双(G/G',1/G)展开法求解(3+1)维mKdvZK方程和(3+1)维YTSF方程的新孤子解

研究(3+1)维修正Korteweg-devries-Zakharov-Kuznestsov方程和(3+1)维Yu-Toda-Sassa-Fukuymama方程的解。首先利用行波变换和代入变换将(3+1)维mKdvZKE和(3+1)维YTSFE转化为常微分方程,而后选择双(G/G’,1/G)展开法得到多个与现有的文献不同的精确解。本方法丰富了(3+1)维修正Korteweg-devries-Zakharov-Kuznestsov方程和(3+1)维Yu-Toda-Sassa-Fukuymama方程的解,说明所用方法和过程对构造非线性演化方程的精确解具有科学性和通用性。

The (G'/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations

The （G＇/G, 1/G）-expansion method for finding exact travelling wave solutions of nonlinear evolution equations, which can be thought of as an extension of the （G＇/G）-expansion method proposed recently, is presented. By using this method abundant travelling wave so- lutions with arbitrary parameters of the Zakharov equations are successfully obtained. When the parameters are replaced by special values, the well-known solitary wave solutions of the equations are rediscovered from the travelling waves.

A new approach for selecting best development face ventilation mode based on G1-coefficient of variation method

The current popular methods for decision making and project optimisation in mine ventilation contain a number of deficiencies as they are solely based on either subjective knowledge or objective information.This paper presents a new approach to rank the alternatives by G1-coefficient of variation method.The focus of this approach is the use of the combination weighing,which is able to compensate for the deficiencies in the method of evaluation index single weighing.In the case study,an appropriate evaluation index system was established to determine the evaluation value of each ventilation mode.Then the proposed approach was used to select the best development face ventilation mode.The result shows that the proposed approach is able to rank the alternative development face ventilation mode reasonably,the combination weighing method had the advantages of both subjective and objective weighing methods in that it took into consideration of both the experience and wisdom of experts,and the new changes in objective conditions.This approach provides a more reasonable and reliable procedure to analyse and evaluate different ventilation modes.

Analytical Treatment of the Evolutionary (1 + 1)-Dimensional Combined KdV-mKdV Equation via the Novel (G'/G)-Expansion Method

The novel (G'/G)-expansion method is a powerful and simple technique for finding exact traveling wave solutions to nonlinear evolution equations (NLEEs). In this article, we study explicit exact traveling wave solutions for the (1 + 1)-dimensional combined KdV-mKdV equation by using the novel (G'/G)-expansion method. Consequently, various traveling wave solutions patterns including solitary wave solutions, periodic solutions, and kinks are detected and exhibited.

Exact Solutions of (2+1)-Dimensional Boiti-Leon-Pempinelle Equation with (G'/G)-Expansion Method

In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.

带有两类故障和延迟维修的M/G/1重试排队

研究带两类故障和延迟维修的M/G/1重试排队模型。针对系统平稳性及其平稳分布的问题,首先采用嵌入马尔科夫链和补充变量法得到稳态条件和平稳概率分布,然后用概率母函数研究系统队长分布,最后通过数值算例分析参数对系统性能指标的影响。

Exact Traveling Wave Solutions for the (1 + 1)-Dimensional Compound KdVB Equation via the Novel (G'/G)-Expansion Method

In this work, while applying a new and novel (G'/G)-expansion version technique, we identify four families of the traveling wave solutions to the (1 + 1)-dimensional compound KdVB equation. The exact solutions are derived, in terms of hyperbolic, trigonometric and rational functions, involving various parameters. When the parameters are tuned to special values, both solitary, and periodic wave models are distinguished. State of the art symbolic algebra graphical representations and dynamical interpretations of the obtained solutions physics are provided and discussed. This in turn ends up revealing salient solutions features and demonstrating the used method efficiency.

属性识别和G1-熵权法在电能质量评价中的应用

利用属性识别理论,根据电能质量指标客观数据的测度属性建立指标测度评价矩阵。利用指标客观权重与指标测度矩阵相关的属性,提出利用G1-熵权法来确定各个电能质量指标的综合权重系数,克服了单一赋权法的片面性,减小了计算量。实例分析表明,该方法得到的评价结果更加客观、准确和全面。

基于G_1法的飞行疲劳综合评价指标体系研究

为综合控制并评价飞行疲劳风险,通过对疲劳影响因素的深入分析,运用层次分析法(AHP)确定疲劳风险评价指标,依据G1法编制专家调查问卷,采用专家独立调查方法对指标进行判断,根据G1法确定各指标权重,建立飞行疲劳综合评价指标体系,实现对疲劳风险的量化综合评价。结果表明:运用G1法能有效地综合利用影响疲劳的各种信息评价飞行员的疲劳状况,该指标体系与现有控制飞行疲劳风险的影响因素吻合较好,可以作为进一步实现疲劳风险量化的基础。

优先权的N策略M/G/1排队在通信网中的应用

分析通信网中带有两个优先权的N策略M/G/1排队系统的性能,利用补充变量法对此排队系统的状态转移方程进行分析,获得了带有两个优先权的N策略M/G/1排队系统的队长分布母函数及通信网缓冲器中的平均队长,并对两个优先权排队进一步讨论。

利用(G′/G)-展开法求解2+1维破裂孤子方程组

利用最近提出的(G′/G)-展开法,并借助于计算机代数系统Mathematica,获得了2+1维破裂孤子方程组丰富的显式行波解,分别以含两个任意参数的双曲函数、三角函数和有理函数表示,该方法也适用于其它非线性波方程(组)。

(G'/G,1/G)-展开法在求解非线性演化方程中的应用

(G'/G,1/G)-展开法是求解数学物理问题中非线性演化方程新行波解的一种直接而有效的方法,可以看作是(G'/G)-展开法的扩展方法。利用该方法,Kd V方程和Burgers方程的含任意参数的新行波解被成功求解。当参数赋以特殊值时,从行波解中可以获得著名的孤立波解。

(G^(k+1)/G^k)展开法以及KdV方程的行波解（英文）

本文中,(G(k+1)/G(k))展开法被首次提出,其中k为非负整数,并且G=G(ξ)满足k+2阶常系数齐次线性微分方程(LODE),同时给出表达式(G(k+1)/G(k))的解析公式,并由此得到非线性发展方程的双曲函数解、有理函数解及三角函数周期解,最后给出一个利用(G(k+1)/G(k))展开法求解KdV方程的实例.

用(1/G)-展开法求修正Kawahara方程的孤立波解

利用(1/G)-展开法,借助于计算机代数系统M athem atica,获得了修正Kawahara方程的孤立波解,这里的G=G(ξ)是一阶线性常微分方程的解,(1/G)-展开法可看作是(G′/G)-展开法的一种特殊情形。

服务速度有变化的可修M/G(M/G)/1排队系统

通过对系统中顾客数设置门限 N ,研究了当服务台对某顾客服务完毕时如发现系统中顾客数超过门限N时就提高服务速度的 M/G( M/G) /1排队系统模型 ,通过 L -变换、母函数及补充变量法得到了瞬态队长分布、稳态队长分布及可靠度等指标 .

利用改进的(G′/G)-展开法求广义的(2+1)维Boussinesq方程的精确解

利用改进的(G′/G)-展开法,求广义的(2+1)维Boussinesq方程的精确解,得到了该方程含有较多任意参数的用双曲函数、三角函数和有理函数表示的精确解,当双曲函数表示的行波解中参数取特殊值时,便得到广义的(2+1)维Boussinesq方程的孤立波解.

应用(1/G)-展开法求解五阶KdV方程(英文)

本篇论文首次提出(1/G)-展开法,用于求解非线性演化方程的行波解.将该法应用于五阶KdV方程的求解,当参数满足一定条件时,该方程可化为Sawada-Kotera(SK)方程、Caudrey-Dodd-Gibbon(CDG)方程、Kaup-Kupershmidt(KK)方程、Lax方程和Ito方程.其解可被表示为含两个任意参数的双曲函数解和三角函数解,作为示例,文中仅给出了SK方程和Ito方程的行波解.(1/G)-展开法具有直接、简捷与基本的特点,可以适用于数学物理中其它非线性演化方程的求解.

构造非线性偏微分方程精确解的(1/G)-展开法

精确解是研究非线性偏微分方程的重要课题。许多自然现象都可以由非线性偏微分方程的精确解描述。利用(1/G)-展开法,并借助符号计算系统Maple,获得了Sharma-Tasso-Olver方程和Ablowitz-Kaup-Newell-Segur水波方程的精确解,其中包括一些新的结果。未来这一方法也可用来构造其他非线性偏微分方程的精确解。

基于G1法的高校财务风险预警指标体系权重确定

随着近几年高校招生规模的扩大、投资的增加、举债经营风险和校办产业风险的加大等新问题对高校总体财务状况的影响越来越大。针对这些问题,文章根据高校财务风险评价指标构建原则,构建一套高校财务风险预警指标体系。在此基础上,运用G1法确定指标权重,建立财务风险预警指数计算模型,使管理者能方便、快捷计算出风险综合指数,判断财务状况,作出正确决策。

学生发展导向的高校创新创业教育质量评价研究--基于群组G1法

高校创新创业教育质量评价对于高校推进创新创业教育改革、提升创新创业教育质量具有重大意义。将学生发展作为创新创业教育的出发点和落脚点,以学生发展为导向,建立高校创新创业教育质量评价指标体系,并采用群组G1法和非线性加权法完成了评价指标的赋权和评价模型的构建。最后,根据评价指标的赋权结果,得出各指标对高校创新创业教育质量的影响程度,并提出质量提升的具体建议。