摘要:

In this note we introduce the concept of completely prime and completely semiprime ideals for Γ-rings and study some of the properties of these ideals. Furthermore we introduce the concept of the completely prime radical of an ideal of a Γ-ring and also show that the upper radical determined by a class of completely prime rings is a special radical. We define an mc-system to give an elementwise characterization of the completely prime radical. Finally we show that if R is the right operator ring of a Γ ring H and W has a strong right unity, then there is a one-to-one correspondence between the completely prime ideals of R and that of M.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632161

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

It is shown that the rank of the projective added to the state space of a system in dynamic feedback can be decreased by assigning some poles to the original system first and by using these to obtain a new system with state space of lower rank on which dynamic feedback can be applied.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632162

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

An investigation is made of Cartesian closedness of monotopological categories A which are not necessarily c-categories. Results include: a description of the underlying sets of the power-objects in terms of the horn-sets of a certain monotopological subcategory of A; the fact that if A is Cartesian closed then it is subconcretely so; and the fact that if A is not topological and contains an initial source which is not a mono-source then A cannot be Cartesian closed. Various criteria concerning the existence of splitting objects in A are given, as well as the proofs of the exponential, distributive and other laws when A is Cartesian closed.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632163

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

IfGis a graph of order p and size q, we associate with each vertexvεGthe pair(d(v)—σ, Δ—d(v))which we call the coordinate (representation) ofvinG.The Cartesian graph ofG, denoted by cart(G), is defined as{(d(v)—σ,Δ- d(v)) | vε V}. The coordinate (a,a) of a vertex ofGis said to be simple inGwhile non-simple coordinate representations (a, b), (b, a) of vertices ofGform a mirror coordinate pair ofG.We characterise graphs for whichcart(G)=cart(G)and call such graphs Cartesian perfect. The Cartesian number of a graphG, denoted byxcart(G), is the sum of (i) the number of mirror coordinate pairs in a maximum setSof mirror coordinate pairs ofGand (ii) either 1 or 0 depending on whethercart(G)has a simple coordinate or not, respectively and (iii) the number of distinct non-simple coordinate representations of vertices ofGwhich do not belong to any mirror coordinate pair inS.GraphsGfor whichXcart(G)= x(G) are considered and we characterise k-Cartesian critical graphs (connected graphsGwith Xcart(G) =kandxcart(H) > kfor each connected subgraphHofG)for k=1,2 and 3. With each nonregular graphGwe associate the equationy =—x +Δ—σwhich we call the linear equation ofGwith intercept p = Δ—σ. A graphGis said to be (r)-linear with respect to its intercept p if (-p+r,q) satisfies its linear equation. For r ≥ 0 we characterise those Cartesian perfect graphsGfor which bothGand Ǥ are (r)-linear with respect to their interceptsp.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632164

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Techniques from the theories of partial differential equations and indefinite inner product spaces are used to prove the uniform convergence of the eigenfunction expansion associated with a two-parameter system of ordinary differential equations of the second order under left definiteness, left semi-definiteness, and indefiniteness assumptions.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632165

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Yesl Any equation of conservation of the form ∂x{P(∂xφ, ∂tφ) = ∂t{Q(∂xφ, ∂tφ)is shown to admit an infinite-dimensional, Abellan group of symmetries that is not a prolongation symmetry group. Explicit equations are given for the determination of the generators of the Lle algebra of this Abellan symmetry group, and for the generators of Its underlying Poisson algebra.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632166

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

In the article “Geodetic games for graphs” by F. Buckley and F. Harary the geodetic game on a generalized wheel Wm,nis stated to be won by the first player iff m + n is odd. This is incorrect; in this paper we show that the necessary and sufficient condition for the first player is that (1) n ⋚ 4 and m + n is odd or m = 1 and n is even, (2) m = 2 and n = 5, (3) n < 5 and m ≥ 2 and either m or n is odd.

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632167

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632168

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1988.9632160

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor