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1.
在振动论、控制论等方面,方程 f(x,) g(x)=p(t)都有很重要的应用.早在四、五十年代N.Lavinson,C.E.Langenhop和G.Siefert等人对此方程周期解的存在性就进行了研究.本文引进了两个辅助方程,定义了半能量函数.引用了[3—6]中的“等零斜率曲线”得到了一些结果. 1.引理及定义对下列方程:  相似文献   

2.
由系统x^..+f(x,x^.)x^.+g(x)=0的内侧轨线找外侧轨线,再由庞卡莱定理推知系x^..+f(x,x^.)x^.+g(x)=0存在稳定极限环.  相似文献   

3.
几类非线性微分方程闭轨线的不存在性   总被引:1,自引:0,他引:1  
赵丽琴  吕宝红 《数学进展》2007,36(4):476-484
本文研究几类非线性微分方程不存在闭轨线的条件,所得结果可用于判别方程■ f_1(x)■ f_2(x)■ g(x)=0和■ f(x,■)■ g(x)=0闭轨线的不存在性.  相似文献   

4.
方程=h(y)-F(x),=-g(x)的极限环存在定理   总被引:3,自引:0,他引:3  
在保证 Liénard 系统=y-F(x),=-g(x)(1)存在极限环的定理中, 定理要求的条件普遍认为是最少的.对作为定理的特例之定理,近年有不少加以改进和推广之结果.但对定理本身加以推广,除文[3]外不多见.我们讨论较(1)更广泛的系统(?)=h(y)-F(x),(?)=-g(x).(2)记 G(x)=integral from n=0 to x g(ξ)dξ,令 z=G(x),作变换,记 F_i(z)=F(G_i~(-1)(z)),其中x_1=G_1~(-1)(z),x_2=G_2~(-1)(z)分别是 z=G(x)在 x>0和 x<0时的反函数,在xg(x)>0的前提下,上述反函数存在,这时系统(2)变为  相似文献   

5.
首先看一道选择题:设全集为实数集R,M={x|f(x)=0},N={x|g(x)=0},那么集合P={x|f(x)g(x)=0}可表示为(A)M∩N;(B)M∪N;(C)M∪N;(D)M∪N.这是一道广为流传的题目.如1998年福州市高中毕业班质量检查卷(理科)第一题.参考答案都选(D).其实这是一道错题.例如,设f(x)=x2-1,g(x)=lg(x-1).则M={x|f(x)=0}={-1,1},N={x|g(x)=0}={2},M∪N={-1,1,2},但P={x|f(x)g(x)=0}={x|(x2-1)lg(x-1)=0}={2}≠M∪N.又如设f(x)=sinx,g(x)=cosx,M={x|f(x)=0}={x|x=kπ,k∈Z},N={x|g(x)=0}={x|cosx=0}={x|x=kπ π2,k∈Z}.M∪N={x|x=kπ或kπ π2,k∈Z}…  相似文献   

6.
利用Picard-Fuchs方程法得到了Abelian积分I(h)=∮_(Г_h)g(x,y)dx-f(x,y)dy的零点个数的上界,其中Γ_h是由H(x,y)=x~2+y~2+2xy+a(x~4+y~4)=h定义的闭轨线,a0,h∈(0,+∞),f(x,y)和g(x,y)是关于x和y的n次多项式.进而得到该系统极限环个数的上界.  相似文献   

7.
本文不作假设integral from 0 to ±∞ (f(x)+|g(x)|dx=±∞),得到方程(?)+f(x)(?)+g(?)=p(t)调和解的存在性,以及当integral from 0 to ±∞(g(x)dx=+∞时,其解的正向有界性和当g(x)=x,f(x)>0时,其调和解的渐近稳定性、唯一性。  相似文献   

8.
一类三次系统的极限环与分支问题   总被引:2,自引:0,他引:2  
讨论了E31系统中一类属于广义Liénard型方程x。 f1(x)x。 f2(x)x。2 g(x)=0的系统x。=yy。=-x δy nx2 mxy ly2 bxy2在m,n,l同号及b≠0情况下的极限环的存在惟一性与分支问题.  相似文献   

9.
本文§1讨论方程组 (?)=(?)(y)-F(x),(?)=-g(x)极限环的存在性,推广了作者的结果和方法. §2建立了各种类型的极限环存在唯一性定理.包括(E)的一切轨线是否绕原点打转,积分integral from 0 to ±∞(g(x)dx)和integral from 0 to ±∞(F′(x)dx)是否发散,奇点为一个及两个等情况;包括(E)的一切异于零的轨线当t→+∞时都趋于此唯一的极限环,以及可用以确定极限环的位置  相似文献   

10.
通过估计方程 g(x)=p(t)之解绕原点一周的时间,讨论了周期解存在的条件及调和解的存在唯一性。  相似文献   

11.
黄飞  陈晓剑 《运筹与管理》1999,8(3):106-109
企业集团是资本的集合体,它在资本本质的推动下,不断寻求资本增值的最大化。但是我国企业集团由于受经济体制转换期的影响,以及自身经验的不足,未能正确定位集团的发展领域,从而未能实现资本的增值。文章根据我国企业集团当前存在的问题,结合项目实践中的体会,讨论了如何正确认识资本增值域,以及如何正确选择与优化资本增值域  相似文献   

12.
The survey is devoted to line graphs and a new multivalued function called the line hypergraph. This function generalizes two classical concepts at once, namely the line graph and the dual hypergraph. In a certain sense, line graphs and dual hypergraphs are extreme values of the function . There are many publications about line graphs, but our considerations are restricted to papers concerning Krausz global characterization of line graphs or Whitneys theorem on edge isomorphisms. The survey covers almost all known results on the function because they are concentrated around Krausz and Whitneys theorems. These results provide evidence that the notion of the line hypergraph is quite natural. It enables one to unify the classical theorems on line graphs and to obtain their more general versions in a simpler way.  相似文献   

13.
人们对市场竞争状态的描述,大多从微观角度出发,研究微观主体自身在市场竞争中的地位和变化状态,本文从宏观角度出发,定义统计熵的性质和数学公式,从数学上证明统计熵的取值特征,进而分析出统计熵取值与市场竞争的关系,这种质量描述可为政府进行宏观调控,维持较好的市场结构提供科学依据。  相似文献   

14.
This paper evaluates a set of constructive heuristic methods developed to solve the novel Alternative Subgraphs Assembly Line Balancing Problem (ASALBP), which considers variants for different parts of a production or manufacturing process. Each variant is represented by a precedence subgraph that defines the tasks to be performed and their processing times. The proposed methods use priority rules and random choice to select the assembly subgraphs and to assign the tasks to the stations in order to minimize the number of required workstations. The methods are evaluated by a computational experiment based on medium- and large-scale benchmark problems. This work is supported by the Spanish MCyT project DPI2004-03472, co-financed by FEDER, and by a Venezuelan Grant by the University of Los Andes.  相似文献   

15.
In this paper, we introduced learning effect into assembly line balancing problems. In many realistic settings, the produced worker(s) (or machine(s)) develops continuously by repeated the same or similar activities. Therefore, the production time of product shortens if it is processed later. We show that polynomial solutions can be obtained for both simple assembly line balancing problem (SALBP) and U-type line balancing problem (ULBP) with learning effect.  相似文献   

16.
A new branch-and-bound algorithm is presented to solve the two-sided assembly line balancing problem of type 1 (TALB-1). First, a pair of two directly facing station is defined as a position, and then the two-sided assembly line (TAL) is relaxed to a one-sided assembly line (OAL). Some new lower bound on positions are computed, and dominance rules and reduction rules for the one-sided assembly line balancing problem of type 1 (OALB-1) are extended and incorporated into a station-oriented assignment procedure for the TALB-1 problem. Finally, the tests are carried out on a well-known benchmark set of problem instances, and experimental results demonstrate that the proposed procedure is efficient.  相似文献   

17.
Let A be the incidence matrix of lines and points of the classical projective plane PG(2, q) with q odd. With respect to a conic in PG(2, q), the matrix A is partitioned into 9 submatrices. The rank of each of these submatrices over Fq, the defining field of PG(2, q), is determined. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 224–236, 2010  相似文献   

18.
19.
本文给出了过任意空间Ck(k≥3)类光滑曲线的直纹面是可展曲面的充要条件.同时得到了该空间曲线为相应直纹面的曲率线,测地线和渐近曲线的充要条件  相似文献   

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