共查询到20条相似文献,搜索用时 318 毫秒
1.
Jana Jurečková Pranab Kumar Sen 《Annals of the Institute of Statistical Mathematics》1990,42(2):345-357
For a general (real) parameter, let M
nbe the M-estimator and M
n
(1) be its one-step version (based on a suitable initial estimator M
n
(0)). It is known that, under certain regularity conditions, n(M
n
(1)-M
n)=O
p(1). The asymptotic distribution of n(M
n
(1)-M
n) is studied; it is typically non-normal and it reveals the role of the initial estimator M
n
(0).Work of this author was partially supported by the Office of Naval Research, Contract No. N00014-83-K-0387 相似文献
2.
WangShiying ZhangYuren LiuYan 《高校应用数学学报(英文版)》1999,14(4):492-494
Abstract. Let Sn be the symmetric group 相似文献
3.
An SOLS (self-orthogonal latin square) of order v with ni missing sub-SOLS (holes) of order hi (1ik), which are disjoint and spanning (i.e. ∑i=1k nihi=v), is called a frame SOLS and denoted by FSOLS(h1n1h2n2 hknk). It has been proved that for b2 and n odd, an FSOLS(anb1) exists if and only if n4 and n1+2b/a. In this paper, we show the existence of FSOLS(anb1) for n even and FSOLS(an11) for n odd. 相似文献
4.
Klaus-Hilmar Sprenger 《Mathematical Logic Quarterly》1997,43(2):251-286
We compare two different Grzegorczyk hierarchies {Hnσ}n≥0 and {Lnσ}n≥1 on term algebras, which grow according to the height and length of terms, respectively. The solution of almost all inclusion problems among the Grzegorczyk classes and the (simultaneous) recursion number classes Rnσ and Snσ on term algebras shows {Hnσ}n≥0 to generalize Weihrauch's Grzegorczyk hierarchy on words {Enk}n≥0 to arbitrary term algebras. However, by regarding terms as words, {Lnσ}n≥1 turns out to be computationally equivalent to Weihrauch's hierarchy {Enσ}n≥0 on the whole. Especially, L2σ} is equivalent to polynomial time computability and contains several natural term algebra functions. This establishes a notion of feasible term algebra functions and predicates. 相似文献
5.
《Quaestiones Mathematicae》2013,36(3):297-309
We have proved that for all compact linear operator u from R into an Lp ([0,1], ν) (0 < p < 1) extends to L 1 ([0,1], ν), where R denotes the closed linear subspace in L 1 ([0,1], ν) of the Rademacher functions {rn }n ? N. In this paper, we study this type of extension for En ? L2n 1 where En is the n–dimensional subspace which appears in Kasin's theorem such that L2n 1 = En ⊕ E ⊥ n and the L2n 1 , L2n 2 norms are universally equivalent on both En , E ⊥ n. We show that, the precedent extension fails for the pair (En , L2n 1 ) and we generalize this to any E in an L 1(Ω, A, P) by giving some conditions on E. 相似文献
6.
Paul Purdom Jr. 《BIT Numerical Mathematics》1970,10(1):76-94
An algorithm is given for computing the transitive closure of a directed graph in a time no greater thana
1
N
1
n+a
2
n
2 for largen wherea
1 anda
2 are constants depending on the computer used to execute the algorithm,n is the number of nodes in the graph andN
1 is the number of arcs (not counting those arcs which are part of a cycle and not counting those arcs which can be removed without changing the transitive closure). For graphs where each arc is selected at random with probabilityp, the average time to compute the transitive closure is no greater than min{a
1
pn
3+a
2
n
2, 1/2a
1
n
2
p
–2+a
2
n
2} for largen. The algorithm will compute the transitive closure of an undirected graph in a time no greater thana
2
n
2 for largen. The method uses aboutn
2+n bits and 5n words of storage (where each word can holdn+2 values). 相似文献
7.
Zhen Guo 《数学学报(英文版)》2009,25(1):77-84
Let x : Mn^n→ R^n+1 be an n(≥2)-dimensional hypersurface immersed in Euclidean space Rn+1. Let σi(0≤ i≤ n) be the ith mean curvature and Qn = ∑i=0^n(-1)^i+1 (n^i)σ1^n-iσi. Recently, the author showed that Wn(x) = ∫M QndM is a conformal invariant under conformal group of R^n+1 and called it the nth Willmore functional of x. An extremal hypersurface of conformal invariant functional Wn is called an nth order Willmore hypersurface. The purpose of this paper is to construct concrete examples of the 3rd order Willmore hypersurfaces in Ra which have good geometric behaviors. The ordinary differential equation characterizing the revolutionary 3rd Willmore hypersurfaces is established and some interesting explicit examples are found in this paper. 相似文献
8.
We show that for each n ≥ 1, if T2n does not prove the weak pigeonhole principle for Σbn functions, then the collection scheme B Σ1 is not finitely axiomatizable over T2n. The same result holds with Sn2 in place of T 2n (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
The complementarity problem with a nonlinear continuous mappingf from the nonnegative orthantR
+
n
ofR
n intoR
n can be written as the system of equationsF(x, y) = 0 and(x, y) R
+
2n
, whereF denotes the mapping from the nonnegative orthantR
+
2n
ofR
2n intoR
+
n
× Rn defined byF(x, y) = (x
1y1,,xnyn, f1(x) – y1,, fn(x) – yn) for every(x, y) R
+
2n
. Under the assumption thatf is a uniformP-function, this paper establishes that the mappingF is a homeomorphism ofR
+
2n
ontoR
+
n
× Rn. This result provides a theoretical basis for a new continuation method of tracing the solution curve of the one parameter family of systems of equationsF(x, y) = tF(x
0, y0) and(x, y) R
+
2n
from an arbitrary initial point(x
0, y0) R
+
2n
witht = 1 until the parametert attains 0. This approach is an extension of the one used in the polynomially bounded algorithm recently given by Kojima, Mizuno and Yoshise for solving linear complementarity problems with positive semi-definite matrices. 相似文献
10.
We determine all square-free odd positive integers n such that the 2-Selmer groups S
n
and Ŝ
n
of the elliptic curve E
n
: y
2 = x(x − n)(x − 2n) and its dual curve ê
n
: y
2 = x
3 + 6nx
2 + n
2
x have the smallest size: S
n
= {1}, Ŝ
n
= {1, 2, n, 2n}. It is well known that for such integer n, the rank of group E
n
(ℚ) of the rational points on E
n
is zero so that n is a non-congruent number. In this way we obtain many new series of elliptic curves E
n
with rank zero and such series of integers n are non-congruent numbers.
Dedicated to Professor Sheng GONG on the occasion of his 75th birthday 相似文献
11.
Humio Ichimura 《Archiv der Mathematik》2011,96(6):555-563
Let p be an odd prime number, and pn0{p^{n_0}} the highest power of p dividing 2
p−1 − 1. Let Kn=Q(zpn+1){K_n={\bf Q}(\zeta_{p^{n+1}})} and Ln,j=Kn+(z2j+2){L_{n,j}=K_n^+(\zeta_{2^{j+2}})} for j ≥ 0. Let hn*{h_n^*} be the relative class number of K
n
, and h
n,j
the class number of L
n,j
, respectively. Let n be an integer with n ≥ n
0. We prove that if the ratio hn*/hn-1*{h_n^*/h_{n-1}^*} is odd, then h
n,j
/h
n−1,j
is odd for any j ≥ 0. 相似文献
12.
Thomas Meixner 《Israel Journal of Mathematics》1985,51(1-2):68-78
For a (finite) groupG and some prime powerp
n, theH
p
n
-subgroupH
pn (G) is defined byH
p
n
(G)=〈xεG|x
pn≠1〉. A groupH≠1 is called aH
p
n
-group, if there is a finite groupG such thatH is isomorphic toH
p
n
(G) andH
p
n
(G)≠G. It is known that the Fitting length of a solvableH
p
n
-group cannot be arbitrarily large: Hartley and Rae proved in 1973 that it is bounded by some quadratic function ofn. In the following paper, we show that it is even bounded by some linear function ofn. In view of known examples of solvableH
p
n
-groups having Fitting lengthn, this result is “almost” best possible. 相似文献
13.
Li Xin Zhang 《数学学报(英文版)》2002,18(2):311-326
Let {X
n
;n≥1} be a sequence of i.i.d. random variables and let X
(r)
n
= X
j
if |X
j
| is the r-th maximum of |X
1|, ..., |X
n
|. Let S
n
= X
1+⋯+X
n
and
(r)
S
n
= S
n
−(X
(1)
n
+⋯+X
(r)
n
). Sufficient and necessary conditions for
(r)
S
n
approximating to sums of independent normal random variables are obtained. Via approximation results, the convergence rates
of the strong law of large numbers for
(r)
S
n
are studied.
Received March 22, 1999, Revised November 6, 2000, Accepted March 16, 2001 相似文献
14.
Stephen L. Lipscomb 《Semigroup Forum》1992,44(1):96-106
The idea of an even permutation has recently been generalized, via path notation, to one-one partial transformations (charts)
in the symmetric inverse semigroupsC
n. The even charts form the alternating semigroupA
n
c
⊂C
n
. Generators ofA
n
c
are identified: It then follows that forn≥5,A
n
c
is the collection of restrictions of the even permutations (of rankn). Like theC
n
case, the congruences ofA
n
c
form a chain.
Part of this research was supported by a Mary Washington College faculty development grant. 相似文献
15.
Let {Xn} be a strictly stationary φ-mixing process with Σj=1∞ φ1/2(j) < ∞. It is shown in the paper that if X1 is uniformly distributed on the unit interval, then, for any t [0, 1], |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log log n)3/4) a.s. and sup0≤t≤1 |Fn−1(t) − t + Fn(t) − t| = (O(n−3/4(log n)1/2(log log n)1/4) a.s., where Fn and Fn−1(t) denote the sample distribution function and tth sample quantile, respectively. In case {Xn} is strong mixing with exponentially decaying mixing coefficients, it is shown that, for any t [0, 1], |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log n)1/2(log log n)3/4) a.s. and sup0≤t≤1 |Fn−1(t) − t + Fn(t) − t| = O(n−3/4(log n)(log log n)1/4) a.s. The results are further extended to general distributions, including some nonregular cases, when the underlying distribution function is not differentiable. The results for φ-mixing processes give the sharpest possible orders in view of the corresponding results of Kiefer for independent random variables. 相似文献
16.
Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 |Sn/n^1/r|^p(0 〈 r 〈 2,p 〉 0) are given,which are the same as that in the independent case. 相似文献
17.
Let h(t) = Σn ≥ 1hntn, h1 > 0, and exp(xh(t)) = Σn ≥ 0Pn(x) tn/n!. For f C[0,1], the associated Bernstein-Sheffer operator of degree n is defined by Bhnf(x) = Pn− 1 Σnk = 0f(k/n)(nk) Pk(x) Pn − k(1 − x) where pn = pn(1). We characterize functions h for which Bhn is a positive operator for all n ≥ 0. Then we give a necessary and sufficient condition insuring the uniform convergence of Bhnf to f. When h is a polynomial, we give an upper bound for the error f − Bhnf ∞. We also discuss the behavior of Bhnf when h is a series with a finite or infinite radius of convergence. 相似文献
18.
Let {Xn, n1} be a sequence of independent random variables (r.v.'s) with a common distribution function (d.f.) F. Define the moving maxima Yk(n)=max(Xn−k(n)+1,Xn−k(n)+2,…,Xn), where {k(n), n1} is a sequence of positive integers. Let Yk(n)1 and Yk(n)2 be two independent copies of Yk(n). Under certain conditions on F and k(n), the set of almost sure limit points of the vector consisting of properly normalised Yk(n)1 and Yk(n)2 is obtained. 相似文献
19.
Michael Voit 《Journal of multivariate analysis》1996,59(2):230-248
Forn2, let (μxτ, n)τ0be the distributions of the Brownian motion on the unit sphereSn
n+1starting in some pointxSn. This paper supplements results of Saloff-Coste concerning the rate of convergence ofμxτ, nto the uniform distributionUnonSnforτ→∞ depending on the dimensionn. We show that,[formula]forτn:=(ln n+2s)/(2n), where erf denotes the error function. Our proof depends on approximations of the measuresμxτ, nby measures which are known explicitly via Poisson kernels onSn, and which tend, after suitable projections and dilatations, to normal distributions on
forn→∞. The above result as well as some further related limit results will be derived in this paper in the slightly more general context of Jacobi-type hypergroups. 相似文献
20.
Timothy J. Killeen 《Annals of the Institute of Statistical Mathematics》1979,31(1):315-317
Suppose thatX
1,X
2, ... is a sequence of absolutely continuous or integer valued random variables with corresponding probability density functionsf
n
(x). Let {φ
n
}
n=1
∞
be a sequence of real numbers, then necessary and sufficient conditions are given forn
−1 logf
n
(φ
n
)-n
−1 log P (X
n
>φ
n
)=0(1) asn→∞. 相似文献