共查询到20条相似文献,搜索用时 31 毫秒
1.
R.A. Maller 《Stochastic Processes and their Applications》1978,8(2):171-179
Let Xi be iidrv's and Sn=X1+X2+…+Xn. When EX21<+∞, by the law of the iterated logarithm for some constants αn. Thus the r.v. is a.s.finite when δ>0. We prove a rate of convergence theorem related to the classical results of Baum and Katz, and apply it to show, without the prior assumption EX21<+∞ that EYh<+∞ if and only if for 0<h<1 and δ> , whereas whenever h>0 and . 相似文献
2.
Takahiko Nakazi 《Journal of Functional Analysis》1983,53(3):224-230
If φ ∈ L∞, we denote by Tφ the functional defined on the Hardy space H1 by . Let Sφ be the set of functions in H1 which satisfy . It is known that if φ is continuous, then Sφ is weak-1 compact and not empty. For many noncontinuous φ each Sφ is weak-1 compact and not empty. A complete descr ption of Sφ if Sφ is weak-1 compact and not empty is obtained. Sφ is not empty if and only if for some nonzero ? in H1. It is shown that if and , where p is an analytic polynomial and g is a strong outer function, then Sφ is weak-1 compact. As the consequence, if , then Sφ is weak-1 compact. 相似文献
3.
Yuliang Wen 《Comptes Rendus Mathematique》2004,338(3):229-234
Let M2n be a 2n-dimensional compact, simply connected Riemannian manifold without boundary and S2n be the unit sphere of 2n+1 dimension Euclidean space . We prove in this note that if the sectional curvature KM varies in (0,1] and the volume V(M) is not larger than for some positive number η depending only on n, then M2n is homeomorphic to S2n. To cite this article: Y. Wen, C. R. Acad. Sci. Paris, Ser. I 338 (2004). 相似文献
4.
Grzegorz Banaszak 《Comptes Rendus Mathematique》2003,337(9):575-580
Let l be an odd prime number, F denote any totally real number field and E/F be an Abelian CM extension of F of conductor f. In this paper we prove that for every n odd and almost all prime numbers l we have where Sn(E/F,l) is the Stickelberger ideal (Ann. of Math. 135 (1992) 325–360; J. Coates, p-adic L-functions and Iwasawa's theory, in: Algebraic Number Fields by A. Fröhlich, Academic Press, London, 1977). In addition if we assume the Quillen–Lichtenbaum conjecture then To cite this article: G. Banaszak, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
5.
Witold Lipski 《Discrete Mathematics》1978,21(3):253-259
Let Sπ be the length of a shortest sequence of positive integers which contains every Y ?{1,…,n} as a subsequence of |Y| consecutive terms. We give the following asymptotic estimation: . The upper bound is derived constructively. 相似文献
6.
Let C(S) be the space of real-valued continuous functions on a compact metric space S. Let {Xn, n ? 1} be a sequence of independent identically distributed C(S)-valued random variables with mean zero and supt?sE[X12(t)] = 1. We show that the measures induced by ( converge weakly to a Gaussian measure on C(S) under different conditions on X1, one of which consolidates and extends results of Strassen and Dudley, Giné, and Dudley. Our method of proof is different from the methods employed by these authors. 相似文献
7.
《Topology and its Applications》1987,26(1):83-92
We modify various lemmas from Dydak's paper on the Vietoris-Smale theorem to obtain more general results. We consider closed subsets X and Y of paracompact spaces M, N respectively, and a map F:M→N such that F∥X:X→Y is closed and surjective and X=F-1(Y) to obtain the following result.(Theorem). If for each y ϵ Y and N is LCn+1, then the morphism in-pro- induced by the morphism is an isomorphism of in-pro-Grp for k⩽n and an epimorphism for k=n+1. 相似文献
8.
Shlomo Moran 《Journal of Combinatorial Theory, Series B》1984,37(2):113-141
Let V be a set of n points in Rk. Let d(V) denote the diameter of V, and l(V) denote the length of the shortest circuit which passes through all the points of V. (Such a circuit is an “optimal TSP circuit”.) lk(n) are the extremal values of l(V) defined by lk(n)=max{l(V)|V∈Vnk}, where Vnk={V|V?Rk,|V|=n, d(V)=1}. A set V∈Vnk is “longest” if l(V)=lk(n). In this paper, first some geometrical properties of longest sets in R2 are studied which are used to obtain l2(n) for small n′s, and then asymptotic bounds on lk(n) are derived. Let δ(V) denote the minimal distance between a pair of points in V, and let: δk(n)=max{δ(V)|V∈Vnk}. It is easily observed that . Hence, exists. It is shown that for all , and hence, for all . For k=2, this implies that , which generalizes an observation of Fejes-Toth that . It is also shown that . The above upper bound is used to improve related results on longest sets in k-dimensional unit cubes obtained by Few (Mathematika2 (1955), 141–144) for almost all k′s. For k=2, Few's technique is used to show that . 相似文献
9.
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
10.
Detlef Müller 《Journal of Functional Analysis》1982,47(2):247-280
Let F1(Rn) denote the Fourier algebra on n, and (n) the space of test functions on n. A closed subset E of n is said to be of spectral synthesis if the only closed ideal J in F1(Rn) which has E as its hull is the ideal . We consider sufficiently regular compact subsets of smooth submanifolds of n with constant relative nullity. For such sets E we give an estimate of the degree of nilpotency of the algebra , where j(E) denotes the smallest closed ideal in F1(Rn) with hull E. Especially in the case of hypersurfaces this estimate turns out to be exact. Moreover for this case we prove that k(E)∩D(Rn) is dense in k(E). Together this solves the synthesis problem for such sets. 相似文献
11.
Let be an elliptic curve with complex multiplication, defined over . We consider linear forms on with coefficients in the CM field of . Within this framework, we present a new measure of linear independence for elliptic logarithms in (logb)(loga)n. Like recent advances in this domain (works by Ably, David, Hirata-Kohno), our result is best possible in terms of the height of the linear forms (logb) while providing a better estimate in the height of algebraic points considered (loga), removing a term in logloga. To cite this article: M. Ably, É. Gaudron, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
12.
Wolfgang Wasow 《Linear algebra and its applications》1977,18(2):163-170
Let A(x,ε) be an n×n matrix function holomorphic for |x|?x0, 0<ε?ε0, and possessing, uniformly in x, an asymptotic expansion , as ε→0+. An invertible, holomorphic matrix function P(x,ε) with an asymptotic expansion , as ε→0+, is constructed, such that the transformation y = P(x,ε)z takes the differential equation a positive integer, into , where B(x,ε) is asymptotically equal, to all orders, to a matrix in a canonical form for holomorphic matrices due to V.I. Arnold. 相似文献
13.
R.S. Singh 《Journal of multivariate analysis》1976,6(2):338-342
Let Xj = (X1j ,…, Xpj), j = 1,…, n be n independent random vectors. For x = (x1 ,…, xp) in Rp and for α in [0, 1], let Fj(x) = αI(X1j < x1 ,…, Xpj < xp) + (1 ? α) I(X1j ≤ x1 ,…, Xpj ≤ xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, α max1 ≤ N ≤ n |Σ0n(Fj(x) ? Fj(x))|. It is shown that P[Dn ≥ L] < 4pL exp{?2(L2n?1 ? 1)} for each positive integer n and for all L2 ≥ n; and, as n → ∞, with probability one. 相似文献
14.
K.B. Athreya 《Statistics & probability letters》1983,1(3):147-150
Let X1, X2, X3, … be i.i.d. r.v. with E|X1| < ∞, E X1 = μ. Given a realization X = (X1,X2,…) and integers n and m, construct Yn,i, i = 1, 2, …, m as i.i.d. r.v. with conditional distribution for 1 ? j ? n. ( denotes conditional distribution given X). Conditions relating the growth rate of m with n and the moments of X1 are given to ensure the almost sure convergence of toμ. This equation is of some relevance in the theory of Bootstrap as developed by Efron (1979) and Bickel and Freedman (1981). 相似文献
15.
Stephen M Tanny 《Journal of Combinatorial Theory, Series A》1976,21(2):196-202
Let π = (π(1), π(2),…, π(n)) be a permutation on {1, 2, …, n}. A succession (respectively, 1-succession) in π is any pair π(i), π(i + 1), where π(i + 1) = π(i) + 1 (respectively, π(i + 1) ≡ π(i) + 1 (mod n)), i = 1, 2, …, n ? 1. Let R(n, k) (respectively, ) be the number of permutations with k successions (respectively, 1-successions). In this note we determine R(n, k) and . In addition, these notions are generalized to the case of circular permutations, where analogous results are developed. 相似文献
16.
Jesper Michael Møller 《Topology and its Applications》1983,16(3):279-286
Let π: E→X be a principal n-bundle and p:V→X an m-dimensional complex vector bundle over, say, a connected CW-complex X. An equivariant embedding of π into p is an embedding h:E → V commuting with projections such that h(e · z)=zh(e) for all eεE and . We compute the primary obstruction to embedding π equivariantly into p. If dim X?2m, then c=0 if and only if π admits an equivariant embedding into p. If dim X>2m and π embeds equivariantly into p, then c=0. Other embedding criteria exist in case p is the trivial m-plane bundle εm. We use these criteria for a discussion of the classification of the equivalence classes of principal -bundles that admit equivariant embeddings into εm. Finally, we offer an example of a principal -bundle that admit an ordinary but not an equivariant embedding into ε1. 相似文献
17.
G.F Clements 《Journal of Combinatorial Theory, Series A》1974,17(2):227-244
Let S(n) denote the set of subsets of an n-element set. For an element x of S(n), let Γx and Px denote, respectively, all (|x| ?1)-element subsets of x and all (|x| + 1)-element supersets of x in S(n). Several inequalities involving Γ and P are given. As an application, an algorithm for finding an x-element antichain in S(n) satisfying for all x-element antichains X in S(n) is developed, where YX is the set of all elements of S(n) contained in an element of X. This extends a result of Kleitman [9] who solved the problem in case x is a binomial coefficient. 相似文献
18.
Let A be a -algebra, B be a -subalgebra of A, and φ be a factorial state of B. Sometimes, φ may be extended to a factorial state of A by a tensor product method of Sakai (“-algebras and -algebras, Springer-Verlag, Berlin/Heidelberg/ New York 1971”). Sometimes, there is a weak expectation of A into , and then factorial extensions may be found by a method of Sakai and Tsui (Yokohama Math. J.29 (1981), 157–160). These two methods are shown to have the same effect, and the factorial extensions produced by them are analysed. 相似文献
19.
Michel Talagrand 《Comptes Rendus Mathematique》2003,337(7):477-480
Consider a random Hamiltonian for We assume that the family is jointly Gaussian centered and that for =ξ(N?1∑i?Nσ1iσ2i) for a certain function ξ on . F. Guerra proved the remarkable fact that the free energy of the system with Hamiltonian is bounded below by the free energy of the Parisi solution provided that ξ is convex on . We prove that this fact remains (asymptotically) true when the function ξ is only assumed to be convex on . This covers in particular the case of the p-spin interaction model for any p. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
20.