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1.
大家都知道斐波那契(Fibonacci Number)关于兔子繁殖的故事.兔子每月的数量依次为一个数列:1,1,2,3,5,8,13,21,34,55,89,144,233,377…,设这个数列记为{Fn}:F1,F2,F3,F4,…,Fn,…,易知,F1=F2=1,从第3项起每一项都等于它的前两项的和,  相似文献   

2.
文[1]中,王方汉老师有如下猜想:当n为形如4m-1(mEN)的素数时,生成数列凡一l=(1,2,…,牛/,M,…,2,l)所确定的数列B,,具有遍历性.也就是说,设数列凡1=(r,12,…,r。-l),h为正整数,B。=(hi,bZ,…,b。),1=hi<bZ<…<b。且均为整数,设凡;与B。之间有如下映射关系:。。。。,;;=(1,2,…,宁,宁,…,2,1)且n为形如4m-1的素数时,数列B。各项被n除的余数恰是0,1,2,…,n-1的一个全排列.显然,数列B。=(hi,bZ,…,b。)各项被n除的余数恰是0,1,2,…,n一且的一个全排列等价于…  相似文献   

3.
设A为由K个相互独立的成败型元件组成的串联系统,第i个元件的可靠性pi,pi未知,i=1,2,…,K.设对第i个元件,对于给定的mi,有ni个巴斯卡试验数据:Xi1,Xi2,…,Xini,其中Xij表示对第i个元件进行试验,试验进行到mi次成功时所需要的试验次数j=1,2,…,ni,i=1,2,…,K.记Ti=Xi1+Xi2+…+Xini,i=1,2,…,k.本文研究基于统计量(T1,T2,…,Tk)求串联系统A的可靠性经典精确最优置信下限.  相似文献   

4.
设{Xn,n≥0}是可列非齐次马尔可夫链,Sn(i0,i1,…,im-1,ω)表示m元状态序组(i0,i1,…,im-1)在序列(X0,X1,…,Xm-1),(X1,X2,…,Xm),…,(Xn-1,Xn,…,Xn+m-2)中出现的次数.本文给出了关于Sn(i0,i1,…,im-1,ω)的一个对任意可列非齐次马尔可夫链普遍成立的随机偏差定理,即用不等式表示的一个强极限定理.  相似文献   

5.
关于方程xy+yz+zx=n的正整数解   总被引:1,自引:1,他引:0  
陈锡庚  乐茂华 《数学学报》1998,41(3):577-582
本文在广义Riemann猜想成立的条件下证明了:当且仅当正整数n=1,2,4,6,10,18,22,30,42,58,70,78,102,130,190,210,330,462时,方程xy+yz+zx=n无正整数解(x,y,z).  相似文献   

6.
沈杰 《数学通讯》2006,(9):42-43
在数学竞赛试题中经常出现形如max{min{f1(x1,X2,…,xn),f2(x1,x2,…,xn),…,fm(x1,x2,…,xn)}}或min{max{f1(x1,x2,…,xn),f2(x1,x2,…,xn),…,fm(x1,x2,…,xn)}}的多变元、多个函数的复合最值问题,即求函数最大值的最小值或求函数最小值的最大值。这类问题复杂、抽象且综合性强,解题时不能孤立地研究每一个函数,宜采用整体思想。  相似文献   

7.
全文约定:用Ω表示三维欧氏空间的多面体,其顶点集为{A1,A2,…,An},重心为G,令{A1,A2,…,An}={A’1,A’2,…,A’n},由Ω的任意k个顶点A’1,A’2,…,A’k组成的多面体为Ωjk,其重心为Gjk,由Ω的剩余n-k个顶点A’k+1,A'k+2,…,A’n所组成的多面体为Ωjk,其重心为Gjk(j=1,2,…,Cn^k).  相似文献   

8.
这个会非常重要,我很高兴,主动来参加这个会.近年在国内,关于教育方面的种种问题都在考虑,不仅在中国,在美国也一样,例如在加州围绕教学改革,打了一场"数学之战",最近这一年我与华中师大路刚同志谈的较多,无锡的徐沥泉老师,试着把数学方法论用于数学教学,做了很好的工作,数学教学问题的研究,郁很大的发展,英藉匈牙利人拉卡托斯,通过研究多面体的欧拉公式,以此为素材,为案例,搞助探论(heuristic,康宏逵先生的译法是准确的,有人译为探索法,亦可,译成"启发法"就在些勉强了),起初在一个杂志登出来,后来他的学生把它…  相似文献   

9.
不难验证,选择适当的空间直角坐标系,正四面体的四个顶点的坐标就可以设为:(a,a,a),(a,-a,-a),(-a,a,-a),(-a,-a,a),其中a〉0. 利用距离公式得:正四面体的棱长为2√2a. 利用上述正四面体顶点坐标的巧妙设法,本文给出四面体中的几个有趣的定值,供参考.  相似文献   

10.
关于C~∞-字的幂是C~∞-字的条件(Ⅰ)   总被引:1,自引:0,他引:1  
本文证明了关于C∞-字的导数的下列重要结果:对任意C∞-字w,若w2是C∞-字,则对任意的自然数k,一定存在u∈Σ使得Dk(w2)=Dk(w)uDk(w),其中Σ={Λ,1,2,12,21,11,22,112,211,221,122,121,212,1121,1211,1212,2121,2112,1221,1122,2211,11211}.这个结果对彻底解决沈传龙与黄允宝(1994)提出的对任意C∞-字w都有w3不是C∞-字的猜想将起关键作用  相似文献   

11.
龚舒  龚循华 《运筹学学报》2013,17(2):107-123
在局部凸空间中引进了向量均衡问题的强超有效解、C-强超有效解、弱超有效解, C-弱超有效解、齐次超有效解、 C-齐次超有效解的概念,并在局部凸空间中用极理论为工具讨论了向量均衡问题的 C-弱超有效解, C-超有效解, C-齐次超有效解,以及C-强超有效解的对偶形式. 又在赋范线性空间中讨论了向量均衡问题的以上各种超有效解之间的等价性,并且在赋范线性空间具正规锥的条件下讨论了向量均衡问题的以上各种超有效解的对偶形式. 作为它的应用,给出了向量优化问题各种超有效解的对偶形式.  相似文献   

12.
Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.  相似文献   

13.
In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector equilibrium problem. This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jinxing Province, China.  相似文献   

14.
In this paper, the integral bifurcation method is used to study a nonlinearly dispersive wave equation of Camassa-Holm equation type. Loop soliton solution and periodic loop soliton solution, solitary wave solution and solitary cusp wave solution, smooth periodic wave solution and non-smooth periodic wave solution of this equation are obtained, their dynamic characters are discussed. Some solutions have an interesting phenomenon that one solution admits multi-waves when parameters vary.  相似文献   

15.
基于多目标优化问题的McRow模型,该文确定了W-鲁棒有效解(也称为McRow最优解)与弱有效解、有效解以及真有效解的关系.首先, 针对确定多目标优化问题,研究了W-鲁棒有效解与各种精确解的关系.随后,针对随机多目标优化问题,引进McRow最优解的概念,给出了它与其余各种解的关系.算例表明,利用McRow模型所得到的解更具有鲁棒性.  相似文献   

16.
该文在L2中讨论了第一类算子方程Au=f当A-1无定义和A-1不是单值的情形下的不适定求解问题,给出了解存在的充要条件,当有解时,得到了形式解,多解时形式解就是最小范数解,并且得到了近似解表达式,给出了误差估计.  相似文献   

17.
We present a numerical method for computing a local Nash (saddle-point) solution to a zero-sum differential game for a nonlinear system. Given a solution estimate to the game, we define a subproblem, which is obtained from the original problem by linearizing its system dynamics around the solution estimate and expanding its payoff function to quadratic terms around the same solution estimate. We then apply the standard Riccati equation method to the linear-quadratic subproblem and compute its saddle solution. We then update the current solution estimate by adding the computed saddle solution of the subproblem multiplied by a small positive constant (a step size) to the current solution estimate for the original game. We repeat this process and successively generate better solution estimates. Our applications of this sequential method to air combat simulations demonstrate experimentally that the solution estimates converge to a local Nash (saddle) solution of the original game.  相似文献   

18.
In this paper, we focus on a treatment of a linear programming problem with an interval objective function. From the viewpoint of the achievement rate, a new solution concept, the maximin achievement rate solution, is proposed. Nice properties of this solution are shown: a maximin achievement rate solution is necessarily optimal when a necessarily optimal solution exists, and if not, then it is still a possibly optimal solution. An algorithm for a maximin achievement rate solution is proposed based on a relaxation procedure together with a simplex method. A numerical example is given to demonstrate the proposed solution algorithm.  相似文献   

19.
对(0,1)格上的无限Fuzzy关系方程,给出其可解的充要条件.利用可达解与不可达解的概念,给出方程存在可达解与不可达解的充要条件.进一步,在解集非空时,刻画了方程的解集的结构及性质.  相似文献   

20.
The Riemann solutions to the isentropic relativistic Euler system for Chaplygin gas with a small parameter are considered. Unlike the polytropic or barotropic gas cases, we find that firstly, as the parameter decreases to a certain critical number, the two-shock solution converges to a delta shock wave solution of the same system. Moreover, as the parameter goes to zero, that is, the pressure vanishes, the solution is nothing but the delta shock wave solution to the zero-pressure relativistic Euler system. Meanwhile, the two-rarefaction wave solution tends to the vacuum solution to the zero-pressure relativistic system, and the solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution to the zero-pressure relativistic system as pressure vanishes.  相似文献   

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