A strong law of large numbers for generalized random sets from the viewpoint of empirical processes

In this article we prove a strong law of large numbers for Borel measurable nonseparably valued random elements in the case of generalized random sets.

     

正系数多项式倒数逼近的点态和整体估计

利用Ditzian-Totik光滑模对于[0,1]上定义的非角连续函数f(x)，且f(x)≠0，文中证明存在正系数多项式Pn(x)及常数C，使得|f9x)-1/Pn(x)|≤Cωψ^λ（f,n^-1/2(ψ(x) 1/√n)^1-λ)。当λ＝1时，上述结果导出已有的整体估计，而当0≤λ＜1时，得到倒数逼近一个新的点态局部估计。     

Integral Method o Reciprocity in the Spectroscopy of Laser Crystals with Impurity Centers

A new method of determining the stimulated emission cross-section spectra from the absorption cross-section spectra, which we call the integral method of reciprocity, is suggested it does not require knowledge of the structure of the impurity-center electron levels. Based on this method, formulas for calculating the radiation lifetime of impurity centers in crystals have been derived. The effectiveness of the integral method of reciprocity was demonstrated in determining the stimulated emission cross sections and radiation lifetime of an ytterbium ion in the laser crystals Yb³⁺:KYW and Yb³⁺:KGW.     

Application of the Volterra filter in experimental diffraction data processing

The effective signal in x-ray diffraction analysis of material properties often contains high frequency (noise) and low frequency (trend) components as additive parts. It is necessary to extract the effective signal from the noise to ensure high quality of signal processing. Digital filters of Volterra type are proposed for filtering purposes and a comparison of Volterra filtration implemented on x-ray diffraction data versus results from a set of other digital filters is given.     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.     

A new VOF‐based numerical scheme for the simulation of fluid flow with free surface. Part II: application to the cavity filling and sloshing problems

Finite element analysis of fluid flow with moving free surface has been performed in 2‐D and 3‐D. The new VOF‐based numerical algorithm that has been proposed by the present authors (Int. J. Numer. Meth. Fluids, submitted) was applied to several 2‐D and 3‐D free surface flow problems. The proposed free surface tracking scheme is based on two numerical tools; the orientation vector to represent the free surface orientation in each cell and the baby‐cell to determine the fluid volume flux at each cell boundary. The proposed numerical algorithm has been applied to 2‐D and 3‐D cavity filling and sloshing problems in order to demonstrate the versatility and effectiveness of the scheme. The proposed numerical algorithm resolved successfully the free surfaces interacting with each other. The simulated results demonstrated applicability of the proposed numerical algorithm to the practical problems of large free surface motion. It has been also demonstrated that the proposed free surface tracking scheme can be easily implemented in any irregular non‐uniform grid systems and can be extended to 3‐D free surface flow problems without additional efforts. Copyright © 2003 John Wiley & Sons, Ltd.     

Measurement of wire diameter by optical diffraction

A combined interference and diffraction pattern, in the form of equidistant interference fringes, resulting from illuminating a vertical metallic wire by a laser beam is analyzed to measure the diameter of four standard wires. The diameters range from 170 to 450 μm. It is found that the error in the diameter measurements increases for small metallic wires and for small distances between the wire and the screen due to scattering effects. The intensity of the incident laser beam was controlled by a pair of sheet polaroids to minimize the scattered radiation. The used technique is highly sensitive, but requires controlled environmental conditions and absence of vibration effects. The expanded uncertainty for k=2 is calculated and found to decrease from U(D)=±1.45 μm for the wire of nominal diameter 170 μm to ±0.57 μm for the diameter 450 μm.     

The Dual Properties of Lk-UR and k-SS Space

In this paper, we get some properties in the dual space of Lk-UR and k-SS Banach space.AMS Subject Classification: 46B09     

Solid state phase equilibria in the Gd-Si-B system at 1270 K

Solid state phase equilibria in the ternary Gd-Si-B phase diagram have been proposed at 1270 K using X-ray diffraction, scanning electron microscopy and electron probe microanalysis. Prior to this work, the binary systems Gd-B, Gd-Si and Si-B have also been reinvestigated. The main characteristic of the ternary diagram is the occurrence of two new ternary compounds Gd₅Si₂B₈ and Gd₅Si₃B_0.64. The former crystallizes in tetragonal symmetry, space group P4/mbm with unit cell parameters a=7.2665(3), c=8.2229(7) Å, the second one presents hexagonal symmetry, space group P6₃/mcm with unit cell parameters a=8.5080(4),c=6.4141(2) Å. The X-ray structures of the two structurally related phases Gd₅Si₃B_0.64 and host binary Gd₅Si₃ have been refined from three-dimensional single-crystal intensity data to the final R values of 0.036 (R_w=0.046) and 0.046 (R_w=0.055) for 457 and 401 reflections, respectively with [F>4σ(F)]. Both structures exhibit the Mn₅Si₃-type structure, with in addition for Gd₅Si₃B_0.64 a partial occupancy by boron of the normally vacant interstitial site at the center of the Gd₆ octahedron, which corresponds to the origin of the unit cell. Bonding between the interstitial boron atoms and the gadolinium ones forming the Gd₆B polyhedra is indicated by the decrease in the corresponding Gd-Gd distances and consequently in the unit cell volume. Finally, the Gd-Si-B phase diagram is compared with the previously reported Er-Si-B, at 1070 K.     

关于"太阳在银河系中所受引力与到银心距离r的关系"的讨论

讨论了银道面内的引力场强分布和太阳在银河系中所受引力与到银心距离r的关系，指出引力场强g并不是与r的平方成反比，这是由于银河系的大小和形状不能忽略造成的．强调了万有引力定律的适用条件．