Novel halogenated cyclopentasilylene-2,4-dienes via DFT

In view of immense importance of silylenes and the fact that their properties undergo significant changes on substitution with halogens, here, we have used B3LYP/6-311++G** level of theory to access the effects of 1–4 halogens (X = F, Cl, Br, and I) on four unprecedented sets of cyclopentasilylene-2,4-dienes; with the following formulas: SiC₄H₃X ( 1 _X ), SiC₄H₂X₂ ( 2 _X ), SiC₄HX₃ ( 3 _X ), and SiC₄X₄ ( 4 _X ). In going down from F to I, the singlet (s)-triplet (t) energy gap (ΔE_s-t, a possible indication of stability), and band gap (ΔE_H-L) decrease while nucleophilicity (N), chemical potential (μ), and proton affinity (PA) increase. The overall order of N, μ, and PA for each X is 2 _X > 1 _X > 3 _X > 4 _X . Precedence of 2 _X over 1 _X is attributed to the symmetric cross conjugation in the former. The highest and lowest N are shown by 2 _I and 4 _F . The trend of divalent angle () for each X is 4 _X > 1 _X > 3 _X > 2 _X . The results show that in going from electron withdrawing groups (EWGs) to electron donating groups (EDGs), the ΔE_s-t and ΔE_H-L decrease while N, μ, and PA increase. Also, rather high N of our scrutinized silylenes may suggest new promising ligands in organometallic chemistry.     

FEM study of palladium and molybdenum clusters on an alumina covered field emitter

Palladium and molybdenum polycrystalline layers (clusters) have been deposited in a stainless steel UHV system onto a layer of alumina (Al₂O₃). This layer has been prepared by high temperature oxidation of an aluminium layer. The interaction of this system with nitrogen has been investigated at room temperature by an FEM technique. Under these conditions nitrogen spillover from molybdenum to palladium has been observed.     

Recursive partition and amalgamation with the exponential family: Theory and applications

The theory of tree-growing (RECPAM approach) is developed for outcome variables which are distributed as the canonical exponential family. The general RECPAM approach (consisting of three steps: recursive partition, pruning and amalgamation), is reviewed. This is seen as constructing a partition with maximal information content about a parameter to be predicted, followed by simplification by the elimination of ‘negligible’ information. The measure of information is defined for an exponential family outcome as a deviance difference, and appropriate modifications of pruning and amalgamation rules are discussed. It is further shown how the proposed approach makes it possible to develop tree-growing for situations usually treated by generalized linear models (GLIM). In particular, Poisson and logistic regression can be tree-structured. Moreover, censored survival data can be treated, as in GLIM, by observing a formal equivalence of the likelihood under random censoring and an appropriate Poisson model. Three examples are given of application to Poisson, binary and censored survival data.     

关于(?)-拟微分核的连续性

Supposa that f(x) is a quasidifferentiable function, defined on S(?)R~n where S is an open set, with a -equivalent bounded quasidifferential subfam ily. Lenma I     

A STUDY OF VARIOUS BARRIERS IN ENCLOSED SOUND FIELD BY USING THE COMPUTER PROGRAM—SOFIS

In the study of the behaviors of barriers in an enclosed field, one should take into account such phenomena as sound energy reflection, absorption, scattering and diffraction. Therefore, the study is much more difficult than that in free field. In this paper, sound barriers are classified into four kinds according to their size, number and shape. Each kind of barriers is modelled by a corresponding method based on a computer program—SOFIS. The program combines the ray-tracing technique and statistical method. The impulse response and some acoustical parameters such as sound pressure level at different positions can be calculated by the program, no matter there are a certain kind of barriers in the field or the field is empty. The ray-tracing program and the algorithms for various barriers are validated by the comparison between measurement and prediction of the reverberation room and the anechoic room of the Northwestern Polytechnic University.     

Canonical Modules of Semigroup Rings and a Conjecture of Reiner

We prove that the homotopy types of two naturally defined simplicial complexes are related in the following way: one is homotopy equivalent to a multiple suspension of the canonical Alexander dual of the other. These simplicial complexes arise in free resolutions of semigroup rings and modules. The relation between their homotopy types was conjectured by Reiner, and was suggested by a homological consequence of a result due independently to Danilov and Stanley on canonical modules of normal semigroup rings. Our proof is purely topological, and gives an alternative proof of their result. We also prove a generalization of a result of Hochster saying that these rings are Cohen—Macaulay, and indicate a new proof of Ehrhart's reciprocity law for rational polytopes. Received October 3, 2000, and in revised form April 2, 2001, and May 10, 2001. Online publication November 7, 2001.     

重写系统和的合流性

在实际应用中,常常使用多个重写系统。本文主要讨论重写系统和的合流性,并给出了一个重写系统和具有合流性的充分条件。     

High-temperature expansions to fifteenth order

High-temperature series expansions of the susceptibility and second moment to 15th order are calculated for zero external field on the linear chain (LC), plane square (PSQ), simple cubic (SC), and body-centered cubic (BCC) lattices. Checks for specific models against pertinent work in the literature are detailed.