214.