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91.
Alternatives based on polynomial expansions of gaussian basis set exponents are introduced and evaluated. The formulas presented here outperform methods based upon the even-tempered formula or combinations of it. They closely match the performance of other methods based upon larger polynomial expansions of the logarithm of the exponents using the same or one less parameter per orbital angular symmetry. 相似文献
92.
设G是一个简单连通图,若分离G的余一独立集S的最小点数等于连接S的点之间的内部不相交路的最大个数,则称G是Menger图。我们考虑了图的几种运算并给出了运算后的图是Menger图的条件。 相似文献
93.
In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group Sk, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35. 相似文献
94.
Two main properties of the subgradient mapping of convex functions are transposed for quasiconvex ones. The continuity of the functionxf(x)–1f(x) on the domain where it is defined is deduced from some continuity properties of the normal coneN to the level sets of the quasiconvex functionf. We also prove that, under a pseudoconvexity-type condition, the normal coneN(x) to the set {x:f(x)f(x)} can be expressed as the convex hull of the limits of type {N(x
n)}, where {x
n} is a sequence converging tox and contained in a dense subsetD. In particular, whenf is pseudoconvex,D can be taken equal to the set of points wheref is differentiable.This research was completed while the second author was on a sabbatical leave at the University of Montreal and was supported by a NSERC grant. It has its origin in the doctoral thesis of the first author (Ref. 1), prepared under the direction of the second author.The authors are grateful to an anonymous referee and C. Zalinescu for their helpful remarks on a previous version of this paper. 相似文献
95.
For one-dimensional expanding mapsT with an invariant measure we consider, in a parameter space, the envelope
n
of the real lines associated to any couple of points of the orbit, connected byn iterations ofT. If the map hass inverses and is piecewise linear, then the sets
n
are just the union ofs
n
points and converge to the invariant Cantor set ofT. A correspondence between all the sets and their measures is established and allows one to associate the atomic measure on 1 to the completly continuous measure on the Cantor set. If the map is nonlinear, hyperbolic, and hass inverses, the sets
n
are homeomorphic to the Cantor set; they converge to the Cantor set ofT and their measures converge to the measure of the Cantor set whenn. The correspondence between the sets
n
allows one to define converging approximation schemes for the map an its measure: one replaces each of thes
n
disjoint sets with a point in a convenient neighborhood and a probability equal to its measure and transforms it back to the original set 1. All the approximations with linear Cantor systems previously proposed are recovered, the converging proprties being straightforward in the present scheme. Moreover, extensions to higher dimensionality and to nondisconnected repellers arte possible and are briefly examined. 相似文献
96.
Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG()
D
. The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably. 相似文献
97.
98.
The addition of the macrocyclic polyether 18-Crown-6 (18C6) increases the selectivity of oxidation of ethylbenzene to -phenylethylhydroperoxide (PEH) in the presence of Ni(acac)2. The initial oxidation rate, selectivity and degree of conversion of ethylbenzene to PEH are greater than those catalyzed by Ni(acac)2 only. The efficiency of the macrocyclic ligand as an activator of Ni(acac)2 exceeds that of monodentate donor ligands. The high selectivity of the process is due to both the primary Ni(acac)2 · 18C6 complexes and the products of their transformation in the course of oxidation. The mechanism of ethylbenzene oxidation catalyzed by Ni(acac)2 · 18C6 complexes is discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1406–1411, August, 1994. 相似文献
99.
100.
A three-dimensional pharmacophore model was developed from a series of inhibitors of Aurora A kinase to discover new potent anti-cancer agents using the HypoGen module in the Catalyst software. The pharmacophore model was developed based on the structure of 20 currently available inhibitors, which were carefully selected from the literature. The best hypothesis (Hypo 1) was defined by four features: one hydrogen-bond donor and three hy- drophobic points, with the best correlation coefficient of 0.909, the lowest rms deviation of 1.563, and the highest cost difference of 99.075. The Hypo 1 was then validated by a test set consisting of 24 compounds and by a cross-validation of 95% confidence level through randomizing the data using the CatScramble program, which suggested that a predictive pharmacophore model had been successfully obtained. 相似文献