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许德祥 《湖南师范大学教育科学学报》2000,(5)
设S={x1,x2 ,…xn}是一个由非零整数且｜xi ≠｜xj (i≠j,1≤i,j≤n)组成的集合 .我们先定义了在集S上的广义GCD(GGCD)矩阵和广义LCM(GLCM)矩阵 ,研究了定义在广义factor closed集和广义gcd closed集S上的GGCD矩阵和GLCM矩阵的行列式 相似文献
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本文在贵刊文[1]的基础上,探讨平面闭折线A(n)关于点P的k号心与它的一级顶点子集V j(1≤j≤n)关于点P的k号心之间的关系.定理1设闭折线A(n)关于P的k号心为Q.闭折线A(n)一级顶点子集V j关于点P的k号心为Q j(1≤j≤n),过点P任作一直线l,且Q、Q j、Aj三点到直线l的有向距离分别为d(Q)、d(Q j)、d(Aj),则d(Q)=d(Q j)+d(A j)/k.证明以任意一点P为原点建立平面直角坐标系xPy,则可设直线l的方程为ax+by=0.设各点的坐标分别为:Ai(xi,y i),Q(x,y),Q j(x'j,y'j)(i=1,2L,n且1≤j≤n),则11niix=k∑=x,y=1k∑in=1yi,'1j1(ni j)ix=k∑=x?x,y'j=… 相似文献
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研究了如下形式的时滞型Hopfield神经网络u′i(t)=-biui(t) nj=1aijfj(uj(t-τij)) Ji, i=1,2,…,n的全局吸引性和平衡点的全局指数稳定。通过构建合适的Lyapunov泛函和利用不等式pxyp-1≤xp (p-1)yp,获得了几个新的判定条件,这些结论推广了已知文献中的结果。 相似文献
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第一天1.给定实数a1,a2,…,an.对每个i(1≤i≤n),定义:di=max{aj|1≤j≤i}-min{aj|i≤j≤n},且令d=max{di|1≤i≤n}.(1)证明:对任意实数x1≤x2≤…≤xn,有max{|xi-ai||1≤i≤n}≥2d.(2)证明:存在实数x1≤x2≤…≤xn,使得式①中的等号成立.(新西兰供题)2.设A、B、C、D、E五点中,四边形ABCD是平行四边形,四边形BCED是圆内接四边形.设l是通过点A的一条直线,l与线段DC交于点F(F是线段DC的内点),且l与直线BC交于点G.若EF=EG=EC,求证:l是∠DAB的平分线.(卢森堡供题)3.在一次数学竞赛活动中,有一些参赛选手是朋友,朋友关系是相互的.如… 相似文献
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蒋岳祥 《浙江大学学报(A卷英文版)》2005,6(4):315-321
The sequences {Zi,n, l≤i≤n}, n≥l have multi-nomial distribution among i.i.d. random variables {X1,i, i≥1}, {X2,i,u≥l }, …, {Xm,i, i≥1 }. The extreme value distribution Gz(x) of this particular triangular array of i.i.d, random variables Z1,n, Z2Zn,n is discussed in this paper. We found a new type of not max-stable extreme value distributions, i) Gz(x) = r-1∏i=1ФAiαi(x) × Фαr (x);ii) Gz (x) = r-1∏i=1ψAiαi (x) × ψαr (x); iii) Gz (x) = r-1∏i=1 ∧Ai (λix) × A(x), r≥2, 0＜α1≤α2≤…≤αr and λi∈ (0,1] for i, l≤i≤r-1 which occur if Fj, …, Fm belong to the same MDA. 相似文献
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1.(法国)设m和n是正整数,a_1,a_2,…,a_m是集合{1,2,…,n}中的不同元素,每当a_i a_j≤n,1≤i≤j≤m,就有某个k,1≤k≤m,使得a_i a_j=a_k。求证:(a_1 a_2 … a_m)/m≥(n 1)/2。 证明 不妨设a_1>a_2>…>a_m,关键在于证明,对任意i,当1≤i≤m时,有 相似文献
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<数学通讯>1997年第7期上征解问题173是: 设xi＞0,i=1,...,n,Sn=x1 ... xn,Pi,j=(xi/xj)(Sn-xi-xj),则Tn=P1,2 P2,3 ... Pn-1,n Pn,1≥(n-2)Sn(n≥3).(1) 相似文献
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三、C(s~m,r)数的三组求和公式引理1.任一和式f(x)=∑a_kx~k,记w为1的n次根 (w=cos(2π)/n+isin(2π)/n-e~(i(2π)/n)), 则对任二整数n>k≥0,有 a_kx~k+a_(k+u)x~(k+k)+a_(k+2n)x~(k+2n)+… =(1/n)sum from j=0 to n-1 (w~(-jk)·f(w~j,x).(A) 相似文献
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把容斥原理形式进一步的推广得到一些更普遍的形式.对于任何一个集合S,推广到在性质a1,a2,…,aq中具有r个性质,在性质aq+1,…,an中具有k个性质的元素的个数为:N(r,k)=∑0≤i≤q-r 0≤j≤n-q-k(-1)i+j(r+i r)(k+j k)N r+i,k+j,使得容斥原理的应用范围扩大化. 相似文献
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Concave resource allocation problem is an integer programming problem of minimizing a nonincreasing concave function subject to a convex nondecreasing constraint and bounded integer variables. This class of problems are encountered in optimization models involving economies of scale. In this paper, a new hybrid dynamic programming method was proposed for solving concave resource allocation problems. A convex underestimating function was used to approximate the objective function and the resulting convex subproblem was solved with dynamic programming technique after transforming it into a 0-1 linear knapsack problem. To ensure the convergence, monotonicity and domain cut technique was employed to remove certain integer boxes and partition the revised domain into a union of integer boxes. Computational results were given to show the efficiency of the algorithm. 相似文献
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Multi-dimensional nonlinear knapsack problems are often encountered in resource allocation, industrial planning and computer networks. In this paper, a surrogate dual method was proposed for solving this class of problems. Multiply constrained problem was relaxed to a singly constrained problem by using the surrogate technique. To compute tighter bounds of the primal problem, the cutting plane method was used to solve the surrogate dual problem, where the surrogate relaxation problem was solved by the 0-1 linearization method. The domain cut technique was employed to eliminate the duality gap and thus to guarantee the convergence of tile algorithm. Numerical results were reported for large-scale multi-dimensional nonlinear knapsack problems. 相似文献
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1IntroductionReliability opti mization plays an i mportant role inthe planning and design of moderntechnological syste-ms[1,2].Although components with high reliability canbe manufactured as the modern technology deve-lops,the requirements for the systems reliability are oftenbeyond the capability of manufacturing.This is spe-cially true for systems where a failure of the systemwill result in catastrophic consequence.On the otherhand,adopting high reliability components in a systemmay be infea… 相似文献
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In this paper, a new branch-and-bound algorithm based on the Lagrangian dual relaxation and continuous relaxation is proposed for discrete multi-factor portfolio selection model with roundlot restriction in financial optimization. This discrete portfolio model is of integer quadratic programming problems. The separable structure of the model is investigated by using Lagrangian relaxation and dual search. Computational results show that the algorithm is capable of solving real-world portfolio problems with data from US stock market and randomly generated test problems with up to 120 securities. 相似文献
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In this paper, the discrete mean-variance model is considered for portfolio selection under concave transaction costs. By using the Cholesky decomposition technique, the convariance matrix to obtain a separable mixed integer nonlinear optimization problem is decomposed. A brand-and-bound algorithm based on Lagrangian relaxation is then proposed. Com-putational results are reported for test problems with the data randomly generated and those from the US stock market. 相似文献
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In this paper, a branch-and-bound method for solving multi-dimensional quadratic 0-1 knapsack problems was studied. The method was based on the Lagrangian relaxation and the surrogate constraint technique for finding feasible solutions. The Lagrangian relaxations were solved with the maximum-flow algorithm and the Lagrangian bounds was determined with the outer approximation method. Computational results show the efficiency of the proposed method for multi-dimensional quadratic 0-1 knapsack problems. 相似文献
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In this paper, a new method named as the gradually descent method was proposed to solve the discrete global optimization problem. With the aid of an auxiliary function, this method enables to convert the problem of finding one discrete minimizer of the objective function f to that of finding another at each cycle. The auxiliary function can ensure that a point, except a prescribed point, is not its integer stationary point if the value of objective function at the point is greater than the scalar which is chosen properly. This property leads to a better minimizer of f found more easily by some classical local search methods. The computational results show that this algorithm is quite efficient and reliable for solving nonlinear integer programming problems. 相似文献
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介绍了非线性规划中的一种近似增广拉格朗日函数,建立了基于这种增广拉格朗日函数的对偶映射和相应的对偶问题,得到了原问题和对偶问题的强近似对偶和弱近似对偶结果。我们的结果推广了一些已有的结论。 相似文献
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1 IntroductionThenonlinearconstrainedoptimizationproblemisaveryimportantmathematicalprogrammingprob lem .Ithasbeenstudiedextensively ,andmanyalgo rithmsforsolvingthis problemhasbeen pro posed[1,2 ] .Mostalgorithmsforsolvingthenonlinearcon strainedoptimization problemislocallyconvergent ,suchastheNewtonmethod ,theBFGSmethodandtheSQPmethod ,etc .Toovercomethisdrawback ,manyextendediterativemethodshavebeendevel oped .Forexample ,theNewtonmethodincorporatedwiththelinesearch[1] andhomotopymeth… 相似文献
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采用一种快速的新型算法,即交替方向乘子法求解图像重建的全变分模型.首先,对全变分模型进行等价变形,使之转化成带有等式约束的可分的凸优化问题.然后,通过引入增广拉格朗日函数,并采用Gauss-Seidel迭代的思想,对问题中2块变量交替极小化,最后更新乘子.因为该方法充分利用了问题的特殊结构,将原问题分解成一系列容易求解... 相似文献