共查询到20条相似文献,搜索用时 31 毫秒
1.
Vernon Watts 《Probability Theory and Related Fields》1980,54(3):281-285
Summary Let {X
n} be independent and identically distributed and let X
kn
(n)
denote the k
n-th order statistic for X
1 ..., X
n, where k
n but k
n/n0. A representation for X
kn
(n)
in terms of the empirical distribution function is developed. The conditions include those under which X
kn
(n)
is asymptotically normal.Research partially supported by the University of North Carolina at Chapel Hill under Office of Naval Research Contract No. N00014-75-C-0809 and by The Florida State University under Office of Naval Research Contract No. N00014-76-C-0608. 相似文献
2.
James R. Holub 《Israel Journal of Mathematics》1985,52(3):231-238
LetW(D) denote the set of functionsf(z)=Σ
n=0
∞
A
n
Z
n
a
nzn for which Σn=0
∞|a
n
|<+∞. Given any finite set lcub;f
i
(z)rcub;
i=1
n
inW(D) the following are equivalent: (i) The generalized shift sequence lcub;f
1(z)z
kn
,f
2(z)z
kn+1, …,f
n
(z)z
(k+1)n−1rcub;
k=0
∞
is a basis forW(D) which is equivalent to the basis lcub;z
m
rcub;
m=0
∞
. (ii) The generalized shift sequence is complete inW(D), (iii) The function
has no zero in |z|≦1, wherew=e
2πiti
/n. 相似文献
3.
Given n vectors {i} ∈ [0, 1)d, consider a random walk on the d‐dimensional torus ??d = ?d/?d generated by these vectors by successive addition and subtraction. For certain sets of vectors, this walk converges to Haar (uniform) measure on the torus. We show that the discrepancy distance D(Q*k) between the kth step distribution of the walk and Haar measure is bounded below by D(Q*k) ≥ C1k?n/2, where C1 = C(n, d) is a constant. If the vectors are badly approximated by rationals (in a sense we will define), then D(Q*k) ≤ C2k?n/2d for C2 = C(n, d, j) a constant. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 相似文献
4.
This paper is concerned with double sequencesC={C
n}
n
=–/
of Hermitian matrices with complex entriesC
n
M
s×s
) and formal Laurent seriesL
0(z)=–
k=1
C
–k
z
k
andL
(z)=
k=0
C
k
z
–k
. Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L
0,L
) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given. 相似文献
5.
Susana Elena Trione 《Studies in Applied Mathematics》1988,79(2):127-141
Let t = (t1,…,tn) be a point of ?n. We shall write . We put, by the definition, Wα(u, m) = (m?2u)(α ? n)/4[π(n ? 2)/22(α + n ? 2)/2Г(α/2)]J(α ? n)/2(m2u)1/2; here α is a complex parameter, m a real nonnegative number, and n the dimension of the space. Wα(u, m), which is an ordinary function if Re α ≥ n, is an entire distributional function of α. First we evaluate {□ + m2}Wα + 2(u, m) = Wα(u, m), where {□ + m2} is the ultrahyperbolic operator. Then we express Wα(u, m) as a linear combination of Rα(u) of differntial orders; Rα(u) is Marcel Riesz's ultrahyperbolic kernel. We also obtain the following results: W?2k(u, m) = {□ + m2}kδ, k = 0, 1,…; W0(u, m) = δ; and {□ + m2}kW2k(u, m) = δ. Finally we prove that Wα(u, m = 0) = Rα(u). Several of these results, in the particular case µ = 1, were proved earlier by a completely different method. 相似文献
6.
For a code C=C(n,M) the level
k code of C, denoted C
k
, is the set of all vectors resulting from a linear combination of precisely k distinct codewords of C. We prove that if k is any positive integer divisible by 8, and n=k, M=k2k then there is a codeword in C
k
whose weight is either 0 or at most
. In particular, if <(4–2)2/48 then there is a codeword in C
k
whose weight is n/2–(n). The method used to prove this result enables us to prove the following: Let k be an integer divisible by p, and let f(k,p) denote the minimum integer guaranteeing that in any square matrix over Z
p
, of order f(k,p), there is a square submatrix of order k such that the sum of all the elements in each row and column is 0. We prove that lim inf f(k,2)/k<3.836. For general p we obtain, using a different approach, that f(k,p)p(
k
/ ln
k
)(1+
o
k
(1)). 相似文献
7.
Vito Lampret 《Central European Journal of Mathematics》2012,10(2):775-787
An asymptotic approximation of Wallis’ sequence W(n) = Π
k=1
n
4k
2/(4k
2 − 1) obtained on the base of Stirling’s factorial formula is presented. As a consequence, several accurate new estimates
of Wallis’ ratios w(n) = Π
k=1
n
(2k−1)/(2k) are given. Also, an asymptotic approximation of π in terms of Wallis’ sequence W(n) is obtained, together with several double inequalities such as, for example,
W(n) ·(an + bn ) < p < W(n) ·(an + b¢n )W(n) \cdot (a_n + b_n ) < \pi < W(n) \cdot (a_n + b'_n ) 相似文献
8.
Fort=2,3 andk2t–1 we prove the existence oft–(n,k,) designs with independence numberC
,k
n
(k–t)/(k–1)
(ln n)
1/(k–1)
. This is, up to the constant factor, the best possible.Some other related results are considered.Supported by NSF Grant DMS-9011850 相似文献
9.
Cordero Luis A. Fernández Marisa Ugarte Luis 《Annals of Global Analysis and Geometry》2002,22(4):355-373
For any compact complex manifold M with a compatible symplectic form, we consider the homomorphisms L
1,0: H
1,0(M) H
{n, n–1(M) and L
0, 1: H
0, 1(M) H
n – 1, n
(M) given by the cup product with []
n – 1, n being the complex dimension of M andH
*, *(M) the Dolbeault cohomology of M. We say that Mhas Lefschetz complex type (1, 0) (resp. (0, 1)) if L
1, 0 (resp.L
0, 1) is injective. Such conditions can be considered as complexversions of the (real) Lefschetz condition studied by Benson and Gordonin [Topology
27 (1988), 513–518]for symplectic manifolds. Within the class of compactcomplex nilmanifolds, we prove that the injectivity of L
1, 0characterizes those complex structures which are Abelian in the sense ofBarberis et al. [Ann. Global Anal. Geom.
13 (1995), 289–301]. In contrast, complex tori are the only nilmanifolds having Lefschetz complex type (0, 1). 相似文献
10.
LetF(W) be a Wiener functional defined byF(W)=I
n(f) whereI
n(f) denotes the multiple Wiener-Ito integral of ordern of the symmetricL
2([0, 1]
n
) kernelf. We show that a necessary and sufficient condition for the existence of a continuous extension ofF, i.e. the existence of a function ø(·) from the continuous functions on [0, 1] which are zero at zero to which is continuous in the supremum norms and for which ø(W)=F(W) a.s, is that there exists a multimeasure (dt
1,...,dt
n
) on [0, 1]
n
such thatf(t
1, ...,t
n
) = ((t
1, 1]), ..., (t
n
, 1]) a.e. Lebesgue on [0, 1]
n
. Recall that a multimeasure (A
1,...,A
n
) is for every fixedi and every fixedA
i,...,Ai-1, Ai+1,...,An a signed measure inA
i
and there exists multimeasures which are not measures. It is, furthermore, shown that iff(t
1,t
2, ...,t
n
) = ((t
1, 1], ..., (t
n
, 1]) then all the tracesf
(k),
off exist, eachf(k) induces ann–2k multimeasure denoted by (k), the following relation holds
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