A topological classification of linear differential equations on Banach spaces

In the present work, we give necessary and sufficient conditions for linear differential non-autonomous equations on a Banach space, that satisfy exponential dichotomy, to be topologically equivalent. We shall also prove that such equations are structurally stable.     

Energy moments of scattering phase shift for partly non-local momentum dependent interaction

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.     

关于有限群模范畴的商范畴及其等价函子

将所有能被p-可除kG-模分解的同态映射做成一个理想,利用该理想构造了有限群G的模范畴的商范畴,分析了该商范畴中的零对象,并得到该商范畴的3个等价函子。     

On the asymptotic equivalence between the Enskog and the Boltzmann equations

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.     

New light on the optical equivalence theorem and a new type of discrete diagonal coherent state representation

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.     

Measurement of coupling constants in symmetrical spin systems using a full multiple-step cross-polarization-driven NMR pulse scheme

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.     

Decreasing Subsequences in Permutations and Wilf Equivalence for Involutions

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”     

Lie symmetries of a system arising in plasma physics

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.