弱Lp空间的Marcienkiewicz型内插定理及其应用

在弱$L_p$空间之间建立一类Marcienkiewicz型内插定理并且给出它在现代调和分析理论中的某些应用.     

Toeplitz-Bezout矩阵的若干性质

从定义出发,利用矩阵生成函数的方法来研究Toeplitz-Bezout若干基本性质,同时利用极限的思想将其对角约化.     

Equidistribution of Random Walks on Spheres

We study the equidistribution on spheres of the n-step transition probabilities of random walks on graphs. We give sufficient conditions for this property being satisfied and for the weaker property of asymptotical equidistribution. We analyze the asymptotical behaviour of the Green function of the simple random walk on ² and we provide a class of random walks on Cayley graphs of groups, whose transition probabilities are not even asymptotically equidistributed.     

Curvature walls and focal conic domains in a lyotropic lamellar phase

In the quasi-ternary CPCl/brine/hexanol lyotropic system, the interface of the lamellar and L₃ sponge phases displays a phenomenon of epitaxy: the layers of the lamellar phase tend to make a constant non-trivial angle with the interface. Thin samples of lamellar phase embedded in the sponge phase are thus submitted to oblique anchoring conditions and defects are created in the lamellar phase in order to satisfy the bulk lamellar ordering and the boundary conditions. We have studied small droplets of lamellar phase in the sponge phase. They do not exhibit the classic defects (focal conic domains) but wall defects, which appear in order to satisfy the smectic elasticity and the boundary conditions. Moreover we show through experiments in controlled geometry that, even in the presence of focal conic domains, wall defects control the size and periodicity of the textures which are observed at the interface. Received 4 November 1998     

Discrete Green's Function for Lattice Random Walk

A lattice random walk model based on particles scattering on discrete lattice of homogenous space is introduced. The discrete Green's function (DFG) for two-dimensional and three-dimensional lattice random walk of photon is found and proved by mathematical induction. The convolution theorem of photon lattice random walk is presented. They can be used with the method of images to calculate the photon density distribution in semi-infinite and finite slab homogenous turbid media such as tissue.     

On the convergence of a class of derivative-free minimization algorithms

A convergence analysis is presented for a general class of derivative-free algorithms for minimizing a functionf(x) for which the analytic form of the gradient and the Hessian is impractical to obtain. The class of algorithms accepts finite-difference approximation to the gradient, with stepsizes chosen in such a way that the length of the stepsize must meet two conditions involving the previous stepsize and the distance from the last estimate of the solution to the current estimate. The algorithms also maintain an approximation to the second-derivative matrix and require that the change inx made at each iteration be subject to a bound that is also revised automatically. The convergence theorems have the features that the starting pointx ¹ need not be close to the true solution andf(x) need not be convex. Furthermore, despite the fact that the second-derivative approximation may not converge to the true Hessian at the solution, the rate of convergence is still Q-superlinear. The theorry is also shown to be applicable to a modification of Powell's dog-leg algorithm.     

等效电子组态(l1+l1-)的谱项波函数及能量矩阵的电子杨表表示

把电子组态（l^1 l^1-）给出的填布杨图称为电子杨表,给出了有关电子杨表与无微扰波函数之间的对应关系式,证明了电子杨表的正交归一性质,给出了电子组态（l^1 l^1-）谱项波函数的电子杨表表示,证明了由电子杨表给出的（l^1 l^1-）电子组态的能量矩阵为对角矩阵。     

腔内倍频法测量KDP类晶体损耗系数

用腔内倍频方法测量无源腔内晶体吸收和散射共同作用带来的损耗,其特点是响应时间很短,约100ns,并具有很高的灵敏度（约10-4）,可望应用于高功率激光照射下非线性光学晶体无损损伤以及快速损伤的研究。将测量KDP类晶体的损耗结果与文献资料作了比较。     

Properties of an exact crystalline many-body ground state

A new quantum many-body Hamiltonian is introduced, for which the exact ground state is a Jastrow-type product. This Hamiltonian is interpreted as a one-component |x|-potential Coulomb system in free boundary conditions, and by explicit calculation it is shown that the ground state is crystalline. The generaln-body density matrix is calculated, and is related to then-body density matrix calculated in periodic boundary conditions.     

Optimization of the heavy nuclei track etching in olivine crystals from meteorites

The investigation of the track etching velocity dependence for nuclei with Z50 on pH of the etching solution in the olivine crystals from Marjalahti and Eagle Station meteorites, containing galactic cosmic-ray nuclear tracks and also the crystals from Marjalahti meteorite, calibrated at the UNILAC (GSI, Darmstadt) with 14.17 MeV/N ²⁰⁸Pb nuclei, were performed.

The pH of the etching solution were changed from 7.8 to 9.4. It is shown that the optimal track etch condition were realised at pH of etching solution in the interval from 8.4 to 8.8.

The results of the Galactic cosmic-ray nuclei tracks with Z83 revealed in olivine crystals are presented. They were additionally irradiated at 90% to the surface with accelerated 14 MeV/N ¹³²Xe nuclei.