差分方程解对初值连续性问题

本文讨论了差分方程的解对初值的连续性问题，对较一般的方程给出了保证解对初值连续的充分条件，对线性方程（组）利用系数矩阵的特征值给出其解对初值连续的条件．     

On spectral radii of matrices governing some numerical estimating algorithms with incomplete data

Summary Many estimating procedures are carried out with incomplete data by means of different types of EM algorithms. They allow us to obtain maximum likelihood parameter estimates in classical inference and also estimates based on the posterior mode in Bayesian inference. This paper analyzes in detail the spectral radii of the Jacobian matrices algorithm as a possible way to evaluate convergence rates. The eigenvalues of such matrices are explicitly obtained in some cases and, in all of them, a geometric convergence rate is, at least, guaranteed near the optimum. Finally, a comparison between the leading eigenvalues of EM and direct and approximate EM-Bayes algorithms may suggest the efficiency of each case.     

Integrating modeling,algorithm design,and computational implementation to solve a large-scale nonlinear mixed integer programming problem

This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings. This research was supported in part by the Office of Naval Research Contract N00014-78-C-0222, by the Center for Business Decision Analysis*, by the University of Texas at Austin, and by the David Bruton, Jr., Centennial Chair in Business Decision Support Systems. Reproduction in whole or in part is permitted for any purpose of the U.S. Government. Center for Business Decision Analysis, Graduate School of Business — GSB 3.126, University of Texas, Austin, Texas 78712, USA.     

The lion and man problem revisited

A pursuerP, whose speed is bounded by 1, wants to get closer to an evaderE, whose speed is bounded by >1.P wants to reduce his distancePE fromE below the capture radius . Both players are confined to a circular arena. This problem is equivalent to a problem discussed by Flynn, who characterized and gave numerical bounds to the least upper boundd* on the values ofPE thatE can maintain. He used direct methods and did not use Isaacs' theory.We solve our problem relying on the theory of singular surfaces in differential games. We construct and investigate barriers of the game of kind, and we replace Flynn's bounds ond* by analytical (exact) values for various speeds .The support of the TW Department of THT, Enschede, Holland, is gratefully acknowledged.     

Almost sure comparison of birth and death processes with application to M/M/s queueing systems

Given conditions, which concern the infinitesimal parameters of two birth and death processes, the processes are constructed on the same probability space such that one process is almost surely larger than the other. Application is made to M/M/s queueing systems. Stochastic comparisons of queue length and virtual waiting time in two M/M/s systems are obtained.     

Asymptotic distribution of the increase of the largest canonical correlation when one of the vectors is augmented

Let r₁ > r₂ > … be the sample canonical correlations in a sample of size n from a multivariate normal population partitioned into two subvectors with population canonical correlations ₁ > ₂ > …. Let one of the subvectors be augmented by adding one or more variables to it. For the increase in the largest canonical correlation, Δr in the sample and Δ in the population, it is shown that √n(Δr − Δ) → ^DN(0, σ²) and a formula for σ² is derived.     

The asteroidal belt and Kirkwood gaps—II. Kinematical theory

We have developed a kinematical theory for the asteroidal belt and Kirkwood gaps from the point of view of stellar dynamics. We have generated the potential that would produce these gaps and have made a spectral analysis study. We have shown that these gaps could be due to spiral tubes of matter in the ecliptic plane as a consequence of differential rotation and spatial interference of density waves. We have also shown that this mechanism could account for depletion of matter from this region.     

Small polaron electron transport in reduced CeO2 single crystals

An investigation of the electrical properties of reduced ceria, CeO_2?x, carried out on single crystals, shows that CeO_2?x provides one of the clearest examples of hopping conduction and the small polaron mechanism. Included are conductivity and Seebeck coefficient measurements at constant x, obtained by sealing off the specimen chamber after reduction. The Seebeck coefficient is independent of temperature, suggesting that the number of carriers is constant. On the other hand, the mobility is activated, with activation energy E_h = 0.40 eV at small x and increasing to 0.52 eV at x = 0.25. The results for the mobility preexponential are consistent with the adiabatic theory of small polaron behavior. A puzzling feature of the Seebeck data as a function of x is that, for low x, the data fit the well-known Heikes formula, without a degeneracy factor of 2 for spin. Nevertheless, these data are interpreted to show that the proportion of mobile carriers decreases as x increases, presumably because of the presence of short-range ordered configurations which immobilize some carriers.     

Electron diffraction data as a constraint in the determination of force field of thallous halide dimers

Electron diffraction data have been used as a constraint in the determination of force field for Tl₂F₂ having planar rhombic structure. The L-F approximation method, recently given by us, has also been applied to evaluate force constants for thallous halide dimers,e.g. T1₂F₂ and T1₂Cl₂. The results have been compared with the available experimental data in order to check the validity of the present work. It is concluded that non-bond experimental mean amplitudeU ₁..._Tl for Tl₂F₂ is capable of fixing the force field and L-F approximation gives reasonably good force fields for the two thallous halide dimers now under study.     

不同月经周期乳腺增生的超声图像分析

本文对不同月经周期乳腺增生的超声图像特征进行了分析.研究对象为选取2017年6月～2019年6月本院乳腺增生患者102例,所有患者均于不同月经周期(月经期、增殖期、分泌期)给予彩色多普勒超声检查,并检测性激素[雌二醇(E2)、孕酮(P)],分析不同月经周期乳腺增生的超声图像特征.结果 显示,102例乳腺增生患者中,彩色...