解非光滑方程组的广义数值延拓算法(Ⅰ)──基本理论

本文研究了求解Ｂ－可微方程组的广义数值延拓算法的基本理论．其基本出发点是利用同伦廷拓思想,建立相应的非光滑同伦方程组,论证其跟踪路径的存在唯一性及连续性．据此,在另文中进一步获得了广义数值延拓算法的适定性、收敛性,进而将新算法应用于几类重要的规划问题．     

非线性高阶抛物双曲型耦合方程组的第一边界问题

本文研究了一类广义Sine-Gordon型非线性高阶双曲方程组、非线性高阶拟双曲型方程组、非线性高阶拟抛物型方程组以及非线性高阶广义Sehrdinger型方程组的耦合方程组的第一边界问题,作者证明了此耦合方程组第一边界问题的整体广义解和整体古典解的存在性、唯一性和光滑性。     

一类完全非线性抛物方程组的高次有限体积元方法及分析

1 引言有限体积元方法(FVEMs)作为处理偏微分方程的有效数值方法,得到了广泛的应用．已有文献多为处理单个方程,对于方程组的情形此类文献甚少．羊丹平对于一维抛物型方程组构造了一次广义差分格式．Douglas就一类抛物型方程组讨论了一般的     

用Lebesgue－Stieltjes积分定义的双曲型方程广义解

该文用Ｌｅｂｅｓｇｕｅ－Ｓｔｉｅｌｔｊｅｓ积分给出一个双曲型方程组广义解的新定义，在这个意义下证明了Ｃａｕｃｈｙ问题整体广义解的存在性．这种解自然地包含了δ－激波．     

在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题

研究了在分子晶体中的一类广义非线性Schroedinger方程组的初边值问题．应用先验估计的方法，得到了整体解的存在性．     

用Lebesgue-Stieltjes积分定义的间断解的存在唯一性

在Lebesgue-Stieltjies积分定义的广义解的意义下,证明了一个双曲型方程组Cauchy问题整体广义解的存在性和唯一性.作为经典广义解的自然推广,文中的广义解可以包含某些具奇性的双曲波如δ-波.也适用更一般的方程组.     

一类非线性双曲偶合方程组广义解的存在性

本文考虑了具有形式ｎ的弱偶合双曲守恒方程组广义解的存在性问题．极大值原理导出了粘性解Ｌ∞模先验估计，关于单个守恒律简化的补偿列紧方法给出了粘性解的收敛性，即广义解的存在性．     

高阶非线性双曲型拋物型耦合方程组的周期边界问题和初值问题

本文研究了广义Sine—Gordon型非线性高阶双曲方程组、高阶非线性拟双曲型方程组、高阶非线性拟抛物型方程组以及高阶非线性Schrodinger型方程组的耦合方程组的周期边界问题和初值问题。证明了此耦合方程组的周期边界问题和初值问题整体广义解和整体古典解的存在性、唯一性和光滑性。     

关于一类非线性双曲方程组的二维Cauchy问题

本文通过引进新的广义解定义，对一类非线性双曲方程组的二维Ｃａｕｃｈｙ问题，证明了解的存在唯一性．并且，解可能含δ波．     

带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解的极限

研究了带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解的极限.由于非齐次项的影响,带有源项的广义Chaplygin气体磁流体Euler方程组Riemann解不再是自相似的.当压力和磁感强度同时消失时,它的解会收敛到零压流输运方程组的Riemann解,解中会出现δ-激波和真空现象.同时研究还得到了仅当磁感强度消失时,它的解会收敛到非齐次广义Chaplygin气体Euler方程组的Riemann解,并且解中只出现δ-激波.     

Self-triggered filter design for a class of nonlinear stochastic systems with Markovian jumping parameters

This paper is concerned with the self-triggered filtering problem for a class of Markovian jumping nonlinear stochastic systems. The event-triggered mechanism (ETM) is employed between the sensor and the filter to reduce unnecessary measurement transmission. Governed by the ETM, the measurement is transmitted to the filter as long as a predefined condition is satisfied. The purpose of the addressed problem is to synthesize a filter such that the dynamics of the filtering error is bounded in probability (BIP). A sufficient condition is first given to ensure the boundedness in probability of the filtering error dynamics, and the characterization of the desired filter gains is then realized by means of the feasibility of certain matrix inequalities. Furthermore, a self-triggered mechanism is designed to guarantee the filtering error dynamics to be BSP with excluded Zeno phenomenon. In the end, numerical simulation is carried out to illustrate the usefulness of the proposed self-triggered filtering algorithm.     

Non-Convex Strong Duality Via Subdifferential

In this article, the strong duality is treated. It is shown that the strong duality is equivalent to the non-emptiness of the subdifferential of a sort map involving the constraint functions. It is also noted that this technique is useful to verify the Assumption S. Indeed, the linearity of a constraint function h is not required as usually seen in the literature. Moreover, it is shown that this condition is easer to verify in the applications. We apply this new principle to the bi-obstacle problem, to the elastic-plastic torsion problem and to the continuum model of transportation.     

Torsional oscillations in symmetrical structures

A two-time perturbation technique is used to study the lateral and torsional motions of a nonlinear symmetrical structure subject to a lateral sinusoidal ground motion. It is shown that when the ground acceleration frequency is about one-third of or three times the natural frequency of the lateral motion, the symmetrical structure is particularly susceptible to torsional oscillations even when the natural frequency of torsion is not close to the natural frequency of the lateral motion. The implication of this type of nonlinear coupling between the lateral and torsional motions in real structures subject to earthquakes is also discussed.     

Discrete dynamic programming with outcomes in random variable structures

Multiobjective approach is the common way of generalization single-criterion dynamic programming models. Another way is to consider partially ordered criteria structures. That approach is rather rare. The aim of the paper is to present such a model. Generalization of Bellman’s principle of optimality is employed to create a forward procedure to find the set of all maximal elements. As this set is usual large, the second problem under consideration is to find its subsets. To reduce the number of solutions presented to decision maker we propose to apply a family of narrowing relations. That approach is similar to scalarization in multiobjective programming. Ordered structures of random variables based on mean–variance, stochastic dominance and inverse stochastic dominance are considered. Numerical illustration is given at the end of the paper.     

二项线性随机效应模型的拟蒙特卡罗估计

讨论了如何运用拟蒙特卡罗方法对二项线性随机效应模型进行参数估计.首先写出观测数据的边缘对数似然函数,然后用拟蒙特卡罗方法将函数中的积分写成求和的形式,接着利用Newton-Raphson算法计算参数的极大似然估计.以一组种子数据为例,说明该方法是简单可行的.     

A defense of indeterminism

My goal is to defend the indeterminist approach to vagueness, according to which a borderline vague utterance is neither true nor false. Indeterminism appears to contradict bivalence and the disquotational schema for truth. I agree that indeterminism compels us to modify each of these principles. Kit Fine has defended indeterminism by claiming that ordinary ambiguous sentences are neither true nor false when one disambiguation is true and the other is false. But even if Fine is right about sentences, his point does not seem to generalize to utterances. What the indeterminist needs -- and what ordinary ambiguity does not provide -- is an ambiguous utterance where what is being said is indeterminate between two different propositions. I will show that such cases exist. These cases imply that the modifications that indeterminism makes to bivalence and the disquotational schema are required independently of indeterminism, in fact independently of vagueness.     

连续区间数的中位算子及其灵敏度分析

研究决策信息以区间数形式给出的方案决策问题。考虑到区间数非均匀分布的特点,为避免区间极端值在区间数确定中产生较大误差,本文将中位数概念运用到区间数的确定上,提出OIP(Ordered Interval Point)有序中位算子。取单位区间单调函数(BUM函数)为二分之一所表示的值为权重,将区间数确定为一个实数,并研究算子单调性和有界性的初等运算性质。通过比较OIP算子与COWA算子对态度参数和区间长度的反应灵敏度,获得了在一定条件下OIP算子对态度参数反应更稳健,对区间长度反应更灵敏的结论。最后用算例证明该算子的可行性和有效性。     

Two warehouse inventory models for single vendor multiple retailers with price and stock dependent demand

Here a single vendor multiple retailer inventory model of an item is developed where demand of the item at every retailer is linearly dependent on stock and inversely on some powers of selling price. Item is produced by the vendor and is distributed to the retailers following basic period policy. According to this policy item is replenished to the retailers at a regular time interval (T₁) called basic period (BP) and replenishment quantity is sufficient to last for the period T₁. Due to the scarcity of storage space at market places, every retailer uses a showroom at the market place and a warehouse to store the item, little away from the market place. Item is sold from the showroom and is filled up from the warehouse in a bulk release pattern. Some of the inventory parameters are considered as fuzzy in nature and model is formulated to maximize the average profit from the whole system. Imprecise objective is transformed to equivalent deterministic ones using possibility/necessity measure of fuzzy events with some degree of optimism/pessimism. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover and random mutation and is used to solve the model. In some complex cases, with the help of above GA, fuzzy simulation process is used to derive the optimal decision. The model is illustrated through numerical examples and some sensitivity analyses are presented.     

B-Spline Collocation Method for Nonlinear Singularly-Perturbed Two-Point Boundary-Value Problems

A B-spline collocation method is presented for nonlinear singularly-perturbed boundary-value problems with mixed boundary conditions. The quasilinearization technique is used to linearize the original nonlinear singular perturbation problem into a sequence of linear singular perturbation problems. The B-spline collocation method on piecewise uniform mesh is derived for the linear case and is used to solve each linear singular perturbation problem obtained through quasilinearization. The fitted mesh technique is employed to generate a piecewise uniform mesh, condensed in the neighborhood of the boundary layers. The convergence analysis is given and the method is shown to have second-order uniform convergence. The stability of the B-spline collocation system is discussed. Numerical experiments are conducted to demonstrate the efficiency of the method.     

基于区间数贴近度的不确定多属性决策模型

针对只有部分权重信息且属性值以区间数形式给出的多属性决策问题,提出了一种基于区间数贴近度的决策方法.首先讨论了区间数贴近度的定义和性质;然后给出了解决不确定多属性决策问题的一般步骤.并依据传统的逼近理想解的基本思路,以实际评价值与理想解之间的贴近度最大化为目标建立优化模型,从而得到指标权重.进而计算出每个方案与正理想解的相对贴近度,即可得到所有方案的排序结果.方法能充分利用规范化评价的先验信息,评价结果客观可靠,不具有主观随意性.最后通过实例分析验证了该方法的有效性和实用性.