An approximated principal component prediction model for continuous-time stochastic processes

In this paper, a linear model for forecasting a continuous-time stochastic process in a future interval in terms of its evolution in a past interval is developed. This model is based on linear regression of the principal components in the future against the principal components in the past. In order to approximate the principal factors from discrete observations of a set of regular sample paths, cubic spline interpolation is used. An application for forecasting tourism evolution in Granada is also included. © 1997 by John Wiley & Sons, Ltd.     

Simultaneously Definitizable and Spectralizable Operators in Krein Space

We study the spectral properties of a self–adjoint operator in Krein space such that one of its natural powers is J–non–negative and some other power is a spectral operator in the Dunford sense.     

A novel method of temperature control for a crystal growth puller

A facile method to control the contracting rate of the thermal expansible bars for pulling crystal is first suggested. The thermal expansible bars, set in a modified Dewar flask whose vacuum degree is controlled, are heated to designed temperature and then switch off the power to let it cool down at a desired rate, which depends largely on the changeable vacuum degree. This new approach is expected to completely eliminate the effects, which possibly reduces the smooth extent of thermal expansion, caused by the minor temperature fluctuations during crystal growth process and to realize the utmost smooth and slow pulling rate. It is expected to install this apparatus in optical floating zone furnace, instead of traditional motor, to grow peritectic crystal, such as crystal Bi‐2223, since for the peritectic reaction, in principle, the extremely slow growing rate is considerably essential.     

线性常微分方程参数稳定性的统计推断

对具有随机误差的观测数据, 讨论了常系数线性常微分方程参数稳定性的统计推断问题. 通过残差项的Karhunen-Loeve 分解, 给出了变点检验步骤及其在原假设下的极限分布. 在对立假设下定义了变点的估计, 证明了检验以及估计的一致性. 对常系数二阶常微分方程进行了统计模拟, 结果表明原假设下的极限分布是对真实分布非常好的近似; 对立假设下, 即使输入函数的频率存在0.75% 的变化, 上述检验也能以大概率拒绝原假设. 最后利用上述方法研究了英国中部地区的气温数据, 揭示了数据一些新的特点.     

de Sitter空间S1m+1中具有平行Blaschke张量的正则类空超曲面

本文引入两个以de Sitter空间为模型的非齐性坐标来覆盖共形空间Q₁^m+1.利用球面S^m+1中超曲面的Möbius几何的方法,本文研究了Q₁^m+1中正则类空超曲面的共形几何.作为其结果,本文对所有具有平行Blaschke张量的正则类空超曲面进行了完全分类.     

Undecaborates M2[B11H11]: Facile Synthesis,Crystal Structure,and Reactions

closo-Undecaborates were synthesized by the deprotonation of B₁₁H₁₃(SMe₂) with LitBu in thp or K[BHEt₃] in thf, [Li(thp)₃]₂[B₁₁H₁₁] and K₂[B₁₁H₁₁] being obtained in 83 and 93% yield, respectively. K₂[B₁₁H₁₁] can be transformed into A₂[B₁₁H₁₁] with the corresponding ammonium chlorides in aqueous solution (A = [NMe₃Ph], [NBzlEt₃], [N(PPh₃)₂]). The crystal structure analysis of [Li(thp)₃]₂[B₁₁H₁₁] (space group P2₁/c) reveals a rather distorted octadecahedron for the [B₁₁H₁₁]^2– anion, whereas the corresponding octadecahedron in [NBzlEt₃]₂[B₁₁H₁₁] (space group P2₁2₁2₁) exhibits a structure close to C_2v symmetry, expected for the free anion. The protonation of [B₁₁H₁₁]^2– at low temperature gives [B₁₁H₁₂]^–, whose structure could be elucidated by NMR methods; it is formed, apparently, by the opening of the B1–B4 edge of [B₁₁H₁₁]^2– in the course of its known degenerate skeletal rearrangement, followed by the protonation of the B2–B4 edge. The reaction of [B₁₁H₁₂]^– with a second molecule of the acid HX (X = CF₃COO) gives nido-[B₁₁H₁₃X]^–. The addition of BH₃ to [B₁₁H₁₁]^2– yields closo-[B₁₂H₁₂]^2– under loss of H₂. Two [B₁₁H₁₁]^2– units are fused by the aid of FeCl₃, with the known anion [B₂₂H₂₂]^2– as the product, whose ¹¹B-NMR signals could completely be assigned on the basis of C_s symmetry. The compound [NBzlEt₃][N(PPh₃)₂][B₂₂H₂₂] crystallizes in the space group Pna2₁.     

New translation method for STOs and its application to calculation of two-center two-electron integrals

The new translation method for Slater-type orbitals (STOs) previously tested in the case of the overlap integral is extended to the calculation of two-center two-electron molecular integrals. The method is based on the exact translation of the regular solid harmonic part of the orbital followed by the series expansion of the residual spherical part in powers of the radial variable. Fair uniform convergence and stability under wide changes in molecular parameters are obtained for all studied two-center hybrid, Coulomb, and exchange repulsion integrals. Ten-digit accuracy in the final numerical results is achieved through multiple precision arithmetic calculation of common angular coefficients and Gaussian numerical integration of some of the analytical formulas resulting for the radial integrals. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 91–100, 2000     

Banach空间中线性流形上的度量投影的表达式

借助于正规对偶映射,建立了一般Banach空间中线性流形上的(集值)度量投影存在的 充要条件,同时给出了度量投影的表达式和点到线性流形上的距离公式.这些本质地推广和改进了 王玉文和于金凤在空间自反、严格凸和光滑强假定下的相应结果.     

POST-BUCKLING AND IMPERFECTION SENSITIVITY OF A COLUMN WITH AN EQUILATERAL TRIANGULAR CROSS-SECTION IN THE PLASTIC RANGE

The asymmetric initial post-buckling corresponding to the lowest bifurcation load andthe imperfection sensitivity are analysed in detail for a compressed simply supported column with anequilateral triangular cross-section in the plastic range.The effect of elastic unloading is taken into ac-count in the analysis.The asymptotic relations,including high order terms,among the load,the am-plitude of imperfection and the amplitude of the bifurcation mode are realized.The results show thatthe maximum supported load is very sensitive to imperfection.