共查询到20条相似文献,搜索用时 15 毫秒
1.
Huanyin Chen 《Czechoslovak Mathematical Journal》2009,59(1):145-158
A matrix A ∈ M
n
(R) is e-clean provided there exists an idempotent E ∈ M
n
(R) such that A-E ∈ GL
n
(R) and det E = e. We get a general criterion of e-cleanness for the matrix [[a
1, a
2,..., a
n
+1]]. Under the n-stable range ondition, it is shown that [[a
1, a
2,..., a
n
+1]] is 0-clean iff (a
1, a
2,..., a
n
+1) = 1. As an application, we prove that the 0-cleanness and unit-regularity for such n × n matrix over a Dedekind domain coincide for all n ⩾ 3. The analogous for (s, 2) property is also obtained.
相似文献
2.
3.
Let R be a noetherian ring,
\mathfraka{\mathfrak{a}} an ideal of R, and M an R-module. We prove that for a finite module M, if
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is minimax for all i ≥ r ≥ 1, then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is artinian for i ≥ r. A local–global principle for minimax local cohomology modules is shown. If
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is coatomic for i ≤ r (M finite) then
Hi\mathfraka(M){{\rm H}^{i}_{\mathfrak{a}}(M)} is finite for i ≤ r. We give conditions for a module which is locally minimax to be a minimax module. A non-vanishing theorem and some vanishing
theorems are proved for local cohomology modules. 相似文献
4.
We study the asymptotic behavior of a set of random vectors ξi, i = 1,..., m, whose coordinates are independent and identically distributed in a space of infinitely increasing dimension. We investigate
the asymptotics of the distribution of the random vectors, the consistency of the sets M
m(n) = ξ1,..., ξm and X
nλ = x ∈ X
n: ρ(x) ≤ λn, and the mutual location of pairs of vectors.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1706–1711, December, 1998. 相似文献
5.
A. I. Martikainen 《Journal of Mathematical Sciences》2006,133(3):1308-1313
Let {Xi, Yi}i=1,2,... be an i.i.d. sequence of bivariate random vectors with P(Y1 = y) = 0 for all y. Put Mn(j) = max0≤k≤n-j (Xk+1 + ... Xk+j)Ik,j, where Ik,k+j = I{Yk+1 < ⋯ < Yk+j} denotes the indicator function for the event in brackets, 1 ≤ j ≤ n. Let Ln be the largest index l ≤ n for which Ik,k+l = 1 for some k = 0, 1, ..., n - l. The strong law of large numbers for “the maximal gain over the longest increasing runs,”
i.e., for Mn(Ln) has been recently derived for the case where X1 has a finite moment of order 3 + ε, ε > 0. Assuming that X1 has a finite mean, we prove for any a = 0, 1, ..., that the s.l.l.n. for M(Ln - a) is equivalent to EX
1
3+a
I{X1 > 0} < ∞. We derive also some new results for the a.s. asymptotics of Ln. Bibliography: 5 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 179–189. 相似文献
6.
For a graph G, we define σ2(G) := min{d(u) + d(v)|u, v ≠ ∈ E(G), u ≠ v}. Let k ≥ 1 be an integer and G be a graph of order n ≥ 3k. We prove if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
of length at most four such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k. And show if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k, V(C
1) ∪...∪ V(C
k
) = V(G), and |C
i
| ≤ 4 for all 1 ≤ i ≤ k − 1.
The condition of degree sum σ2(G) ≥ n + k − 1 is sharp.
Received: December 20, 2006. Final version received: December 12, 2007. 相似文献
7.
Michel Talagrand 《Israel Journal of Mathematics》1992,79(2-3):207-224
Consider a setA of symmetricn×n matricesa=(a
i,j)
i,j≤n
. Consider an independent sequence (g
i)
i≤n
of standard normal random variables, and letM=Esupa∈A|Σi,j⪯nai,jgigj|. Denote byN
2(A, α) (resp.N
t(A, α)) the smallest number of balls of radiusα for thel
2 norm ofR
n
2 (resp. the operator norm) needed to coverA. Then for a universal constantK we haveα(logN
2(A, α))1/4≤KM. This inequality is best possible. We also show that forδ≥0, there exists a constantK(δ) such thatα(logN
t≤K(δ)M.
Work partially supported by an N.S.F. grant. 相似文献
8.
André Adler 《Central European Journal of Mathematics》2006,4(1):1-4
Consider independent and identically distributed random variables {X
nk, 1 ≤ k ≤ m, n ≤ 1} from the Pareto distribution. We select two order statistics from each row, X
n(i) ≤ X
n(j), for 1 ≤ i < j ≤ = m. Then we test to see whether or not Laws of Large Numbers with nonzero limits exist for weighted sums of the random variables
R
ij = X
n(j)/X
n(i). 相似文献
9.
Harish Seshadri 《Proceedings Mathematical Sciences》2009,119(2):197-201
Using elementary comparison geometry, we prove: Let (M, g) be a simply-connected complete Riemannian manifold of dimension ≥ 3. Suppose that the sectional curvature K satisfies −1 − s(r) ≤ K ≤ −1, where r denotes distance to a fixed point in M. If lim
r → ∞ e2r
s(r) = 0, then (M, g) has to be isometric to ℍ
n
.
The same proof also yields that if K satisfies −s(r) ≤ K ≤ 0 where lim
r → ∞
r
2
s(r) = 0, then (M, g) is isometric to ℝ
n
, a result due to Greene and Wu.
Our second result is a local one: Let (M, g) be any Riemannian manifold. For a ∈ ℝ, if K ≤ a on a geodesic ball B
p
(R) in M and K = a on ∂B
p
(R), then K = a on B
p
(R). 相似文献
10.
. For each vertex v in a graph G, the maximum length of a cycle which passes through v is called the cycle number of v, denoted by c(v). A sequence a
1,a
2,…,a
n
of nonnegative integers is called a cycle sequence of a graph G if the vertices of G can be labeled as v
1,v
2,…,v
n
such that a
i
=c(v
i
) for 1≤i≤n. We give some sufficient and necessary conditions for a sequence to be a cycle sequence. We can thereby derive a polynomial
time procedure for recognizing cycle sequences.
Received: July 14, 1997 Final version received: June 15, 1998 相似文献
11.
Li Wenxia 《数学学报(英文版)》1998,14(4):487-494
Corresponding to the irreducible 0–1 matrix (a
ij
)
n×n
, take similitude contraction mappingsϕ
ij
for eacha
ij
=1, ina
ij
=1, in R
d
with ratio 0<r
ij
<1. There are unique nonempty compact setsF
1,…,F
n
satisfying for each1≤i≤n, F
i. We prove that open set condition holds if and only ifF
i
is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r
ij
3
)
n x n
is 1.
Partly supported by Natural Science Foundation of China, and partly by Natural Science Foundation of Hubei Province 相似文献
12.
LetH
i, 1 ≤ i ≤n be complex finite-dimensional Hilbert spaces of dimension di,1 ≤ i ≤n respectively withd
i ≥ 2 for everyi. By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using
a key lemma of Jaikumar [1] we show that every unitary operator on the tensor productH =H
1 ⊗H
2 ⊗... ⊗H
n can be expressed as a composition of a finite number of unitary operators living on pair productsH
i ⊗H
j,1 ≤i,j ≤n. An estimate of the number of operators appearing in such a composition is obtained.
Dedicated to Prof. A.K. Roy on his 62nd birthday. 相似文献
13.
Let G be a connected graph. We denote by σ(G,x) and δ(G) respectively the σ-polynomial and the edge-density of G, where
. If σ(G,x) has at least an unreal root, then G is said to be a σ-unreal graph. Let δ(n) be the minimum edgedensity over all n vertices graphs with σ-unreal roots. In this paper, by using the theory of adjoint polynomials, a negative answer to a problem posed by Brenti et
al. is given and the following results are obtained: For any positive integer a and rational number 0≤c≤1, there exists at least a graph sequence {G
i}1≤i≤a
such that G
i is σ-unreal and δ(G
i)→c as n→∞ for all 1 ≤i≤a, and moreover, δ(n)→0 as n→∞.
Supported by the National Natural Science Foundation of China (10061003) and the Science Foundation of the State Education
Ministry of China. 相似文献
14.
Extremes of independent Gaussian processes 总被引:1,自引:0,他引:1
Zakhar Kabluchko 《Extremes》2011,14(3):285-310
For every n ∈ ℕ, let X
1n
,..., X
nn
be independent copies of a zero-mean Gaussian process X
n
= {X
n
(t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process a
n
(M
n
− b
n
), where M
n
(t) = max
i = 1,...,n
X
in
(t), and a
n
, b
n
are normalizing constants. We also provide an analogous characterization for the limits of the process a
n
L
n
, where L
n
(t) = min
i = 1,...,n
|X
in
(t)|. 相似文献
15.
David M. Bressoud 《Proceedings Mathematical Sciences》1987,97(1-3):61-66
Given a basic hypergeometric series with numerator parametersa
1,a
2, ...,a
r and denominator parametersb
2, ...,b
r, we say it isalmost poised ifb
i, =a
1
q
δ,i
a
i,δi = 0, 1 or 2, for 2 ≤i ≤r. Identities are given for almost poised series withr = 3 andr = 5 when a1, =q
−2n.
Partially supported by N.S.F. Grant No. DMS-8521580. 相似文献
16.
Peter Adams Elizabeth J. Billington Darryn E. Bryant Saad I. El-Zanati 《Graphs and Combinatorics》2002,18(1):31-51
The Hamilton-Waterloo problem asks for a 2-factorisation of K
v
in which r of the 2-factors consist of cycles of lengths a
1,a
2,…,a
t
and the remaining s 2-factors consist of cycles of lengths b
1,b
2,…,b
u
(where necessarily ∑
i=1
t
a
i
=∑
j=1
u
b
j
=v). In this paper we consider the Hamilton-Waterloo problem in the case a
i
=m, 1≤i≤t and b
j
=n, 1≤j≤u. We obtain some general constructions, and apply these to obtain results for (m,n)∈{(4,6),(4,8),(4,16),(8,16),(3,5),(3,15),(5,15)}.
Received: July 5, 2000 相似文献
17.
We extend the scalar curvature pinching theorems due to Peng-Terng, Wei-Xu and Suh-Yang. Let M be an n-dimensional compact minimal hypersurface in S n+1 satisfying Sf 4 f_3~2 ≤ 1/n S~3 , where S is the squared norm of the second fundamental form of M, and f_k =sum λ_i~k from i and λ_i (1 ≤ i ≤ n) are the principal curvatures of M. We prove that there exists a positive constant δ(n)(≥ n/2) depending only on n such that if n ≤ S ≤ n + δ(n), then S ≡ n, i.e., M is one of the Clifford torus S~k ((k/n)~1/2 ) ×S~... 相似文献
18.
Summary We give a survey of known results regarding Schur-convexity of probability distribution functions. Then we prove that the
functionF(p
1,...,pn;t)=P(X1+...+Xn≤t) is Schur-concave with respect to (p
1,...,pn) for every realt, whereX
i are independent geometric random variables with parametersp
i. A generalization to negative binomial random variables is also presented. 相似文献
19.
Yaochen Zhu 《数学学报(英文版)》2000,16(3):395-398
Let f (x) be a continued fraction with elements a
n
x, where coefficients a
n
are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with a
n
. For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.
Received March 27, 1998, Accepted September 28, 1998 相似文献
20.
In Part I of the paper, we have proved that, for every α > 0 and a continuous function f, which is either convex (s = 0) or changes convexity at a finite collection Y
s
= {y
i
}
s
i=1 of points y
i
∈ (-1, 1),
sup{ na En(2)( f,Ys ):n \geqslant N* } \leqslant c( a, s )sup{ na En(f):n \geqslant 1 }, \sup \left\{ {{n^\alpha }E_n^{(2)}\left( {f,{Y_s}} \right):n \geqslant \mathcal{N}*} \right\} \leqslant c\left( {\alpha, s} \right)\sup \left\{ {{n^\alpha }{E_n}(f):n \geqslant 1} \right\}, 相似文献
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