矩孔金属光栅矢量模式理论的数值计算

根据矩孔金属光栅的矢量模式理论，计算了不同入射方向，波长及偏振态情况下衍射场的分布，研究了不同光栅结构对衍射效率，偏振态变化的影响；同时，根据实际需要，加工制作了一批不同深度的矩孔光栅样品，进行了实验测量，并将计算值与实验值进行了比较，两者基本相符。     

Enumerating disjunctions and conjunctions of paths and cuts in reliability theory

Let G=(V,E) be a (directed) graph with vertex set V and edge (arc) set E. Given a set P of source-sink pairs of vertices of G, an important problem that arises in the computation of network reliability is the enumeration of minimal subsets of edges (arcs) that connect/disconnect all/at least one of the given source-sink pairs of P. For undirected graphs, we show that the enumeration problems for conjunctions of paths and disjunctions of cuts can be solved in incremental polynomial time. Furthermore, under the assumption that P consists of all pairs within a given vertex set, we also give incremental polynomial time algorithm for enumerating all minimal path disjunctions and cut conjunctions. For directed graphs, the enumeration problem for cut disjunction is known to be NP-complete. We extend this result to path conjunctions and path disjunctions, leaving open the complexity of the enumeration of cut conjunctions. Finally, we give a polynomial delay algorithm for enumerating all minimal sets of arcs connecting two given nodes s₁ and s₂ to, respectively, a given vertex t₁, and each vertex of a given subset of vertices T₂.     

Time Asymptotic Behaviour for a One-Velocity Transport Operator with Maxwell Boundary Condition

This paper is concerned with the spectral analysis of a one-velocity transport operator with Maxwell boundary condition in L ₁-space. After a detailed spectral analysis it is shown that the associated Cauchy problem is governed by a C ₀-semigroup. Next, we discuss the irreducibility of the transport semigroup. In particular, we show that the transport semigroup is irreducible. Finally, a spectral decomposition of the solutions into an asymptotic term and a transient one which will be estimated for smooth initial data is given.     

Interacting Spin 0 Fields with Torsion via Duffin-Kemmer-Petiau Theory

Here we study the behaviour of the spin 0 sector of the DKP field in spaces with torsion. First we show that in a Riemann-Cartan manifold the DKP field presents an interaction with torsion when minimal coupling is performed, contrary to the behaviour of the KG field, a result that breaks the usual equivalence between the DKP and the KG fields.Next we analyse the case of the Teleparallel Equivalent of General Relativity (Weitzenböck manifold), showing that in this case there is a perfect agreement between KG and DKP fields. The origins of both results are also discussed.On leave from     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.     

L-shell/subshell ionization of Au,Pb and Bi by low energy proton impact

Proton induced X-ray emission has been used to measureL-subshell and total ionization cross-sections of Au, Pb and Bi in the energy range of 200–350 keV. The ionization cross-sections have been extracted using the X-ray spectra and other quantities like fluorescence yields, transition probabilities, relative widths and Coster-Krönig fraction etc. involved in the process. The results have been compared with the cross-sections measured before and discussed in the light of known theories regarding the ion-atom collisions.     

Projector formalism of generalized Brownian motion theory applied to dissipative and noisy systems

The projector formalism of Zwanzig-Mori type is extended to obtain generalized Fokker-Planck and generalized nonlinear Langevin equations for coarse-grained variables when the underlying microscopic dynamics is dissipative and noisy (stochastic).     

一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算

利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.