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1.
2.
It is proved that (i) for
survives to E∞; (ii) for
survives to E∞.
Project supported by the Doctoral Program Foundation of China. 相似文献
3.
Zhengyan Lin 《中国科学A辑(英文版)》1997,40(4):337-349
Let
be a sequence of independent Gaussian processes with (h)
Put
. The large increments forY(·) with bounded σ(p, h) are investigated. As an example the large increments of infinite-dimensional fractional Ornstein-Uhlenbeck process in IP are given. The method can also be applied to certain processes with stationary increments.
Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province. 相似文献
4.
The asymptotic expansions are studied for the vorticity
to 2D incompressible Euler equations with-initial vorticity
, where ϕ0(x) satisfies |d ϕ0(x)|≠0 on the support of
and
is sufficiently smooth and with compact support in ℝ2 (resp. ℝ2×T) The limit,v(t,x), of the corresponding velocity fields {v
ɛ(t,x)} is obtained, which is the unique solution of (E) with initial vorticity ω0(x). Moreover,
(ℤ2)) for all 1≽p∞, where
and ϕ(t,x) satisfy some modulation equation and eikonal equation, respectively. 相似文献
5.
By means of a method of analytic number theory the following theorem is proved. Letp be a quasi-homogeneous linear partial differential operator with degreem,m > 0, w.r.t a dilation
given by ( a1, …, an). Assume that either a1, …, an are positive rational numbers or
for some
Then the dimension of the space of polynomial solutions of the equationp[u] = 0 on ℝn must be infinite 相似文献
6.
M. Zippin 《Israel Journal of Mathematics》1966,4(3):199-204
A basis
is constructed inc
0 such that there exists no bounded linear projection ofc
0 onto the subspace spanned by a certain subsequence
of
.
This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor
A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice. 相似文献
7.
Di Zhao 《中国科学A辑(英文版)》1999,42(9):897-904
LetM be a compact Riemann manifold with the Ricci curvature ≽ - R(R = const. > 0) . Denote by d the diameter ofM. Then the first eigenvalue λ1 ofM satisfies
. Moreover if
, then
相似文献
8.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
9.
Zeng Guangxing 《中国科学A辑(英文版)》1999,42(3):272-280
For an ordered field (K,T) and an idealI of the polynomial ring
, the construction of the generalized real radical
ofI is investigated. When (K,T) satisfies some computational requirements, a method of computing
is presented.
Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project. 相似文献
10.
Chen Debao 《分析论及其应用》1993,9(3):17-28
In this paper we study the degree of approximation by superpositions of a sigmoidal function. We mainly consider the univariate
case. If f is a continuous function, we prove that for any bounded sigmoidal function σ,
. For the Heaviside function H(x), we prove that
. If f is a continuous function of bounded variation, we prove that
and
. For he Heaviside function, the coefficient 1 and the approximation orders are the best possible. We compare these results
with the classical Jackson and Bernstein theorems, and make some conjectures for further study. 相似文献
11.
The exit measures of super-Brownian motions with branching mechanism
from a bounded smooth domain D in ℝd+1 are known to be absolutely continuous with respect to the surface area on ϑD if
whereas in the case
they are singular. However, if the branching is restricted to a singular hyperplane, it is proved that they have absolutely
continuous states for alld≥1.
Project supported by the National Natural Science Foundation of China (Grant No. 16931063). 相似文献
12.
Strong consistency of nearest neighbor kernel regression estimation for stationary dependent samples
Under quite mild conditions onk
n
. the strong consistency is proved for the nearest neighbor density, the nearest neighbor kernel regression and the modified
nearest neighbor kernel regression of an a-mixing stationary sequence in time series context. The condition imposed on the
mixing coefficients is
,
. which is simple and weak. 相似文献
13.
We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks
with the form of
, where the input-output function is defined as a generalized sigmoid function, such asv
i
=2/π arctan(π/2μiμi),
and
, etc. Numerical simulations are also provided to demonstrate the theoretical results. 相似文献
14.
Let F be a subfield of a commutative field extending ℝ. Let
We say thatf :
preserves distanced ≥ 0 if for eachx,y ∈ ℝ ∣x- y∣= d implies ϕ2(f(x),f(y)) = d2
. We prove that each unit-distance preserving mappingf :
has a formI o (ρ,ρ), where
is a field homomorphism and
is an affine mapping with orthogonal linear part. 相似文献
15.
Furstenberg family and chaos 总被引:3,自引:0,他引:3
Jin-cheng XlONG~ Jie L Feng TAN School of Mathematical Sciences South China Normal University Guangzhou China 《中国科学A辑(英文版)》2007,50(9):1325-1333
A Furstenberg family F is a family,consisting of some subsets of the set of positive integers,which is hereditary upwards,i.e.A■B and A∈F imply B∈F.For a given system (i.e.,a pair of a complete metric space and a continuous self-map of the space) and for a Furstenberg family F, the definition of F-scrambled pairs of points in the space has been given,which brings the well-known scrambled pairs in Li-Yorke sense and the scrambled pairs in distribution sense to be F-scrambled pairs corresponding respectively to suitable Furstenberg family F.In the present paper we explore the basic properties of the set of F-scrambled pairs of a system.The generically F-chaotic system and the generically strongly F-chaotic system are defined.A criterion for a generically strongly F-chaotic system is showed. 相似文献
16.
17.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献
18.
Sums of five almost equal prime squares II 总被引:3,自引:0,他引:3
It is proved that every large integerN≡5 (mod 24) can be written as
with each primep
j
satisfying
, which gives a short interval version of a classical theorem of Hua.
Project supported by the Trans-Century Training Programme Foundation for the Talents by the State Education Commission and
the National Natural Science Foundation of China (Grant No. 19701019). 相似文献
19.
Let 1<q<∞, 1-1/q≤α<∞, 0<p<∞ and G be a locally compact Vilenkin group.The authors first introduce the general Herz-type Hardy spaces HKα,pq(G) and hKα,pq(G), then present the central atom or the central block and atom decompositions of these spaces. Using this characterization, they discuss some properties of these spaces and investigate the boundedness on the spaces HKα,pq(G) of the fractional integral operators and the boundedness on the spaces hKα,pq(G) of the pseudo-differential operators of order zero. 相似文献
20.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献