共查询到20条相似文献,搜索用时 31 毫秒
1.
David J. Grynkiewicz 《Combinatorica》2006,26(4):445-453
An n-set partition of a sequence S is a collection of n nonempty subsequences of S, pairwise disjoint as sequences, such that every term of S belongs to exactly one of the subsequences, and the terms in each subsequence are all distinct so that they can be considered
as sets. If S is a sequence of m+n−1 elements from a finite abelian group G of order m and exponent k, and if
is a sequence of integers whose sum is zero modulo k, then there exists a rearranged subsequence
of S such that
. This extends the Erdős–Ginzburg–Ziv Theorem, which is the case when m = n and wi = 1 for all i, and confirms a conjecture of Y. Caro. Furthermore, we in part verify a related conjecture of Y. Hamidoune, by showing that
if S has an n-set partition A=A1, . . .,An such that |wiAi| = |Ai| for all i, then there exists a nontrivial subgroup H of G and an n-set partition A′ =A′1, . . .,A′n of S such that
and
for all i, where wiAi={wiai |ai∈Ai}. 相似文献
2.
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
3.
V. V. Vysotsky 《Journal of Mathematical Sciences》2007,147(4):6873-6883
Let Si be a random walk with standard exponential increments. The sum ∑
i=1
k
Si is called the k-step area of the walk. The random variable
∑
i=1
k
Si plays an important role in the study of the so-called one-dimensional sticky particles model. We find the distribution of
this variable and prove that
for 0 ≤ t ≤ 1. We also show that
, where the Ui,n are order statistics of n i.i.d. random variables uniformly distributed on [0, 1]. Bibliography: 6 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 341, 2007, pp. 48–67. 相似文献
4.
C. M. Reidys 《Annals of Combinatorics》2006,10(4):481-498
In this paper we study sequential dynamical systems (SDS) over words. An SDS is a triple consisting of: (a) a graph Y with vertex set {v1, ..., vn}, (b) a family of Y-local functions
, where K is a finite field and (c) a word w, i.e., a family (w1, ..., wk), where wi is a Y-vertex. A map
is called Y-local if and only if it fixes all variables
and depends exclusively on the variables
, for
. An SDS induces an SDS- map,
, obtained by the map-composition of the functions
according to w. We show that an SDS induces in addition the graph G(w,Y) having vertex set {1, ..., k} where r, s are adjacent if and only if ws, wr are adjacent in Y. G(w, Y) is acted upon by Sk via
and Fix(w) is the group of G(w, Y) graph automorphisms which fix w. We analyze G(w, Y)-automorphisms via an exact sequence involving the normalizer of Fix(w) in Aut(G(w, Y)), Fix(w) and Aut(Y). Furthermore we introduce an equivalence relation over words and prove a bijection between word equivalence classes and
certain orbits of acyclic orientations of G(w, Y).
Received September 12, 2004 相似文献
5.
LetH
ibe a finite dimensional complex Hilbert space of dimensiond
i associated with a finite level quantum system Ai for i = 1, 2, ...,k. A subspaceS ⊂
is said to becompletely entangled if it has no non-zero product vector of the formu
1⊗u
2 ⊗ ... ⊗u
k with ui inH
i for each i. Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic
algebraic geometry we prove that
where ε is the collection of all completely entangled subspaces.
When
andk = 2 an explicit orthonormal basis of a maximal completely entangled subspace of
is given.
We also introduce a more delicate notion of aperfectly entangled subspace for a multipartite quantum system, construct an example using the theory of stabilizer quantum codes and pose a
problem. 相似文献
6.
E.M.E.ZAYED 《数学学报(英文版)》2004,20(2):209-222
The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1 κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1 κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. 相似文献
7.
E.M.E.ZAYED 《应用数学学报(英文版)》2004,20(2):215-230
The asymptotic expansion of the heat kernel Θ(t)=sum from ∞to j=1 exp(-tλ_j) where {λ_j}_(j=1)~∞are the eigen-values of the negative Laplacian -Δ_n=-sum from n to k=1((?))~2 in R~n(n=2 or 3) is studied for short-time t for a generalbounded domain Ωwith a smooth boundary (?)Ω.In this paper,we consider the case of a finite number of theDirichlet conditions φ=0 on Γ_i (i=1,...,J) and the Neumann conditions (?)=0 on Γ_i (i=J 1,...,k) andthe Robin conditions ((?) γ_i)φ=0 on Γ_i (i=k 1,...,m) where γ_i are piecewise smooth positive impedancefunctions,such that (?)Ωconsists of a finite number of piecewise smooth components Γ_i(i=1,...,m) where(?)Ω=(?)Γ_i.We construct the required asymptotics in the form of a power series over t.The senior coefficients inthis series are specified as functionals of the geometric shape of the domain Ω.This result is applied to calculatethe one-particle partition function of a“special ideal gas”,i.e.,the set of non-interacting particles set up in abox with Dirichlet,Neumann and Robin boundary conditions for the appropriate wave function.Calculationof the thermodynamic quantities for the ideal gas such as the internal energy,pressure and specific heat revealsthat these quantities alone are incapable of distinguishing between two different shapes of the domain.Thisconclusion seems to be intuitively clear because it is based on a limited information given by a one-particlepartition function;nevertheless,its formal theoretical motivation is of some interest. 相似文献
8.
Dr. Wolfgang Stadje 《Monatshefte für Mathematik》1980,89(4):315-322
It is proved that iff∈L 1(?),f'∈L 1(?) and ∫∣x∣ i ∣f(x)∣dx<∞ fori=1, ...,k?1 and ifA=(a ij ) is a (k×k)-matrix with non-vanishing determinant, for $$\tilde f_A (\zeta ): = \smallint \exp (i\zeta _1 \sum\limits_{j = 1}^k {a_{1j} x^j } + ... + i\zeta _k \sum\limits_{j = 1}^k {a_{kj} x^j } )f(x)dx$$ the following relation holds: $$\tilde f_A (\zeta ) = O(\left\| \zeta \right\|)^{ - b_k } with b_k : = (\sum\limits_{j = 1}^k {j!)^{ - 1} } for k \in \mathbb{N}$$ . 相似文献
9.
In this paper, we obtain all possible general solutions of the sum form functional equations
and
valid for all complete probability distributions (p
1, ..., p
k), (q
1, ..., q
l
), k ≥ 3, l ≥ 3 fixed integers; λ ∈ ℝ, λ ≠ 0 and F, G, H, f, g, h are real valued mappings each having the domain I = [0, 1], the unit closed interval. 相似文献
10.
J. S. Hwang 《数学学报(英文版)》1998,14(1):57-66
Letf(X) be an additive form defined by
wherea
i
≠0 is integer,i=1,2…,s. In 1979, Schmidt proved that if ∈>0 then there is a large constantC(k,∈) such that fors>C(k,∈) the equationf(X)=0 has a nontrivial, integer solution in σ1, σ2, …, σ3,x
1,x
2, …,x
3 satisfying
Schmidt did not estimate this constantC(k,∈) since it would be extremely large. In this paper, we prove the following result 相似文献
11.
De-xiang Ma Wei-gao Ge Xue-gang Chen 《应用数学学报(英文版)》2005,21(4):661-670
In this paper, we obtain positive solution to the following multi-point singular boundary value problem with p-Laplacian operator,{( φp(u'))'+q(t)f(t,u,u')=0,0〈t〈1,u(0)=∑i=1^nαiu(ξi),u'(1)=∑i=1^nβiu'(ξi),whereφp(s)=|s|^p-2s,p≥2;ξi∈(0,1)(i=1,2,…,n),0≤αi,βi〈1(i=1,2,…n),0≤∑i=1^nαi,∑i=1^nβi〈1,and q(t) may be singular at t=0,1,f(t,u,u')may be singular at u'=0 相似文献
12.
In this paper, we use Laguerre calculus to find theLP spectrum (λ, Μ) of the pair (L, iT). Here
md T = ∂/∂t with
a basis for the left-invariant vector fields on the Heisenberg group. We find kernels for the spectral projection operators
on the ray λ > 0 in the Heisenberg brush and show that they are Calderón-Zygmund-Mikhlin operators. Estimates for these operators
in L
k
p
(Hn), HP(Hn), and S
k
pv
(Hn) spaces can therefore be deduced. 相似文献
13.
Francesco Leonetti 《Annali dell'Universita di Ferrara》1985,31(1):169-184
Riassunto In questo lavoro si prova la regolarità h?lderiana delle derivate, fino all'ordinek, dei minimi locali
dei funzionali
sotto opportune ipotesi suA
ij
αβ
e sug.
Summary In this paper we prove h?lder-continuity of the derivates, up to orderk, of local minima of functionals under suitable hypotheses forA ij αβ andg.相似文献
14.
Let {zk=xk+iyk} be a sequence on upper half plane
and {si} be the number of appearence of zk in {z1,z2,...,zk}. Suppose sup si<+∞. Let ω(x) be a weight belonging to A∞ and
. We Consider the weighted Hardy space
and operator Tp mapping f(z)∈H
+w
p
into a sequence defined by
, 0<p≤+∞, j=1,2,.... Then Tp(H
+w
p
)=lp if and only if {zk} is uniformly separated. Besides the effective solution for interpolation is obtained.
Supported by National Science Foundation of China and Shanghai Youth Science Foundation 相似文献
15.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
16.
Dong Sheng Kang 《数学学报(英文版)》2009,25(3):435-444
Suppose Ω belong to R^N(N≥3) is a smooth bounded domain,ξi∈Ω,0〈ai〈√μ,μ:=((N-1)/2)^2,0≤μi〈(√μ-ai)^2,ai〈bi〈ai+1 and pi:=2N/N-2(1+ai-bi)are the weighted critical Hardy-Sobolev exponents, i = 1, 2,..., k, k ≥ 2. We deal with the conditions that ensure the existence of positive solutions to the multi-singular and multi-critical elliptic problem ∑i=1^k(-div(|x-ξi|^-2ai△↓u)-μiu/|x-ξi|^2(1+ai)-u^pi-1/|x-ξi|^bipi)=0with Dirichlet boundary condition, which involves the weighted Hardy inequality and the weighted Hardy-Sobolev inequality. The results depend crucially on the parameters ai, bi and #i, i -- 1, 2,..., k. 相似文献
17.
Zhang Lixin 《数学学报(英文版)》1998,14(1):113-124
Let {X, X
n
;n>-1} be a sequence of i.i.d.r.v.s withEX=0 andEX
2=σ2(0 < σ < ∞).
we obtain some sufficient and necessary conditions for
to hold, get the widest range ofk’s and answer a question of Hanson and Russo (1983).
Supported by National Natural Science Foundation of China and China Postdoctoral Science Foundation 相似文献
18.
Jin-hong You Gemai Chen Min Chen Xue-lei JiangUniversity of Regina Regina Saskatchewan SS OA CanadaUniversity of Calgary Calgary Alberta TN N CanadaAcademy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《应用数学学报(英文版)》2003,19(3):363-370
Consider the partly linear regression model ,where yi's are responses, xi = (xi1, xi2,…,xip)' and ti ∈T are known and nonrandom design points, T is a compact set in the real line is an unknown parameter vector, g(·) is an unknown function and {Ei} isa linear process, i.e., random variables with zeromean and variance o2e. Drawing upon B-spline estimation of g(·) and least squares estimation of 0, we construct estimators of the autocovariances of {Ei}- The uniform strong convergence rate of these estimators to their true values is then established. These results not only are a compensation for those of [23], but also have some application in modeling error structure. When the errors {Ei} are an ARMA process, our result can be used to develop a consistent procedure for determining the order of the ARMA process and identifying the non-zero coefficients of the process. Moreover, our result can be used to construct the asymptotically efficient estimators for parameters in the ARMA error process. 相似文献
19.
Henrik Petersson 《Integral Equations and Operator Theory》2007,57(3):413-423
We prove that for any weighted backward shift B = Bw on an infinite dimensional separable Hilbert space H whose weight sequence w = (wn) satisfies
, the conjugate operator
is hypercyclic on the space S(H) of self-adjoint operators on H provided with the topology of uniform convergence on compact sets. That is, there exists an
such that
is dense in S(H). We generalize the result to more general conjugate maps
, and establish similar results for other operator classes in the algebra B(H) of bounded operators, such as the ideals K(H) and N(H) of compact and nuclear operators respectively. 相似文献
20.
污染线性模型的非参数估计 总被引:1,自引:0,他引:1
Abstract. In this paper, the following contaminated linear model is considered: 相似文献