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121.
黄文林 《浙江大学学报(理学版)》1959,46(6):651-655
122.
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
123.
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
124.
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
125.
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
126.
127.
《Mathematical Methods in the Applied Sciences》2018,41(4):1331-1343
Lie group classification for a diffusion‐type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. Certain initial value problems are reduced to problems with the governing equations being ordinary differential equations. Examples of potential symmetries are also presented. 相似文献
128.
In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜C(R) and that in the Bass class ?C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories. 相似文献
129.
Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions. 相似文献
130.
Vladimir Ivanovich Mironenko Vladimir Vladimirovich Mironenko 《Journal of Applied Analysis & Computation》2016,6(3):876-883
In the paper we are giving the new method for searching periodic solutions of periodic differential systems. For this we construct a differential system with the same Reflecting Function as the Reflecting Function of the given system and with a known periodic solution. Then the initial data of the periodic solutions of this two systems coincide. In such a way the problem of existance periodic solutions goes to the Cauchy problem. 相似文献