非线性动力系统多阶段辨识模型、算法及应用

本文针对一类发酵过程中的发育期、生长期及稳定期的不同特性，提出一种非线性多阶段动力系统及其辨识模型。论述了该模型是一种特殊的多阶段最优控制问题。根据子控制问题性能指标下水平集的局部一致有界性及下半连续性，证明了子控制问题可控性及最优解集为非空紧集。依此性质构造优化算法，研制相应的数学软件，并应用于间歇发酵过程中的参数辨识。其数值结果表明：该多阶段模型比已有模型更能逼近实际过程，提高了模型的精度，使模型更为有效。     

Calculation of the Probabilities of Molecular Transitions in Modeling Interisomeric Structural Transformations

The problems of a computational procedure in modeling structural isomer–isomer transitions in multiatomic molecules are considered. A number of approximations that allow one to considerably simplify calculation of the probabilities of these transformations are suggested. In comparison with traditional calculations of potential surfaces and determination of their saddle points, in the proposed approach the relationship between the electronic and vibrational components of a general problem is virtually changed. A particular emphasis is put on the vibrational part, which seems to be more physical. It is shown that the problem of structural isomer–isomer conversions can be solved without resorting at all to explicit calculation of the contribution of an electronic matrix element to the probability of transition. There is no need to study in detail the shapes of potential surfaces; it suffices only to know the positions of their minima. The calculation of multidimensional vibrational integrals is replaced by calculation of one-dimensional integrals. The results obtained form a basis for constructing methods for modeling the dynamic spectra of complex molecules considering their structural transformations.     

Multiperiod Portfolio Optimization with Terminal Liability: Bounds for the Convex Case

This paper is concerned with an investor trading in multiple securities over many time periods in order to meet an outstanding liability at some future date. The investor is concerned with maximizing the expected profits from portfolio rebalancing under an initial wealth restriction to meet the future liabilities. We formulate the problem as a discrete-time stochastic optimization model and allow asset prices to have continuous probability distributions on compact domains. For the case of Markovian price uncertainty and convex terminal liability, we develop a simplicial approximation, under which bounds on the problem can be computed efficiently. Computations only require evaluating a dynamic programming recursion, which thus, allows its application to problems with a large number of trading periods. The bounds are tight in that they are exact in certain cases. Numerical results are given to demonstrate the computational efficiency of the procedure.     

The kernel theorem for Cauchy ultradistribution

Kernel theorems for spaces of Cauchy ultradistribution, supported by an n-dimensional tube and cone of the product type, are investigated.     

基于动力系统的线性不等式组的解法

本文提出了一种新的求解线性不等式组可行解的方法-基于动力系统的方法．假设线性不等式组的可行域为非空,在可行域的相对内域上建立一个非线性关系表达式,进而得到一个结构简单的动力系统模型．同时,定义了穿越方向。文章最后的数值实验结果表明此算法是有效的．     

白噪声分析中的梯度算子和散度算子

在白噪声分析的框架中，我们给出了广义Weiner泛函空间上的梯度算子和散度算子的定义与公式，并利用梯度和散度算子以及适应投影建立了广义泛函的表示公式．也证明了积分核算子可用梯度与散度算子表出．     

p—级数与几个广义积分

本文给出了ｐ—级数与广义积分∫１０ｌｎｋ－１ｘ１－ｘｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘｄｘ，∫１０ｌｎｋ－１ｘ１－ｘ２ｄｘ，∫１０ｌｎｋ－１ｘ１＋ｘ２ｄｘ之间的关系．并通过一些ｐ—级数的求和，给出了上述广义积分中某些积分的积分值．     

The ‘Temperature Integral’ — Its use and abuse

This paper first reviews the history of the temperature dependence of reaction rate in reaction kinetics. The various equations which are in use today for expressing this dependence were delineated by van't Hoff almost one hundred years ago. Since an exponential form best describes this dependence for most thermal analysis reactions and, due to the fact that the simple Arrhenius equation (with a temperature-independent preexponential factor) has traditionally been used for this purpose, the mathematically intractable temperature integral often has become a necessary evil in the analysis of thermal analysis kinetics. Methods which avoid the temperature integral in kinetics analysis are discussed. The merits of various evaluations and approximations for the temperature integral are described and assessed in this paper.     

三次数域的整基和幂元整基

如何有效地找出数域的整基，是人们长期思考的问题.本文给出了求三次数域的整基的一个简单方法.此外，人们还对数域是否存在幂元整基的问题感兴趣.二次域和分圆域均存在幂元整基，而对于三次数域情形，则尚不清楚.本文给出了三次数域存在幂元整基的充要条件，从而对于三次数域情形给出了完整的答案.