共查询到20条相似文献,搜索用时 421 毫秒
1.
G. Lepsveridze 《Georgian Mathematical Journal》1998,5(2):157-176
It is proved that for any given sequence (σ
n
,n ∈ ℕ)=Γ0 ⊂ Γ, where Γ is the set of all directions in ℝ2 (i.e., pairs of orthogonal straight lines) there exists a locally integrable functionf on ℝ2 such that: (1) for almost all directionsσ ∈ Γ\Γ0 the integral ∫f is differentiable with respect to the familyB
2σ
of open rectangles with sides parallel to the straight lines fromσ: (2) for every directionσ
n
∈ Γ0 the upper derivative of ∫f with respect toB
2σ
n
equals +∞; (3) for every directionσ ∈ Γ the upper derivative of ∫ |f| with respect toB
2σ
equals +∞. 相似文献
2.
3.
WU SHIQUAN 《高校应用数学学报(英文版)》1995,10(2):223-228
MAXIMUMTREESOFFINITESEQUENCES¥WUSHIQUANAbstract:Letn,s1,s2,...,snbenon-negativeintegersandM(s1,s2,...,sn)={(a1,a2,...,a.)|aii... 相似文献
4.
Sam Gutmann 《Journal of multivariate analysis》1978,8(4):573-578
Let (X1, X2,…, Xk, Y1, Y2,…, Yk) be multivariate normal and define a matrix C by Cij = cov(Xi, Yj). If (i)
(X1,…, Xk) =
(Y1,…, Yk) and (ii) C is symmetric positive definite, then 0 < varf(X1,…, Xk) < ∞ corr(f(X1,…, Xk),f(Y1,…, Yk)) > 0. Condition (i) is necessary for the conclusion. The sufficiency of (i) and (ii) follows from an infinite-dimensional version, which can also be applied to a pair of jointly normal Brownian motions. 相似文献
5.
José Luis Cereceda 《International Journal of Mathematical Education in Science & Technology》2017,48(2):267-277
In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, Pk(n) and Qk(n), such that Pk(n) = Qk(n) = fk(n) for n = 1, 2,…?, k, where fk(1), fk(2),…?, fk(k) are k arbitrarily chosen (real or complex) values. Then, we focus on the case that fk(n) is given by the sum of powers of the first n positive integers Sk(n) = 1k + 2k + ??? + nk, and show that Sk(n) admits the polynomial representations Sk(n) = Pk(n) and Sk(n) = Qk(n) for all n = 1, 2,…?, and k ≥ 1, where the first representation involves the Eulerian numbers, and the second one the Stirling numbers of the second kind. Finally, we consider yet another polynomial formula for Sk(n) alternative to the well-known formula of Bernoulli. 相似文献
6.
Ofelia T. Alas Salvador Hernández Manuel Sanchis Michael G. Tkachenko Richard G. Wilson 《Acta Mathematica Hungarica》2006,112(3):199-219
Summary We study subposets of the lattice L_1(X) of all T1-topologies on a set X, namely Σt(X), Σ3(X) and Σlc(X), being respectively the collections of all Tychonoff, all T3 and all locally compact Hausdorff topologies on X, with a view to deciding which elements of these partially ordered sets have and which do not have covers, that is to say
immediate successors, in the respective posets. In the final section we discuss the subposet Σ G of all Hausdorff group topologies on a group G. 相似文献
7.
Aude Maignan 《Numerical Algorithms》2001,27(2):153-167
In this paper we present a new method for enclosing all the real roots in a bounded box of a system of n elementary-algebraic equations depending on n variables. This system is denoted by h(x)=P(x,f
1(x
1),...,f
k
(x
1),f
1(x
2),...,f
k
(x
n
)), where x=(x
1,x
2,...,x
n
) R
n
, P is a system of polynomials depending on n+kn variables and the univariate functions f
i
are simple. This method arises from the exclusion method of Dedieu and Yakoubsohn. We provide both a theoretical complexity bound and some numerical experiments. 相似文献
8.
A. K. Aleskeviciene 《Lithuanian Mathematical Journal》2005,45(4):359-367
Let X
1, X
2,... be independent identically distributed random variables with distribution function F, S
0 = 0, S
n
= X
1 + ⋯ + X
n
, and Sˉ
n
= max1⩽k⩽n
S
k
. We obtain large-deviation theorems for S
n
and Sˉ
n
under the condition 1 − F(x) = P{X
1 ⩾ x} = e−l(x), l(x) = x
α
L(x), α ∈ (0, 1), where L(x) is a slowly varying function as x → ∞.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 447–456, October–December, 2005. 相似文献
9.
Barry C. Arnold 《Journal of multivariate analysis》1985,17(3):316-332
Let X1, X2,…, Xn be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by X1:n, X2:n,…, Xn:n. Bounds are derived for E(Xn:n) when it is assumed that the Xi's are (i) arbitrarily dependent and (ii) independent. The effect of assuming a symmetric common distribution for the Xi's is discussed. Analogous bounds are described for the expected range of the sample. Bounds on expectations of general linear combinations of order statistics are described in the independent case. 相似文献
10.
Let R be a local ring and let (x
1, …, x
r) be part of a system of parameters of a finitely generated R-module M, where r < dimR
M. We will show that if (y
1, …, y
r) is part of a reducing system of parameters of M with (y
1, …, y
r) M = (x
1, …, x
r) M then (x
1, …, x
r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ε Supp M ∩ V
R(x
1, …, x
r) with dimR
R/P = dimR
M − r the localization M
P of M at P is an r-dimensional Cohen-Macaulay module over R
P.
Furthermore, we will show that M is a Cohen-Macaulay module iff y
d is a non zero divisor on M/(y
1, …, y
d−1) M, where (y
1, …, y
d) is a reducing system of parameters of M (d:= dimR
M). 相似文献
11.
Jaka Cimprič 《代数通讯》2013,41(11):4035-4041
12.
The construction of the extended double cover was introduced by N. Alon [1] in 1986. For a simple graph G with vertex set V = {v
1, v
2, ..., v
n
}, the extended double cover of G, denoted G
*, is the bipartite graph with bipartition (X, Y) where X = {x
1, x
2, ..., x
n
} and Y = {y
1, y
2, ..., y
n
}, in which x
i
and y
j
are adjacent iff i = j or v
i
and v
j
are adjacent in G.In this paper we obtain formulas for the characteristic polynomial and the spectrum of G
* in terms of the corresponding information of G. Three formulas are derived for the number of spanning trees in G
* for a connected regular graph G. We show that while the extended double covers of cospectral graphs are cospectral, the converse does not hold. Some results on the spectra of the nth iterared double cover are also presented. 相似文献
13.
We consider the number Kn of clusters at a distance level dn ∈ (0, 1) of n independent random variables uniformly distributed in [0, 1], or the number Kn of connected components in the random interval graph generated by these variables and dn, and, depending upon how fast dn → 0 as n → ∞, determine the asymptotic distribution of Kn, with rates of convergence, and of related random variables that describe the cluster sizes. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
14.
V. V. Bavula 《代数通讯》2013,41(8):3219-3261
The left quotient ring (i.e., the left classical ring of fractions) Qcl(R) of a ring R does not always exist and still, in general, there is no good understanding of the reason why this happens. In this article, existence of the largest left quotient ring Ql(R) of an arbitrary ring R is proved, i.e., Ql(R) = S0(R)?1R where S0(R) is the largest left regular denominator set of R. It is proved that Ql(Ql(R)) = Ql(R); the ring Ql(R) is semisimple iff Qcl(R) exists and is semisimple; moreover, if the ring Ql(R) is left Artinian, then Qcl(R) exists and Ql(R) = Qcl(R). The group of units Ql(R)* of Ql(R) is equal to the set {s?1t | s, t ∈ S0(R)} and S0(R) = R ∩ Ql(R)*. If there exists a finitely generated flat left R-module which is not projective, then Ql(R) is not a semisimple ring. We extend slightly Ore's method of localization to localizable left Ore sets, give a criterion of when a left Ore set is localizable, and prove that all left and right Ore sets of an arbitrary ring are localizable (not just denominator sets as in Ore's method of localization). Applications are given for certain classes of rings (semiprime Goldie rings, Noetherian commutative rings, the algebra of polynomial integro-differential operators). 相似文献
15.
Ozer TALO Feyzi BASAR 《数学学报(英文版)》2008,24(7):1205-1212
Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55(1)(2003), 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp(F) of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp(F) includes the space lp(F) and also shown that the spaces bvp(F) and lp(F) axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given. 相似文献
16.
W. J. Park 《Journal of multivariate analysis》1974,4(4):479-485
Strassen's version of the law of the iterated logarithm is extended to the two-parameter Gaussian process {X(s, t); ε(s, t) [0, ∞)2} with the covariance function R((s1,t1),(s2,t2)) = min(s1,s2)min(t1,t2). 相似文献
17.
A hereditary property of graphs is any class of graphs closed under isomorphism and subgraphs. Let 𝒫1, 𝒫2,…, 𝒫n be hereditary properties of graphs. We say that a graph G has property 𝒫1°𝒫2°···°𝒫n if the vertex set of G can be partitioned into n sets V1, V2,…, Vn such that the subgraph of G induced by Vi belongs to 𝒫i; i = 1, 2,…, n. A hereditary property is said to be reducible if there exist hereditary properties 𝒫1 and 𝒫2 such that ℛ = 𝒫1°𝒫2; otherwise it is irreducible. We prove that the factorization of a reducible hereditary property into irreducible factors is unique whenever the property is additive, i.e., it is closed under the disjoint union of graphs. © 2000 John Wiley & Sons, Inc. J Graph Theory 33: 44–53, 2000 相似文献
18.
A note on the interlacing of zeros and orthogonality 总被引:1,自引:0,他引:1
Kathy Driver 《Journal of Approximation Theory》2009,161(2):508-510
Let be a sequence of monic polynomials with deg(tn)=n such that, for each n∈N, the zeros of tn are real and simple and tn and tn+1 have no common zeros. We discuss the connection between the orthogonality of the sequence, the positivity of a certain ratio, and the interlacing of the zeros of tn and tn+1 for n≥1, n∈N. 相似文献
19.
C. Y. Dang 《Journal of Optimization Theory and Applications》1992,75(1):51-67
We construct a new triangulation of (0, 1] ×R
n
, calledD
3-triangulation, with continuous refinement of grid sizes for simplicial deformation algorithms for computing solutions of nonlinear equations. It is proved that theD
3-triangulation is superior to the well-knownK
3-triangulation andJ
3-triangulation in the number of simplices. The surface density of theD
3-triangulation also must be less than that of theK
3-triangulation and theJ
3-triangulation. Numerical tests show that the simplicial deformation algorithm based on theD
3-triangulation indeed is much more efficient.The author would like to thank Dolf Talman for his remarks on an earlier version of this paper, three anonymous referees for their constructive suggestions, and Gerard van der Laan, Kaizhou Chen, and Xuchu He for their encouragement. 相似文献
20.
Amparo Gil Javier Segura Nico M. Temme 《Journal of Computational and Applied Mathematics》2006,190(1-2):270-286
Each member of the family of Gauss hypergeometric functions
fn=2F1(a+ε1n,b+ε2n;c+ε3n;z),