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991.
B. Yousefi 《Archiv der Mathematik》2004,83(6):536-539
Let
be a Hilbert space of functions analytic on a plane domain such that for every in the functional of evaluation at is bounded. Assume further that
contains the constants and admits multiplication by the independent variable z, Mz, as a bounded operator. We give sufficient conditions for Mz to be reflexive.Received: 17 February 2004 相似文献
992.
Let L(x, v) be a Lagrangian which is convex and superlinear in the velocity variable v, and let H(x, p) be the associated Hamiltonian. Conditions are obtained under which every viscosity solution
of the Hamilton-Jacobi equation
is an action function in the large, i.e.,
for all
Received: 13 June 2003 相似文献
993.
We characterize the relation between the geometrical properties of Weyl manifolds and the algebraic properties of the Weyl
algebras (§1) and the deformation algebras associated to two conformal Weyl connections (§2). The last section is devoted
to the study of the Weyl-Lyra algebras associated to a conformal Weyl connection and a conformal semisymmetric connection. 相似文献
994.
Manuel del Pino Jean Dolbeault Monica Musso 《Journal de Mathématiques Pures et Appliquées》2004,83(12):1405-1456
We consider the problem of finding positive solutions of Δu+λu+uq=0 in a bounded, smooth domain Ω in , under zero Dirichlet boundary conditions. Here q is a number close to the critical exponent 5 and 0<λ<λ1. We analyze the role of Green's function of Δ+λ in the presence of solutions exhibiting single and multiple bubbling behavior at one point of the domain when either q or λ are regarded as parameters. As a special case of our results, we find that if , where λ∗ is the Brezis-Nirenberg number, i.e., the smallest value of λ for which least energy solutions for q=5 exist, then this problem is solvable if q>5 and q−5 is sufficiently small. 相似文献
995.
This paper is concerned with the existence, smoothness and attractivity of invariant manifolds for evolutionary processes on general Banach spaces when the nonlinear perturbation has a small global Lipschitz constant and locally Ck-smooth near the trivial solution. Such a nonlinear perturbation arises in many applications through the usual cut-off procedure, but the requirement in the existing literature that the nonlinear perturbation is globally Ck-smooth and has a globally small Lipschitz constant is hardly met in those systems for which the phase space does not allow a smooth cut-off function. Our general results are illustrated by and applied to partial functional differential equations for which the phase space (where r>0 and being a Banach space) has no smooth inner product structure and for which the validity of variation-of-constants formula is still an interesting open problem. 相似文献
996.
H.?IshikawaEmail author J.?M.?ThuswaldnerEmail author 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2004,74(1):11-32
Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan
and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration
admit a functional equation.
The second author was supported by the FWF project S381O. 相似文献
997.
For any monoid M, any universal variety contains arbitrarily large algebras
whose endomorphism monoid is isomorphic to M. A variety universal modulo a group
G contains arbitrarily large algebras whose endomorphism monoid is isomorphic to the
direct product M x G. One of the results of this
paper structurally characterizes all finitely generated varieties of distributive double
p-algebras universal modulo a group, and shows
that any unavoidable direct factor G is a Boolean group with at most eight elements. 相似文献
998.
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
999.
1000.
Let v be a valuation of terms of type , assigning to each term
t of type a value v(t) 0. Let
k 1 be a natural number. An identity
of type is called
k-normal
if either s = t or both
s and t have value
k, and otherwise is called non-k-normal. A
variety V of type is said to be k-normal if
all its identities are k-normal, and non-k-normal
otherwise. In the latter case, there is a unique smallest k-normal variety
to contain V , called the k-normalization of
V. Inthe case k = 1, for the usual depth valuation
of terms, these notions coincide with the well-known concepts of normal identity, normal variety, and
normalization of a variety. I. Chajda has characterized the normalization of a variety by means of choice algebras. In
this paper we generalize his results to a characterization of the k-normalization of
a variety, using k-choice algebras. We also introduce the concept of a
k-inflation algebra, and for the case that v is the
usual depth valuation of terms, we prove that a variety V is
k-normal iff it is closed under the formation of k-inflations,
and that the k-normalization of V consists
precisely of all homomorphic images of k-inflations of algebras in V . 相似文献