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1.
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
2.
3.
Abstract
With Littlewood–Paley analysis, Peetre and Triebel
classified, systematically, almost all the usual function spaces
into two classes of spaces: Besov spaces
and Triebel–Lizorkin
spaces
; but the structure of
dual spaces
of
is very different from
that of Besov spaces or that of Triebel–Lizorkin spaces, and
their structure cannot be analysed easily in the
Littlewood–Paley analysis. Our main goal is to characterize
in tent spaces with
wavelets. By the way, some applications are given: (i)
Triebel–Lizorkin spaces for p
= ∞ defined by Littlewood–Paley analysis cannot serve as the dual
spaces of Triebel–Lizorkin spaces for p = 1; (ii) Some inclusion relations
among these above spaces and some relations among
and
L
1
are studied.
Supported by NNSF of China (Grant No.
10001027) 相似文献
4.
Xiao Chun FANG Shu Dong LIU 《数学学报(英文版)》2007,23(10):1745-1750
Let A be a separable unital nuclear simple C*-algebra with torsion K0 (A), free K1 (A) and with the UCT. Let T : A→M(K)/K be a unital homomorphism. We prove that every unitary element in the commutant of T(A) is an exponent, thus it is liftable. We also prove that each automorphism α on E with α ∈ Aut0(A) is approximately inner, where E is a unital essential extension of A by K and α is the automorphism on A induced by α. 相似文献
5.
Rejeb HADIJI 《数学年刊B辑(英文版)》2007,28(3):327-352
The authors consider the problem: -div(p▽u) = uq-1 λu, u > 0 inΩ, u = 0 on (?)Ω, whereΩis a bounded domain in Rn, n≥3, p :Ω→R is a given positive weight such that p∈H1 (Ω)∩C(Ω),λis a real constant and q = 2n/n-2, and study the effect of the behavior of p near its minima and the impact of the geometry of domain on the existence of solutions for the above problem. 相似文献
6.
For an l-graph
, the Turán number
is the maximum number of edges in an n-vertex l-graph
containing no copy of
. The limit
is known to exist [8]. The Ramsey–Turán density
is defined similarly to
except that we restrict to only those
with independence number o(n). A result of Erdős and Sós [3] states that
as long as for every edge E of
there is another edge E′of
for which |E∩E′|≥2. Therefore a natural question is whether there exists
for which
.
Another variant
proposed in [3] requires the stronger condition that every set of vertices of
of size at least εn (0<ε<1) has density bounded below by some threshold. By definition,
for every
. However, even
is not known for very many l-graphs
when l>2.
We prove the existence of a phenomenon similar to supersaturation for Turán problems for hypergraphs. As a consequence, we
construct, for each l≥3, infinitely many l-graphs
for which
.
We also prove that the 3-graph
with triples 12a, 12b, 12c, 13a, 13b, 13c, 23a, 23b, 23c, abc, satisfies
. The existence of a hypergraph
satisfying
was conjectured by Erdős and Sós [3], proved by Frankl and R?dl [6], and later by Sidorenko [14]. Our short proof is based
on different ideas and is simpler than these earlier proofs.
* Research supported in part by the National Science Foundation under grants DMS-9970325 and DMS-0400812, and an Alfred P.
Sloan Research Fellowship.
† Research supported in part by the National Science Foundation under grants DMS-0071261 and DMS-0300529. 相似文献
7.
RenZiYANG JunXiangXU 《数学学报(英文版)》2004,20(3):525-532
In this paper we consider the effective reducibility of the following linear differentialequation: x = (A ∈Q(t,∈))x, |∈| ≤ ∈0, where A is a constant matrix, Q(t,e) is quasiperiodic in t, and e is a small perturbation parameter. We prove that if the eigenvalues of A and the basic frequencies of Q satisfy some non-resonant conditions, the linear differential equation can be reduced to y = (A^*(∈) R^*(t, ∈))y, |∈| ≤ ∈o, where R^* is exponentially small in ∈. 相似文献
8.
Hui-qiong Li Zhen-long Chenu 《应用数学学报(英文版)》2007,23(4):579-592
Let{(t);t∈R_ ~N}be a d-dimensional N-parameter generalized Brownian sheet.Necessaryand sufficient conditions for a compact set E×F to be a polar set for(t,(t))are proved.It is also provedthat if 2N≤αd,then for any compact set ER_>~N,d-2/2 Dim E≤inf{dimF:F ∈ B(R~d),P{(E)∩F≠φ}>0}≤d-2/β DimE,and if 2N>αd,then for any compact set FR~d\{0},α/2(d-DimF)≤inf{dimE:E∈B(R_>~N),P{(E)∩F≠φ}>0}≤β/2(d-DimF),where B(R~d)and B(R_>~N)denote the Borel σ-algebra in R~d and in R_>~N respectively,dim and Dim are Hausdorffdimension and Packing dimension respectively. 相似文献
9.
Chaohui ZHANG 《数学年刊B辑(英文版)》2007,28(1):55-66
Let S be a Riemann surface with genus p and n punctures. Assume that 3p - 3 n > 0 and n ≥ 1. Let a be a puncture of S and let (~S) = S ∪ {a}. Then all mapping classes in the mapping class group Mods that fixes the puncture a can be projected to mapping classes of Mod(~S) under the forgetful map. In this paper the author studies the mapping classes in Mods that can be projected to a given hyperbolic mapping class in Mod(~S). 相似文献
10.
Mikkel Thorup 《Combinatorica》2007,27(1):91-127
We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic graph in
worst-case time per edge insertion or deletion. Within logarithmic factors, this matches the best time bound for 1-edge connectivity.
Previously, no o(n) bound was known for edge connectivity above 3, and even for 3-edge connectivity, the best update time was O(n2/3), dating back to FOCS'92.
Our algorithm maintains a concrete min-cut in terms of a pointer to a tree spanning one side of the cut plus ability to list
the cut edges in O(log n) time per edge.
By dealing with polylogarithmic edge connectivity, we immediately get a sampling based expected factor (1+o(1)) approximation to general edge connectivity in
time per edge insertion or deletion. This algorithm also maintains a pointer to one side of a near-minimal cut, but if we
want to list the cut edges in O(log n) time per edge, the update time increases to
.
* A preliminary version of this work was presented at the The 33rd ACM Symposium on Theory of Computing( STOC) [22], Crete, Greece, July 2001. 相似文献
11.
Di He HU Zheng Yan XIAO 《数学学报(英文版)》2007,23(1):41-56
There are two parts in this paper. In the first part we construct the Markov chain in random environment(MCRE), the skew product Markov chain and p-θ^→ chain from a random transition matrix and a two-dimensional probability distribution, and in the second part we prove that the invarianee principle for p-θ^→ chain, a more complex non-homogeneous Markov chain, is true under some reasonable conditions. This result is more powerful. 相似文献
12.
13.
On the Range of the Aluthge Transform 总被引:1,自引:0,他引:1
Let
be the algebra of all bounded linear operators on a complex separable Hilbert space
For an operator
let
be the Aluthge transform of T and we define
for all
where T = U|T| is a polar decomposition of T. In this short note, we consider an elementary property of the range
of Δ. We prove that R(Δ) is neither closed nor dense in
However R(Δ) is strongly dense if
is infinite dimensional.
An erratum to this article is available at . 相似文献
14.
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
15.
Ming Yi LEE Chin Cheng LIN Yu Tien LIN 《数学学报(英文版)》2006,22(5):1509-1518
In this article, we apply the molecular characterization of the weighted Hardy space developed by the first two authors to show the boundedness of Hormander multiplier on the weighted Herz-type Hardy spaces HK^α,p 2(|x|^t; |x|^t) and HK^α,P 2(|x|^t; |x|^t). 相似文献
16.
For an arbitrary set E and a given closure operator
, we want to construct a symmetric closure operator
via some – possibly infinite – iteration process. If E is finite, the corresponding symmetric closure operator .
defines a matroid. If
and
is the convex closure operator,
turns out to be the affine closure operator. Moreover, we apply the symmetrization process to closure operators induced by
visibility.
Received March 9, 2005 相似文献
17.
In this paper, we will give some optimal estimates on the rotation number of the linear equation
and that of the asymmetric equation:
where p(t) and q(t) are almost periodic functions and
These estimates are obtained by introducing some kind of new norms in the spaces of almost periodic functions.
Supported by the National Natural Science Foundation of China (no. 10325102), TRAPOYT-M.O.E. of China (2001), and the National
973 Project of China (no. G1999075108).
Received: April 6, 2004; revised: July 7, 2004 相似文献
18.
Xiu Gui LIU 《数学学报(英文版)》2007,23(6):1025-1032
Abstract Let A be the mod p Steenrod algebra and S the sphere spectrum localized at p, where p is an odd prime. In 2001 Lin detected a new family in the stable homotopy of spheres which is represented by (b0hn-h1bn-1)∈ ExtA^3,(p^n+p)q(Zp,Zp) in the Adams spectral sequence. At the same time, he proved that i.(hlhn) ∈ExtA^2,(p^n+P)q(H^*M, Zp) is a permanent cycle in the Adams spectral sequence and converges to a nontrivial element ξn∈π(p^n+p)q-2M. In this paper, with Lin's results, we make use of the Adams spectral sequence and the May spectral sequence to detect a new nontrivial family of homotopy elements jj′j^-γsi^-i′ξn in the stable homotopy groups of spheres. The new one is of degree p^nq + sp^2q + spq + (s - 2)q + s - 6 and is represented up to a nonzero scalar by hlhnγ-s in the E2^s+2,*-term of the Adams spectral sequence, where p ≥ 7, q = 2(p - 1), n ≥ 4 and 3 ≤ s 〈 p. 相似文献
19.
Abstract A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in ℝn+1, and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of M in a hyperplane Xn+1 =constant in case M satisfies: for any two points (X′,Xn+1),
on M, with
, the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper,
we establish it under some additional conditions. Some variations of the Hopf Lemma are also presented. Several open problems
are described. Part I dealt with corresponding one dimensional problems.
(Dedicated to the memory of Shiing-Shen Chern)
* Partially supported by NSF grant DMS-0401118. 相似文献
20.
Given a closed ideal I in a C*-algebra A, an ideal J (not necessarily closed) in I , a *-homomorphism α : A → M(I ) and a map L : J → A with some properties, based on earlier works of Pimsner and Katsura, we define a C*-algebra
which we call the Crossed Product by a Partial Endomorphism. We introduce the Crossed Product by a Partial Endomorphism
induced by a local homeomorphism σ : U → X where X is a compact Hausdorff space and U is an open subset of X. A bijection between the gauge invariant ideals of
and the σ, σ-1- invariant open subsets of X is showed. If (X, σ) has the property that
is topologically free for each closed σ, σ-1-invariant subset X′ of X then we obtain a bijection between the ideals of
and the open σ, σ-1-invariant subsets of X.
*Partially supported by CNPq.
**Supported by CNPq. 相似文献