摘要:

The survey is devoted to two of the most common topologies on the set of all subspaces of a Banach space. The first part contains definitions of the topologies and a description of their properties. The main topics of the rest of the paper are: (1) Comparison of the introduced topologies; (2) Stability of properties of subspaces with respect to the topologies. The last section contains a list of open problems

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631766

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

In ring theory it is well known that a ringRwith identity is isomorphic to a matrix ring if and only ifRhas a set of matrix units. In this paper, the above result is extended to matrix near-rings and it is proved that a near-ringRwith identity is isomorphic to a matrix near-ring if and only ifRhas a set of matrix units and satisfies two other conditions. As a consequence of this result several examples of matrix near-rings are given and for a finite group (Γ, +) witho(Γ)> 2 it is proved thatM0(Γn)is (isomorphic to) a matrix near-ring.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631767

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

We introduce the notion of separability to locales. We prove the localic version of Urysohn's metrization theorem and show that, as in spaces, separability is countably productive. We also show that a normal regular locale is separable only if its Stone-Cech compactification is separable.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631768

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

For n a positive integer and v a vertex of a graphG, the nth order degree ofvinG, denoted bydegnv, is the number of vertices at distance n from v. The graphGis said to be nth order regular of degreekif, for every vertexvofG, degnv = k.The following conjecture due to Alavi, Lick, and Zou is proved: For n ≥ 2, ifGis a connected nth order regular graph of degree 1, thenGis either a path of length 2n—1 orGhas diameter n. Properties of nth order regular graphs of degreek, k ≥1, are investigated.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631769

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

The properties of the limit cycle of a generalised van der Pol equation of the form ü + u = ε (1—u2n)u, where ε is small and n is any positive integer, are investigated by applying a time transformation perturbation method due to Burton. It is found that asnincreases the amplitude of the limit cycle oscillation decreases and its period increases. The time transformation solution is compared with the solution derived using the method of multiple scales and with a numerical solution. It is found that, to first order in ε, the time transformation solution for the limit cycle agrees better with the numerical solution than the multiple scales solution. Both perturbation solutions give the same result for the period of the limit cycle to second order in ε. The accuracy of the time transformation solution decreases as n increases.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631770

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

摘要:

For a torsion radical, δ, we study various types of relative flatness and regularity. We obtain conditions valid when every R-module is δ-flat, when every R-module is semi-δ-flat and when every R-module is semi-δ-injective, and hence we characterize quasi-Frobenius rings R together with any torsion radical, δ, on R-mod. We define a ring to be δ perfect whenever every δ-flat module is projective and obtain extensions of some known results on perfect rings. We also introduce a relative form of the Jacobson Radical defined in terms of δ-flatness.

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631771

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631772

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1994.9631765

出版商:Taylor & Francis Group    

年代:1994

数据来源: Taylor