共查询到20条相似文献,搜索用时 421 毫秒
1.
2.
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
3.
Humio Ichimura 《Archiv der Mathematik》2006,87(6):539-545
Let p be an odd prime number and
. Let
be the classical Stickelberger ideal of the group ring
. Iwasawa [6] proved that the index
equals the relative class number
of
. In [2], [4] we defined for each subgroup H of G a Stickelberger ideal
of
, and studied some of its properties. In this note, we prove that when
mod 4 and [G : H] = 2, the index
equals the quotient
.
Received: 13 January 2006 相似文献
4.
We prove Tolokonnikov’s Lemma and the inner-outer factorization for the real Hardy space
, the space of bounded holomorphic (possibly operator-valued) functions on the unit disc all of whose matrix-entries (with
respect to fixed orthonormal bases) are functions having real Fourier coefficients, or equivalently, each matrix entry f satisfies
for all z ∈
.
Tolokonnikov’s Lemma for
means that if f is left-invertible, then f can be completed to an isomorphism; that is, there exists an F, invertible in
, such that F = [ f f
c
] for some f
c
in
. In control theory, Tolokonnikov’s Lemma implies that if a function has a right coprime factorization over
, then it has a doubly coprime factorization in
. We prove the lemma for the real disc algebra
as well. In particular,
and
are Hermite rings.
The work of the first author was supported by Magnus Ehrnrooth Foundation.
Received: December 5, 2006. Revised: February 4, 2007. 相似文献
5.
J. J. Grobler 《Integral Equations and Operator Theory》2007,57(1):83-99
For a probability space
we denote the marginal measures of
, defined on Σ and Λ respectively, by
and
. If ρ is a function norm defined on
marginal function norms ρ1 and ρ2 are defined on
and
. We find conditions which guarantee Lρ 1 + Lρ 2 to be embedded in Lρ as a closed subspace. The problem is encountered in Statistics when estimating a bivariate distribution with known marginals.
We find a condition which, applied to the binormal distribution in L2, improves some known conditions. 相似文献
6.
Abstract
By
we denote the set of all propositional formulas. Let
be the set of all clauses. Define
. In Sec. 2 of this paper we prove that for normal modal logics
, the notions of
-expansions and
-expansions coincide. In Sec. 3, we prove that if I consists of default clauses then the notions of
-expansions for I and
-expansions for I coincide. To this end, we first show, in Sec. 3, that the notion of
-expansions for I is the same as that of
-expansions for I.
The project is supported by NSFC 相似文献
7.
Fazli Kh 《Statistical Inference for Stochastic Processes》2007,10(2):181-208
We observe a realization X
(n) of a Poisson process on the set
with intensity function
depending on the unknown real parameter
. Based on X
(n) we test simple null hypothesis
against one sided alternative
for given
. We improve the level of the well-known locally asymptotically uniformly most powerful (LAUMP) test by using the Edgeworth
type expansion for stochastic integral. We show that the improved test is second-order efficient under certain regularity
conditions.
相似文献
8.
S. Asserda 《Integral Equations and Operator Theory》2006,55(1):1-18
Let
denote the closed subspace of
consisting of analytic functions in the unit disc
. For certain class of subharmonic functions
and
, it is shown that the essential norm of Hankel operator
is comparable to the distance norm from Hf to compact Hankel operators. 相似文献
9.
Let H be a finite group,
a field and V a finite dimensional
H-module. We introduce the Fitting submodule FV (H), an
H submodule of V which has properties similar to the generalized Fitting subgroup of a finite group.
Received: 26 August 2005 相似文献
10.
Let X, Y be Banach spaces. We say that a set
is uniformly p–summing if the series
is uniformly convergent for
whenever (xn) belongs to
. We consider uniformly summing sets of operators defined on a
-space and prove, in case X does not contain a copy of c0, that
is uniformly summing iff
is, where T (φ x) = (T#φ) x for all
and x∈X. We also characterize the sets
with the property that
is uniformly summing viewed in
.
Received: 1 July 2005 相似文献
11.
B. Klartag 《Geometric And Functional Analysis》2006,16(6):1274-1290
Let
be a convex body and ɛ > 0. We prove the existence of another convex body
, whose Banach–Mazur distance from K is bounded by 1 + ɛ, such that the isotropic constant of K’ is smaller than
, where c > 0 is a universal constant. As an application of our result, we present a slight improvement on the best general upper
bound for the isotropic constant, due to Bourgain.
The author is a Clay Research Fellow, and was also supported by NSF grant #DMS-0456590.
Received: November 2005; Accepted: February 2006 相似文献
12.
Dietmar Vogt 《Archiv der Mathematik》2006,87(2):163-171
It is shown that for open convex
, d > 1 and a nontrivial polynomial P the space
does not have property
. If P is elliptic or homogeneous, then this holds for every open Ω. For
even
cannot occur and if it occurs for some Ω, then P must be hypoelliptic.
Received: 18 July 2005 相似文献
13.
This paper exhibits an interesting relationship between arbitrary order Bessel functions and Dirac type equations.
Let
be the Euclidean Dirac operator in the n-dimensional flat space
the radial symmetric Euler operator and α and λ be arbitrary non-zero complex parameters. The goal of this paper is to describe
explicitly the structure of the solutions to the PDE system
in terms of arbitrary complex order Bessel functions and homogeneous monogenic polynomials.
Received: 27 October 2005 相似文献
14.
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
15.
The purpose of this paper is to give new and general characterizations for uniform dichotomy and uniform exponential dichotomy
of evolution families on the real line. We consider two general classes denoted
and
and we prove that if V,W are Banach function spaces with
and
, then the admissibility of the pair
for an evolution family
implies the uniform dichotomy of
. In addition, we consider a subclass
and we prove that if
, then the admissibility of the pair
implies the uniform exponential dichotomy of the family
. This condition becomes necessary if
. Finally, we present some applications of the main results. 相似文献
16.
Let k 1 and
be a system of rational functions forming a strongly linearly independent set over a finite field
. Let
be arbitrarily prescribed elements. We prove that for all sufficiently large extensions
, there is an element
of prescribed order such that
is the relative trace map from
onto
We give some applications to BCH codes, finite field arithmetic and ordered orthogonal arrays. We also solve a question of Helleseth et~al. (Hypercubic 4 and 5-designs from Double-Error-Correcting codes, Des. Codes. Cryptgr. 28(2003). pp. 265–282) completely.classification 11T30, 11G20, 05B15 相似文献
17.
18.
Summary.
Let
be a field of real or complex numbers and
denote the set of nonzero elements of
.
Let
be an abelian group. In this paper, we solve the functional equation
f
1
(x +
y) +
f
2
(x -
y) =
f
3
(x) +
f
4
(y) +
g(xy)
by modifying the domain of the unknown functions
f
3,
f
4, and
g from
to
and using a method different from [3]. Using this result,
we determine all functions
f
defined on
and taking values on
such that the difference
f(x + y) + f
(x -
y) - 2
f(x) - 2
f(y)
depends only on the product
xy for all
x and
y in
相似文献
19.
Imre Kocsis 《Aequationes Mathematicae》2007,73(3):280-284
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