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1.
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
2.
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
3.
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
4.
Let
be a continuous semimartingale and let
be a continuous function of bounded variation. Setting
and
suppose that a continuous function
is given such that F is C1,2 on
and F is
on
. Then the following change-of-variable formula holds:
where
is the local time of X at the curve b given by
and
refers to the integration with respect to
. A version of the same formula derived for an Itô diffusion X under weaker conditions on F has found applications in free-boundary problems of optimal stopping. 相似文献
5.
F. Ben SaÏd 《The Ramanujan Journal》2005,9(1-2):63-75
Let IN be the set of positive integers,
= {b1 < ⋅s < bh}⊂IN, N∊IN and N≥ bh.
=
0(
,N) is the set (introduced by J.-L. Nicolas, I.Z. Ruzsa and A. Sárközy) such that
{1,..., N} =
and p(
,n)≡ 0 (mod 2) for n∊IN and n > N, where p(
,n) denotes the number of partitions of n with parts in
. Let us denote by σ (
,n) the sum of the divisors of n belonging to
. In a paper jointly written with J.-L. Nicolas, we have recently proved that, for all k≥ 0, the sequence (σ(
,2k n))n≥ 1mod 2k+1 is periodic with an odd period qk. In this paper, we will characterize for any fixed odd positive integer q, the sets
and the integers N such that q0 = q, and those for which qk = q for all k≥ 0. Moreover, a set
=
0(
,N) is constructed with the property that its period, i.e. the period of (σ(
,n))n≥ 1mod 2, is 217, and for which the counting function is asymptotically equal to that of
0({1,2,3,4,5},5) which is a set of period 31.Dedicated to Professor J.-L. Nicolas on the occasion of his 60th birthday2000 Mathematics Subject Classification: Primary—11P81, 11P83Research supported by MIRA 2002 program no 0203012701, Number Theory, Lyon-Monastir. 相似文献
6.
Some Processes Associated with Fractional Bessel Processes 总被引:1,自引:0,他引:1
Let
be a d-dimensional fractional Brownian motion with Hurst parameter H and let
be the fractional Bessel process. Itôs formula for the fractional Brownian motion leads to the equation
. In the Brownian motion case
is a Brownian motion. In this paper it is shown that Xt is not an
-fractional Brownian motion if H 1/2. We will study some other properties of this stochastic process as well. 相似文献
7.
Frank Müller 《Calculus of Variations and Partial Differential Equations》2005,24(3):289-308
We study surfaces of prescribed bounded mean curvature H in a partially free boundary configuration
. If
is projectable onto and
is a cylinder surface over the x1,x2-plane, we show that also the spanned H-surface
is projectable onto this plane. Besides certain conditions on
and H, we have to suppose that
is stationary and freely stable w.r.t. the generalized area functional
, and the vector field
is assumed to be tangential on
. Consequences are uniqueness of freely stable H-surfaces and solvability of a mixed boundary problem for the nonparametric prescribed mean curvature equation.
Mathematics Subject Classification (2000): 53 A 10, 35 J 65, 35 R 35, 49 Q 05 相似文献
8.
Minimum-Volume Enclosing Ellipsoids and Core Sets 总被引:3,自引:0,他引:3
We study the problem of computing a (1+ε)-approximation to the minimum-volume enclosing ellipsoid of a given point set
. Based on a simple, initial volume approximation method, we propose a modification of the Khachiyan first-order algorithm. Our analysis leads to a slightly improved complexity bound of
operations for
. As a byproduct, our algorithm returns a core set
with the property that the minimum-volume enclosing ellipsoid of
provides a good approximation to that of
. Furthermore, the size of
depends on only the dimension d and ε, but not on the number of points n. In particular, our results imply that
for
.We thank the Associate Editor and an anonymous referee for handling our paper efficiently and for helpful comments and suggestions.This author was supported in part by NSF through Grant CCR-0098172.This author was supported in part by NSF through CAREER Grant DMI-0237415. 相似文献
9.
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
10.
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
11.
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
12.
Jie FANG 《数学学报(英文版)》2007,23(9):1611-1620
An algebraic structure A is said to have the endomorphism kernel property if every congruence on A, other than the universal congruence, is the kernel of an endomorphism on A. In this paper, we consider the EKP (that is, endomorphism kernel property) for an extended Ockham algebra A. In particular, we describe the structure of the finite symmetric extended de Morgan algebras having EKP. 相似文献
13.
Asymptotic Normality for Non-linear Functionals of Non-causal Linear Processes with Summable Weights
Let
be a non-causal linear process with weights ajs satisfying certain summability conditions, and the iid sequence of innovation {i} having zero mean and finite second moment. For a large class of non-linear functional K which includes indicator functions and polynomials, the present paper develops the
central limit theorem for the partial sums
相似文献
14.
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
15.
B. Bouchard 《Journal of Theoretical Probability》2005,18(2):439-467
Motivated by applications in financial mathematics, Ref. 3 showed that, although
fails to be locally convex, an analogue to the classical bipolar theorem can be obtained for subsets of
: if we place this space in polarity with itself, the bipolar of a set of non-negative random variables is equal to its closed (in probability), solid, convex hull. This result was extended by Ref. 1 in the multidimensional case, replacing
by a closed convex cone K of [0, )d, and by Ref. 12 who provided a conditional version in the unidimensional case. In this paper, we show that the conditional bipolar theorem of Ref. 12 can be extended to the multidimensional case. Using a decomposition result obtained in Ref. 3 and Ref. 1, we also remove the boundedness assumption of Ref. 12 in the one dimensional case and provide less restrictive assumptions in the multidimensional case. These assumptions are completely removed in the case of polyhedral cones K. 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.
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
19.
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
20.
D. Jakubíková-Studenovská 《Algebra Universalis》2009,60(2):125-143
In the present paper we prove that the collection of all convexities of partial monounary algebras is finite; namely, it has exactly 23 elements. Further, we show that for
each element there exists a subset of such that is generated by and card .
This work was supported by the Science and Technology Assistance Agency under the contract No. APVT-20-004104. Supported by
Grant VEGA 1/3003/06. 相似文献