共查询到20条相似文献,搜索用时 50 毫秒
1.
Ramez N. Maalouf 《Archiv der Mathematik》2007,89(5):442-451
We consider sequences {f
n
} of analytic self mappings of a domain and the associated sequence {Θ
n
} of inner compositions given by . The case of interest in this paper concerns sequences {f
n
} that converge assymptotically to a function f, in the sense that for any sequence of integers {n
k
} with n
1 < n
2 < ... one has that locally uniformly in Ω. Most of the discussion concerns the case where the asymptotic limit f is the identity function in Ω.
Received: 16 December 2006 相似文献
2.
In this paper we prove that any residue class λ modulo a large prime number p can be represented in the form
for some positive integers m1, n1,... ,m5, n5 of the size O(p27/28). This improves one of the results from [6] on representability of λ modulo p in the form
with
. We also prove that any residue class modulo p can be represented in the form
with
. This improves the result of [7].
Received: 27 March 2006 相似文献
3.
4.
Let pi, 1≦ i ≦ 5, be prime numbers. It is proved that every sufficiently large integer N that satisfies N ≡ 5(mod 24) can be written as N = p21 + p22 + p23 + p24 + p25, where
Received: 10 February 2005 相似文献
5.
Sun Zhonghua Qi Wenfeng 《高校应用数学学报(英文版)》2007,22(4):469-477
Let Z/(pe) be the integer residue ring modulo pe with p an odd prime and integer e ≥ 3. For a sequence (a) over Z/(pe), there is a unique p-adic decomposition (a) = (a)0 (a)1·p … (a)e-1 ·pe-1, where each (a)i can be regarded as a sequence over Z/(p), 0 ≤ i ≤ e - 1. Let f(x) be a primitive polynomial over Z/(pe) and G' (f(x), pe) the set of all primitive sequences generated by f(x) over Z/(pe). For μ(x) ∈ Z/(p)[x] with deg(μ(x)) ≥ 2 and gcd(1 deg(μ(x)),p- 1) = 1,set ψe-1 (x0, x1,…, xe-1) = xe-1·[ μ(xe-2) ηe-3 (x0, x1,…, xe-3)] ηe-2 (x0, x1,…, xe-2),which is a function of e variables over Z/(p). Then the compressing map ψe-1: G'(f(x),pe) → (Z/(p))∞,(a) (→)ψe-1((a)0, (a)1,… ,(a)e-1) is injective. That is, for (a), (b) ∈ G' (f(x), pe), (a) = (b) if and only if ψe - 1 ((a)0, (a)1,… , (a)e - 1) =ψe - 1 ((b)0,(b)1,… ,(b)e-1). As for the case of e = 2, similar result is also given. Furthermore, if functions ψe-1 and ψe-1 over Z/(p) are both of the above form and satisfy ψe-1((a)0,(a)1,… ,(a)e-1) = ψe-1((b)0,(b)1,… ,(b)e-1) for (a),(b) ∈ G'(f(x),pe), the relations between (a) and (b), ψe-1 and ψe-1 are discussed. 相似文献
6.
Bhagwati Prashad Duggal Slavisa V. Djordjević 《Mediterranean Journal of Mathematics》2005,2(4):395-406
It is known that if
and
are Banach space operators with the single-valued extension property, SVEP, then the matrix operator
has SVEP for every operator
and hence obeys Browder’s theorem. This paper considers conditions on operators A, B, and M0 ensuring Weyls theorem for operators MC. 相似文献
7.
J. V. Manojlović 《Lithuanian Mathematical Journal》2009,49(1):71-92
We consider a class of fourth-order nonlinear difference equations of the form
where α and β are the ratios of odd positive integers, and {p
n
} and {q
n
} are positive real sequences defined for all
satisfying the condition
We classify the nonoscillatory solutions of (Ω) and establish necessary and/or sufficient conditions for the existence of
nonoscillatory solutions with specific asymptotic behavior.
Supported by Ministry of Science, Technology and Development of Republic of Serbia – Grant No. 144003. 相似文献
8.
We establish a new bound for the exponential sum
where λ is an element of the residue ring modulo a large prime number
and
are arbitrary subsets of the residue ring modulo p − 1 and γ (n) are any complex numbers with | γ (n)| ≦ 1.
Received: 15 June 2005 相似文献
9.
Zong-mao Cheng Xiu-yun Wang Zheng-yan Lin 《应用数学学报(英文版)》2006,22(1):81-90
In this paper, we introduce a class of Gaussian processes Y={Y(t):t∈R^N},the so called hifractional Brownian motion with the indcxes H=(H1,…,HN)and α. We consider the (N, d, H, α) Gaussian random field x(t) = (x1 (t),..., xd(t)),where X1 (t),…, Xd(t) are independent copies of Y(t), At first we show the existence and join continuity of the local times of X = {X(t), t ∈ R+^N}, then we consider the HSlder conditions for the local times. 相似文献
10.
Yah SUN Gen Xiang CHAI 《数学学报(英文版)》2007,23(4):685-696
In this article the following random intercept mixed effects model will be considered: yij = vi =v^τijβ+ εij,i=1,…,m;j=1,2,…,ni, where {vi} are i.i.d, random effects with mean α 2. 2 and finite variance σ^2 v, {εij} are i.i.d, random errors with finite variance ε^2 ε. Here we will estimate α,σ^2 v,σ^2 ε,β and study their large sample properties, such as strong consistency, strong convergence rates and asymptotic normality. 相似文献
11.
Jun Wu 《Monatshefte für Mathematik》2008,19(1):83-87
For an irrational number x and n ≥ 1, we denote by k
n
(x) the exact number of partial quotients in the continued fraction expansion of x given by the first n decimals of x. G. Lochs proved that for almost all x, with respect to the Lebesgue measure
In this paper, we prove that an iterated logarithm law for {k
n
(x): n ≥ 1}, more precisely, for almost all x,
for some constant σ > 0.
Author’s address: Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, P.R. China 相似文献
12.
Kâzim Ilhan Ikeda 《Proceedings Mathematical Sciences》2003,113(2):99-137
This paper which is a continuation of [2], is essentially expository in nature, although some new results are presented. LetK be a local field with finite residue class fieldK
k. We first define (cf. Definition 2.4) the conductorf(E/K) of an arbitrary finite Galois extensionE/K in the sense of non-abelian local class field theory as wheren
G is the break in the upper ramification filtration ofG = Gal(E/K) defined by
. Next, we study the basic properties of the idealf(E/K) inO
k in caseE/K is a metabelian extension utilizing Koch-de Shalit metabelian local class field theory (cf. [8]).
After reviewing the Artin charactera
G : G → ℂ ofG := Gal(E/K) and Artin representationsA
g G → G →GL(V) corresponding toa
G : G → ℂ, we prove that (Proposition 3.2 and Corollary 3.5)
where Χgr
: G → ℂ is the character associated to an irreducible representation ρ: G → GL(V) ofG (over ℂ). The first main result (Theorem 1.2) of the paper states that, if in particular,ρ : G → GL(V) is an irreducible representation ofG(over ℂ) with metabelian image, then
where Gal(Eker(ρ)/Eker(ρ)•) is any maximal abelian normal subgroup of Gal(Eker(ρ)/K) containing Gal(Eker(ρ)
/K)′, and the break nG/ker(ρ) in the upper ramification filtration of G/ker(ρ) can be computed and located by metabelian local class field theory. The
proof utilizes Basmaji’s theory on the structure of irreducible faithful representations of finite metabelian groups (cf.
[1]) and on metabelian local class field theory (cf. [8]).
We then discuss the application of Theorem 1.2 on a problem posed by Weil on the construction of a ‘natural’A
G ofG over ℂ (Problem 1.3). More precisely, we prove in Theorem 1.4 that ifE/K is a metabelian extension with Galois group G, then
Kazim İlhan ikeda whereN runs over all normal subgroups of G, and for such anN, V
n denotes the collection of all ∼-equivalence classes [ω]∼, where ‘∼’ denotes the equivalence relation on the set of all representations
ω : (G/N)• → ℂΧ satisfying the conditions Inert(ω) = {δ ∈ G/N : ℂδ} = ω =(G/N) and
where δ runs over R((G/N)•/(G/N)), a fixed given complete system of representatives of (G/N)•/(G/N), by declaring that ω1 ∼ ω2 if and only if ω1
= ω
2,δ for some δ ∈ R((G/N)•/(G/N)).
Finally, we conclude our paper with certain remarks on Problem 1.1 and Problem 1.3. 相似文献
13.
Summary. Let k ≥ 1 be any integer. Let G be a finite abelian group of exponent n. Let sk(G) be the smallest positive integer t such that every sequence S in G of length at least t has a zero-sum subsequence of length kn. We study this constant for groups
when d = 3 or 4. In particular, we prove, as a main result, that
for every k ≥ 4,
and
for every prime p ≥ 5. 相似文献
14.
15.
Let X1, X2,... be, i.i.d. random variables, and put
. We find necessary and sufficient moment conditions for
, where δ≥ 0 and q>0, and
with an>0 and bn is either
or
The series f(x) we deal with are classical series studied by Hsu and Robbins, Erdős, Spitzer, Baum and Katz, Davis, Lai, Gut, etc 相似文献
16.
Melvin Hausner 《Combinatorica》1985,5(3):215-225
Ifμ is a positive measure, andA
2, ...,A
n
are measurable sets, the sequencesS
0, ...,S
n
andP
[0], ...,P
[n] are related by the inclusion-exclusion equalities. Inequalities among theS
i
are based on the obviousP
[k]≧0. Letting
=the average average measure of the intersection ofk of the setsA
i
, it is shown that (−1)
k
Δ
k
M
i
≧0 fori+k≦n. The casek=1 yields Fréchet’s inequalities, andk=2 yields Gumbel’s and K. L. Chung’s inequalities. Generalizations are given involvingk-th order divided differences. Using convexity arguments, it is shown that forS
0=1,
whenS
1≧N−1, and
for 1≦k<N≦n andv=0, 1, .... Asymptotic results asn → ∞ are obtained. In particular it is shown that for fixedN,
for all sequencesM
0, ...,M
n
of sufficiently large length if and only if
for 0<t<1. 相似文献
17.
Y. Rakotondratsimba 《Acta Mathematica Hungarica》2000,86(3):213-236
A sufficient condition on nonnegative double-sequences
is derived in order that the two-dimensional discrete Hardy operator His bounded from
into
whenever 1 < p q < . 相似文献
18.
We prove that if f belongs to the Morrey space
, with λ ∊ [0, n−2], and u is the solution of the problem
then Du belongs to the space
, for any
Mathematics Subject Classification (2000) 35J25, 35D10 相似文献
19.
Bin Heng SONG Huai Yu JIAN 《数学学报(英文版)》2005,21(5):1183-1190
We establish the existence of fundamental solutions for the anisotropic porous medium equation, ut = ∑n i=1(u^mi)xixi in R^n × (O,∞), where m1,m2,..., and mn, are positive constants satisfying min1≤i≤n{mi}≤ 1, ∑i^n=1 mi 〉 n - 2, and max1≤i≤n{mi} ≤1/n(2 + ∑i^n=1 mi). 相似文献
20.
T. Levasseur 《Transformation Groups》1998,3(4):337-353
Let
u
be a compact Lie algebra and let
u
be its complexification. Let ζ−1/2 be the inverse on the set of regular elements of
u
of a square root of the discriminant of
. Generalizing a result of W. Lichtenstein in the case
u
=
(n, ℂ) or
(nℝ), we prove that ∂(q).ζ1/2 is non zero for all harmonic polynomialsq ∈S(
) \ {0}. This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of
. 相似文献