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排序方式: 共有10000条查询结果,搜索用时 31 毫秒
981.
If E is a vector space over a field K, then any regular symmetric bilinear form on E induces a polarity
on the lattice of all subspaces of E. In the particular case where E is 3-dimensional, the set of all subspaces M of E such that both M and
are not N-subspaces (which, in most cases, is equivalent to saying that M is nonisotropic), ordered by inclusion and endowed with the restriction of the above polarity, is an orthomodular lattice T(E, ). We show that if K is a proper subfield of K, with K F2, and E a 3-dimensional K -subspace of E such that the restriction of to E × E is, up to multiplicative constant, a bilinear form on the K -space E , then T(E , ) is isomorphic to an irreducible 3-homogeneous proper subalgebra of T(E, ). Our main result is a structure theorem stating that, when K is not of characteristic 3, the converse is true, i.e., any irreducible 3-homogeneous proper subalgebra of T(E, ) is of this form. As a corollary, we construct infinitely many finite orthomodular lattices which are minimal in the sense that all their proper subalgebras are modular. In fact, this last result was our initial aim in this paper.Received June 4, 2003; accepted in final form May 18, 2004. 相似文献
982.
We investigate local polynomial functions on Stone algebras and on Kleene
algebras. We find a generating set for the clone of all local polynomial functions. We also
represent local polynomial functions on a given algebra by polynomial functions of some
canonical extension of this algebra. 相似文献
983.
Let X be a Banach space and let
A be a closed linear operator on
X. It is shown that the abstract Cauchy problem
enjoys maximal regularity in weighted
L
p
-spaces with weights
, where
,
if and only if it has the property of maximal
L
p
-regularity.
Moreover, it is also shown that the derivation operator
admits an
-calculus in weighted
L
p
-spaces.
Received: 26 February 2003 相似文献
984.
The solutions of the equation
in
, where
are investigated,
Bessel potentials of higher order are defined, and recurrence relations
between these solutions and these Bessel potentials are obtained. It is
also proved that these solutions and the solutions of
, under certain conditions, are identical.
Received: 6 November 2002 相似文献
985.
In this paper we establish a multiplicity theorem for critical points of
functionals on reflexive Banach spaces. Precisely, we deduce the main result
using a general variational principle proved by Ricceri. Moreover,
we present an application to a Neumann problem which gives a
positive answer to some questions formulated by the previous
author.Received: 6 February 2003 相似文献
986.
Let T = T(A, D) be a self-affine attractor in
defined by an integral expanding matrix A and
a digit set D. In the
first part of this paper, in connection with canonical number systems,
we study connectedness of T when
D corresponds to the set of
consecutive integers
. It is shown that in
and
, for any integral expanding matrix A, T(A, D) is connected.
In the second part, we study connectedness of Pisot dual tiles, which
play an important role in the study of
-expansions, substitutions and
symbolic dynamical systems. It is shown that each tile of the dual
tiling generated by a Pisot unit of degree 3 is arcwise connected. This
is naturally expected since the digit set consists of consecutive
integers as above. However surprisingly, we found families of
disconnected Pisot dual tiles of degree 4. We even give a simple
necessary and sufficient condition of connectedness of the Pisot dual
tiles of degree 4. Detailed proofs will be given in [4].
Received: 2 March 2003 相似文献
987.
988.
Existence of multiple and sign-changing solutions for a problem involving p-Laplacian and jumping nonlinearities are considered via the construction of descent flow in . Sign-changing and multiple solutions are obtained under additional assumption on the nonlinearity. The uniqueness of positive (negative) solution theorem is included too. 相似文献
989.
Joachim Toft 《Journal of Functional Analysis》2004,207(2):399-429
Let Mp,q denote the modulation space with parameters p,q∈[1,∞]. If 1/p1+1/p2=1+1/p0 and 1/q1+1/q2=1/q0, then it is proved that . The result is used to get inclusions between modulation spaces, Besov spaces and Schatten classes in calculus of Ψdo (pseudo-differential operators), and to extend the definition of Toeplitz operators. We also discuss continuity of ambiguity functions and Ψdo in the framework of modulation spaces. 相似文献
990.
We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2. 相似文献