共查询到19条相似文献,搜索用时 62 毫秒
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定理:不等式 (sum from i=1 to m(a_(1i) a_(2i)…a_(ni)))~n≤≤sum from i=1 to m(a_(1i))~n sum from i=1 to m(a_(2i))~n…sum from i=1 to m(a_(ni))~n對於任意自然數n都成立,其中a_(ki)為正數(K=1,2,…,n,i=1,2,…,m). 證明: 設 A_K~n=sum from i=1 to m(a_(Ki))~n (K=1,2,…,n), x_(Ki)=a_(Ki)/A_K,(K=1,2,…,n i=1,2,…,m)則從n侗正數的幾何平均值小於或等於其算術平均值這個結果可得 x_(1i)x_(2i)…x_(ni)≤((x_(1i))~n+(x_(2i))~n+…+(x_(ni))~n)/n由此更推得a_(1i)a_(2i)…a_(ni)=A_1A_2…A_n(x_(1i)x_(2i)…x_(ni)≤ 相似文献
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常系数非齐线性递推式的解的显式表示 总被引:1,自引:0,他引:1
薛访存 《数学的实践与认识》1991,(4)
本文给出常系数非齐线性递推式(?)的解的显式表达式 H(m)=sum from i=0 to k-1(sum from j=i to k-1 b_ja_(k-j+i))D_(m-k-i)+sum from i=0 to m-k D_if(m-i)(m≥k)其中D_m=sum x_1+2x_2+…+kx_k=m x_j≥0(i=1,2,…,k)(?)a_1~x1a_2~x2…a_k~xk. 相似文献
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Let N denote the set of positive integers. The sum graph G^+(S) of a finite subset S belong to N is the graph (S, E) with uv ∈ E if and only if u + v ∈ S. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N. By using the set Z of all integers instead of N, we obtain the definition of the integral sum graph. A graph G = (V, E) is a mod sum graph if there exists a positive integer z and a labelling, λ, of the vertices of G with distinct elements from {0, 1, 2,..., z - 1} so that uv ∈ E if and only if the sum, modulo z, of the labels assigned to u and v is the label of a vertex of G. In this paper, we prove that flower tree is integral sum graph. We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph, and give the sum number of Dm. 相似文献
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Let p(n) denote the largest prime factor of an integer n≥2, and let Q(n) denote the largest prime power which divides n≥2. The purpose of this paper is to give asymptotic formula for the sum. 相似文献
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Let p be a prime number, q=p^f and m|q-1. For a multiplicative character x of Fq with order m, the Gauss sum G(x) over Fq is defined by 相似文献
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Let f be a meromorphic function of finite order in the plane. If its Nevanlinnadeficiency sum is 2,then we say that f has maximum deficiency sum. Drasin con-jectured that if f has maximum deficiency sum and the infinity is not its Nevanlinna'sdeficient value, then zero is the only Nevaulinna's deficient value of f' with defi-ciency 1. Yang Lo gave a positive answer of this conjecture by proving that under theabove assumption, zero is the only Nevanlinna's deficient value of f(h) with,deficie-ncy 2/(1 + k) for k = 1,2,…. Now, omitting the condition δ(∞,f) = 0, we prove 相似文献
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本文讨论如下类型二阶泛函微分方程(E) [r(t)x′(t)]′ sum from 1 to m(f_i(t,x(g_(il)(t)),…,x(g_(in)(t))))=0解的渐近性与振动性。 假设i)r(t)对t≥a连续且为正; ii)对一切t≥a,有g_(ij)(t)≥t(或≤t),连续,且当t→∞时,趋于 ∞,i=1,2,…,m,j=1,2,…,n; 相似文献
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Sufficient conditions are established for the asymptotic behavior of solutionsof nonlinear delay differential equations x′(t)+sum from i=1 to m(pi(t)x(t-т_i))=F(t,x_t),t≥0where 0<т_1<т_2<…<т_m≤r,pi∈C([0,∞)),i=1,2,…,m,F∈C([0,∞)×C_0,R).C_0=C([-r,0],R)equipped with the sup norm ||·|| forsome r>0. A new result is established, some known results are improved. 相似文献
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Using the notion of biconnected sum we define the biconnected sum (T1, M1)§(T2,M2) of two involutions (T1M1) and (T2,M2) which is an involution on the biconnected sum M1,§M2. A connected involution is said to be reducible if it can be expressed as a biconnected sum of two connected involutions.Theorem Each connected involution (T, M) can be decomposed into a bi-connected sum of connected irreducible involutions (T, M)=(T1, M1)§…§(Tq,Mq),and (?) where the coefficients of Hn_1(M) are in Z/2 Z if M is unoriented, in Z if is oriented . 相似文献
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Let N denote the set of positive integers.The sum graph G (S) of a finite subset S (C) N is the graph (S,E) with uv ∈ E if and only if u v ∈ S.A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S С N.By using the set Z of all integers instead of N,we obtain the definition of the integral sum graph.A graph G=(V,E) is a mod sum graph if there exists a positive integer z and a labelling,λ,of the vertices of G with distinct elements from {0,1,2,...,z-1} so that uv ∈ E if and only if the sum,modulo z,of the labels assigned to u and v is the label of a vertex of G.In this paper,we prove that flower tree is integral sum graph.We prove that Dutch m-wind-mill (Dm) is integral sum graph and mod sum graph,and give the sum number of Dm. 相似文献
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Let p ≥ 5 be a prime.For any integer h,the Hardy sum is defined by H(h,p) =p-1Σj=1(-1)j+1+[hj/p],which is related to the classical Dedekind sum.The mean values of the Hardy sum in short intervals are studied by using the mean value theorems of Dirichlet L-functions. 相似文献
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一个类似广义Dedekind和S_2(h,n,k)的二次均值 总被引:1,自引:0,他引:1
王阳 《数学的实践与认识》2003,33(7):129-136
本文的主要目的是利用 Dirichlet L -函数的均值研究 n为奇数时 ,类似广义 Dedekind和 S2 ( h,n,k)的二次均值 ,得到了两个有趣的渐近公式 . 相似文献
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何淦瞳 《数学的实践与认识》2005,35(10):153-156
讨论了矩阵的和与其加项之间,在等价关系及(对称阵的)合同关系上的联系.并进一步讨论了矩阵和的非零特征值与其加项的非零特征值之间的联系,给出了C ra ig定理的一个代数形式和代数证明. 相似文献
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马海成 《数学的实践与认识》2009,39(24)
给出了求函数和分的一种表格式算法.对于函数f(x)g(x),如果f(x)为多项式,而g(x)的高阶和分都能算出,那么f(x)g(x)的和分就可以利用这种表格式算法较快速的算出,它对数列求和有一定的益处. 相似文献
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Within this paper we study the Minkowski sum of prisms (“Cephoids”) in a finite dimensional vector space. For a vector
with positive components we write
and denote by
the associated prism. We provide a representation of a finite sum of prisms in terms of inequalities.
Dedicated to the 65th birthday of Alexander Rubinov. 相似文献
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