The classical maximum principle for homogeneous, second order, uniformly elliptic equations implies that non-negative, classical supersolutions are either positive or vanish identically in the interior of their domain of definition. This paper is concerned with an extension of this result to weak supersolutions of non-uniformly elliptic equations subject to only mild coefficient restrictions.

In this brief note new characterizations of open mappings and closed mappings are presented which involve the compact order of the domain. The paper answers some of the questions which resulted from the study of the ordinal monotonicity of pseudo-open mappings and thus constitutes an extension of that work. Another characterization of open mappings is introduced.

It is shown that if с is a finitely productive and hereditary class of uniformly pointed finite discrete universal algebras then any injective in с is an injective in Proс.

The theory of differentiation in locally convex spaces constructed by the author in Memoirs Amer. Math. Soc. 17 (1979) is used to give a new form of the definition of Omori-Lie groups.

Ostrom proposed classifications of translation planes on the basis of the action of the collineation group of the plane on the ideal points. There are examples of translation planes in which ideal points form a single orbit (flag transitive planes) and also several orbits (Hall, André, Foulser, and so forth, planes). In this paper the authors have constructed a translation plane in which the ideal points are divided into two orbits of lengths 18 and 8 respectively. A few collineatlons are computed together with their actions. The group of collineations G1 which is transitive on the two sets of 18 and 8 lines separately is calculated. All the collineations that fix L0 are also calculated and they form a group of. If G2 is the group of translations then the full collineation group is shown to be 〈G1, G2, G3〉.

In this paper we consider a nonlinear differential-integral equation which arises in the problems of ecology and study the questions of convergent solutions and asymptotic equivalence of the solutions.

The aim of the paper is to study the interrelation between several natural smallness conditions on an algebraic theory with a proper class of operations. The conditions concern the existence of sets of data determining algebras, homomorphisms, subalgebras, and congruences.

The object of this paper is to establish some relations between two generalized Nörlund methods and also between two absolute generalized Nörlund methods. Our theorems obtained here generalize many known results, including McFadden's Theorems which state the inclusion relations between two absolute Nörlund methods, and results of Ikuko Kayashima.

Using the notions of orthogonality in normed linear spaces such as isosceles, pythagorean, and Birkhoff-James orthogonality, in this paper we provide some new characterizations of inner product spaces besides giving simpler proofs of existing similar characterizations. In addition we prove that in a normed linear space pythagorean orthogonality is unique and that isosceles orthogonality is unique if and only if the space is strictly convex.

A new class of algebraic systems known as loop near-rings are introduced, which includes near-rings and consequently rings. Different types of radicals are introduced in a loop near-ring N which coincide with the Jacobson radical when N happens to be a ring, and several characterizations of these radicals are obtained.

In this paper we study the existence and uniqueness of solutions for the following complex nonlinear complementarity problem: find z ∈ S such that g(z) ∈ S* and re(g(z), z) = 0, where S is a closed convex cone in Cn, S* the polar cone, and g is a continuous function from Cn into itself. We show that the existence of a z ∈ S with g(z) ∈ int S* implies the existence of a solution to the nonlinear complementarity problem if g is monotone on S and the solution is unique if g is strictly monotone. We also show that the above problem has a unique solution if the mapping g is strongly monotone on S.

Let V denote the symmetric monoidal closed category of limit-space abelian groups and let L denote the full subcategory of locally compact Hausdorff abelian groups. Results of Samuel Kaplan on extension of characters to products of L–groups are used to show that each closed subgroup of a product of L-groups is a limit of L–groups. From this we deduce that the limit closure of L in V is reflective in V and has every group Pontryagin reflexive with respect to the structure of continuous convergence on the character groups. The basic duality L ≃ Lop is then extended.

In this present paper we shall prove the following. Suppose that λ1, λ2, λ3 are any non-zero real numbers not all of the same sign and that λ1/λ2 is irrational. If η is any real number and, 0 < α < 1/9, then there are infinitely many prime triples (p1, p2, p3) for which

An algebraic formulation of the density theorem for loop near-rings is presented, which generalizes the same result for near-rings.

We show that a certain class of Fibonacci groups can not be right ordered. A question remaining is: Are the torsion-free members of this class unique products groups?