共查询到20条相似文献,搜索用时 31 毫秒
1.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
2.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
3.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,129(2):3772-3786
Let an n × n Hermitian matrix A be presented in block 2 × 2 form as
, where A12 ≠ 0, and assume that the diagonal blocks A11 and A22 are positive definite. Under these assumptions, it is proved that the extreme eigenvalues of A satisfy the bounds
where
and ‖ ⋅ ‖ is the spectral norm. Further, in the positive-definite case, several equivalent conditions necessary and sufficient for both of the above bounds to be attained are provided. Bibliography: 6 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 172–194. 相似文献
4.
Chang Jen-Chun Chen Rong-Jaye Hwang Frank K. 《Methodology and Computing in Applied Probability》2001,3(4):379-386
A d-within-consecutive-k-out-of-n system, abbreviated as Con(d, k, n), is a linear system of n components in a line which fails if and only if there exists a set of k consecutive components containing at least d failed ones. So far the fastest algorithm to compute the reliability of Con(d, k, n) is Hwang and Wright's
algorithm published in 1997, where
. In this paper we use automata theory to reduce
to
. For d small or close to k, we have reduced
from exponentially many (in k) to polynomially many. The computational complexity of our final algorithm is
, where
. 相似文献
5.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
6.
Nikolaos Marmaridis 《manuscripta mathematica》1984,47(1-3):55-83
Let
be a triangular matrix algebra, uhere k is an algebraically closed field, B is the path algebra of an oriented Dynkin diagram of type E6 or E7 or E8 and M is a finite dimensional k-B-bimodule. The aim of this paper is to determine the representation type of A for any orientation of the Dynkin diagram and for any indecomposable B-module M. This classification is obtained by comparing the representation types of the algebras
and
using the theory of tilting modules. 相似文献
7.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
8.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
9.
Let PG2(2) be the Fano plane, i. e., the unique hypergraph with 7 triples on 7 vertices in which every pair of vertices is contained
in a unique triple. In this paper we prove that for sufficiently large n, the maximum number of edges in a 3-uniform hypergraph on n vertices not containing a Fano plane is
Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlier
result of de Caen and Füredi, and proves an old conjecture of V. Sós. In addition, we also prove a stability result for the
Fano plane, which says that a 3-uniform hypergraph with density close to 3/4 and no Fano plane is approximately 2-colorable.
* Research supported in part by NSF grant DMS-0106589. 相似文献
10.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0+. 相似文献
11.
Let
be a unit sphere of the d–dimensional Euclidean space ℝ
d
and let
(0 < p ≤ 1) denote the real Hardy space on
For 0 < p ≤ 1 and
let
E
j
(f,H
p
) (j = 0, 1, ...) be the best approximation of f by spherical polynomials of degree less than or
equal to j, in the space
Given a distribution f on
its Cesàro mean of order δ > –1 is
denoted by
For 0 < p ≤ 1, it is known that
is the critical index for the uniform
summability of
in the metric H
p
. In this paper, the following result is proved:
Theorem
Let
0<p<1 and
Then for
where
A
N
(f)≈B
N
(f) means that there’s a positive constant C, independent of N and f, such that
In the case
d = 2, this result was proved by Belinskii in 1996.
The authors are partially supported by NNSF of China under the grant # 10071007 相似文献
12.
Jiong Sheng LI Jian Hua YIN 《数学学报(英文版)》2006,22(4):1133-1138
Let σ(k, n) be the smallest even integer such that each n-term positive graphic sequence with term sum at least σ(k, n) can be realized by a graph containing a clique of k + 1 vertices. Erdos et al. (Graph Theory, 1991, 439-449) conjectured that σ(k, n) = (k - 1)(2n- k) + 2. Li et al. (Science in China, 1998, 510-520) proved that the conjecture is true for k 〉 5 and n ≥ (k2) + 3, and raised the problem of determining the smallest integer N(k) such that the conjecture holds for n ≥ N(k). They also determined the values of N(k) for 2 ≤ k ≤ 7, and proved that [5k-1/2] ≤ N(k) ≤ (k2) + 3 for k ≥ 8. In this paper, we determine the exact values of σ(k, n) for n ≥ 2k+3 and k ≥ 6. Therefore, the problem of determining σ(k, n) is completely solved. In addition, we prove as a corollary that N(k) -= [5k-1/2] for k ≥6. 相似文献
13.
Huaning Liu 《Bulletin of the Brazilian Mathematical Society》2007,38(2):179-188
For integers a,
b and n
> 0, define
and
where
denotes the summation over all
r such that (r, n) = 1, and
is defined by the equation
. The two sums are analogous to the
homogeneous Dedekind sum S(a,b,
n). The functional equations for
A
Γ and B
Γ are established. Furthermore, Knopp's
identity on Dedekind sum is extended.
*This work is supported by the N.S.F. (10271093,
60472068) of P.R. China. 相似文献
14.
Letn>1. The number of all strictly increasing selfmappings of a 2n-element crown is
. The number of all order-preserving selfmappings of a 2n-element crown is
相似文献
15.
Werner Burau 《Annali di Matematica Pura ed Applicata》1956,42(1):381-393
Sunto Conoscendo il modello minimo
per la totalità degli S
k
I
d'una schiera giacenti su di una quadrica Q2k di S2k+1 si definisce il ? complesso lineare di S
k
I
? come imagine d'una sezione iperpiana di
. Il problema della classificazione projettiva di tali complessi lineari è posto e risolto per k≤5.
相似文献
16.
The Existence of Solutions of Elliptic Equations
with Neumann Boundary Condition for Superlinear Problems 总被引:1,自引:0,他引:1
ChongLI 《数学学报(英文版)》2004,20(6):965-976
In this paper, we study and discuss the existence of multiple solutions of a class of non-linear elliptic equations with Neumann boundary condition, and obtain at least seven non-trivial solutions in which two are positive, two are negative and three are sign-changing. The study of problem (1.1):{-△u αu=f(u),x∈Ω, x∈Ω,δu/δr=0,x∈δΩ,is based on the variational methods and critical point theory. We form our conclusion by using the sub-sup solution method, Mountain Pass Theorem in order intervals, Leray-Schauder degree theory and the invariance of decreasing flow. 相似文献
17.
We give an asymptotic formula for
|
设为首页 | 免责声明 | 关于勤云 | 加入收藏 |
Copyright©北京勤云科技发展有限公司 京ICP备09084417号 |