Kirby C. Smith

A stochastic model of a temperature-dependent population☆

Abstract The theoretical basis is developed for a population model which allows the use of constant temperature experimental data in predicting the size of an insect population for any variable temperature environment. The model is based on a stochastic analysis of an insects mortality, development, and reproduction response to temperature. The key concept in the model is the utilization of a physiological time scale. Different temperatures affect the population by increasing an individuals physiological age by differing rates. Conditions for the temperature response properties are given which establish the validity of the model for variable temperature regimes. These conditions refer to the relationship between chronological and physiological age. Reasonable agreement between the model and field populations demonstrates the practicality of this approach.

The centralizer of a set of group automorphisms

Let A be a set of automorphisms of a finite group G. The structure of the near-ring C(A) of identity preserving functions which commute with every element of A is investigated.

An internal characterisation of structural matrix rings

It is known that structural matrix rings pro-vide a natural passage from complete matrix rings to upper and lower triangular matrix rings, and they often explain the peculiarities regarding certain properties of complete matrix rings on the one hand and of triangular matrix rings on the other hand. In this paper the concept of a set of matrix units in a ring associated with a quasi-order relation is introduced and used to provide an internal char-acterisation of structural matrix rings.

Generalized matrix near-rings

Let R be a right near-ring with identity. The k×k matrix near-ring over R, Matk(R R), as defined by Meldrum and van der Walt, regards R as a left mod-ule over R. Let M be any faithful left R-module. Using the action of R on M, a generalized k×k matrix near-ring, Matk(R M), is defined. It is seen that Matk(R M) has many of the features of Matk(R R). Differences be-tween the two classes of near-rings are shown. In spe- cial cases there are relationships between Matk(R M) and Matk(R R). Generalized matrix near-rings Matk(R M) arise as the “right near-ring” of finite centraiizer near-rings of the form M A{G)> where G is a finite group and A is a fixed point free automorphism group on G.

Simple near-ring centralizers of finite rings

For a finite ring R with identity and a finite unital R-module V we call C(R) = {f: V-VIf(av) = af(v) for all a E R, v E V} the nearring centralizer of R. We investigate the structure of C(R) and obtain a characterization of those rings R for which C(R) is a simple nonring.

Simple near-rings associated with meromorphic products

Let H be a subgroup of G2 and let Mo(G, 2, H) = {f e Mo(G)lf (H) C H}. In this paper we characterize in terms of properties of H when Mo(G, 2, H) is a simple near-ring.

Endomorphisms of linear automata

Relationships between the group, Aut(M), of automorphisms of a linear automaton M and the structure of M are determined. Linear automata in which Aut(M) is a group of translations are characterized in terms of the structure of the state space of M. Also, conditions are determined as to when Aut(M) contains only linear transformations.

Rings which are a Homomorphic Image of a Centralizer Near-Ring

In this work the near-rings under consideration will be exclusively centralizer near-rings M A(G) where G is a finite group and A is a group of automorphisms of G.

When is a centralizer near-ring isomorphic to a matrix near-ring? Part 2

Necessary conditions are found for a centralizer near-ring MA(G) to be isomorphic to a matrix near-ring, where G is a finite group which is cyclic as an MA(G)-module There are centralizer near-rings which are matrix near-rings. A class of such near-rings is exhibited. Examples of centralizer near-rings which are not matrix near-rings are given.

Algebraically closed noncommutative polynomial rings

Let R be a noncommutative polynomial ring over the division ring K where K has center F. Then R = K[x,σ,D]where σ is a monomorphism of K and D is a σ-derivaton K. R is called dimension finite if (K: Fσ)<∞ and (K: FD)<∞ where Fσ is the subfield of F fixed under σand FD is the subfied of F of D-constants. R is algebraically closed if every nonconstant polynomial in Rfactors completely into linear factors. The algebraically closed dimension finite polynomial rings are determined. s done by reducing the problem to two classes: skew polynomial rings and differential polynomial rings. Examples algebraically closed polynomial rings which are not dimensfinite are given.