Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.     

Compulsorily Phase Locked Interferometer Using Orthogonally Polarized Light Source of a Modulated LD with High Extinction Ratio

This paper describes a compulsorily phase locked differential interferometer using an orthogonally polarized light source of a modulated LD with high extinction ratio to reduce non-linearity of the interferometer caused by polarization cross-talk. The current modulated LD is used as a light source to make the interferometer compact and for the scanning phase of the interferometer. The interferometer is operated compulsorily at the maximum inclination point of the fringe intensity curve by fringe scanning and an electric system. A Wollaston prism of high extinction ratio (50 dB) is used to combine the polarizing beams and to make the polarization cross-talk very small. In one light source the polarized output beams are on the same propagation axis; in the other they have a small crossing angle (2.5 mrad ∼ 10 mrad) to completely exclude non-linearity of the interferometer causded by polarization cross-talk. Using jets of a gas mixture of nitrogen and ethylene, this interferometer was demonstrated to be useful in detecting the photothermal effect of a photothermal velocimeter under phase fluctuation in a turbulent flow.     

T 1 theorem for Besov spaces on nonhomogeneous spaces

Suppose μ is a Radon measure on ℝ ^d , which may be non doubling. The only condition assumed on μ is a growth condition, namely, there is a constant C₀>0 such that for all x∈supp(μ) and r>0, μ(B(x, r))⪯C₀rⁿ, where 0<n⪯d. We prove T1 theorem for non doubling measures with weak kernel conditions. Our approach yields new results for kernels satisfying weakened regularity conditions, while recovering previously known Tolsa’s results. We also prove T1 theorem for Besov spaces on nonhomogeneous spaces with weak kernel conditions given in [7].     

Ternary univariate curvature-preserving subdivision

We present an interpolating, univariate subdivision scheme which preserves the discrete curvature and tangent direction at each step of subdivision. Since the polygon have a geometric information of some original (in some sense) curve as a discrete curvature, we can expect that the limit curve has the same curvature at each vertex as the control polygon. We estimate the curvature bound of odd vertices and give an error estimate for restoring a curve from sampled vertices on curves.     

加权二次有理Bézier插值曲线

在本文中,给定一组有序空间数据点列及每个数据点的切矢向量,利用加权二次有理Bézier曲线对数据点作插值曲线,使该曲线具有C1连续性,并且权因子只是对相应顶点曲线附近产生影响,同调整两个相邻的权因子可以调整这两个相邻顶点之间的曲线和它的控制多边形.     

Representations of Positive Projections II

In this paper we obtain a number of Maharam-type slice integral representations, with respect to scalar measures, for positive projections in Dedekind complete vector lattices and f-algebras. AMS Classification: 47B65, 46A40, 06F25     

Leptonic constant of the pseudoscalar <Emphasis Type="Italic">B</Emphasis><Subscript><Emphasis Type="Italic">c</Emphasis></Subscript> meson

We calculate the leptonic constant for the pseudoscalar ground state of the B _c meson in the framework of a QCD-motivated potential model taking into account the two-loop anomalous dimension for the heavy quark current in nonrelativistic QCD as matched with full QCD.     

Fonctions analytiques Cliffordiennes

We define analytic functions within Clifford Algebras CL, and study their trigonometric properties. We write the addition formulas when their arguments, A and B in CL, commute, this generalizes ordinary trigonometry. We examine in particular the case A² = 1.      

Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups

In the present paper it is shown that if S₁ and S₂ are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S₁*) onto LUC(S₂*), then T maps S₁ topologically isomorphically onto S₂. Furthermore, T maps M ^l _n(S₁) (M(S₁), respectively) isometrically isomorphically onto M ^l _n(S₂) (M(S₂), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.     

Experiences in Expert Systems

This paper describes some work carried out in the Scientific Research and Development Branch (SRDB) of the Home Office, intended to contribute to an overall aim of building up internal expertise in the field of expert systems. This was done by carrying out a number of pilot and demonstrator projects, two of which are described in some detail. The plan, which proved successful, was to build as far as possible on the relevant skills already possessed by an OR group in the branch. The lessons learned from these are summarized in the hope that they will be of use to other groups who wish to become involved in this important area.