共查询到20条相似文献,搜索用时 31 毫秒
1.
令$k,\ell \geq 2$是正整数.令$A$是无限非负整数的集合.对$n\in \mathbb{N}$, 令$r_{1,k,\ldots,k^{\ell-1}}(A, n)$表示方程$n=a_0+ka_1+\cdots +k^{\ell-1}a_{\ell-1}$, $a_0, \ldots, a_{\ell-1}\in A$解的个数. 在本文中, 我们证明了对所有$n\geq 0$, $r_{1,k,\ldots,k^{\ell-1}}(A, n)=1$当且仅当$A$是$k^\ell$进制展开中数位小于$k$的所有非负整数的集合. 这个结果部分回答了S\''{a}rk\"{o}zy and S\''{o}s关于多维线性型表示的一个问题. 相似文献
2.
Let N denote the set of all nonnegative integers and A be a subset of N.Let W be a nonempty subset of N.Denote by F~*(W) the set of all finite,nonempty subsets of W.Fix integer g≥2,let A_g(W) be the set of all numbers of the form sum f∈Fa_fg~f where F∈F~*(W)and 1≤a_f≤g-1.For i=0,1,2,3,let W_i = {n∈N|n≡ i(mod 4)}.In this paper,we show that the set A = U_i~3=0 A_g(W_i) is a minimal asymptotic basis of order four. 相似文献
3.
Artūras DUBICKAS 《数学学报(英文版)》2013,29(12):2251-2260
Let u be a sequence of positive integers which grows essentially as a geometric progression. We give a criterion on u in terms of its distribution modulo d, d = 1, 2,..., under which the set of positive integers expressible by the sum of a prime number and an element of u has a positive lower density. This criterion is then checked for some second order linear recurrence sequences. It follows, for instance, that the set of positive integers of the form p + [(2 + √3)n], where p is a prime number and n is a positive integer, has a positive lower density. This generalizes a recent result of Enoch Lee. In passing, we show that the periods of linear recurrence sequences of order m modulo a prime number p cannot be "too small" for most prime numbers p. 相似文献
4.
Franz A. Delahan 《Journal of Graph Theory》1998,29(1):1-9
Fix any positive integer n. Let S be the set of all Steinhaus graphs of order n(n − 1)/2 + 1. The vertices for each graph in S are the first n(n − 1)/2 + 1 positive integers. Let I be the set of all labeled graphs of order n with vertices of the form i(i − 1)/2 + 1 for the first n positive integers i. This article shows that the function ϕ : S → I that maps a Steinhaus graph to its induced subgraph is a bijection. Therefore, any graph of order n is isomorphic to an induced subgraph of a Steinhaus graph of order n(n − 1)/2 + 1. This considerably tightens a result of Brigham, Carrington, and Dutton in [Brigham, Carrington, & Dutton, Combin. Inform. System Sci. 17 (1992)], which showed that this could be done with a Steinhaus graph of order 2n−1. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 1–9, 1998 相似文献
5.
Ajai Choudhry 《Journal of Number Theory》2005,110(2):403-412
This paper deals with the problem of finding n integers such that their pairwise sums are cubes. We obtain eight integers, expressed in parametric terms, such that all the six pairwise sums of four of these integers are cubes, 9 of the 10 pairwise sums of five of these integers are cubes, 12 pairwise sums of six of these integers are cubes, 15 pairwise sums of seven of these integers are cubes and 18 pairwise sums of all the eight integers are cubes. This leads to infinitely many examples of four positive integers such that all of their six pairwise sums are cubes. Further, for any arbitrary positive integer n, we obtain a set of 2(n+1) integers, in parametric terms, such that 5n+1 of the pairwise sums of these integers are cubes. With a choice of parameters, we can obtain examples with 5n+2 of the pairwise sums being cubes. 相似文献
6.
Simon R. Blackburn 《Journal of Combinatorial Theory, Series A》2006,113(7):1572-1581
The paper contains proofs of the following results. For all sufficiently large odd integers n, there exists a set of 2n−1 permutations that pairwise generate the symmetric group Sn. There is no set of 2n−1+1 permutations having this property. For all sufficiently large integers n with n≡2mod4, there exists a set of 2n−2 even permutations that pairwise generate the alternating group An. There is no set of 2n−2+1 permutations having this property. 相似文献
7.
<正> §1.問題的提出及解法 錢学森在[1]中提出了有时滞的系統的无条件稳定性的問題,并叙述了Satche的作图法.对于有时滞的系統的稳定性問題,一般化为超越方程的根的实部的符号的判定問題,这方面有及,Hayes及Bellman等人的工 相似文献
8.
Let n = n1 + n2 + … + nj a partition Π of n. One will say that this partition represents the integer a if there exists a subsum nil + ni2 + … + nil equal to a. The set
(Π) is defined as the set of all integers a represented by Π. Let
be a subset of the set of positive integers. We denote by p(
,n) the number of partitions of n with parts in
, and by
((
,n) the number of distinct sets represented by these partitions. Various estimates for
(
,n) are given. Two cases are more specially studied, when
is the set {1, 2, 4, 8, 16, …} of powers of 2, and when
is the set of all positive integers. Two partitions of n are said to be equivalent if they represent the same integers. We give some estimations for the minimal number of parts of a partition equivalent to a given partition. 相似文献
9.
研究了高阶线性微分方程f~(k)+A_(k-1)(z)f~(k-1)+…+A_1(z)f′+A_0(z)f=0的非零解f,及其一阶、二阶导数,f~(i)(i=1,2)的不动点性质,这里A_j(z)(j=0,1,…k-1)为亚纯函数,得到了若δ(∞,A_0)>0,且满足max{i(A1),i(A2),…,i(A_(k-1))}相似文献
10.
For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n − 1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n − 2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. © 1998 John Wiley & Sons, Inc. J Combin Designs 6:91–110, 1998 相似文献
11.
12.
Yu. F. Bilu B. Brindza P. Kirschenhofer Á. Pintér R. F. Tichy A. Schinzel 《Compositio Mathematica》2002,131(2):173-188
Given m, n 2, we prove that, for sufficiently large y, the sum 1
n
+···+ y
n
is not a product of m consecutive integers. We also prove that for m n we have 1
m
+···+ x
m
1
n
+···+ y
n
, provided x, y are sufficiently large. Among other auxiliary facts, we show that Bernoulli polynomials of odd index are indecomposable, and those of even index are almost indecomposable, a result of independent interest. 相似文献
13.
研究了非齐次线性微分方程f^{(k)}+A_{k-1}(z)f^{(k-1)}+...+A_{s}(z)f^{(s)}+...+A_{0}(z)f=F(z)
解的增长性,其中A_{j}(j=0,1,\cdots,k-1)及F是整函数. 在A_{s}比其他系数有较快增
长的情况下,得到了上述非齐次微分方程在一定条件下的超越整函数解的超级的精确估计. 相似文献
14.
假设A0,A1,…,Ak-1在某个角域内解析,讨论高阶线性微分方程,f(k) Ak-1f (k-1) … A1f' A0f=0在特定角域内解的增长性和渐近性,改进了一些结果. 相似文献
15.
It is proved that (i) for
survives to E∞; (ii) for
survives to E∞.
Project supported by the Doctoral Program Foundation of China. 相似文献
16.
对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数
Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1∑j=1r(1+xi3/1- xi3)1/r,
其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式. 相似文献
17.
The path spectrum of a graph is the set of lengths of all maximal paths in the graph. A set S of positive integers is spectral if it is the path spectrum of a tree. We characterize the spectral sets containing at most two odd integers (and arbitrarily many even ones) and obtain several necessary conditions for a set to be spectral. We show that for each even integer s≥2 at least 1/4 of all subsets of the set {2,3,…,s} are spectral and conjecture that all the subsets with at least 3s/4 integers are spectral. 相似文献
18.
本文主要考虑以下两个问题: (1) 建立非齐次线性微分方程$$f''+A_2(z)f''+A_1(z)f''+A_0(z)f=A_3(z),$$ 系数增长性与解的零点的几何分布的相互关系, 其中 $A_0(z),\ldots, A_3(z)$为单位圆内的解析函数; (2) 找到一些使方程$$f^{(k)}+A_{k-1}(z)f^{(k-1)}+\cdots+A_1(z)f''+A_0(z)f=0,$$ 所有解属于Zygmund-型空间的充分条件. 我们得到的结果推广了Heittokangas, Gr\"{o}hn, Korhoneon 和 R\"{a}tty\"{a}的部分结果. 相似文献
19.
A. I. Galochkin 《Mathematical Notes》1975,18(4):911-917
Lower bounds are obtained for linear forms of values of Siegel's G functions. In particular, it is found that ifα 1...,α m are pairwise distinct nonzero rational numbers, then for any positive ? and a natural q>q0(?,α 1,...,α m) we have for any nonzero set (x0 x1,..., xm) of integers the inequality $$|x_0 + x_1 In(i + a_1 q^{ - 1} ) + ... + x_m In(i + a_m q^{ - 1} )|q^{ - \lambda } (h_1 ...h_m )^{ - 1 - \varepsilon } ,$$ where hi=max(i, ¦xi¦), andλ=λ (?,α 1,...,α m). 相似文献
20.