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131.
Martin Schader 《Mathematical Social Sciences》1982,2(2):189-197
Transfer algorithms are usually used to optimize an objective function that is defined on the set of partitions of a finite set X. In this paper we define an equivalence relation ? on the set of fuzzy equivalence relations on X and establish a bijection from the set of hierarchies on X to the set of equivalence classes with respect to ?. Thus, hierarchies can be identified with fuzzy equivalence relations and the transfer algorithm can be modified in order to optimize an objective function that is defined on the set of hierarchies on X. 相似文献
132.
Amiya Mukherjee Aniruddha C. Naolekar 《Proceedings of the American Mathematical Society》1997,125(12):3747-3752
In this paper we apply a recently developed new version of the Bredon-Illman cohomology theory to obtain an equivariant analogue of a result of Kan and Thurston, which implies that a connected CW-complex has the homotopy type of a space obtained by applying the plus construction of Quillen to certain Eilenberg-MacLane spaces.
133.
本文讨论了n维欧氏空间Rn(n>2)上的多项式向量场集合的系数拓扑不变量,可分为具有不同全局拓扑性质的两类不交的子集合;证明了Rn上的多项式向量场可连续地延拓成n维射影空间RPn上的连续多项式向量场的充要条件,反应了其次数与系数相关的拓扑性质;还证明了平面上的多项式向量场的赤道是闭轨线和不变集的充要条件. 相似文献
134.
The phase shift sum rules recently derived by Puff are extended for a general partly non-local momentum dependent potential.
In achieving this, one must use Fredholm determinant of the outgoing solution of the Schrodinger equation instead of the Jost
function as was done by Puff. The constants appearing in the moment relations are explicitly defined in terms of the momentum
representation of the interaction. 相似文献
135.
黄文林 《浙江大学学报(理学版)》1959,46(6):651-655
136.
An asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the Boltzmann and Enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations. The proof is given starting from the solution of the Boltzmann equation, then the proof line is simply indicated when one starts from the Enskog equation. The proof holds for Knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the Enskog equation tends to zero.On leave from Department of Mathematics, University of Warsaw, Poland. 相似文献
137.
In many instances we find it advantageous to display a quantum optical density matrix as a generalized statistical ensemble
of coherent wave fields. The weight functions involved in these constructions turn out to belong to a family of distributions,
not always smooth functions. In this paper we investigate this question anew and show how it is related to the problem of
expanding an arbitrary state in terms of an overcomplete subfamily of the overcomplete set of coherent states. This provides
a relatively transparent derivation of the optical equivalence theorem. An interesting by-product is the discovery of a new
class of discrete diagonal representations.
Work supported in part by the Energy Research and Development Administration, Contract No. E(40-I)3992. 相似文献
138.
New NMR pulse schemes completely driven under homonuclear and heteronuclear cross-polarization conditions are proposed for the study and the measurement of coupling constants in symmetrical molecules in solution. The appropriate superimposition of independent magnetization components can afford several spin-selective multiplet patterns that are suitable for the determination of the magnitude and the sign of proton-proton and proton-carbon coupling constants with optimum sensitivity levels. A detailed product operator formalism analysis for the proposed doubly selective 1D and nonselective 2D HCP-TOCSY versions is provided and experimental verification for the configurational analysis of symmetric olefinic systems having chemical equivalence is demonstrated. 相似文献
139.
Mireille?Bousquet-MélouEmail author Einar?Steingrímsson 《Journal of Algebraic Combinatorics》2005,22(4):383-409
In a recent paper, Backelin, West and Xin describe a map φ* that recursively replaces all occurrences of the pattern k... 21 in a permutation σ by occurrences of the pattern (k−1)... 21 k. The resulting permutation φ*(σ) contains no decreasing subsequence of length k. We prove that, rather unexpectedly, the map φ* commutes with taking the inverse of a permutation.
In the BWX paper, the definition of φ* is actually extended to full rook placements on a Ferrers board (the permutations correspond to square boards), and the construction
of the map φ* is the key step in proving the following result. Let T be a set of patterns starting with the prefix 12... k. Let T′ be the set of patterns obtained by replacing this prefix by k... 21 in every pattern of T. Then for all n, the number of permutations of the symmetric group
n that avoid T equals the number of permutations of
n that avoid T′.
Our commutation result, generalized to Ferrers boards, implies that the number of involutions of
n that avoid T is equal to the number of involutions of
n avoiding T′, as recently conjectured by Jaggard.
Both authors were partially supported by the European Commission's IHRP Programme, grant HPRN-CT-2001-00272, “Algebraic Combinatorics
in Europe” 相似文献
140.