函数一致连续的一个充要条件

给出了一元函数在区间上一致连续的一个充分必要条件,举例说明了使用它来讨论函数在区间上的一致连续性将更为简单.     

用导数判别函数的一致连续性

本文主要给出了用导数判别函数在一般区间上一致连续的方法,并举例说明不可以建立关于一致连续的比较判别法．     

函数列在不同区间上一致收敛性的研究

函数列的一致收敛性与所讨论的区间有关.在区间的子区间或不同的区间上,函数列的一致收敛性表现如何呢?通过几个命题和几个实例,并利用几何画板可以帮助我们辨别函数列在不同区间上的一致收敛性.     

函数一致连续的比较判别法

在一般教材上对无穷区间上的函数,通常都采用定义的方法判别其一致连续性,对于复杂的函数,判别其是否一致连续一般来说常常比较困难.本文给出了判别无穷区间上函数一致连续性的一种比较判别法.     

一种具有不同形式效用值的群决策方法

研究了具有实数值、区间数和语言短语等三种形式效用值信息的群决策问题．首先给出了具有不同形式效用值的群决策问题的描述；然后给出了具有三种形式效用值的群决策方法的计算步骤．在该方法中，将不同形式的效用值均转化为区间数形式的效用值，通过加权法则得到每个方案的区间数群体综合效用值，并依据群体综合效用值进行方案的排序．最后通过给出一个算例说明了本给出的方法．     

函数一致连续性的判别新法

分别给出了各类区间上函数一致连续性的新的判定方法,使得一些复杂函数的一致连续性可以借助于较易判别出一致连续性的初等函数去判定.最后举例验证了方法的可行性和有效性.     

一道全国大学生数学竞赛决赛题的推广

解答一道全国大学生数学竞赛非数学类决赛试题,该试题涉及微分方程,定积分及一元函数求极限.针对以积分形式表示的函数求极限问题,将定义在[0,1]区间上特定的被积函数分别推广到单调连续函数、连续函数及[-1,1]区间上的连续函数这三种形式.利用夹逼准则、连续函数的定义及反常积分一致收敛的性质可证推广命题成立.     

用导数判别函数的一致连续性

本主要给出了用导数判别函数在一般区间上一致连续的方法．并举例说明不可以建立关于一致连续的比较判别法。     

幂级数在收敛区间端点收敛时的性质

讨论幂级数及其逐项积分、逐项求导后的级数在收敛区间端点收敛时的若干性质,给出它们之间敛散性的关系,并把连续性和逐项可积性推广到幂级数的收敛域上.     

判别函数项级数不一致收敛的一种方法

本文利用一致收敛函数列的一个性质,给出了判别函数项级数（包括函数列）不一致收敛的一种方法;这种方法为教科书所忽视,然而它对于一类函数列与函数项级数来说,却十分有用;特别对于一类函数项级数,判别的方法和技巧都有它们的特点,有一定启发性;１　一致收敛函数列的一个性质一致收敛函数列有一个不为人注意的性质：命题１　设各项连续的函数列｛Ｓｎ（ｘ）｝在区间Ｉ上一致收敛于Ｓ（ｘ）,则对Ｉ中任何以ｘ０（ｘ０∈Ｉ）为极限的数列｛ｘｎ｝,都有ｌｉｍｎ→∞Ｓｎ（ｘｎ）＝Ｓ（ｘ０）．（１）这个性质仅在某些数学分析教科书…     

Generation Supply Bidding in Perfectly Competitive Electricity Markets

This paper reports on the development of a comprehensive framework for the analysis and formulation of bids in competitive electricity markets. Competing entities submit offers of power and energy to meet the next day's load. We use the England and Wales Power Pool as the basis for the development of a very general competitive power pool (CPP) framework. The framework provides the basis for solving the CPP dispatcher problem and for specifying the optimal bidding strategies. The CPP dispatcher selects the winning bids for the right to serve load each period of the scheduling horizon. The dispatcher must commit sufficient generation to meet the forecasted load and reserve requirements throughout the scheduling horizon. All the unique constraints under which electrical generators operate including start-up and shut-down time restrictions, reserve requirements and unit output limits must be taken into account. We develop an analytical formulation of the problem faced by a bidder in the CPP by specifying a strategy that maximizes his profits. The optimal bidding strategy is solved analytically for the case of perfect competition. The study in this work takes into account the principal sources of uncertainty—the load forecast and the actions of the other competitors. The formulation and solution methodology effectively exploit a Lagrangian relaxation based approach. We have conducted a wide range of numerical studies; a sample of numerical results are presented to illustrate the robustness and superiority of the analytically developed bidding strategies.     

Multiple level production planning in rolling horizon assembly environments

In this paper, nine multiple level planning heuristics are evaluated to characterize how rolling horizon results relate to fixed horizon results in a deterministic demand environment. The weighted order cycle (WOC) is introduced as a single expression of cost structure within a multiple item bill of materials. When planning horizons are restated in terms of WOC (versus time buckets), it becomes apparent that the cost performance of the majority of the heuristics is essentially the same for fixed horizon and rolling horizon conditions when the planning horizon is at least two WOC in length. The horizon sensitive logic of the best two heuristics in cost performance also exhibited less nervousness then several horizon myopic rules, a counter intuitive result. An established multiple level cost modification technique was found to reduce the nervousness of single item rules, in addition to its original goal of schedule cost reduction. To gauge cost performance, Lagrangian relaxation of a binary formulation of the problem was used to find bounds within an average of 1% of the optimal solution cost of each simulation.     

轴对称Einstein-Maxwell-Dilaton-Axion黑洞熵与能斯特定理

该文利用Ｂｒｉｃｋ Ｗａｌｌ方法，计算轴对称Ｅｉｎｓｔｅｉｎ Ｍａｘｗｅｌｌ Ｄｉｌａｔｏｎ Ａｘｉｏｎ 黑洞背景下标量场的自由能和熵．结果表明，当黑洞具有内外视界时，所得熵不仅与外视界面积有关，而且也是内视界面积的函数．当内视界面积于零时，可回到已知结论．并且表明，用内外视界位置参量表达的熵，在黑洞辐射温度趋于绝对零度时，黑洞的熵也趋于零，它满足能斯特定理，可视为黑洞的普朗克绝对熵．     

On the single item fill rate for a finite horizon

We investigate expressions for expected item fill rate in a periodic inventory system. The typical treatment of fill rate found in many operations management texts assumes infinite horizon, independent and stationary demand. For the case when the horizon is finite, we show that the expected value of the actual fill rate is greater than the value given by the infinite horizon expression. The implication of our results is that an inventory manager in a finite horizon situation who uses the infinite horizon expression to set stocking levels will achieve a higher than desired expected fill rate at greater than necessary inventory expense.     

A stochastic programming approach for planning horizons of infinite horizon capacity planning problems

Planning horizon is a key issue in production planning. Different from previous approaches based on Markov Decision Processes, we study the planning horizon of capacity planning problems within the framework of stochastic programming. We first consider an infinite horizon stochastic capacity planning model involving a single resource, linear cost structure, and discrete distributions for general stochastic cost and demand data (non-Markovian and non-stationary). We give sufficient conditions for the existence of an optimal solution. Furthermore, we study the monotonicity property of the finite horizon approximation of the original problem. We show that, the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem, when the time horizon goes to infinity. These convergence results, together with the integrality of decision variables, imply the existence of a planning horizon. We also develop a useful formula to calculate an upper bound on the planning horizon. Then by decomposition, we show the existence of a planning horizon for a class of very general stochastic capacity planning problems, which have complicated decision structure.     

一类稳定的连续时间广义预测控制

引入无穷时域的1-范数性能指标,通过施加新的终端等式约束确定出无穷时域性能指标的一个上界,将不可解的优化问题转化为可解的优化问题,从而提出保证连续时间广义预测控制闭环稳定性的准无穷时域方法.仿真例子证明了算法的有效性.     

Three kinds of horizon-like hypersurface of a uniformly accelerating, non-stationary charged black hole

Three kinds of horizon-like hypersurface of a uniformly rectilinearly accelerating, non-stationary charged black hole: event horizon, apparent horizon and time-like limit surface are studied. The result is that the event horizon is apart from the time-like limit surface and the apparent horizon in the case where the black hole is charged, uniformly accelerating and its mass is varying (evaporating and accreting). Some other new results are also given. Project supported by the National Natural Science Foundation of China.     

Degeneracy in infinite horizon optimization

We consider sequential decision problems over an infinite horizon. The forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique. We show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy. We then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon. We also present a general near-optimal forecast horizon.This material is based on work supported by the National Science Foundation under Grants ECS-8409682 and ECS-8700836.     

Ergodic Control in L∞

The infinite horizon discounted L ^∞ problem is studied as the discount factor goes to zero. It is related to the limit of the finite horizon problem as the horizon becomes infinite. The deterministic problem with and without a running cost is considered.     

Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide

We show how infinite horizon stochastic optimal control problems can be solved via studying their finite horizon approximations. This often leads to analytical solutions for the infinite horizon problem by studying phase diagrams, even in cases where the complexity of the finite horizon case does not permit analytic solutions. Our approach can be applied to many problems in dynamic economics.