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1.
Precise asymptotics in the Baum-Katz and davis law of large numbers for positively associated sequences 总被引:6,自引:1,他引:5
§ 1 Introduction and resultsL et { X,Xi;i≥ 1} be a sequence of i.i.d.random variables,and set Sn= ni=1 Xi,n≥1.Hsu and Robbins[1 ] introduced the conceptof complete convergence.They together withErdos[2 ] proved n≥ 1 P(|Sn|≥εn) <∞ ,ε>0 (1)if and only if EX=0 and EX2 <∞ .L ater,Spitzer[3] proved n≥ 11n P(|Sn|≥εn) <∞ ,ε>0if and only if EX =0 and E|X|<∞ .More generally,it was shown by Baum and Katz[4 ]that,for 0
0 (… 相似文献
2.
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
3.
Solutions
of a semilinear elliptic boundary value problem,
(with
bounded below) can be put into a one-to-one correspondence with zeros
of a function
. Often d is small. The function
is called the bifurcation function. It can also be shown that the eigenvalues of the matrix
characterize the stability properties of the solutions of the elliptic problem as rest points of
. A finite element method that can be used for computing B and B
c has recently been proposed. An overview of these results and the finite element method is given.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
4.
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
5.
O. V. Kulikova 《Journal of Mathematical Sciences》2007,142(2):1942-1948
Under the condition of asphericity of a quotient group
, mutual commutants of the form
in hyperbolic groups G are investigated together with the structure of central subgroups
in central extensions
of
. In particular, quotients of the form G/[g
m
, G] are considered, where g is an element of infinite order from a hyperbolic group G and m is sufficiently large (depending on g).
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 115–125, 2005. 相似文献
6.
We compute in this paper the distribution of the area
swept under the occupation process of an M/M/1 queue during a busy period. For this purpose, we use the expression of the Laplace transform
of the random variable
established in earlier studies as a fraction of Bessel functions. To get information on the poles and the residues of
, we take benefit of the fact that this function can be represented by a continued fraction. We then show that this continued
fraction is the even part of an S fraction and we identify its successive denominators by means of Lommel polynomials. This allows us to numerically evaluate
the poles and the residues. Numerical evidence shows that the poles are very close to the numbers
as
. This motivated us to formulate some conjectures, which lead to the derivation of the asymptotic behaviour of the poles and
the residues. This is finally used to derive the asymptotic behaviour of the probability survivor function
. The outstanding property of the random variable
is that the poles accumulate at 0 and its tail does not exhibit a nice exponential decay but a decay of the form
for some positive constants c and
, which indicates that the random variable
has a Weibull-like tail.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
8.
A. M. Arkhipov 《Journal of Mathematical Sciences》2006,139(6):7013-7024
In this paper, we consider the Kuramoto-Sivashinskii equation on the multidimensional torus with a Riemannian metric:
where
. For this equation the theorem on energy transfer holds. It is formulated in the following way. Let
be the Fourier expansion of the function u. Denote by P
N
and P
N
⊥
the operators of rejection of the “leading” and, respectively, “lowest” terms of the Fourier expansion (harmonics), i.e.,
.
For any ρ > 0,N ∈ ℕ, s ≥ n/2+5, and λ ∈ (0, 1), there exists R such that for any function. ϕ ∈
lying outside the ball
in the ball
, there exists an instant of time t ∈ (0, 1) such that g
KS
t
ϕ=ψ and
. Here, R is a constant depending on the metric (g), n
s
is the sth Sobolev norm, and
is the C
1-norm.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
9.
Deirdre Longacher Smeltzer 《Designs, Codes and Cryptography》1999,16(3):291-306
A ( v, k, λ)-difference set D in a group G can be used to create a symmetric 2-( v, k, λ) design,
, from which arises a code C, generated by vectors corresponding to the characteristic function of blocks of
. This paper examines properties of the code C, and of a subcode, C
o=JC, where J is the radical of the group algebra of G over
. When G is a 2-group, it is shown that Co is equivalent to the first-order Reed-Muller code,
, precisely when the 2-divisor of Co is maximal. In addition, ifD is a non-trivial difference set in an elementary abelian 2-group, and if D is generated by a quadratic bent function, then Co is equal to a power of the radical. Finally, an example is given of a difference set whose characteristic function is not
quadratic, although the 2-divisor of Co is maximal. 相似文献
10.
§ 1 IntroductionIn[1 ] ,Karakostas and Tsamatos studied the existence of positive solutions for two-pointboundary value problemx″+ sign( 1 -c) q( t) f( x,x′) x′=0 ,( 1 .1 )x( 0 ) =0 ,x′( 1 ) =cx′( 0 ) ,( 1 .2 )where c∈ ( 0 ,1 )∪ ( 1 ,∞ ) .By using indices ofconvergence ofthe nonlinearity at0 and +∞and fixed point theorem in cones,they provided a priori upper and lower bounds for theslope of the solutions.The“c∈ ( 0 ,1 ) part”of their results has been extended to the fol-lowing … 相似文献