共查询到20条相似文献,搜索用时 31 毫秒
1.
Let {X, X
n;n≥1} be a strictly stationary sequence of ρ-mixing random variables with mean zero and finite variance. Set
. Suppose lim
n→∞
and
, where d=2, if −1<b<0 and d>2(b+1), if b≥0. It is proved that, for any b>−1,
, where Γ(•) is a Gamma function.
Research supported by the National Natural Science Foundation of China (10071072). 相似文献
2.
Adimurthi K. Sandeep 《NoDEA : Nonlinear Differential Equations and Applications》2007,13(5-6):585-603
Let Ω be a bounded domain in
, we prove the singular Moser-Trudinger embedding:
if and only if
where
and
. We will also study the corresponding critical exponent problem. 相似文献
3.
Wang Lei Pan Ting Dept. of Math. Zhejiang Univ. Hangzhou China. Univ. of International Relation Hangzhou China. 《高校应用数学学报(英文版)》2004,19(2):212-222
Ibαf ( x) =∫R ∏mj=1( bj( x) - bj( y) ) 1| x - y| n-αf ( y) dyare considered.The following priori estimates are proved.For 1
01Φ1t| {y∈Rn:| Ibαf( y) | >t}| 1q ≤csupt>01Φ1t| {y∈Rn:ML( log L) 1r ,α(‖b‖f ) ( y) >t}| 1q,where‖b‖=∏mj=1‖bj‖Oscexp Lrj,Φ( t) =t( 1 + log+t) 1r,1r =1r1+ ...+ 1rm,ML(… 相似文献
4.
Aleksandar Ivić 《Central European Journal of Mathematics》2005,3(2):203-214
Let Δ(x) denote the error term in the Dirichlet divisor problem, and E(T) the error term in the asymptotic formula for the mean square of
. If E
*(t)=E(t)-2πΔ*(t/2π) with
, then we obtain
and
It is also shown how bounds for moments of | E
*(t)| lead to bounds for moments of
. 相似文献
5.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
6.
A SIMPLIFIED BRAUER'S THEOREM ON MATRIX EIGENVALUES 总被引:1,自引:0,他引:1
Luoluo Li 《高校应用数学学报(英文版)》1999,14(3):259-264
Let A=(a
ij)∈C
n×n
and
. Suppose that for each row of A there is at least one nonzero off-diagonal entry. It is proved that all eigenvalues of A are contained in
. The result reduces the number of ovals in original Brauer’s theorem in many cases. Eigenvalues (and associated eigenvectors)
that locate in the boundary of
are discussed.
The project is supported in part by Natural Science Foundation of Guangdong. 相似文献
7.
Jiang Chaowei Yang Xiaorong 《高校应用数学学报(英文版)》2007,22(1):87-94
In the case of Zd (d ≥ 2)-the positive d-dimensional lattice points with partial ordering ≤, {Xk,k ∈ Zd } i.i.d. random variables with mean 0, Sn = ∑k≤nXk and Vn2 = ∑j≤nX2j, the precise asymptotics for ∑n1/|n|(log|n|)dP(|Sn/vn|≥ ε√loglog|n|) and ∑n(logn|)δ/|n|(log|n|)d-1 P(|Sn/Vn| ≥ ε√log n), as ε ↘ 0, is established. 相似文献
8.
Let
be i.i.d. random variables and let, for each
and
. It is shown that
a.s. whenever the sequence of self-normalized sums S
n
/V
n is stochastically bounded, and that this limsup is a.s. positive if, in addition, X is in the Feller class. It is also shown that, for X in the Feller class, the sequence of self-normalized sums is stochastically bounded if and only if
相似文献
9.
J. Steuding 《Acta Mathematica Hungarica》2002,96(4):259-308
We calculate in a new way (following old ideas of Atkinson and new ideas of Jutila and Motohashi) the mean square of the product
of a function F(s), involving the Riemann zeta-function ζ(s), and a certain Dirichlet polynomial A(s) of length M=Tθ in short intervals on σ=a near the critical line: if θ<3/8, then
The main term I(T,H) is well known, but the error term is much smaller than the one obtained by other approaches (e.g.
). It follows from Levinson"s method that the proportion of zeros of the zeta-function with imaginary parts in [T,T+H] which
are simple and on the critical line is positive, when H≥T0.552.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
10.
§1 Introduction and preliminariesA set T Rn×Rnis called a monotone operator on Rn,if T has the property(x,y) ,(x′,y′)∈T 〈x -x′,y -y′〉≥0 ,where〈·,·〉denotes the inner product on Rn.T is maximal if(considered as a graph) itis not strictly contained in any other monotone operator on Rn.It is well known that thetheory of maximal monotone operators plays an important role in the study of convexprogramming and variational inequalities since itcan provide a powerful general framework… 相似文献
11.
O. L. Vinogradov 《Journal of Mathematical Sciences》2001,107(4):3987-4001
In what follows, C is the space of
-periodic continuous real-valued functions with uniform norm,
is the first continuity modulus of a function
with step h, H
n is the set of trigonometric polynomials of order at most n,
is the set of linear positive operators
(i.e., of operators such that
for every
),
is the space of square-integrable functions on
,
It is proved that
coincides with the smallest eigenvalue of some matrix of order n+1. The main result of the paper states that, for every
does not exceed and, for
, is equal to the minimum of the quadratic functional
over the unit sphere of
. Then it is calculated that
Bibliography: 19 titles. 相似文献
12.
姚奎 《高校应用数学学报(英文版)》2001,16(2):161-170
§ 1 PreliminariesWe considerψ( x)∈ L1 ( Rn) satisfying the mean valuezero,i.e.∫Rnψdx=0 ,and definethe square function g( f) on Rnbyg( f) ( x) =( k|ψk* f|2 ) 1 2 ( x)for f∈ S( Rn) ,the Schwartz space,whereψk( x) =ψ2 k( x) . Whenψ has some smooth property,one can obtain the weak type estimate by viewingthe square function g( f) as the vector-valued singularintegrals,which the readercan referto [1 ,2 ] .As for the results aboutthe Lp-estimates,see [3,4 ] .In this paper,we sha… 相似文献
13.
This article improves results of Hamada, Helleseth and Maekawa on minihypers in projective spaces and linear codes meeting the Griesmer bound.In [10,12],it was shown that any
-minihyper, with
, where
, is the disjoint union of
points,
lines,...,
-dimensional subspaces. For q large, we improve on this result by increasing the upper bound on
non-square, to
non-square,
square,
, and (4) for
square, p prime, p<3, to
. In the case q non-square, the conclusion is the same as written above; the minihyper is the disjoint union of subspaces. When q is square however, the minihyper is either the disjoint union of subspaces, or the disjoint union of subspaces and one subgeometry
. For the coding-theoretical problem, our results classify the corresponding
codes meeting the Griesmer bound. 相似文献
14.
The following assertion is proved. Let
be the set of integers the number of the prime power of which is
. Let
be the size of
. Then for each irrational
, uniformly in
, \begin{equation*} \frac{1}{\pi_k(x)} \bigg|\sum _{\alul{n\le x}{n\in\cN_k}} f(n) e^{2\pi in\alpha}\bigg|\to 0, \end{equation*}
where
is an arbitrary multiplicative function with
,
is a positive constant.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
15.
Let
be a nondecreasing sequence of positive numbers and let l
1,α be the space of real sequences
for which
. We associate every sequence ξ from l
1,α with a sequence
, where ϕ(·) is a permutation of the natural series such that
, j ∈ ℕ. If p is a bounded seminorm on l
1,α and
, then
Using this equality, we obtain several known statements.
__________
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 1002–1006, July, 2005. 相似文献
16.
On a Binary Diophantine Inequality Involving Prime Numbers 总被引:1,自引:0,他引:1
M. B. S. Laporta 《Acta Mathematica Hungarica》1999,83(3):179-187
Let 1 < c < 15/14 and N a sufficiently large real number. In this paper we prove that, for all (N, 2N\ A with
, the inequality
has solutions in primes
. 相似文献
17.
The sequence of orthogonal polynomials
is said to be classical if
is also orthogonal. The aim of this paper is to find the sequences
which have the property that
is also orthogonal. We prove that sequences, with this property have to be, classical and belong either to the set of Laguerre or Jacobi polynomials, where in the Laguerre case c has to be zero and in the Jacobi case c = ±1. 相似文献
18.
A. N. Petrov 《Journal of Mathematical Sciences》2001,107(4):4067-4072
A new numerical inequality for average power means is presented. Let
and let
be a sequence of positive numbers. Consider the operator
. We denote by
the superposition of these operators. The following assertion is proved: if
. Bibliography: 2 titles. 相似文献
19.
The paper deals with the problem of recovering the parameters (functions)
and
of the Maxwell dynamical system
(tan is the tangent component;
is a solution) by the response operator
(
is the normal). The parameters determine the velocity
, the c-metric
, and the time
. It is shown that for any fixed
, the operator
determines
and
in
uniquely. Bibliography: 15 titles. 相似文献
20.
We prove new pointwise inequalities involving the gradient of a function
, the modulus of continuity
of the gradient
, and a certain maximal function
and show that these inequalities are sharp. A simple particular case corresponding to
and
is the Landau type inequality
, where the constant 8/3 is best possible and
. 相似文献