共查询到20条相似文献,搜索用时 46 毫秒
1.
Oleg Pikhurko 《Discrete Mathematics》2006,306(17):2097-2107
A graph G of order n and size m is edge-magic if there is a bijection l:V(G)∪E(G)→[n+m] such that all sums l(a)+l(b)+l(ab), ab∈E(G), are the same. We present new lower and upper bounds on M(n), the maximum size of an edge-magic graph of order n, being the first to show an upper bound of the form . Concrete estimates for ε can be obtained by knowing s(k,n), the maximum number of distinct pairwise sums that a k-subset of [n] can have.So, we also study s(k,n), motivated by the above connections to edge-magic graphs and by the fact that a few known functions from additive number theory can be expressed via s(k,n). For example, our estimate
2.
Shaun Cooper 《Journal of Number Theory》2003,103(2):135-162
Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p,
3.
Sherry Gong 《Journal of Number Theory》2009,129(12):2924-2932
Let an(k) be the coefficient of tk in the nth cyclotomic polynomial
4.
5.
6.
In this paper we discuss the asymptotic distribution of the approximation numbers of the finite sections for a Toeplitz operator T(a)∈L(?p), 1<p<∞, where a is a piecewise continuous function on the unit circle. We prove that the behavior of the approximation numbers of the finite sections Tn(a)=PnT(a)Pn depends heavily on the Fredholm properties of the operators T(a) and . In particular, if the operators T(a) and are Fredholm on ?p, then the approximation numbers of Tn(a) have the so-called k-splitting property. But, in contrast with the case of continuous symbols, the splitting number k is in general larger than . 相似文献
7.
J. Lang 《Journal of Approximation Theory》2006,140(2):141-146
Consider the Hardy-type operator T : Lp(a,b)→Lp(a,b),-∞a<b∞, which is defined byIt is shown thatwhere ρn(T) stands for any of the following: the Kolmogorov n-width, the Gel’fand n-width, the Bernstein n-width or the nth approximation number of T. 相似文献
8.
9.
Stefan De Wannemacker 《Journal of Combinatorial Theory, Series A》2007,114(7):1332-1349
Let n and k be natural numbers and let S(n,k) denote the Stirling numbers of the second kind. It is a conjecture of Wilf that the alternating sum
10.
11.
Oleksiy A. Ignatyev 《Applied mathematics and computation》2010,216(2):388-394
The linear autonomous system of difference equations x(n+1)=Ax(n) is considered, where is a real nonsingular k×k matrix. In this paper it has been proved that if W(x) is any homogeneous polynomial of m-th degree in x, then there exists a unique homogeneous polynomial V(x) of m-th degree such that ΔV=V(Ax)-V(x)=W(x) if and only if where are the eigenvalues of the matrix A. The theorem on the instability has also been proved. 相似文献
12.
Taekyun Kim 《Journal of Mathematical Analysis and Applications》2008,339(1):598-608
In this paper we study a two-variable p-adic q-l-function lp,q(s,t|χ) for Dirchlet's character χ, with the property that
13.
Jason P. Bell 《Journal of Number Theory》2006,117(1):160-190
This paper shows that the natural setting for the Bateman and Erd?s study of monotonicity of the kth difference of partition functions a(n) is the class of partition identities
14.
Let 1 ? p ? ∞, 0 < q ? p, and A = (an,k)n,k?0 ? 0. Denote by Lp,q(A) the supremum of those L satisfying the following inequality:
15.
16.
Let , 1?μ?n, be a polynomial of degree n such that p(z)≠0 in |z|<k, k>0, then for 0<r?R?k, Dewan, Yadav and Pukhta [K.K. Dewan, R.S. Yadav, M.S. Pukhta, Inequalities for a polynomial and its derivative, Math. Inequal. Appl. 2 (2) (1999) 203-205] proved
17.
Matthew Boylan 《Journal of Number Theory》2003,98(2):377-389
Let F(z)=∑n=1∞a(n)qn denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that
18.
Florian Luca 《Discrete Mathematics》2007,307(13):1672-1678
In this note, we supply the details of the proof of the fact that if a1,…,an+Ω(n) are integers, then there exists a subset M⊂{1,…,n+Ω(n)} of cardinality n such that the equation
19.
Mitsunori Imaoka 《Topology and its Applications》2010,157(15):2435-2445
We study the stable extendibility of R-vector bundles over the (2n+1)-dimensional standard lens space Ln(p) with odd prime p, focusing on the normal bundle to an immersion of Ln(p) in the Euclidean space R2n+1+t. We show several concrete cases in which is stably extendible to Lk(p) for any k with k?n, and in several cases we determine the exact value m for which is stably extendible to Lm(p) but not stably extendible to Lm+1(p). 相似文献
20.
Yong-Gao Chen 《Journal of Number Theory》2003,100(2):326-331
Let p1,p2,… be the sequence of all primes in ascending order. The following result is proved: for any given positive integer k and any given , there exist infinitely many positive integers n with