Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

化学与社会:跨学科视角下的通识课教学新探索

从通识教育的时代要求和化学的学科地位出发，首先讨论了在化学类通识课程建设中引入跨学科视角的意义和可操作性。随后以通识课"化学与社会"的建设为例，系统地分享了引入跨学科视角后的课程设计理念和内容框架建设，通过课堂实施方案的论述和特色实例的分享总结了课程实施经验，并以学生访谈资料分析讨论了课程取得的效果和需要进一步完善的方向。以期为跨学科理念在化学教育教学实践中的转化和落地开拓思路、提供经验。     

带缓冲串行生产系统预防性维护建模及运行参数优化研究

为了保证串行生产系统的产能和提高系统可靠性,提出了带缓冲区的串行生产系统预防性维护决策模型。首先,分析了生产线各执行单元可靠性和运行参数之间的关系,建立了考虑执行单元运行参数和缓冲库存的维护模型。在此基础上,结合串行生产线的特点,建立综合考虑维护成本、有效运行速度和缓冲库存的多目标优化函数。最后,构建启发式算法求解目标函数,并以串行包装生产线为例进行仿真实验分析,结果表明本文所建模型是有效且实用的。     

Reliability bounds in DFRA class with known mean and variance

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Randomized algorithms for the separation of point sets and for solving quadratic programs

A randomized algorithm for finding a hyperplane separating two finite point sets in the Euclidean space ^d and a randomized algorithm for solving linearly constrained general convex quadratic problems are proposed. The expected running time of the separating algorithm isO(dd! (m + n)), wherem andn are cardinalities of sets to be separated. The expected running time of the algorithm for solving quadratic problems isO(dd! s) wheres is the number of inequality constraints. These algorithms are based on the ideas of Seidel's linear programming algorithm [6]. They are closely related to algorithms of [8], [2], and [9] and belong to an abstract class of algorithms investigated in [1]. The algorithm for solving quadratic problems has some features of the one proposed in [7].This research was done when the author was supported by the Alexander von Humboldt Foundation, Germany.On leave from the Institute of Mathematics and Mechanics, Ural Department of the Russian Academy of Sciences, 620219 Ekaterinburg, S. Kovalevskaya str. 16, Russia.     

Bayesian sequential reliability for Weibull and related distributions

Assume that the probability density function for the lifetime of a newly designed product has the form: [H(t)/Q()] exp{–H(t)/Q()}. The Exponential(), Rayleigh, WeibullW(, ) and Pareto pdf's are special cases.Q() will be assumed to have an inverse Gamma prior. Assume thatm independent products are to be tested with replacement. A Bayesian Sequential Reliability Demonstration Testing plan is used to eigher accept the product and start formal production, or reject the product for reengineering. The test criterion is the intersection of two goals, a minimal goal to begin production and a mature product goal. The exact values of various risks and the distribution of total number of failures are evaluated. Based on a result about a Poisson process, the expected stopping time for the exponential failure time is also found. Included in these risks and expected stopping times are frequentist versions, thereof, so that the results also provide frequentist answers for a class of interesting stopping rules.This research was supported by NSF grants DMS-8703620 and DMS-8923071, and forms part of the Ph.D. Thesis of the first author, the development of which was supported in part by a David Ross grant at Purdue University. The authors thank the editors and a referee for insightful comments and suggestions.     

The strong coupling constant: Its theoretical derivation from a geometric approach to hadron structure

Since more than a decade, abi-scale, unified approach to strong and gravitational interactions has been proposed, that uses the geometrical methods of general relativity, and yielded results similar to strong gravity theory's. We fix our attention, in this note, on hadron structure, and show that also the strong interaction strength _S, ordinarily called the (perturbative) coupling-constant square, can be evaluated within our theory, and found to decrease (increase) as the distancer decreases (increases). This yields both the confinement of the hadron constituents (for large values ofr) and their asymptotic freedom (for small values ofr inside the hadron): in qualitative agreement with the experimental evidence. In other words, our approach leads us, on a purely theoretical ground, to a dependence of _S onr which had been previously found only on phenomenological and heuristic grounds. We expect the above agreement to be also quantitative, on the basis of a few checks performed in this paper, and of further work of ours on calculating meson mass spectra.     

Intramolecular Catalysis in Reactions of Hydroxamic Acids

Among hydroxamate ions (typical nucleophiles), anomalously high nucleophilicity relative to 4-nitrophenyl diethyl phosphonate is seen in anions which have general basic catalytic sites that provide anchimeric assistance for proton transfer in the transition state.     

Rapidly converging lattice sums for nonelectrostatic interactions

The relative energies of one-, two-, and three-dimensional Bravais lattice Lennard-Jones particles can be calculated by lattice sums. The expression of lattice sums over a Lennard-Jones potential can be manipulated into a form that converges rapidly. A formalism capable of calculating the lattice potential at arbitrary points of a completely general lattice has been developed. This method provides an alternative way to calculate the relative energies from the surface and the interior bulk sites of many chemical systems. The method is illustrated with application to hcp and fcc Lennard-Jonesium, both for the relative binding energy and for calculating the potential along the geometric diffusion pathway between tetrahedral and octahedral interstitial sites. Diffusion from the tetrahedral site to the octahedral site experiences a barrier of 752.600 in units of 4 epsilon. The reverse pathway experiences a barrier of 1035.614 in units of 4 epsilon.     

An investigation of the reliability of the Galerkin-Petrov method

It is shown that the Galerkin-Petrov method if applied in a controlled way yields reliable results for excited states of the same symmetry classifications as the ground state. Computations are performed for the 2¹ S and 3¹ S states of He. The problem of optimizing nonlinear parameters of the basis functions by means of the GP method is discussed. A special optimization scheme is suggested and numerically illustrated for someS states of He.