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1.
Let M be a right R-module,
the class of all M-small modules, and P a projective cover of M in
[M]. We consider the torsion theories
= (
),
= (
), and
= (
) in
[M], where
is the torsion theory generated by
is the torsion theory cogenerated by
, and
is the dual Lambek torsion theory. We study some conditions for
to be cohereditary, stable, or split, and prove that Rej(M,
) = M
=
(=
=
)
=
GenM(P)
.2000 Mathematics Subject Classification: 16S90 相似文献
2.
Let
be the Poisson point process with intensity 1 in Rd and let
be
. We obtain a strong invariance principle for the total length of the nearest-neighbor graph on
. 相似文献
3.
Let M be a four-holed sphere and Γ the mapping class group of M fixing the boundary ∂M. The group Γ acts on
which is the space of completely reducible SL (2,
-gauge equivalence classes of flat SL
-connections on M with fixed holonomy
on ∂M. Let
and
be the compact component of the real points of
. These points correspond to SU(2)-representations or SL(2,
-representations. The Γ-action preserves
and we study the topological dynamics of the Γ-action on
and show that for a dense set of holonomy
, the Γ-orbits are dense in
. We also produce a class of representations
such that the Γ-orbit of [ρ] is finite in the compact component of
, but
is dense in SL(2,
.Mathematics Subject Classiffications (2000). 57M05, 54H20, 11D99 相似文献
4.
Jaeyoung Byeon Junsang Park 《Calculus of Variations and Partial Differential Equations》2005,24(4):459-477
Let
be a connected compact smooth Riemannian manifold of dimension
with or without smooth boundary
We consider the following singularly perturbed nonlinear elliptic problem on
where
is the Laplace-Beltrami operator on
,
is an exterior normal to
and a nonlinearity
of subcritical growth. For certain
there exists a mountain pass solution
of above problem which exhibits a spike layer. We are interested in the asymptotic behaviour of the spike layer.
Without any non-degeneracy condition and monotonicity of
we show that if
the peak point
of the solution
converges to a maximum point of the scalar curvature
on
(the mean curvature
on
as
respectively.
The research of the first author was supported in part by KRF-2002-070-C000005 of Korea Research Foundation. 相似文献
5.
We generalize the concept of K-convexity to an n-dimensional Euclidean space. The resulting concept of
-convexity is useful in addressing production and inventory problems where there are individual product setup costs and/or
joint setup costs. We derive some basic properties of
-convex functions. We conclude the paper with some suggestions for future research.
Support from Columbia University and University of Texas at Dallas is gratefully acknowledged. Helpful comments from Qi Feng
are appreciated. 相似文献
6.
Frank Müller 《Calculus of Variations and Partial Differential Equations》2005,24(3):283-288
Let $P={\rm \Gamma}\cap{\cal S}Let
be the point of non-tangential intersection of a closed Jordan arc
and an embedded, regular support surface
. Let
be a conformally parametrized solution of
with partially free boundaries
. It is proved, that
is H?lder continuous up to
with
, whenever
meets
orthogonally along its free trace. This provides a regularity result for stationary minimal surfaces and is applicable also
to surfaces of prescribed bounded mean curvature.
Mathematics Subject Classification (2000) 53 A 10, 35 J 65, 35 R 35, 49 Q 05 相似文献
7.
Lutz Strüngmann 《Archiv der Mathematik》2006,86(3):193-204
Let R be a unital associative ring and
two classes of left R-modules. In this paper we introduce the notion of a
In analogy to classical cotorsion pairs as defined by Salce [10], a pair
of subclasses
and
is called a
if it is maximal with respect to the classes
and the condition
for all
and
Basic properties of
are stated and several examples in the category of abelian groups are studied.
Received: 17 March 2005 相似文献
8.
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
9.
Sébastien Dubernet 《Archiv der Mathematik》2006,86(5):430-436
A well known “zero-two law" shows that if
is a strongly continuous one-parameter group of bounded operators on a Banach space X, and if
then
Here we discuss analogous problems for general unital representations θ of a topological group G on a unital Banach algebra A. Let 1 be the unit of G, and I the unit element of A. We show that either
or
if, moreover, θ admits “continuous division by any positive integer”, then, either
or
Our argument also gives automatic continuity results for representations of abelian Baire groups on a separable Banach algebra
and representations of compact non abelian groups on a Banach algebra which are locally bounded and satisfy
Received: 8 June 2005; revised: 13 October 2005 相似文献
10.
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
11.
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
12.
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
13.
Naser Zamani 《Archiv der Mathematik》2006,86(4):321-330
Let
be a homogeneous Noetherian ring with local base ring (R0,m0) and let M,N be two finitely generated graded R-modules. Let
denote the i-th graded generalized local cohomology of N relative to M with support in
. We study the vanishing, tameness and asymptotical stability of the homogeneous components of
.
Received: 22 March 2005; revised: 25 June 2005 相似文献
14.
15.
Gregory D. Landweber 《K-Theory》2005,36(1-2):115-168
Given a Lie superalgebra
, we introduce several variants of the representation ring, built as subrings and quotients of the ring
of virtual
-supermodules, up to (even) isomorphisms. In particular, we consider the ideal
of virtual
-supermodules isomorphic to their own parity reversals, as well as an equivariant K-theoretic super representation ring
on which the parity reversal operator takes the class of a virtual
-supermodule to its negative. We also construct representation groups built from ungraded
-modules, as well as degree-shifted representation groups using Clifford modules. The full super representation ring
, including all degree shifts, is then a
-graded ring in the complex case and a
-graded ring in the real case. Our primary result is a six-term periodic exact sequence relating the rings
, and
. We first establish a version of it working over an arbitrary (not necessarily algebraically closed) field of characteristic
0. In the complex case, this six-term periodic long exact sequence splits into two three-term sequences, which gives us additional
insight into the structure of the complex super representation ring
. In the real case, we obtain the expected 24-term version, as well as a surprising six-term version, of this periodic exact
sequence.
(Received: October 2004) 相似文献
16.
Birkhoff coordinates for KdV on phase spaces of distributions 总被引:1,自引:0,他引:1
The purpose of this paper is to extend the construction of Birkhoff coordinates for the KdV equation from the phase space
of square integrable 1-periodic functions with mean value zero to the phase space
of mean value zero distributions from the Sobolev space
endowed with the symplectic structure
More precisely, we construct a globally defined real-analytic symplectomorphism
where
is a weighted Hilbert space of sequences
supplied with the canonical Poisson structure so that the KdV Hamiltonian for potentials in
is a function of the actions
alone. 相似文献
17.
Let X be a rearrangement-invariant Banach function space
over a complete probability space
, and denote by
the Hardy space consisting of all martingales
such that
. We prove that
implies
for any filtration
if and only if Doobs inequality holds in
X, where
denotes the martingale defined by
, n = 0, 1, 2, ..., and
a.s.Received: 1 August 2000 相似文献
18.
The purpose of this paper is to give characterizations for uniform exponential dichotomy of evolution families on the real
line. We consider a general class of Banach function spaces denoted
and we prove that if
with
and the pair
is admissible for an evolution family
then
is uniformly exponentially dichotomic. By an example we show that the admissibility of the pair
for an evolution family is not a sufficient condition for uniform exponential dichotomy. As applications, we deduce necessary
and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pairs
and
with
相似文献
19.
This paper deals with a class
of pseudorandom bit generators – modified alternating
–generators. This class is constructed similarly to the class
of alternating step generators. Three subclasses of
are distinguished, namely linear, mixed and nonlinear generators. The main attention is devoted to the subclass
of linear and mixed generators generating periodic sequences with maximal period lengths. A necessary and sufficient condition for all sequences generated by the linear generators of
to be with maximal period lengths is formulated. Such sequences have good statistical properties, such as distribution of zeroes and ones, and large linear complexity. Two methods of cryptanalysis of the proposed generators are given. Finally, three new classes of modified alternating
–generators, designed especially to be more secure, are presented. 相似文献
20.
Structure of Degenerate Block Algebras 总被引:13,自引:0,他引:13
Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map
: A
A
F, we define a Lie algebra
=
(A,
) over F with basis {ex | x
A/{0}} and Lie product [ex,ey] =
(x,y)ex+y. We show that
is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der
of
is a complete Lie algebra. We describe the double extension D(
, T) of
by T, where T is spanned by the locally finite derivations of
, and determine the second cohomology group H2(D(
, T),F) using anti-derivations related to the form on D(
, T). Finally, we compute the second Leibniz cohomology groups HL2(
, F) and HL2(D(
, T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee. 相似文献