Stein流形上Bochner-Martinelli型积分的导数的Plemelj公式

运用局部化方法和双全纯映射,通过Stein流形和C~n空间中Bochner-Martinelli核的联系,借助已获得的C~n空间中导数的Plemelj公式,得到Stein流形上导数的Plemelj公式.     

A generalization of Bendixson's criterion

Bendixson's condition on the nonexistence of periodic solutions for planar ordinary differential equations is extended to higher dimensional ordinary differential equations with first integrals to preclude the existence of certain invariant Lipschitz compact submanifolds for those equations.

     

Interionic forces in AgF,AgCl and AgBr crystals

An interionic force model has been used in which the short range nearest neighbour and the next nearest neighbour repulsive interactions and the van der Waals’ interactions are balanced by the long range electrostatic forces. The nearest neighbour and the next nearest neighbour interactions are derived from the overlap integrals for outer shell electrons. The van der Waals’ interactions are estimated from the Slater-Kirkwood variational method. The cohesive energy, the bulk modulus and its pressure dependence for AgF, AgCl and AgBr crystals have been calculated and compared with experimental data.     

On the Growth of Convergence Radii for the Eigenvalues of the Mathieu Equation

It is proved that the convergence radii ρn of the eigenvalues of the Mathieu equation satisfy lim inf ρn/n² > kk′K² = 2.0418., where the modulus k of the complete elliptic integrals is determined by 2E = K.     

Stochastic integrals of empirical-type processes with applications to censored regression

Motivated by the analysis of linear rank estimators and the Buckley-James nonparametric EM estimator in censored regression models, we study herein the asymptotic properties of stochastic integrals of certain two-parameter empirical processes. Applications of these results on empirical processes and their stochastic integrals to the asymptotic analysis of censored regression estimators are also given.     

On computing uniformly valid approximations for viscous waves on a plane beach

Existing expansions for the near- and far-field flow of linear waves in a viscous liquid on a plane beach are supplemented by an approximation in the intermediate region which enables the flow to be matched from the shore line to infinity. Methods of computation are discussed and incorporated are recent improvements on the performance of numerical computation of oscillatory integrals. Sidi's user-friendly W-transform (1988) and Köhler's parameter optimisation (this journal, 1993) for generalised Newton—Cotes quadrature are found to be significant elements particularly with regard to the inversion of the Kontorovich—Lebedev transform. Comprehensive computations are undertaken and diagrams shown to display the behaviour of the stream function for all depths. An attempt is also made to construct a composite expansion of the vorticity and this is computed on a ray bisecting the wedge.     

Feynman diagram approach to atomic collisions

A quantum field theoretic formulation of atomic collision phenomena involving non-relativistic free and bound systems is developed and a calculational procedure in terms of Feynman diagrams is prescribed. Matrix elements of several atomic collision processes have been calculated. In most cases standard quantum mechanical results are reproduced. But in some cases new terms appear in the scattering matrix whose contribution though negligibly small in the low energy region, become important at higher energies. A large portion of this work formed material for an invited talk delivered by one of us (T.P.) at the Second National Workshop on Atomic and Molecular Physics at Visva-Bharati, Santiniketan (India) held from 18–23 November 1979.     

Tensor structure from scalar Feynman matroids

We show how to interpret the scalar Feynman integrals which appear when reducing tensor integrals as scalar Feynman integrals coming from certain nice matroids.     

Calculating contracted tensor Feynman integrals

A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.