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1.
J. A. López Molina M. E. Puerta M. J. Rivera 《Bulletin of the Brazilian Mathematical Society》2006,37(2):191-216
Let
, be a family of compatible couples of Lp-spaces. We show that, given a countably incomplete ultrafilter
in
, the ultraproduct
of interpolation spaces defined by the real method is isomorphic to the direct sum of an interpolation space of type
, an intermediate K?the space between
and
being a purely atomic measure space, and a K?the function space K(Ω3) defined on some purely non atomic measure space (Ω3, ν3) in such a way that Ω2 ∪ Ω3 ≠∅.
The research of first and third authors is partially supported by the MEC and FEDER project MTM2004-02262 and AVCIT group
03/050. 相似文献
2.
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
3.
Huaning Liu 《Bulletin of the Brazilian Mathematical Society》2007,38(2):179-188
For integers a,
b and n
> 0, define
and
where
denotes the summation over all
r such that (r, n) = 1, and
is defined by the equation
. The two sums are analogous to the
homogeneous Dedekind sum S(a,b,
n). The functional equations for
A
Γ and B
Γ are established. Furthermore, Knopp's
identity on Dedekind sum is extended.
*This work is supported by the N.S.F. (10271093,
60472068) of P.R. China. 相似文献
4.
Qi Keng LU Ke WU 《数学学报(英文版)》2007,23(4):577-598
For an integer m ≥ 4, we define a set of 2[m/2] × 2[m/2] matrices γj (m), (j = 0, 1,..., m - 1) which satisfy γj (m)γk (m) +γk (m)γj (m) = 2ηjk (m)I[m/2], where (ηjk (m)) 0≤j,k≤m-1 is a diagonal matrix, the first diagonal element of which is 1 and the others are -1, I[m/2] is a 2[m/1] × 2[m/2] identity matrix with [m/2] being the integer part of m/2. For m = 4 and 5, the representation (m) of the Lorentz Spin group is known. For m≥ 6, we prove that (i) when m = 2n, (n ≥ 3), (m) is the group generated by the set of matrices {T|T=1/√ξ((I+k) 0 + 0 I-K) ( U 0 0 U), (ii) when m = 2n + 1 (n≥ 3), (m) is generated by the set of matrices {T|T=1/√ξ(I -k^- k I)U,U∈ (m-1),ξ=1-m-2 ∑k,j=0 ηkja^k a^j〉0, K=i[m-3 ∑j=0 a^j γj(m-2)+a^(m-2) In],K^-=i[m-3∑j=0 a^j γj(m-2)-a^(m-2) In]} 相似文献
5.
Jiong Sheng LI Jian Hua YIN 《数学学报(英文版)》2006,22(4):1133-1138
Let σ(k, n) be the smallest even integer such that each n-term positive graphic sequence with term sum at least σ(k, n) can be realized by a graph containing a clique of k + 1 vertices. Erdos et al. (Graph Theory, 1991, 439-449) conjectured that σ(k, n) = (k - 1)(2n- k) + 2. Li et al. (Science in China, 1998, 510-520) proved that the conjecture is true for k 〉 5 and n ≥ (k2) + 3, and raised the problem of determining the smallest integer N(k) such that the conjecture holds for n ≥ N(k). They also determined the values of N(k) for 2 ≤ k ≤ 7, and proved that [5k-1/2] ≤ N(k) ≤ (k2) + 3 for k ≥ 8. In this paper, we determine the exact values of σ(k, n) for n ≥ 2k+3 and k ≥ 6. Therefore, the problem of determining σ(k, n) is completely solved. In addition, we prove as a corollary that N(k) -= [5k-1/2] for k ≥6. 相似文献
6.
Yuexu Zhao 《Bulletin of the Brazilian Mathematical Society》2006,37(3):377-391
Let X1, X2, ... be i.i.d. random variables with EX1 = 0 and positive, finite variance σ2, and set Sn = X1 + ... + Xn. For any α > −1, β > −1/2 and for κn(ε) a function of ε and n such that κn(ε) log log n → λ as n ↑ ∞ and
, we prove that
*Supported by the Natural Science Foundation of Department of Education of Zhejiang Province (Grant No. 20060237 and 20050494). 相似文献
7.
Let n and r be positive integers. Suppose that a family
satisfies F1∩···∩Fr ≠∅ for all F1, . . .,Fr ∈
and
. We prove that there exists ε=ε(r) >0 such that
holds for 1/2≤w≤1/2+ε if r≥13. 相似文献
8.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
where (λ
n
) is a sequence of positive steps. Algorithm may be viewed as the discretized equation of a nonlinear oscillator subject to friction. We prove that, if 0 ∈ int (A(0)) (condition of dry friction), then the sequence (x
n
) generated by is strongly convergent and its limit x
∞ satisfies 0 ∈ A(0) + B(x
∞). We show that, under a general condition, the limit x
∞ is achieved in a finite number of iterations. When this condition is not satisfied, we prove in a rather large setting that
the convergence rate is at least geometrical. 相似文献
9.
Multilinear Singular Integrals with Rough Kernel 总被引:9,自引:0,他引:9
ShanZhenLU HuoXiongWU PuZHANG 《数学学报(英文版)》2003,19(1):51-62
For a class of multilinear singular integral operators T
A
,
where R
m
(A; x, y) denotes the m-th Taylor series remainder of A at x expanded about y, A has derivatives of order m − 1 in
is homogeneous of degree zero, the authors prove that T
A
is bounded from L
p
(ℝ
n
) to
and from L
1(ℝ
n
) to L
n/(n−β),∞(ℝ
n
) with the bound
And if Ω has vanishing moments of order m − 1 and satisfies some kinds of Dini regularity otherwise, then T
A
is also bounded from L
p
(ℝ
n
) to
with the bound
Supported by the National 973 Project (G1990751) and SEDF of China (20010027002) 相似文献
10.
Xiu Gui LIU 《数学学报(英文版)》2007,23(3):385-392
In this paper, some groups Ext A^s.t (Zp, Zp) with specialized s and t are first computed by the May spectrM sequence. Then we make use of the Adams spectral sequence to prove the existence of a new nontrivial family of filtration s+5 in the stable homotopy groups of spheres πpnq+(s+3)pq+(s+1)q-5S which is represented (up to a nonzero scalar) by β+2bohh∈ExtA^s+5,P^nq+(n+3)pq+(n+1)q+s(Zp, Zp) in the Adams spectral sequence, where p ≥ 5 is a prime number, n ≥3, 0≤ s 〈 p - 3, q = 2(p - 1). 相似文献
11.
CongWenLIU JiHuaiSHI 《数学学报(英文版)》2003,19(1):187-200
In 1993,Ahern,Flores and Rudin showed that,if f is integrable over the unit ball BC^n of C^n and satisfies∫BC^nfoφdv=f(φ(0)) for every φ∈Aut(BC^n),then f is M-harmonic if and only if n≤11.The present paper is about an analogous question in the context of the unit ball Bn of R^n as well as in the weighted setting. 相似文献
12.
Multivariate Refinement Equations and Convergence of Cascade Algorithms in Lp(0〈p〈1)Spaces 总被引:1,自引:0,他引:1
SongLI 《数学学报(英文版)》2003,19(1):97-106
We consider the solutions of refinement equations written in the form
where the vector of functions ϕ = (ϕ
1, ..., ϕ
r
)
T
is unknown, g is a given vector of compactly supported functions on ℝ
s
, a is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s dilation matrix with m = |detM|. Inhomogeneous refinement equations appear in the construction of multiwavelets and the constructions of wavelets on a finite
interval. The cascade algorithm with mask a, g, and dilation M generates a sequence ϕ
n
, n = 1, 2, ..., by the iterative process
from a starting vector of function ϕ
0. We characterize the L
p
-convergence (0 < p < 1) of the cascade algorithm in terms of the p-norm joint spectral radius of a collection of linear operators associated with the refinement mask. We also obtain a smoothness
property of the solutions of the refinement equations associated with the homogeneous refinement equation.
This project is supported by the NSF of China under Grant No. 10071071 相似文献
13.
Mohammad Sal Moslehian 《Bulletin of the Brazilian Mathematical Society》2007,38(4):611-622
In this paper, we establish the generalized Hyers–Ulam–Rassias stability of C*-ternary ring homomorphisms associated to the Trif functional equation
相似文献
14.
De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
15.
Yu Can ZHU 《数学学报(英文版)》2007,23(9):1707-1718
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where a is a finite subset of positive integers and 1/p+1/q = 1 with p 〉 1, q 〉 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach spaces X and X^* that if {xn}n=1^∞ C X is a q-Besselian frame for X, then there exists a p-Besselian frame {y&*}n=1^∞ belong to X^* for X^* such that x = ∑n=1^∞ yn^*(x)xn for all x ∈ X, and x^* =∑n=1^∞ x^*(xn)yn^* for all x^* ∈ X^*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces. 相似文献
16.
A Note on Certain Block Spaces on the Unit Sphere 总被引:1,自引:0,他引:1
Xiao Feng YE Xiang Rong ZHU 《数学学报(英文版)》2006,22(6):1843-1846
In this note, we clarify a relation between block spaces and the Hardy space. We obtain Bq^0.v belong to H^1(S^n-1)+L(ln+L)^1+v(s^n-1),v〉-1,q〉1,Furthermore,if v≥ 0, q 〉 1. we verify that block spaces Rq^0.v(S^n-1)are proper subspaces of H1 (S^n- 1), 相似文献
17.
Michel WEBER 《数学学报(英文版)》2006,22(2):377-382
Let D be an increasing sequence of positive integers, and consider the divisor functions:
d(n, D) =∑d|n,d∈D,d≤√n1, d2(n,D)=∑[d,δ]|n,d,δ∈D,[d,δ]≤√n1,
where [d,δ]=1.c.m.(d,δ). A probabilistic argument is introduced to evaluate the series ∑n=1^∞and(n,D) and ∑n=1^∞and2(n,D). 相似文献
18.
Ian M. Wanless 《Combinatorica》2006,26(6):743-745
Let
denote the set of n×n binary matrices which have each row and column sum equal to k. For 2≤k≤n→∞ we show that
is asymptotically equal to (k−1)k−1k2−k. This confirms Conjecture 23 in Minc's catalogue of open problems.
* Written while the author was employed by the Department of Computer Science at the Australian National University. 相似文献
19.
Let
be a universal binary countable homogeneous structure and n∈ω. We determine the equivalence relation
on [U]n with the smallest number of equivalence classes r so that each one of the classes is indivisible. As a consequence we obtain
and a characterization of the smallest number r so that the arrow relation above holds.
For the case of infinitely many colors we determine the canonical set of equivalence relations, extending the result of Erdős
and Rado for the integers to countable universal binary homogeneous structures.
* Supported by NSERC of Canada Grant # 690404.
† Supported by NSERC of Canada Grant # 691325. 相似文献
20.
Qi Kang RAN 《数学学报(英文版)》2005,21(4):705-714
In this paper, we prove that the weak solutions u∈Wloc^1, p (Ω) (1 〈p〈∞) of the following equation with vanishing mean oscillation coefficients A(x): -div[(A(x)△↓u·△↓u)p-2/2 A(x)△↓u+│F(x)│^p-2 F(x)]=B(x, u, △↓u), belong to Wloc^1, q (Ω)(A↓q∈(p, ∞), provided F ∈ Lloc^q(Ω) and B(x, u, h) satisfies proper growth conditions where Ω ∪→R^N(N≥2) is a bounded open set, A(x)=(A^ij(x)) N×N is a symmetric matrix function. 相似文献