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101.
P. Valtazanos S. T. Elbert S. Xantheas K. Ruedenberg 《Theoretical chemistry accounts》1991,78(5-6):287-326
Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH2 groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH2 groups rotate in a disrotatory manner, maintainingC
s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH
2
groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences 相似文献
102.
J. Mogyoródi 《Periodica Mathematica Hungarica》1977,8(3-4):275-279
103.
We have calculated the positions of the avoided level crossings between (n+2)s, np states and nd, k Stark states in the Rydberg Stark states of the potassium atom with principal quantum number n comprised between 12 and 17. We have also studied the adiabatic electric field ionization thresholds for the above Rydberg
states. Both the ionization thresholds and the positions of avoided crossings have been calculated using the recently developed
Stark-adapted quantum defect orbital (SQDO) formalism. The presently reported values appear to be in very good agreement with
the available theoretical and experimental data. 相似文献
104.
In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g
1,g
2) andS = S
1 ×S
2,S
i
are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg
i
are, respectively, convex andS
i
-convex,i = 1, 2. In particular, we consider the special case whenS
2 is in afinite dimensional space,g
2 is affine andS
2 is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g
2 is affine andS = S
2 is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong
2 and the finite dimensionality assumption onS
2, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones. 相似文献
105.
Dale Umbach 《Annals of the Institute of Statistical Mathematics》1981,33(1):81-90
Summary It is desired to estimate a parameter
with the loss function of the formL(θ, a)=W(‖θ−a‖), where
is convex, differentiable, and non-decreasing. With this structure a characterization of Bayes estimators is given. Also
it is noted that if the sample space,
, for the observation,X, is a complete separable metric space then a Bayes estimator exists. 相似文献
106.
Banach空间半线性发展方程的周期解 总被引:8,自引:2,他引:8
把上、下解方法引入到有序Banach空间中的半线性发展方程周期解问题,利用正算子半群特征与单调迭代程序,获得了最大周期解与最小周期解的存在性.所得的结果概括和推广了常微分方程与偏微分方程中的有关结论 相似文献
107.
《Optimization》2012,61(1):77-94
In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors. 相似文献
108.
Affine semigroups are convex sets on which there exists an associative binary operation which is affine separately in either variable. They were introduced by Cohen and Collins in 1959. We look at examples of affine semigroups which are of interest to matrix and operator theory and we prove some new results on the extreme points and the absorbing elements of certain types of affine semigroups. Most notably we improve a result of Wendel that every invertible element in a compact affine semigroup is extreme by extending this result to linearly bounded affine semigroups. 相似文献
109.
Some new inequalities of Hermite-Hadamard's integration are established.As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3],a new upper bound is given.Under special conditions,the bound is smaller than that in [3]. 相似文献
110.
《Physics letters. A》2014,378(5-6):480-483
We have shown in [1] that the invariant varieties of periodic points (IVPP) of all periods of some higher dimensional rational maps can be derived, iteratively, from the singularity confinement (SC). We generalize this algorithm, in this paper, to apply to any birational map, which has more invariants than the half of the dimension. 相似文献