Dual pole eikonal ands-channel singularities

Eikonalization of dual pole amplitudes, such as the Veneziano amplitude, is shown to lead to singularities in the impact parameter plane, which, in the eikonal approximation, may be interpreted as branch points in the direct channel angular momentum plane. This result is discussed in the light of dual absorption models.     

Normal modes and quality factors of spherical dielectric resonators: I — shielded dielectric sphere

Electromagnetic theoretic analysis of shielded homogeneous and isotropic dielectric spheres has been made. Characteristic equations for the TE and TM modes have been derived. Dielectric spheres of radii of the order of μm size are found suitable for the optical frequency region whereas for the microwave region radii of the order of mm size are found suitable. Parameters suitable for their application in the optical and microwave frequency ranges have been used to compute the frequencies corresponding to the normal modes for the TE and TM modes. Expressions for the quality factors for realistic resonators, i.e., for a dielectric sphere with a non-zero conductivity and a metal shield with a finite conductivity have also been derived for the TE and TM modes. Computations of the quality factors have been made for resonators with parameters suitable for the optical and the microwave regions.     

Laminar free-convection from spherical segments

An experimental investigation of laminar free-convection heat transfer from heated, isothermal, spherical segments to a high Prandtl number liquid is reported. The effect of an extended insulator base on heat transfer is estimated. The experimentally obtained results are compared with theoretically predicted data.     

Convexity properties,moment inequalities and asymptotic exponential approximations for delay distributions in G1/G/1 systems

Pollaczek distributions pervade the class of delay distibutions in G1/G/1 systems with concave service time distributions. When the service time distribution has finite support and the delay distribution is absolutely continuous on (0, ∞), one can find a distribution with a pure exponential tail that satisfies the corresponding Wiener-Hopf integral equation except for values of the argument that belong to the support in question or to a translate thereof. Again for an exponentially decaying delay distribution, one can formulate sufficient moment inequalities which ensure the existence of asymptotic upper and lower bounds derived from M/D/1 and M/M/1 delay distributions which agree with the former in terms of the first two moments.     

Integration of the boltzmann equation in the relaxation time approximation

We integrate by very simple means the Boltzmann equation in the relaxation time approximation. Our result improves on the solution previously found by Chambers, which does not take into account initial conditions.     

Approximation of boundary values in the boundary element method

Various techniques may be applied to the approximation of the unknown boundary functions involved in the boundary element method (BEM). Several techniques have been examined numerically to find the most efficient. Techniques considered were: Lagrangian polynomials of the zeroth, first and second orders; spline functions; and the novel weighted minimization technique used successfully in the finite difference method (FDM) for arbitrarily irregular meshes. All these approaches have been used in the BEM for the numerical analysis of plates with various boundary conditions.Both coarse and fine grids on the boundary have been assumed. Maximal errors of the deflections of each plate and the bending moments have been found and the effective computer CPU times determined.Analysis of the results showed that, for the same computer time, the greatest accuracy was obtained by the weighted FDM approach. In the case of the Lagrange approximation, higher order polynomials have proved more efficient. The spline technique yielded more accurate results, but with a higher CPU time.Two discretization approaches have been investigated: the least-squares technique and the collocation method. Despite the fact that the simultaneous algebraic equations obtained were not symmetric, the collocation approach has been confirmed as clearly superior to the least-squares technique, because of the amount of computation time used.     

On the calculation of second order properties: An equation of motion approach

In the light of the equation of motion method a general expression for polarisability calculation has been derived. From this general expression, different approximation methods can be deduced for different choices of ground state and excitation manifold. Among these the coupled Hartree-Fock theory is the most extensively used one for polarisability calculations. It has also been shown that this theory has a simple relationship with random phase approximation.     

方差分析模型中参数的经验Bayes估计及其优良性问题

本文考虑单向分类的方差分析模型，构造了Ｐ′α的线性Ｂａｙｅｓ估计和经验Ｂａｙｅｓ（ＥＢ）估计，此处αａ×１是效应参数向量，Ｐａ×ｋ是常数矩阵．在较一般的条件下，基于均方误差矩阵准则和ＰｉｔｍａｎＣｌｏｓｅｎｅｓｓ准则，我们分别证明了ＥＢ估计优于最小二乘估计     

Multipoint Padé-Type Approximants. Exact Rate of Convergence

We study the rate with which sequences of interpolating rational functions, whose poles are partially fixed, approximate Markov-type analytic functions. Applications to interpolating quadratures are given. January 25, 1996. Date revised: December 26, 1996.     

Electron and positron impact ionization of atomic hydrogen and helium using CPB approximation with post-collision interaction

Triple differential cross-sections for the electron and positron impact ionization of atomic hydrogen and helium are calculated in a first order model using a product of two Coulomb wavefunctions for the final state continuum electrons supplemented by post-collision interaction effects.