摘要:

The theory of H-sets was first propounded by L. Collatz [3] and [4]. This concept has been shown to be useful in the study of uniform approximation, and we here consider the form H-sets take in this setting of vector-valued functions and prove a general characterization theorem. A similar exposition for the linear real-valued case can be found in [1].

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631869

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

A stability theory is developed for second order elliptic boundary value problems by considering perturbations of the coefficients, right hand sides and boundary conditions. Systematic use is made of suitable a priori estimates in order to obtain stability results for the solutions in Sobolev spaces of arbitrary order and therefore also for classical solutions.

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631870

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

Other theories that develop topology without points are either excessively artificial or suffer from a lack of rigor. In this paper it is assumed that worlds W are composed of parts that form a complete Boolean algebra [xbar] and that the collection [Wbar] of all points of W is a certain subcollection of all filters defined over [xbar]. Two axioms are given for points which, given suitable definitions, convert [Wbar] into a compact Hausdorff space. Nearness collections of parts of W are defined which satisfy all the axioms of Herrlich for nearness except that closure is defined without mentioning points and consequently one may define closed and open parts. A category of worlds is defined in which the objects are lattices of closed parts of a world and the arrows are roughly speaking the far-preserving mps. It is shown that the category of compact T1-spaces is a reflective subcategory of the category of worlds.

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631871

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

In the paper “Convergence in normed Köthe spaces” (J. Singapore National Academy of Science,4, 146–148 (1975) M.R.52# 11568) Ng Peng-Nung and Lee Peng-Yee obtained a convergence result in the general setting of Banach funcation spaces providing conditions in order that pointwise and weak convergence imply norm convergence. They claim this result to be a generalization of a corresponding well known result in the Lebesgue space L1(X, u). To substantiate their claim it is necessary to show that the class of Banach function spaces for which their theorem holds is larger than the class of L1-spaces. This, we shall show, is unfortunately not the case.

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631872

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

In this paper we show that the definition and construction of radical and semisimple classes of associative rings can be interpreted in a general category K in terms of two subclasses of epimorphisms and mono-morphisms. We also provide answers to the following two questions posed by Wiegandt:

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631873

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

The aim of this note is to apply various factorization properties of module homomorphisms to establish criteria for projectivity and quasi-projectivity.

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631874

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

摘要:

Any multiple integral problem in the calculus of variations gives rise to a pair of distributions on the configuration space. Whenever these distributions are integrable, the Euler-Lagrange equations are equivalent to the condition that the divergences of a set of uniquely defined vector fields vanish. This leads to a simple geometrical interpretation of the Euler-Lagrange equations.

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631875

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631876

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1981.9631868

出版商:Taylor & Francis Group    

年代:1981

数据来源: Taylor