Theoretical Studies on the Abstraction Reaction of Atomic O（^3p） with Si2H6

The hydrogen abstraction reaction of O(^3P) with Si2H6 has been studied theoretially. Two transition states of ^3A″ and ^3A′ symmetries have been located for this abstraction reaction. Geometries have been optimized at the UMP2 leve with 6-311G (d) basis set. G3MP2 has been used for the final single-point energy calculation. The rate constants have been calculated over a wide temperature range of 200-3000K using canonical variational transition-state sheory (CVT) with small curvature tunneling effect(SCT). The calculated CVT/SCT rate constants match well with the experimental value.     

Some difficulties for Clifton,Redhead, and Butterfield's recent proof of nonlocality

Clifton, Redhead, and Butterfield have recently produced a generalization of the new non-locality proof due to Greenberger, Horne, and Zeilinger. Their proof is intended to have certain advantages over the standard Belltype arguments. One of these is that, although the proof allows for causally relevant apparatus hidden variables, it avoids the need for making certain standard locality assumptions about those parameters. On closer inspection, the part of the proof which supposedly removes the need for such assumptions is shown to rest on a fallacy. This renders the proof invalid. Two other, related difficulties are explored along the way.1. CRB actually provide two nonlocality proofs, but our concern here is with the first.2. Cf. p.173 for a precise formulation of these. (Any references in these footnotes are to [1].) Note that, due to the way CRB define the µ's, these conditions are not entirely independent.3. Cf. p.174. Note that CRB claim to derive the independence of outcomes from apparatus existents via our other assumptions without imposing any other conditions on their distributions, citing Lemma 2, which we shall object to in Sec. 4 below. This should be given a careful reading; Lemma 2 only purports to derive the statistical independence of outcomes fromlocal (i.e., nearby) apparatus hidden variables. The independence of outcomes fromdistant apparatus hidden variables is assumed, rather, in OL.4. Here, and in many places, I shall rely on [1] for the details.5. CRB have endorsed this definition of M (personal correspondence).6. More precisely, those values of do so for at least one possible quadruple of apparatus existents, and measurement results; and foruncountably many setting quadruples in (p.167).7. Given CRB's way of defining the µ's so as to include the information found in the 's, the terms in OF and most of those in OL would actually be ill-defined in most cases (for each ) inany theory. This is simply because the measuring devices cannot be set to measure in two different directions at once. However, it should be possible to remedy that situation by simply redefining µ so that it includes only information about the state of the apparatus not covered by .8. CRB endorse the first of these two suggestions (personal correspondence).9. I have omitted the arguments fromA,B,C andD. Wherever they appear without arguments they will implicitly have the three with which they were first introduced. Note that M⁺ should ideally be indexed by and , as there is no reason to think that all the same members of M will makeABCD = +1 for different values of and .10. Cf. note 6 above.11. Note that in light of this objection to their proof, we can see that CRB also fail to establish the link they claim exists between TF, strict correlations, and the condition they call TF.TF is the four-particle analogue of the conjunction of Shimony's outcome independence and his parameter independence (p.162). They rest their claim about the link on Lemma 2 (pp.162 and 165).     

Higher-order necessary conditions for infinite and semi-infinite optimization

In this paper, we present a unified theory of first-order and higher-order necessary optimality conditions for abstract vector optimization problems in normed linear spaces. We prove general multiplier rules, from which nearly all known first-order, second-order, and higher-order necessary conditions can be derived. In the last section, we prove higher-order necessary conditions for semi-infinite programming problems.This work was developed within the Forschungsschwerpunkt Dynamische Systeme, Universität Bremen, Bremen, West Germany.The author wishes to thank Prof. Dr. D. Hinrichsen for his helpful remarks and discussions during the preparation of this work.     

Correlation inequalities for the truncated two-point function of an Ising ferromagnet

We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: _j ; _l ^T _j ; _k ^T _k ; _l ^T , and _j ; _l ^T _{k K j} ; _k ^T _{k l} , whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.NSERC Postgraduate Fellow, 1978–1981. Research supported in part by NSF Grant No. PHY-78-25390-A02.     

Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

再论Pedoe不等式的高维推广及应用

本文对欧氏空间E~n中的两个n维单形,给出了著名的Pedoe不等式的一个实质性推广,并讨论了它的应用.     

Inequalities for linear combinations of monomials in p-Newton sequences

The partial order on monomials that corresponds to domination when evaluated at positive Newton sequences is fully understood. Here we take up the corresponding partial order on linear combinations of monomials. In part using analysis based upon the cone structure of the exponents in p-Newton sequences, an array of conditions is given for this new partial order. It appears that a characterization in general will be difficult. Within the case in which all coefficients are 1, the situation in which, for general sequence length, there are two monomials, each of length two and nonnegative integer exponents, the partial order is fully characterized. The characterization is combinatorial, in terms of indices in the monomials, and, already here there is much more than term-wise domination.     

A Finite Volume Implicit Euler Scheme for the Linearized Shallow Water Equations: Stability and Convergence

The linearized shallow water equations are discretized in space by a finite volume method and in time by an implicit Euler scheme. Stability and convergence of the scheme are proved.     

A convergence for vector valued functions

We give a definition of gamma-convergence (epi-convergence) for the case of vector valued sequences of functions and prove some related properties analogous to the scalar case. We obtain one of the main variational theorems about convergence of ?-minimizers. In the convex case, we consider also variable domains and obtain stability of efficient points and minimal values.