共查询到20条相似文献,搜索用时 15 毫秒
1.
S. Ihara 《Journal of multivariate analysis》1974,4(1):74-87
The message m = {m(t)} is a Gaussian process that is to be transmitted through the white Gaussian channel with feedback: . Under the average power constraint, , we construct causally the optimal coding, in the sense that the mutual information It(m, Y) between the message m and the channel output Y (up to t) is maximized. The optimal coding is presented by , where and A(s) is a positive function such that . 相似文献
2.
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
3.
Hsin Chu 《Journal of Mathematical Analysis and Applications》1982,85(2):566-583
Let X and Y be Banach spaces, ; P is said to be strongly ?-accretive if for some c > 0 and each x,y?X. These mappings constitute a generalization simultaneously of monotone mappings () and accretive mappings (when Y = X). By applying a theorem of 1. Ekeland, it is shown that a localized class of these mappings must be surjective under appropriate geometric assumptions on and continuity assumptions on P. The results generalize two theorems of F. E. Browder and the proofs further refine the methodology for dealing with such mappings. 相似文献
4.
For 1 ? p ? ∞, let , be the lp norm of an m × n complex A = (αij) ?Cm × n. The main purpose of this paper is to find, for any p, q ? 1, the best (smallest) possible constants τ(m, k, n, p, q) and σ(m, k, n, p, q) for which inequalities of the form hold for all A?Cm × k, B?Ck × n. This leads to upper bounds for inner products on Ck and for ordinary lp operator norms on Cm × n. 相似文献
5.
D de Caen 《Journal of Combinatorial Theory, Series B》1983,34(3):340-349
The Turán number T(n, l, k) is the smallest possible number of edges in a k-graph on n vertices such that every l-set of vertices contains an edge. Given a k-graph H = (V(H), E(H)), we let Xs(S) equal the number of edges contained in S, for any s-set S?V(H). Turán's problem is equivalent to estimating the expectation E(Xl), given that min(Xl) ≥ 1. The following lower bound on the variance of Xs is proved: , where m = |E(H)| and . This implies the following: putting t(k, l) = limn→∞T(n, l, k)(kn)?1 then t(k, l) ≥ T(s, l, k)((ks) ? 1)?1, whenever s ≥ l > k ≥ 2. A connection of these results with the existence of certain t-designs is mentioned. 相似文献
6.
Let F be a Sperner family of subsets of {1,…,m}. Bollobás showed that if , and if the parameters of F are p0,…,pm then Here we generalize this result and prove some analogues of it. A corollary of Bollobás' result is that . Purdy proved that if then , which implies Bollobás' corollary. We also show that Purdy's result may be deduced from Bollobás' by a short argument. Finally, we give a canonical form for Sperner families which are also pairwise intersecting. 相似文献
7.
Let Ω = {1, 0} and for each integer n ≥ 1 let (n-tuple) and for all k = 0,1,…,n. Let {Ym}m≥1 be a sequence of i.i.d. random variables such that . For each A in , let TA be the first occurrence time of A with respect to the stochastic process {Ym}m≥1. R. Chen and A.Zame (1979, J. Multivariate Anal. 9, 150–157) prove that if n ≥ 3, then for each element A in , there is an element B in such that the probability that TB is less than TA is greater than . This result is sharpened as follows: (I) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A in , there is an element B also in such that the probability that TB is less than TA is greater than ; (II) for n ≥ 4 and 1 ≤ k ≤ n ? 1, each element A = (a1, a2,…,an) in , there is an element C also in such that the probability that TA is less than TC is greater than if n ≠ 2m or n = 2m but ai = ai + 1 for some 1 ≤ i ≤ n?1. These new results provide us with a better and deeper understanding of the fair coin tossing process. 相似文献
8.
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
9.
Norbert Herrndorf 《Journal of multivariate analysis》1984,15(1):141-146
In this note a functional central limit theorem for ?-mixing sequences of I. A. Ibragimov (Theory Probab. Appl.20 (1975), 135–141) is generalized to nonstationary sequences (Xn)n ∈ , satisfying some assumptions on the variances and the moment condition for some b > 0, ? > 0. 相似文献
10.
A regularity result for singular nonlinear elliptic systems in inverse-power weighted Sobolev spaces
P.D Smith 《Journal of Differential Equations》1984,53(2):125-138
The compactness method to weighted spaces is extended to prove the following theorem:Let H2,s1(B1) be the weighted Sobolev space on the unit ball in Rn with norm Let n ? 2 ? s < n. Let u? [H2,s1(B1) ∩ L∞(B1)]N be a solution of the nonlinear elliptic system , are uniformly continuous functions of their arguments and satisfy: . Then there exists an R1, 0 < R1 < 1, and an α, 0 < α < 1, along with a set such that (1) , (2) Ω does not contain the origin; Ω does not contain BR1, (3) is open, (4) u is ; u is LipαBR1. 相似文献
11.
In College de France, Seminaire E.D.P. II, Nov. 1963–May 1964, Peetre has introduced the smooth distribution semi-group which is discussed here. This notion is redefined by introducing a functional space , which measures the regularity of such a distribution. This allows us to give a spectral characterization of such groups. We show that the iterated resolvent of the infinitesimal generator of a smooth distribution group satisfies the relation , Re λ ≠ 0. The application of this notion is illustrated by the study of the Schrödinger equation in Lp(n). 相似文献
12.
A new method of finding explicit solutions of Lyapunov equations is described based on a lemma on one-dimensional perturbations of invertible operators. If Y satisfies the equation for an appropriate vector b, then X = Y-1 satisfies for a given vector a. A concrete example [with a=(1,0,…,0)T] is given. 相似文献
13.
József Beck 《Journal of Combinatorial Theory, Series A》1981,30(2):117-133
Let {Ai} be a family of sets and let S = ∩iAi. By a positional game we shall mean a game played by two players on {Ai}. The players alternately pick elements of S and that player wins who fist has all the elements of one of the Ai. This paper deals with almost disjoint hypergraphs only, i.e., |Ai∪Aj| ? 1 if i ≠ j. Let be the smallest integer for which there is an almost disjoint n-uniform hypergraph , so that the first player has a winning strategy. It is shown that , which was conjectured by Erdös. The same method is applied to prove a conjecture of Hales and Jewett on r-dimensional tick-tack-toe if r is large enough. Finally we prove that for an arbitrary almost disjoint n-uniform hypergraph the second player has such a strategy that the first player unable to win in his mth move if m < (2 ? ?)n. 相似文献
14.
Alexander Litvak Alain Pajor Mark Rudelson Nicole Tomczak-Jaegermann Roman Vershynin 《Comptes Rendus Mathematique》2004,339(1):33-38
Let be the space equipped with a norm 6·6 whose unit ball has a bounded volume ratio with respect to the Euclidean unit ball. Let Γ be any random N×n matrix with N>n, whose entries are independent random variables satisfying some moment assumptions. We show that with high probability Γ is a good isomorphism from the n-dimensional Euclidean space onto its image in : there exist α,β>0 such that for all , . This solves a conjecture of Schechtman on random embeddings of ?2n into ?1N. To cite this article: A. Litvak et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004). 相似文献
15.
J.H Michael 《Journal of Mathematical Analysis and Applications》1981,79(1):203-217
We consider the mixed boundary value problem , where Ω is a bounded open subset of n whose boundary Γ is divided into disjoint open subsets Γ+ and Γ? by an (n ? 2)-dimensional manifold ω in Γ. We assume A is a properly elliptic second order partial differential operator on and Bj, for j = 0, 1, is a normal jth order boundary operator satisfying the complementing condition with respect to A on . The coefficients of the operators and Γ+, Γ? and ω are all assumed arbitrarily smooth. As announced in [Bull. Amer. Math. Soc.83 (1977), 391–393] we obtain necessary and sufficient conditions in terms of the coefficients of the operators for the mixed boundary value problem to be well posed in Sobolev spaces. In fact, we construct an open subset of the reals such that, if then for is a Fredholm operator if and only if s ∈ . Moreover, = ?xewx, where the sets x are determined algebraically by the coefficients of the operators at x. If n = 2, x is the set of all reals not congruent (modulo 1) to some exceptional value; if n = 3, x is either an open interval of length 1 or is empty; and finally, if n ? 4, x is an open interval of length 1. 相似文献
16.
Gérald Tenenbaum 《Journal of Number Theory》1982,15(3):331-346
The condition , where Ω(n) stands for the number of prime factors, counted according to multiplicity, of the positive integer n, is shown to be necessary and sufficient for the integer sequence with characteristic function χ to have divisor density z, i.e., Σd|nχ(d) = (z + o(1)) Σd|n 1 when n → ∞ if one neglects a sequence of asymptotic density zero. Among the applications, the following result, first conjectured by R. R. Hall, is proved: given any positive α, we have, for almost all n's, and uniformly with respect to z in |0, 1|, 相似文献
17.
18.
This paper is a study of the distribution of eigenvalues of various classes of operators. In Section 1 we prove that the eigenvalues (λn(T)) of a p-absolutely summing operator, p ? 2, satisfy This solves a problem of A. Pietsch. We give applications of this to integral operators in Lp-spaces, weakly singular operators, and matrix inequalities.In Section 2 we introduce the quasinormed ideal Π2(n), P = (p1, …, pn) and show that for T ∈ Π2(n), 2 = (2, …, 2) ∈ Nn, the eigenvalues of T satisfy More generally, we show that for T ∈ Πp(n), P = (p1, …, pn), pi ? 2, the eigenvalues are absolutely p-summable, We also consider the distribution of eigenvalues of p-nuclear operators on Lr-spaces.In Section 3 we prove the Banach space analog of the classical Weyl inequality, namely , 0 < p < ∞, where αn denotes the Kolmogoroff, Gelfand of approximation numbers of the operator T. This solves a problem of Markus-Macaev.Finally we prove that Hilbert space is (isomorphically) the only Banach space X with the property that nuclear operators on X have absolutely summable eigenvalues. Using this result we show that if the nuclear operators on X are of type l1 then X must be a Hilbert space. 相似文献
19.
Let , let , where g2 and g3 are coefficients of the elliptic curve: Y2 = 4X3 ? g2X ? g3 over a finite field and Δ = g23 ? 27g32 and let . Then the p-adic cohomology theory will be applied to compute explicitly the zeta matrices of the elliptic curves, induced by the pth power map on the free -module . Main results are; Theorem 1.1: X2dY and YdX are basis elements for ; Theorem 1.2: YdX, X2dY, Y?1dX, Y?2dX and XY?2dX are basis elements for , where is a lifting of X, and all the necessary recursive formulas for this explicit computation are given. 相似文献
20.
Pedro M Girão 《Comptes Rendus Mathematique》2002,334(2):105-108
Let N?5, a>0, be a smooth bounded domain in , , and 6u62=|?u|22+a|u|22. We prove there exists an α0>0 such that, for all , This inequality implies Cherrier's inequality. To cite this article: P.M. Girão, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 105–108 相似文献