一类双指标线性递归关系的解公式

本文给出了一类双指标线性非齐次递归关系的显式解。     

一类递归关系模型的求解方法

递归关系不仅在数学中有广泛应用,而且在计算机算法设计与分析中也有广泛应用.本文对Josephus问题进行了推广,得到一类更广泛的递归关系模型.讨论了这类模型的求解方法,采用d-进制记数法,给出了这类递归关系模型的解.     

关于一类两个指标的齐次递归关系的解的结构

推广了屠规彰的结果［１］，得到了一类两个指标的常系数齐次递归关系的一个明显解公式．     

一种建立和求解递归关系的方法

本文利用有限差分算子和组合恒等式为工具，给出了线性递归关系中序列｛ａｎ｝求解的新方法，与原来特征多项式法比较，它有两点好处；其一是简化了计算的过程；其二是避免了建立递归关系时复杂的推导。     

一类递归关系存在L解的充要条件

一类递归关系存在Ｌ解的充要条件徐学文（华中师大数学系４３００７０）对于常系数线性齐次递归关系ａｋ是常数且ａｋ≠０．我们将方程为递归关系（１）的特征方程．并有如下结论．结论１若ｘ１．Ｘ２，…．ｘｐ是（２）的ｐ个不同的根，且ｘｉ的重数为λｉ（单根的重数为...     

一类带双指标常系数齐次递推关系的显式解

本文推广了屠规彰＾［１］的结果，得到了一类带双指标的常系数齐次递推关系的一个明显解公式。有关结果，不论是在理论还是在实际方面，都有一定的意义。     

关于无单位间隔组合数求法的注记

本文指出了文［１］中的错误，给出了其正确结果。     

一类递归小波神经网络的稳定性研究

在小波神经网络（WNNs）和递归神经网络（RNNs）的基础上,提出了一类递归小波神经网络（RWNNs）模型,它具有两种网络模型的优点A·D2根据Liapunov渐近稳定理论,对该模型的渐近稳定性进行了研究,并给出了相关的定理和公式．仿真结果表明该模型对非线性动态系统有良好的辨识效果．     

例说建构递归关系证明不等式的模式

众所周知 ,因题而异证明不等式的方法甚多 ,本文旨在介绍一种证明不等式的新方法———建构递归关系法 .为简明见 ,本文举三个例题说明三种典型的建构递归关系证明不等式的模式 .1　建构递归关系模式Ⅰ例 1　在△ＡＢＣ中 ,试证 : ｓｉｎＡ≤332 .(其中和号 关于Ａ ,Ｂ ,Ｃ轮换 ,下同 )证　先证 ｓｉｎＡ≤ ｓｉｎπ -Ａ2 .事实上ｓｉｎＡ ｓｉｎＢ =2ｓｉｎＡ Ｂ2 ｃｏｓＡ -Ｂ2≤ 2ｓｉｎＡ Ｂ2=2ｓｉｎπ -Ｃ2 (1)同理 :ｓｉｎＢ ｓｉｎＣ≤ 2ｓｉｎπ -Ａ2 (2 )ｓｉｎＣ ｓｉｎＡ≤ 2ｓｉｎπ -Ｂ2 (3)由 (1) (2 ) (3)整理得 …     

一类分布自由的回归函数递归核估计的相合性

本文讨论一种回归函数核估计的相合性,所得结果对所有ｘ的分布μ均成立。因此,分布是自由的。     

求解常系数线性齐次递推数列通项的生成函数法

通过引入生成函数,并利用其运算性质以及幂级数展开式,将常系数线性齐次递推数列通项的求解转化为对应特征方程的研究,根据特征根的不同情形,给出了数列通项的一般公式并举例加以应用.     

Double Series Identity and Some Laurent Type Hypergeometric Generating Relations

The main aim of this article is to obtain certain Laurent type hypergeometric generating relations. Using a general double series identity, Laurent type generating functions(in terms of Kampéde Fériet double hypergeometric function) are derived. Some known results obtained by the method of Lie groups and Lie algebras, are also modified here as special cases.     

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??This paper considers the expected penalty functions for a discrete semi-Markov risk model, which includes several existing risk models such as the compound binomial model (with time-correlated claims) and the compound Markov binomial model (with time-correlated claims) as special cases. Recursive formulae and the initial values for the discounted free penalty functions are derived in the two-state model by an easy method. We also give some applications of our results.     

On Functional Relations for the Alternating Analogues of Tornheim's Double Zeta Function

In this paper, new proofs of two functional relations for the alternating analogues of Tornheim's double zeta function are given. Using the functional relations, the author gives new proofs of some evaluation formulas found by Tsumura for these alternating series.     

递推数列极限的初等求法和收敛渐近性

借助实例介绍一些非线性递推数列，特别是分式线性递推数列极限的初等求法。就一般分式线性递推数列，明确其收敛渐近性，并通过相关推论展示其应用。     

The Flagged Double Schur Function

The double Schur function is a natural generalization of the factorial Schur function introduced by Biedenharn and Louck. It also arises as the symmetric double Schubert polynomial corresponding to a class of permutations called Grassmannian permutations introduced by A. Lascoux. We present a lattice path interpretation of the double Schur function based on a flagged determinantal definition, which readily leads to a tableau interpretation similar to the original tableau definition of the factorial Schur function. The main result of this paper is a combinatorial treatment of the flagged double Schur function in terms of the lattice path interpretations of divided difference operators. Finally, we find lattice path representations of formulas for the symplectic and orthogonal characters for sp(2n) and so(2n + 1) based on the tableau representations due to King and El-Shakaway, and Sundaram. Based on the lattice path interpretations, we obtain flagged determinantal formulas for these characters.     

Recursive calculation of moments in priority queues

We reconsider the discrete-time priority queue with two classes. The server serves high-priority customers as long as there are such customers, and only turns to the low-priority customers when there are no high-priority customers. Relying on a multivariate recursive extension of Faà di Bruno's formula, we find recursive equations to calculate the moments of the queue lengths. This allows for calculation of many more moments in much shorter time than conventionally possible.     

空中加油问题的递推模型与调度策略

首先对空中加油问题进行了分析,提取了相关性质,在此基础上建立了问题的递推模型.根据该模型,提出了一种启发式搜索算法.该算法计算复杂度低,适用性好.对应于辅机是否可以多次起飞,该算法分为两子算法.对这两种不同情况下的具体问题,设计了相关的优化函数.所有算法都在计算机中运行,并得到了相应结果.值得指出的是,提出的启发式搜索算法十分高效.对于问题1和问题2,该算法所得解是约束条件下的最优调度策略.对于问题3,问题4,问题5,该算法所得解逼近最优调度策略.