Henry E. Heatherly

SURVIVAL OF THE FITTEST IN A GENERALIZED LOGISTIC MODEL

In this paper we discuss the asymptotic behavior of a logistic model with distributed growth and mortality rates. In particular, we prove that the entire population becomes concentrated within the subpopulation with highest growth to mortality ratio, and converges to the equilibrium defined by this ratio. Finally, we present a numerical example illustrating the theoretical results.

Medial near-rings

In this paper we discuss (left) near-rings satisfying the identities:abcd=acbd,abc=bac, orabc=acb, called medial, left permutable, right permutable near-rings, respectively. The structure of these near-rings is investigated in terms of the additive and Lie commutators and the set of nilpotent elementsN (R). For right permutable and d.g. medial near-rings we obtain a “Binomial Theorem,” show thatN (R) is an ideal, and characterize the simple and subdirectly irreducible near-rings. “Natural” examples from analysis and geometry are produced via a general construction method.

Prime ideals and prime radicals in near-rings

This paper investigates conditions under which a prime ideal is completely prime and conditions for which every prime ideal in a near-ring is completely prime. Various implications of these conditions are examined with respect to the associated radicals.

EXTINCTION IN A GENERALIZED LOTKA- VOLTERRA PREDATOR-PREY MODEL

In this paper we discuss the asymptotic behavior of a predator-prey model with distributed growth and mortality rates. We exhibit simple criteria on the parameters which guarantee that all subpopulations but one predator-prey pair are driven to extinction as t--<x. Finally, we present numeri

Prime Ideals in Near-Rings

An ideal I of a near-ring R is a type one prime ideal if whenever a Rb ⊆ I, then a ∈ I or b ∈ I. This paper considers the interconnections between prime ideals and type one prime ideals in near-rings. It also develops properties of type one prime ideals, gives several examples illustrating where prime and type one prime are not equivalent, and investigates the properties of the type one prime radical. Several different types of conditions are given which guarantee that a prime ideal is type one. The class of all near-rings for which each prime ideal is type one is investigated and many examples of such near-rings are exhibited. Various localized distributivity conditions are found which are useful in establishing when prime ideals will be type one prime.

Permutation identity near-rings and “localized” distributivity conditions

A near-ringR is said to satisfy apermutation identity if there is some non-identity permutation σ of lengthn such that Πaj=Πaσ(j), for eacha1, ...,an∈R. Numerous examples of permutation identity near-rings are given. The theory is then developed making use of various “localized” distributive conditions, which include as special cases most of the standard global ones (e. g., d. g., pseudo-distributive). These localized conditions only assume distributivity among the elements of certain special (and often “small”) sets. Particularly useful for such sets are powers of the ideals generated by the sets of Lie commutators, additive commutators, or distributive elements. Examples are given where a localized condition holds yet none of the usual global ones do. Results are obtained concerning prime, semiprime, or maximal ideals as well as regular, simple, or subdirectly irreducible near-rings.

Involutions on Universal Algebras

The concept of an involution in the category of rings is extended to universal algebras and is further generalized in that setting. This approach yields four distinct types of involutions on algebras with two binary operations and two distinct types on the category of rings. Subdirectly irreducible universal algebras with involution are considered in detail. A subdirectly irreducible universal algebra with involution is either subdirectly irreducible as an algebra without involution or it is the subdirect product of two subdirectly irreducible algebras and the involution is the exchange involution. An example from the category of rings is given to illustrate that this result is sharp: no direct sum decomposition can be achieved in general. Focus then turns to algebras with two binary operations, particularly near-rings and rings. Subdirectly irreducible objects in the categories of distributive near-rings and of rings are characterized in greater detail, with close attention given to their additive structure.

Medial and distributively generated near-rings

In this paper we note some properties of fully invariant additive subgroups of near-rings and apply these results to d.g., medial, or subdirectly irreducible near-rings

Algebras Generated by Semicentral Idempotents

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