Recursion-transform method and potential formulae of the m×n cobweb and fan networks

In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.

Construction of Recursion Formulas for Lax Pairs of (2+1)-Dimensional Equation: Modified Generalized Dispersive Long Wave Equation

In this article, we study the Lax pairs of -dimensional equation: the modified generalized dispersive long wave (MGDLW) equation. Based on the well-known binary Darboux transformation, we dig out the recursion formulas of the first part of the Lax pairs. Then by further discussion and doing some revisional work, we make the recursion formulas fit for the second part of Lax pairs. At last, some solutions to the MGDLW equation are worked out by using the recursion formula.

Recursion Formulae for Obtaining Surfaces with Constant MeanCurvature inR^2,1

Though the Bǎcklund transformation on time-like surfaces with constant mean curvature surfaces in R^2,1 has been obtained, it is not easy to obtain corresponding surfaces because the procedure of solving the related integrable system cannot be avoided when the Bǎcklund transformation is used, For sake of this, in this article, some special work is done to reform the Bǎcklund transformation to a recursion formula, by which we can construct time-like surfaces with constant mean curvature form known ones just by quadrature procedure.

RECURSIVE FORMULA FOR CALCULATING THE CHROMATIC POLYNOMIAL OF A GRAPH BY VERTEX DELETION

A new recursive vertex-deleting formula for the computation of the chromatic polynomial of a graph is obtained in this paper. This algorithm is not only a good tool for further studying chromatic polynomials but also the fastest among all the algorithms for the computation of chromatic polynomials.

HURWITZ-HODGE INTEGRAL IDENTITIES FROM THE ORBIFOLD MARIO-VAFA FORMULA

In this paper, we present some polynomial identities of Hurwitz-Hodge integral. Subsequently, we present how to obtain some Hurwitz-Hodge integral identities from the polynomial identity. Lastly, we give a recursion formula for Hurwitz-Hodge integral （TbL λgλ1）ag.

非对称W-R递推公式

对于AR(p)模型,可用W-R递推公式估计其自回归系数.本文则将对称的W-R递推公式推广到非对称的情况,从而解决了用它来估计ARMA(p,q)模型的自回归系数的问题.

Some Formulas Involving Hypergeometric Functions in Four Variables

Several(generalized)hypergeometric functions and a variety of their extensions have been presented and investigated in the literature by many authors.In the present paper,we investigate four new hypergeometric functions in four variables and then establish several recursion formulas for these new functions.Also,some interesting particular cases and consequences of our results are discussed.

Formulas to Solve the （2＋1）—Dimensional System：The （2＋1）—Extension of Classical Boussinesq System

We deal with the (2 + 1)-extension of classical Boussinesq system,which can reduce to several meaningful(1 + 1)-dimensional systems.By studying its Lax pair,we put forward invariances of Lax pair at first,then a recursionformula depending on an arbitrary function is derived.At last,some solutions of the (2 + 1)-extension of classicalBoussinesq system are digged out by using the formula.

A Geometric Formulation and a Series Approach for Estimating π with Remarks on a Sumerian Tablet

A recursive method based on successive computations of perimeters of inscribed regular polygons for estimating π is formulated by employing the Pythagorean theorem alone without resorting to any trigonometric calculations. The approach is classical but the formulation of coupled recursion relations is new. Further, use of infinite series for computing π is explored by an improved version of Leibniz’s series expansion. Finally, some remarks with reference to π are made on a relatively recently rediscovered Sumerian tablet depicting geometric figures.

Generalized Series of Bernoulli Type

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

广义Fibonacci和Lucas四元数矩阵的行列式

借助递推关系研究了广义m阶Fibonacci和Lucas数,在经典行列式定义的基础上,利用排列组合以及逆序数理论,给出了广义m阶Fibonacci和Lucas四元数矩阵的行列式的定义,基于Binet型公式以及范德蒙行列式的性质,探讨了广义m阶Fibonacci和Lucas四元数矩阵的行列式的计算,特别地,当m=2,3,4时,给出了Fibonacci和Lucas四元数矩阵的行列式的具体值。

Construction of AFLT States by Reflection Method and Recursion Formula

The AFLT states|PY1,Y2has reflection symmetry,Sn|PY1,Y2=|PY2,Y2,nb=2P,where S is the screening charge.AFLT state can be constructed using this reflect symmetry.We propose a recursion formula for this construction.The recursion formula is factorized completely.

四种计算地震反应数值方法的比较研究

本文在简要总结了计算单自由度系统地震反应频域方法和时域方法的特点之后,按照统一的递归公式,系统地对计算单自由度体系的四种时域方法即中心差分方法、Newmark方法、Z变换方法、Duhamel逐步积分法进行了对比研究。通过递归系数b1和b2的不变性、传递函数的低频约束条件和相位特性以及数值分析等几个方面说明了上述方法各自的优缺点、相对精度和适用的范围。根据动力平衡方程的算子不变性,研究了上述方法的共性特征,揭示了相对位移、相对速度、相对加速度递归公式的内在联系,这表明只要知道相对位移的递归公式,相对速度、相对加速度的递归公式也就随之确定。在此基础上推荐了一套计算单自由度系统相对位移、相对速度、相对加速度地震反应的递归公式。

地震道反演面临的问题与进展

常规叠后地震道反演技术 ,受多种因素的影响。在实用中 ,很难获得准确的结果。从地震道反演的主要技术环节来看 ,造成地震道反演错误或解释陷井的原因主要集中在噪声、假设条件、子波提取、时深转换、低频分量、约束条件等方面。PatrickConnolly提出的弹性阻抗 (elasticimpedance)的思想 ,改进了反射系数垂直入射假设的错误 ,巧妙地将AVO问题与地震道反演相结合 ,将地震道反演技术向前推进了一步。在此基础上建立的适合常规叠后资料的、非零炮检距纵波资料的广义弹性阻抗 (generalizedelasticimpedance)模型不仅包含波阻抗 ,还包含了纵横波速度等岩性信息。进一步发展纵波与转换波弹性阻抗的联合反演 ,能更准确地获得纵横波速度信息 ,还能获得流体饱和度及渗透特性的信息 。

有界模型检测的优化

G(p)和G(p→F(q))是有界模型检测(bounded model checking,简称BMC)中的两个重要的常用模态算子.对验证G(p)和G(p→F(q))编码转换公式进行优化.通过分析当验证这些模态算子时FSM(finite state machine)的状态转移和线性时序逻辑(linear-time temporal logic,简称LTL)的语义特征.在现有的编码公式的基础上,给出了简洁、高效的递推公式,该公式有利于高效编码成SAT(satisfiability)实例;证明了递推公式和原转换公式的逻辑关系.通过实验比较分析,在生成SAT实例规模和易求解方面都优于BMC中求解这些模态算子的现有的两种重要方法AA_BMC和Timo_BMC.所给出的方法和思想对于BMC中验证其他模态算子时的编码优化也有参考价值.

单自由度系统地震动力反应的实时计算方法

本文对计算单自由度系统地震动力反应的频域方法和时域方法进行了分析比较,说明了目前时域方法所存在的问题,指出寻找一种在计算精度上与频域方法等价的时域算法是一个值得研究的重要课题。据此,本文提出了一套能较精确模拟单自由度系统传递函数的时域方法,其计算格式采用具有较高计算效率的递归格式。理论分析与数值试验表明,该方法具有精度优于其他时域算法、速度快的特点,可应用于强震观测台网中强地震动参数的实时计算。

起重机n阶伸缩臂架稳定性的递推公式及数值解法

基于纵横弯曲理论建立了n阶伸缩臂阶梯柱的微分方程组,并利用数学归纳法推导出n阶阶梯柱压杆稳定性的递推公式。针对递推公式中的超越方程,结合结构受力特征,列写补充方程,使用Levenberg-Marquardt数值最优化算法求解了具有n个未知数的超越方程组。利用此算法求解出的长度系数与GB/T3811—2008中的结果和ANSYS 17.0结果进行对比,结果表明,此算法的精度优于其他算法的精度,并且长度系数具有一定的非线性,因此在实用过程中,小范围内的线性插值是可行的。对于大截面的阶梯柱,使用线性插值计算,临界力的误差较大。

平面NURBS曲线的导矢及其等距线

本文首先给出了计算NURBS曲线导矢的递推公式,在此基础上,给出了生成平面NURBS曲线等距线的算法。

具有测量数据丢失的离散不确定时滞系统鲁棒Kalman滤波

研究了具有测量数据丢失的离散不确定时滞系统鲁棒Kalman滤波问题,其中时延存在于系统状态和观测值中.模型的不确定性通过在系统矩阵中引入随机参数扰动来表示,测量数据丢失现象则通过一个满足Bernoulli分布且统计特性已知的随机变量来描述.基于最小方差估计准则,利用射影性质和递归射影公式得到一个新的滤波器设计方法,并且保证了滤波器的维数与原系统相等.与传统的状态增广方法相比,当时延比较大时,该方法可以有效降低计算量.最后,给出一个仿真例子说明所提方法的有效性.

火电机组回热系统的通用物理模型及其汽水分布方程的解

在总结各种不同回热系统的特点及不同汽水分布方程的基础上,提出了结构简明的回热系统通用物理模型.在此基础上建立了回热系统汽水分布方程,并进而获得了该汽水分布方程的递推解.该递推解形式简单,可适应于各种不同的回热系统.通用物理模型及所得各级抽汽量的递推解为火电机组的热经济性分析和耗差分析提供了新的分析方法.