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1.
Guang-hui Cai 《Mathematica Slovaca》2007,57(4):381-388
Strong laws are established for linear statistics that are weighted sums of a
-mixing random sample. The results obtained generalize the results of Baxter et al. [SLLN for weighted independent indentically distributed random variables, J. Theoret. Probab. 17 (2004), 165–181] to
-mixing random variables.
This paper is supported by Key discipline of Zhejiang Province (Key discipline of Statistics of Zhejiang Gongshang University)
and National Natural Science Foundation of China. 相似文献
2.
The Commutators of Fractional Integrals on Besov Spaces 总被引:1,自引:0,他引:1
Abstract
In this paper we consider the commutators of fractional integrals
on the Besov spaces
, where b is a locally integrable function and 0 < α < n. We first establish the equivalence between the boundedness of the commutators
and the paraproduct of J. M. Bony. Then we obtain two conditions on the boundedness of the commutators. One of these conditions
is necessary and the other is sufficient.
The first author is supported by NNSF of China (Nos. 19901021, 10371080), Beijing Natural Science Foundation (No. 1013006)
and Scientific Research Foundation for Returned Overseas Chinese Scholars. The second author is supported by the National
973 project (G19990751) 相似文献
3.
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
4.
Abstract
By applying the topological degree theory, we establish some sufficient conditions for the existence on T-periodic solutions for the Liénard-type equation
Our results extend and improve some known results in the literature.
Supported by the National Natural Science Foundation of China (No. 10371034), the Doctor Program Foundation of the Ministry
of Education of China (20010532002) and Key Object of Chinese Ministry of Education ([2002]78). 相似文献
5.
MingXiong 《应用数学学报(英文版)》2004,20(4):665-674
Some results concerning existence of positive solutions for the singular boundary value problems u^(4)(t)=f(t,u(t)) t∈(0,1) u(0)=u(1)=0 u‘(0)=u‘(1)=0 have been given, where f(t, x) may be singular at t = 0, 1. 相似文献
6.
Positive Solutions for Semipositone
<Emphasis Type="Italic">m</Emphasis>-point Boundary-value
Problems 总被引:7,自引:0,他引:7
Abstract
Let ξ
i
∈ (0, 1) with 0 <
ξ1 < ξ2 <
··· < ξ
m−2 < 1,
a
i
, b
i
∈ [0,∞) with
and
. We consider the
m-point boundary-value
problem
where f(x, y) ≥ −M, and M is a positive constant. We show the
existence and multiplicity of positive solutions by applying the
fixed point theorem in cones.
*Supported by the NSFC (10271095).
GG-110-10736-1003, NWNU-KJCXGC-212 and the Foundation of Major
Project of Science and Technology of Chinese Education
Ministry 相似文献
7.
Shuang-jie Peng 《应用数学学报(英文版)》2006,22(1):137-162
Abstract Let Ω be the unit ball centered at the origin in
. We study the following problem
By a constructive argument, we prove that for any k = 1, 2, • • •, if ε is small enough, then the above problem has positive a solution uε concentrating at k distinct points which tending to the boundary of Ω as ε goes to 0+. 相似文献
8.
Generalized random processes are classified by various types of continuity. Representation theorems of a generalized random
process on {M
p
} on a set with arbitrary large probability, as well as representations of a correlation operator of a generalized random
process on {M
p
} and L
r
(R), r > 1, are given. Especially, Gaussian generalized random processes are proven to be representable as a sum of derivatives
of classical Gaussian processes with appropriate growth rate at infinity. Examples show the essence of all the proposed assumptions.
In order to emphasize the differences in the concept of generalized random processes defined by various conditions of continuity,
the stochastic differential equation y′(ω; t) = f(ω; t) is considered, where y is a generalized random process having a point value at t = 0 in the sense of Lojasiewicz.
This paper was supported by the project Functional analysis, ODEs and PDEs with singularities, No. 144016, financed by the
Ministry of Science, Republic of Serbia. 相似文献
9.
Abstract
We give a linear symmetric differential operator L defined by
in the 2π-periodic function space, and study the inverse-definiteness property of L. We obtain a complete result about the inverse-definiteness property of L with real constants a and b when b
2-4a > 0 and a - bk
2 + k
4 ≠ 0 for any k ∈? {1, 2, 3, . . . }.
Supported by GNAFACNR and the Natural Science Foundation of China and Jiangsu Provincial Education Commission 相似文献
10.
Blow-up Solutions for Mixed Nonlinear Schrodinger Equations 总被引:1,自引:0,他引:1
ShaoBinTAN 《数学学报(英文版)》2004,20(1):115-124
This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation: Фt=iαФxx βФ^2Ф^-x γ|Ф|^2Фx ig(|Ф|^2)Ф Under certain conditions on the initial data and the function g(s),we study the existence and nonexistence of global solution for this equation.The blow-up solution and the blow-up time are also investigated. 相似文献
11.
XinPingWANG 《数学学报(英文版)》2003,19(4):765-782
In this paper,we are concerned with the boundedness of all the solutions of the equation x″ ax^ -bx- Ф(x)=p(t),where p(t) is a smooth 2π-periodic function,a and b are positive constants,and the perturbation Ф(x) is bounded. 相似文献
12.
M.Federson R.Bianconi L.Barbanti 《应用数学学报(英文版)》2004,20(4):623-640
We consider the multidimensional abstract linear integral equation of Volterra type x(t) (*)∫Rtα(s)x(s)ds=f(t),t∈R,(1)as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions. The functions x, α and f are Bauach space-valued defined on a compact interval R of R^n Rt is a subinterval of R depending on t ∈ R and (*) f denotes either the Bochner-Lebesgue integral or the Henstock integral. The results presented here generalize those in [1] and are in the spirit of [3]. As a consequence of our approach, it is possible to study the properties of (1) by transferring the properties of the discrete systems, The Henstock integral setting enables us to consider highly oscillating functions. 相似文献
13.
Igor Shparlinski 《Bulletin of the Brazilian Mathematical Society》2008,39(4):587-595
Abdract Given a smooth curve of genus g ≥ 1 which admits a smooth projective embedding of dimension m over the ground field of q elements, we obtain the asymptotic formula q
g+o(g) for the size of set of the -rational points on its Jacobian in the case when m and q are bounded and g → ∞. We also obtain a similar result for curves of bounded gonality. For example, this applies to the Jacobian of a hyperelliptic
curve of genus g → ∞.
相似文献
14.
In this paper we establish results on the existence of nontangential limits for weighted
-harmonic functions in the weighted Sobolev space
, for some q>1 and w in the Muckenhoupt A
q
class, where
is the unit ball in
. These results generalize the ones in Sect. 3 of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996, where the weight was identically equal to one. Weighted
-harmonic functions are weak solutions of the partial differential equation
where
for some fixed q∈(1,∞), where 0<α≤β<∞, and w(x) is a q-admissible weight as in Chap. 1 of Heinonen et al., Nonlinear Potential Theory, 2006.
Later, we apply these results to improve on results of Koskela et al., Trans. Am. Math. Soc. 348(2), 755–766, 1996 and Martio and Srebro, Math. Scand. 85, 49–70, 1999 on the existence of radial limits for bounded quasiregular mappings in the unit ball of
with some growth restriction on their multiplicity function.
相似文献
15.
Changguo Wei 《Proceedings Mathematical Sciences》2008,118(4):517-524
Some results on A
-algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A
-algebras are A
-algebras or A
-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A
-algebra being an A
-algebra. 相似文献
16.
Abstract
The singular second-order m-point boundary value problem
, is considered under some conditions concerning the first eigenvalue of the relevant linear operators, where (Lϕ)(x) = (p(x)ϕ′(x))′ + q(x)ϕ(x) and ξ
i
∈ (0, 1) with 0 < ξ1 < ξ2 < · · · < ξ
m−2 < 1, a
i
∈ [0, ∞). h(x) is allowed to be singular at x = 0 and x = 1. The existence of positive solutions is obtained by means of fixed point index theory. Similar conclusions hold for some
other m-point boundary value conditions.
Supported by the National Natural Science Foundation of China (No.10371066, No.10371013) 相似文献
17.
For a sequence of integrable random variables, we introduce a new set of conditions called Cesàro -Integrability and Strong Cesàro -Integrability and show that, for <1/2, these conditions that are strictly weaker than Cesàro Uniform Integrability and Strong Cesàro Uniform Integrability respectively, are sufficient for WLLN and SLLN to hold for a sequence of pairwise independent random variables. For some special kinds of dependent sequences of random variables also, Cesàro -integrability for appropriate is shown to be sufficient for WLLN to hold. 相似文献
18.
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
19.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献
20.
We investigate the Eden-Staudacher and Beisert-Eden-Staudacher equations for the anomalous dimension of twist-2 operators
at a large spin s in the supersymmetric gauge theory. We reduce these equations to a set of linear algebraic equations and calculate their kernels
analytically. We demonstrate that in the perturbation theory, the anomalous dimension is a sum of products of the Euler functions
ζ(k) having the maximum transcendentality property. We also show that at a large coupling, the “singular” solution of the
Beisert-Eden-Staudacher equation reproduces the anomalous dimension constants predicted from the string side of the AdS/CFT
correspondence.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 117–129, April, 2008. 相似文献