与线性变换的完全环同构的环理论(Ⅲ)

<正> 本文继上文[1,2]的理论,对线性变换完全环的结构作进一步研究.在§1中我们讨论一般无限矩阵的几何意义.在§2中我们用有限维向量空间的线性变换完全环来构作无限维向量空间的线性变换完全环.我们的思想方法是:设是向量空间,     

关于线性算子正合序列的一个同构定理

在Werner Greub所著《Linear Algebra》(第四版)第二章§1中给出了两个短正合序列同构的定义,但未对何种情况下两个短正合序列同构作更多的考察。本文旨在给出两个短正合序列同构的若干条件,并将结果在Banach空间上作进一步推广。     

B值随机元的和的尾概率及其收敛速度

§1.引言及主要结果 设B是一可分Banach空间,‖·‖表示其上的范数,{X_n}是定义在同一概率空间上的B值随机元序列,S_n=sum from n=1 to n X_k(在本文以下内容中,均使用这一记号,始终不变),{t_n}是单调不减的正实数序列,并且本文的目的是研究概率的收敛速度问题,其中ε为任一给定的正数。     

股票指数的时间序列模型分析

借助于SA S软件将工程中的K a lm an滤波方法与时间序列的状态空间模型结合对上海A股指数进行了拟合与预测分析,通过对拟合与预测误差的计算可以发现这种模型是可行的;然后还把与滤波结合的状态空间模型的分析结果和常见的时间序列模型如:AR IM A模型、逐步自回归模型以及指数平滑模型的分析结果进行比较,比较的结果说明结合滤波的状态空间模型分析的结果比后三种的结果更加精确.结果为时间序列数据分析提供了一个较好的分析工具.     

广义函数的泛函对偶关系

§1.引言在广义函数论中所谓基本空间Φ就是由 n 维空间 R~n 上的复数值的无穷可微函数φ所组成的,并且有一定的收敛结构(即在Φ内定义了零序列φ_j→0(Φ))的复数域上的线性空间并满足下列条件     

从Riemann积分到Lebesgue积分——用完备化思想建立Lebesgue积分(续完)

<正> §5 空间L~p(a,b)(P≥1)Lebeague 函数空间L~p(a,b)及其各种变形在泛函分析中占有中心位置。这一节中我们用§3引进L(a,b)的同样方法来建立L~p(a,b)空间的理论     

一类带随机延滞的时间序列模型的遍历性

本利用马氏化方法和一般状态空间马氏链的基本理论研究了一类带随机延滞的时间序列模型的遍历性，得到了该模型伴随几何遍历的一个判别准则．     

输出反馈重极点配置问题的理论与算法

本文主要讨论具有给定特征结构的输出反馈重极点配置问题.§1为重极点配置问题的提出.§2讨论解存在的理论.附录给出§2中两个主要定理的证明。     

黎曼空间的全测地曲面的推广

<正> 在本文中我们给出黎曼空间中全测地曲面的两种推广,即第一类和第二类次测地曲面.首先将全测地曲面概念加以推广的是谷超豪,他在仿射联络空间的研究中引进了ρ型次全测地曲面(在黎曼空间中现称为第一类次测地曲面)的概念,本文就是在这个基础上层开讨论的.在§1我们得到了次测地曲面的充要条件,在§2中将平面公理推广到第一类次测地曲面提出了第一类次平面公理,在§3提出了第二类次平面公理.     

关于变分不等式

本文的目的是研究有用的一类新的变分不等式,推广Lions与Stampacchia等的一些重要结果,包括线性与非线性问题。 §2中研究星集构造,§3中证明双线性型变分不等式的一般存在性定理,§4中解对单调算子的变分不等式,§5考虑与分块定义的算子有关的情况,而在§6中讨论一种逼近方法及其误差估计。     

MODELING REGIONAL IRRIGATION DECISIONS AND DRAINAGE POLLUTION CONTROL

A regional model is proposed for evaluating policies aimed at controlling the quantity and quality of drainage from agricultural lands. The model includes both physical and economic components. The physical component incorporates a crop-water production function which computes the physical soil-water-crop relationships. The multi-farm economic model is a regional income maximization model. The model includes also physical and institutional constraints for each farm and the region. Policies evaluated in this context are varying taxes and constraints on drainage discharge and surface water use. The model was applied to a region in California. Results for alternative control policies are compared on the basis of resource use, regional income, drainage quality and quantity, and the resulting pollution load.     

基于KKT和量子遗传算法的风火电联合上网最优决策

研究了同时考虑节能减排效益和经济效益时,风火电联合上网的决策模型,并采用提出的KKT框架下的量子遗传算法进行模型的求解。综合考虑风电和火电的特点,建立经济效益函数和节能减排效益函数以及相关的约束条件,最终确立多目标决策模型。在KKT框架下将多目标函数转化为单目标,并利用量子遗传算法进行模型的求解。算例分析显示本文提出的KKT框架下的量子遗传算法在决策模型的求解时能够利用更少的CPU运行时间获得更优的决策结果,与其他常用的优化模型相比具有较高的优越性。     

Efficient solutions for weight-balanced partitioning problems

We prove polynomial-time solvability of a large class of clustering problems where a weighted set of items has to be partitioned into clusters with respect to some balancing constraints. The data points are weighted with respect to different features and the clusters adhere to given lower and upper bounds on the total weight of their points with respect to each of these features. Further the weight-contribution of a vector to a cluster can depend on the cluster it is assigned to. Our interest in these types of clustering problems is motivated by an application in land consolidation where the ability to perform this kind of balancing is crucial.Our framework maximizes an objective function that is convex in the summed-up utility of the items in each cluster. Despite hardness of convex maximization and many related problems, for fixed dimension and number of clusters, we are able to show that our clustering model is solvable in time polynomial in the number of items if the weight-balancing restrictions are defined using vectors from a fixed, finite domain. We conclude our discussion with a new, efficient model and algorithm for land consolidation.     

Entropy maximization model for the trip distribution problem with fuzzy and random parameters

Many trip distribution problems can be modeled as entropy maximization models with quadratic cost constraints. In this paper, the travel costs per unit flow between different zones are assumed to be given fuzzy variables and the trip productions at origins and trip attractions at destinations are assumed to be given random variables. For this case, an entropy maximization model with chance constraint is proposed, and is proved to be convex. In order to solve this model, fuzzy simulation, stochastic simulation and a genetic algorithm are integrated to produce a hybrid intelligent algorithm. Finally, a numerical example is presented to demonstrate the application of the model and the algorithm.     

A constrained min‐max algorithm for rival models of the same economic system

There are well established rival theories about the economy. These have, in turn, led to the development of rival models purporting to represent the economic system. The models are large systems of discrete-time nonlinear dynamic equations. Observed data of the real system does not, in general, provide sufficient information for statistical methods to invalidate all but one of the rival models. In such a circumstance, there is uncertainty about which model to use in the formulation of policy. Prudent policy design would suggest that a model-based policy should take into account all the rival models. This is achieved as a pooling of the models. The pooling that yields the policy which is robust to model choice is formulated as a constrained min-max problem. The minimization is over the decision variables and the maximization is over the rival models. Only equality constraints are considered.A successive quadratic programming algorithm is discussed for the solution of the min-max problem. The algorithm uses a stepsize strategy based on a differentiable penalty function for the constraints. Two alternative quadratic subproblems can be used. One is a quadratic min-max and the other a quadratic programming problem. The objective function of either subproblem includes a linear term which is dependent on the penalty function. The penalty parameter is determined at every iteration, using a strategy that ensures a descent property as well as the boundedness of the penalty term. The boundedness follows since the strategy is always satisfied for finite values of the parameter which needs to be increased a finite number of times.The global and local convergence of the algorithm is established. The conditions, involving projected Hessian approximations, are discussed under which the algorithm achieves unit stepsizes and subsequently Q-superlinear convergence.     

Bernoulli substitution in the Ramsey model: Optimal trajectories under control constraints

We consider a neoclassical (economic) growth model. A nonlinear Ramsey equation, modeling capital dynamics, in the case of Cobb-Douglas production function is reduced to the linear differential equation via a Bernoulli substitution. This considerably facilitates the search for a solution to the optimal growth problem with logarithmic preferences. The study deals with solving the corresponding infinite horizon optimal control problem. We consider a vector field of the Hamiltonian system in the Pontryagin maximum principle, taking into account control constraints. We prove the existence of two alternative steady states, depending on the constraints. A proposed algorithm for constructing growth trajectories combines methods of open-loop control and closed-loop regulatory control. For some levels of constraints and initial conditions, a closed-form solution is obtained. We also demonstrate the impact of technological change on the economic equilibrium dynamics. Results are supported by computer calculations.     

An Exact Penalty Method for Free Terminal Time Optimal Control Problem with Continuous Inequality Constraints

In this paper, we consider a class of optimal control problems with free terminal time and continuous inequality constraints. First, the problem is approximated by representing the control function as a piecewise-constant function. Then the continuous inequality constraints are transformed into terminal equality constraints for an auxiliary differential system. After these two steps, we transform the constrained optimization problem into a penalized problem with only box constraints on the decision variables using a novel exact penalty function. This penalized problem is then solved by a gradient-based optimization technique. Theoretical analysis proves that this penalty function has continuous derivatives, and for a sufficiently large and finite penalty parameter, its local minimizer is feasible in the sense that the continuous inequality constraints are satisfied. Furthermore, this local minimizer is also the local minimizer of the constrained problem. Numerical simulations on the range maximization for a hypersonic vehicle reentering the atmosphere subject to a heating constraint demonstrate the effectiveness of our method.     

Optimal inventory policies under decreasing cost functions via geometric programming

In this paper, we establish and analyze two economic order quantity (EOQ) based inventory models under total cost minimization and profit maximization via geometric programming (GP) techniques. Through GP, optimal solutions for both models are found and managerial implications on the optimal policy are determined through bounding and sensitivity analysis. We investigate the effects on the changes in the optimal order quantity and the demand per unit time according to varied parameters by studying optimality conditions. In addition, a comparative analysis between the total cost minimization model and the profit maximization model is conducted. By investigating the error in the optimal order quantity of these two models, several interesting economic implications and managerial insights can be observed.     

Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

Endogenous optimization fisheries models

This paper deals with a special class of fisheries models referred to as endogenous optimization models. The distinctive feature of these models is that behaviour of the agents in the model is not predetermined by exogenous behavioural rules. In endogenous optimization models, the model agents are merely furnished with objectives such as profit or utility maximization. Given these objectives and the various constraints determined by the state of the model at each point of time, the agents solve their maximization problem. The corresponding values of their control variables then constitute their behaviour.Having generated individual agents' behaviour by endogenous optimization, summing over agents yields aggregate behaviour. Aggregate behaviour must conform with the overall constraints of the model, be they physical or otherwise. Within the market system, individual behaviour or rather plans are made compatible via changes in relative prices. Therefore, outside equilibrium, behavioural plans must be repeatedly modified to become mutually compatible. This implies iteratively solving the maximization problem of a number of different agents. Endogenous optimization models therefore tend to be computationally very demanding.Clearly, the basic principles of endogenous optimization are just as applicable to any model involving maximizing agents.