由概率问题导出的两个等价递推公式及其应用

利用某些概率问题可以发现等价的递推公式.以下先从概率模型入手,得到等价的递推公式,再将其进行推广,并在推导Fibonac ci数列通项公式中加以应用.1.由概率模型导出的两个等价递推式设有甲、乙、丙、丁四个人进行传球练习,     

解高考数列问题需要八种意识

数列是高中数学的重要内容之一 ,又是高考考查的重点。由于数列问题涉及的知识点多、覆盖面广 ,且综合性较强 ,因此不少同学在解数列问题时 ,常常因缺乏必要的解题意识 ,短时间内难以找到正确的解题方法 ,而导致解答过程繁难、运算量大 ,甚至半途而废。本文将结合某些高考题或高考模拟题 ,谈谈解高考数列问题需要的八种意识 ,供大家参考。一、递推意识由于数列可以看作是正整数n的函数 ,因此对于以递推关系式出现的问题 ,常常可以从递推关系式中的n =1 ,2 ,3 ,…入手 ,得到一系列的等式 ,通过对它们进行或加、或减、或乘、或除等运算 ,使问…     

关于一类递推数列极限的求法的注解

证明了一类递推数列xn 1=(xn b)/(xn c)(ac≠b,n=1,2,……)的收敛性,并给出这类数列的一些性质.本文所得结果推广和包含了文[1]的相应结果.     

递推数列问题中的函数策略探究

数列是一类特殊的函数,二者之间有着密切联系．对于某些数列问题,应用函数策略进行研究,可取得事半功倍之效．     

利用不动点方法求递推数列的极限

求递推数列的极限是数列极限中一个非常重要的内容,常用单调有界定理,压缩映射原理解决.本文利用不动点给出该类数列的解法,在解决复杂问题中有一定的优越性.     

一个极限问题的两种解法

针对第13届美国普特南数学竞赛的一道数列极限题,将原本不具有单调性质的数列转化为单调数列,并利用单调有界原理及数学归纳法,得出其极限,此方法可推广用以解决同类的一般性数列求极限.此外,此题也可采用不动点原理,简化计算过程.     

三类数列递推公式的相互转化

笔者在研究竞赛数列问题时,发现了一个令人觉得不可思议的结论：三类形式上貌似截然不同的递推公式,竟然可以互相转化,这三类数列实质上是等价的递推数列。     

一类递推数列极限的求法

讨论了一类递推数列xn 1=axn bxn c(ac≠b,n=1,2…)的极限求法,并举例说明.     

由几种典型的递推式构造新数列求通项的方法

已知数列的递推式求其通项公式的方法一般有三种 :“归纳、猜想、证明”、“错位相消 (约 )法”以及构造法 .本文将针对六种最典型的递推式 ,谈谈构造新数列求数列的通项公式的方法 .类型 1　ａｎ +1=ｑａｎ+Ｐｋｎｋ+Ｐｋ - 1ｎｋ- 1+… +Ｐ1ｎ +Ｐ0 (ｑ≠ 0 ,1,ｋ∈Ｎ) .例 1　数列 {ａｎ}中 ,ａ1=1,ａｎ +1=2ａｎ+ 3,求ａｎ.解　令ａｎ +1+ｘ =2 (ａｎ+ｘ) ,可得ｘ =3,故ａｎ+1+ 3=2 (ａｎ+ 3) .又ａ1+ 3=4 ,可见 ,数列 {ａｎ+ 3}是首项为 4 ,以 2为公比的等比数列 ,从而 ,ａｎ+ 3=4·2 ｎ - 1,得ａｎ=2 ｎ +1- 3.例 2　数列 {ａｎ}中 ,…     

GARCH过程的同期聚合

我们首先提出由独立一元变量GARCH过程的同期聚合可得到一个弱GARCH过程 (见Drost和Nijman( 1 993) )过程 ,接着分析同期聚合的参数同原始过程参数间的相依性 ,指出聚合后方差参数依赖于原始方差和参数的峰度 .     

Towards Modeling the Curing Processes of Thermosets

This contribution presents a newly developed phenomenological model to describe the curing processes of thermosets undergoing small strain deformations [1]. The governing equations are derived from a number of physical and chemical assumptions. Some numerical examples demonstrate the model's capability to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Weak Regeneration in Modeling of Queueing Processes

A survey of recent results on weak regeneration in queueing processes is given in which an embedded process of regeneration points is renewal, but unlike classical regeneration, a dependence between adjacent cycles is allowed. We develop a unified two-step approach to stability analysis based on a characterization of the limit behavior of the forward renewal time. This employs an extended construction (initially proposed by Foss and Kalashnikov [13]), which is widely used to transform an original one-dependent regenerative process into weakly regenerative one. It is shown that the approach simplifies stability analysis of many queuing processes. (The tightness of the queueing processes plays an important role in the proofs.) In particular, we consider both well-known classical queues and multi-server queues with regenerative input and non-identical servers. Included is a stability analysis of a feed-forward network with regenerative input and non-identical servers in the nodes.     

工程管理的马尔可夫骨架过程建模

在以前,一个工程项目的进程的管理问题在各工段的施工时间为相互独立且都服从负指数分布的假设下通过一个网络图化为对一个马尔可夫链的控制和优化的研究.本文在一般情况下(放弃对各工程段的时间服从负指数分布的假设)把工程项目进程的管理问题化为对一个马尔可夫骨架过程的控制和优化问题.     

On Modeling Change Points in Non-Homogeneous Poisson Processes

Failures in repairable systems are often described by means of non-homogeneous Poisson processes, identified by their intensity and mean value functions. Intervention on the systems are likely to modify their reliability, and changes in intensities and mean value functions are therefore induced. We consider different scenarios in which interventions take places and propose models describing each of them. Bayesian analyses, relying on Markov-chain Monte Carlo methods, are illustrated along with applications to simulated and real, widely-known, data.     

PROMOT: A Modeling Tool for Chemical Processes

The novel process modeling tool PROMOT supports the object-oriented modeling of chemical processes for the simulation environment DIVA. In PROMOT, differential-algebraic process models can be built by aggregating structural and behavioral modeling entities that represent the topological structure or the dynamic and steady-state behavior, respectively, of the investigated chemical processes. Process models and their modeling entities may be defined either in an object-oriented modeling language or with a graphical user interface. This paper discusses the modeling concept, the modeling language, the knowledge representation aspects, and the implementation of PROMOT.     

Mathematical Modeling of Magnetohydrodynamic Processes in an Aluminum Electrolyzer

We model the electrolysis of aluminum in specific electrolysis baths. A model of the physical process is proposed, allowing for the specific bath design, including the state of the bottom surface. The mathematical model utilizes the information capabilities of the Navier–Stokes equations written for the metal and the electrolyte media. The multidimensional system of equations enables us to consider the magnetohydrodynamic processes in two media and the interaction of the media. The problem is solved numerically. The calculations simulate the interface dynamics and the distribution of velocities and currents in the middle layer in both media. The numerical results are compared with physical experiments.     

Multiphase FEM Modeling of Infiltration Processes in Cohesionless Soils

The aim of this work is to develop a continuum multiphase model to describe infiltration processes for cohesionless soils. For this purpose, a Representative Volume Element (RVE) is considered and described by the continuum mixture theory extended by the concept of volume fractions (Theory of Porous Media – TPM). The thermodynamically consistent TPM is a macroscopical multiphase modeling approach, extended from classical single-phase continuum mechanics. Futhermore a 1-dim example for an infiltration problem is presented. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)