3dsmax在高等数学数列极限概念动画演示教学应用

高等数学是一门比较抽象的学科,极限概念是高等数学中最基本最重要的概念之一,是高等数学入门的难点．本文就教学中运用3dsmax制作高等数学数列极限概念图形动画演示,帮助学生突破数列极限概念的难点进行了探讨。     

利用洛必达法则来求数列的极限

我们知道,利用洛必达法则计算极限很方便,但是用洛必达法则必须满足可导这一条件,而数列就连连续这一条件都不满足,更谈不上可导了。但我们知道,数列是函数的特殊情况,利用这一点,我们可以先求函数的极限,从而求得数列的极限。这体现了由一般到特殊的数学思想。本文将对此方法做进一步的总结和探讨。     

关于微积分中无穷级数讲解的几点看法

在微积分课程的教学当中无穷级数是一个重要的组成部分,但由于与其它章节的联系性不强而相对独立且比较抽象,所以学生在学习无穷级数时常感到比较困难。本文给出了几点看法：（1）重视求数列极限的复习;（2）归纳判别正项级数收敛性的方法。     

函数极限计算的几种方法与应用

极限问题是数学领域中最基本并且最重要的问题之一,无论是在数学分析和高等数学中,还是在微积分中起非常重要的作用。怎样使求极限变得更容易,这是绝大多数学生头疼的问题,由于计算极限的方法很多,所以有时学生都不知道在遇到什么样的问题用哪一种方法最好用。本文介绍几种求极限的方法,并给出相应的应用举例,以便学生更好地掌握关于极限的知识。     

计算机上的“活”函数

函数是中学数学极为重要的内容,贯穿高中数学的始终.方程、不等式、数列、极限、导数与微分等内容都是以函数为中心的,还渗透到三角、立体几何、解析几何,更有内容丰富的函数实际应用性问题,跨学科的综合应用是函数的鲜明特征.     

基于硬币实验的圆周率近似值计算

圆周率π的近似值计算,历史悠久,公式繁多.本文从硬币实验出发,运用数列极限知识让学生亲历体验π的近似值计算过程,领悟思想方法,感受数学魅力。     

数列排列和概率问题与程序的关系

在中学数学中,会遇到数列问题,比如等比数列、等差数列、斐波拉契数列以及这些数列的求和问题,当然还会遇到数列排列、事件发生的概率等典型问题.在做这些题目时,发现这其中有些问题是属于规律性的,而有些是属于随机的.如果有一个类似于经常使用的计算器的工具来帮助人们解决这些问题,就会简单快捷的多.将从程序方面对上述常见问题进行分析,主要说明方法并举例来阐述.     

计算机上的“活”函数

正函数是中学数学极为重要的内容,贯穿高中数学的始终。方程、不等式、数列、极限、导数与微分等内容都是以函数为中心的,还渗透到三角、立体几何、解析几何,更有内容丰富的函     

倒立摆系统中强化学习的极限环问题

倒立摆系统是强化学习的一种重要的应用领域。首先分析指出在倒立摆系统中,常用的强化学习算法存在着极限环问题,算法无法正确收敛、控制策略不稳定。但是由于在简单的一级倒立摆系统中算法的控制策略不稳定的现象还不明显,因此极限环问题常常被忽视。针对强化学习算法中极限环问题,提出基于动作连续性准则的强化学习算法。算法采用修正强化信号和改进探索策略的方法克服极限环对倒立摆系统的影响。将提出的算法用于二级倒立摆的实际系统控制中,实验结果证明算法不仅能成功控制倒立摆,而且可以保持控制策略的稳定。     

激光样式问题的多种算法及其分析

斐波拉契数列问题是使用递归算法的典型问题。激光样式问题属于斐波拉契数列问题。激光样式问题的各种算法、算法的优化和非递归化转换,对所有斐波拉契数列问题都具有借鉴意义。本文对激光样式问题提出两种思路,每一种思路又提出多种算法。并通过对多种算法的分析、程序设计及其效率分析,总结该类问题的较优算法。     

Some results on weak convergence of jump Markov processes and their stability properties

The problem is motivated by stochastic modeling of chemical reactions, but it is studied in a general framework. The fluctuations of a sequence of jump Markov processes around their deterministic limit are considered. It is shown that, if the deterministic limit has an equilibrium point which is at least k-asymptotically stable, the sequence of fluctuations (suitably rescaled) converges to a diffusion process. Moreover, for a particular choice of the rescaling factor, the limit diffusion admits a unique stationary distribution.     

优先归纳逻辑程序的极限行为

虽然对归纳逻辑程序的极限行为至今并没有深入的研究，但是通常在分析正在执行的增量式或在线归纳学习算法时，必须考虑这种程序的极限行为．某些归纳学习算法如果不考虑极限行为可能运行到最后会发生错误．如果给定一个递增的例子集合序列，一个归纳逻辑程序会产生一个相应的具有集合论极限的Horn逻辑程序序列，则此归纳逻辑程序是收敛的，并且如果该Horn逻辑程序序列关于例子集合序列的极限是极限正确的，则此归纳逻辑程序是极限正确的，还说明GOLEM系统不是极限正确的．为了解决这个问题，提出了一个极限正确的称为优先GOLEM系统的归纳逻辑系统，并证明了在一定的限制下，优先GOLEM系统的算法是极限正确的．     

基于标记逻辑的非单调推理（Ⅰ）

我们把标记逻辑定义在一个特殊双格上,通过比较标记选取结论,从而同时捕捉超协调（容错）推理和非单调推理．本文介绍标记逻辑程序的句法与语义构造,提出诱导序列及其极限的概念,给出极限存在的等价条件,并证明一个重要结果：诱导序列基本定理,它是后续讨论的基础．     

卸货顺序约束的单容器矩形装箱问题

解决了基于模拟退火算法求解带卸货顺序约束的单容器装箱问题。提出的方法采用了改进的序列对表示对解空间进行压缩。研究了满足卸货顺序约束的序列对的新性质,以及基于模块删除与插入的新解产生算法,并将该算法集成于模拟退火中。实验结果证明了该模拟退火算法对卸货顺序约束的单容器矩形装箱问题的有效性。     

中国象棋机器博弈的时间自适应分配策略研究

时间分配问题在象棋比赛中是十分重要的策略问题，在机器博弈中也是如此。好的策略可以把宝贵的时间资源用在“刀刃”上；此外，好的时间分配策略还要有好的自适应性，亦即对大多数比赛，无论其限时的长短、步数的多寡，该策略都能合理利用时间。在分析和建立了时间分配的数学模型的基础上，介绍了自适应时间分配与调整的策略和算法。时间分配问题与搜索和评估密切相关，也影响着机器博弈的风格。     

采用观测器的双线性系统最优跟踪控制器设计

研究一类参考输入由外系统描述的双线性系统的最优输出跟踪控制问题.利用逐次逼近的方法,首先构造一族非齐次线性两点边值问题序列将原非线性两点边值问题解耦;然后迭代求解伴随向量的序列,得到由状态向量的线性解析函数和以伴随向量的极限形式给出的非线性部分的补偿项组成的最优输出跟踪控制律.通过构造降维观测器重构外系统的状态,解决了最优输出跟踪控制律的物理可实现问题仿真结果表明了该方法的有效性.     

Online call control in cellular networks revisited

Wireless communication networks based on frequency division multiplexing (FDM in short) play an important role in the field of communications, in which each request can be satisfied by assigning a frequency. To avoid interference, each assigned frequency must be different from the neighboring assigned frequencies. Since frequencies are scarce resources, the main problem in wireless networks is how to fully utilize the given bandwidth of frequencies. In this paper, we consider the online call control problem. Given a fixed bandwidth of frequencies and a sequence of communication requests arriving over time, each request must be either satisfied immediately after its arrival by assigning an available frequency, or rejected. The objective of the call control problem is to maximize the number of accepted requests. We study the asymptotic performance of this problem, i.e., the number of requests in the sequence and the bandwidth of frequencies are very large. In this paper, we give a 7/3-competitive algorithm, say CACO, for the call control problem in cellular networks, improving the previous 2.5-competitive result, and show that CACO is best possible among a class of HYBRID algorithms.     

A Heuristic Algorithm for the Fabric Spreading and Cutting Problem in Apparel Factories

We study the fabric spreading and cutting problem in apparel factories. For the sake of saving the material costs, the cutting requirement should be met exactly without producing additional garment components. For reducing the production costs, the number of lays that corresponds to the frequency of using the cutting beds should be minimized. We propose an iterated greedy algorithm for solving the fabric spreading and cutting problem. This algorithm contains a constructive procedure and an improving loop. Firstly the constructive procedure creates a set of lays in sequence, and then the improving loop tries to pick each lay from the lay set and rearrange the remaining lays into a smaller lay set. The improving loop will run until it cannot obtain any smaller lay set or the time limit is due. The experiment results on 500 cases show that the proposed algorithm is effective and efficient.      

Positive and compartmental systems

When dealing with compartmental systems, an important question is: given an experiment, i.e., an input-output sequence, and supposing there is no error in the data, is the sequence compatible with the compartmental assumption? If the process under analysis is linear, then the previous question is obviously equivalent to asking whether a given transfer function is that of a compartmental system. In this note we provide an answer to the latter question giving necessary and sufficient conditions for a transfer function to be that of a compartmental system of some finite order (i.e., number of compartments). Another problem tackled in this note originates from the observation that in many cases one wants to determine the number of compartments involved in the process. In this note we report a step toward the solution of this fundamental problem by proving necessary and sufficient conditions for a given third order transfer function with real poles to be that of a compartmental system with three compartments     

Feedback Control of Limit Cycle Amplitudes from A Frequency Domain Approach

In this paper, a problem in feedback control of limit cycle amplitudes is studied. A graphical approach for this bifurcation control problem is developed by means of higher-order harmonic balance approximations for both amplitude and frequency of the system oscillatory outputs. The approach starts with the familiar Hopf bifurcation mechanism, and employs the second, fourth, and sixth-order harmonic balance approximations to generate a sequence of graphical tests for convergence analysis of the system oscillatory outputs. This sequential graphical testing leads to accurate approximations of limit cycles of small amplitudes in the system outputs. Degenerate Hopf bifurcation theory is used to formulate an appropriate control objective of capturing small-amplitude limit cycles, which can avoid reaching unstable equilibria or other undesirable limit sets. A rich cubic planar model is presented for illustration of the proposed control method.