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1.
Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m). 相似文献
2.
ZhenFengZHANG 《数学学报(英文版)》2005,21(1):155-168
In this paper, we extend a classical result of Hua to arithmetic progressions with large moduli. The result implies the Linnik Theorem on the least prime in an arithmetic progression. 相似文献
3.
In this paper, we give a necessary and sufficient solvable condition for diagonal cubic equation with prime variable in arithmetic progressions and the outline of the proof. 相似文献
4.
Abstract For relatively prime positive integers u0 and r, and for 0 〈 k ≤ n, define uk := u0 + kr. Let Ln := 1cm(u0,u1,... ,un) and let a,l≥2 be any integers. In this paper, the authors show that, for integers α≥ a, r ≥max(a,l - 1) and n ≥lατ, the following inequality holds Ln≥u0r^(l-1)α+a-l(r+1)^n.Particularly, letting l = 3 yields an improvement on the best previous lower bound on Ln obtained by Hong and Kominers in 2010. 相似文献
5.
Ali AHMAD Kashif ALI Martin BAA Petr KOVR Andrea SEMANIOV-FENOVíKOV 《数学学报(英文版)》2012,28(9):1865-1874
Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An (a, d)-vertex-antimagic total labeling of G is a bijection f from V (G) ∪ E(G) onto the set of consecutive integers 1, 2, . . . , p + q, such that the vertex-weights form an arithmetic progression with the initial term a and difference d, where the vertex-weight of x is the sum of the value f (x) assigned to the vertex x together with all values f (xy) assigned to edges xy incident to x. Such labeling is called super if the smallest possible labels appear on the vertices. In this paper, we study the properties of such labelings and examine their existence for 2r-regular graphs when the difference d is 0, 1, . . . , r + 1. 相似文献
6.
设x是一个实数,a,q是正整数并且满足1≤q≤(logx)3,(a,q)=1。在本文中我们证明了:如果x≥e11.5,则有其中sum from l=1 to q表示 sum from l=1 (l,q)=1 to q。μ(n)表示Mbius函数,φ(x;q,l)=sum from n≡l(mod q) n≤x ∧(n), τ(?)=sum from h=1 to q(?)(h)e(h/q)。当存在模q的实特征使得L(s,)有实零点■≥1-logq/0.1077时■=1;否则■=0。 相似文献
7.
A famous theorem of Szemer'edi asserts that any subset of integers with posi- tive upper density contains arbitrarily arithmetic progressions. Let Fq be a finite field with q elements and Fq((X^-1)) be the power field of formal series with coefficients lying in Fq. In this paper, we concern with the analogous Szemeredi problem for continued fractions of Laurent series: we will show that the set of points x ∈ Fq((X-1)) of whose sequence of degrees of partial quotients is strictly increasing and contain arbitrarily long arithmetic progressions is of Hausdorff dimension 1/2. 相似文献
8.
算术级数中的华罗庚五素数平方定理 总被引:1,自引:1,他引:0
本文给出了华罗庚五素数平方定理的算术级数形式,证明了其中一个素数可 以取在大模的算术级数中. 相似文献
9.
本文考察了几乎所有模的算术级数中的奇数Goldbach问题.证明了对几乎所有的模r≤N1/6-ε,充分大的正奇数N可表为三个素数之和,其中每个素数取在模r 的满足必要同余条件的任意剩余系中. 相似文献
10.
51.IntroductionSupposethatr>Oisafixednumberand[oldenotes,asusuaI,theintegralpartofo.LetForo1wasfirststudiedin1953byPjateckii-Sapiro[']whoprovedthat(1.1)holdsfor1相似文献