By a result of K.B. Lee, the lattice of varieties of pseudo-complemented distributive lattices is the ω + 1 chain

where B−1, B0, B1 are the varieties formed by all trivial, Boolean, and Stone algebras, respectively. General theorems on relative universality proved in the present paper imply that there is a proper class of non-isomorphic algebras in B3 with finite endomorphism monoids, while every infinite algebra from B2 has infinitely many endomorphisms. The variety B4 contains a proper class of non-isomorphic algebras with endomorphism monoids consisting of the identity and finitely many right zeros; on the other hand, any algebra in B3 with a finite endomorphism monoid of this type must be finite.

We give a characterization of monoidal closed structures, “determined by systems of filters” on the category of topological spaces and continuous maps. The method we use to introduce suitable topologies on the product set X × Y of spaces X and Y, and on the set of all continuous maps from X to Y, is essentially that of Wilker.

Necessary and sufficient conditions for a Poisson stable flow to be recurrent are given.

Let K be a closed convex body in Rn containing a finite number of points of lattice Λ in its interior. We show that K is bounded if K contains a certain suitably large simplex.

Let belong to the class of α-spiral functions of order ρ(|α| < π/2, 0 ≤ ρ < 1). In this paper, we determine sharp coefficient estimates for functions of the form f(z)t, where t is a positive integer. We also study the influence of the second coefficient on the other coefficients for such functions. The results obtained not only generalize the results of MacGregor, Boyd, Srivastava, Silverman and Silvia and others, but also give rise to new results.

Let K be a compact Hausdorff space and let E be a Banach space. We denote by C(K, E) the Banach space of all E-valued continuous functions defined on K, endowed with the supremum norm.

Recently, Talagrand [Israel J. Math. 44 (1983), 317–321] constructed a Banach space E having the Dunford-Pettis property such that C([0, 1], E) fails to have the Dunford-Pettis property. So he answered negatively a question which was posed some years ago.

We prove in this paper that for a large class of compacts K (the scattered compacts), C(K, E) has either the Dunford-Pettis property, or the reciprocal Dunford-Pettis property, or the Dieudonné property, or property V if and only if E has the same property.

Also some properties of the operators defined on C(K, E) are studied.

A proof is given for the existence of at least one stable periodic limit cycle solution for the polynomial non-linear differential equation of the form

in some cases where the Levinson-Smith criteria are not directly applicable.

Let R be a commutative ring with unity. Then every factor ring of R has an Artinian total quotient ring if and only if R is a direct sum of one-dimensional Noetherian domains and local Artinian rings.

The purpose of this paper is to give an application of homological methods to game theory. The main theorems give conditions of a homological nature for the existence and uniqueness of the Shapley value for games with continuum players.

A set mapping on a set S is a function f mapping S into the powerset of S such that x ∉ f(x) for each x in S. The set map f has order θ if θ is the least cardinal such that |f(x)| < θ for each x in S. A subset H of S is free for f if x ∉ f(y) for all x, y in H. In this paper we use classical results about set mappings of large order to investigate conditions which ensure a large free set for set mappings of unrestricted order.

The aim of the present paper is to give some general surjectivity theorems for multifunctions using tangent cones and generalized differentiability assumptions.

In this note we point out that a recent result of Leung concerning hypersurfaces of a Euclidean space has a simple generalisation to hypersurfaces of complete simply-connected Riemannian manifolds of non-positive constant sectional curvature.

Let E = {z: |z| < 1} and let H = {w : regular in E, w(0) = 0, |w(z)| < l, z ∈ E}.

Let P(A, B) denote the class of functions in E which can be put in the form (1 + Aw(z))/(1 + Bw(z)), −1 ≤ A < B ≤ 1, w(z) ∈ H. Let S*(A, B) denote the class of functions f(z) of the form such that zf′(z)/f(z) ∈ P(A, B). If f(z) ∈ S*(A, B) and g(z) ∈ S*(C, D) then, in this paper the radius of starlikeness of order β (β ∈ [0, 1]) of the following integral operator

is determined. Conversely, a sharp estimate is obtained for the radius of starlikeness of the class of functions

where g(z) and F(z) belong to the class S*(A, B).

A semigroup is said to be eventually regular if each of its elements has some power that is regular. Regular and group-bound semigroups are each eventually regular. Idempotent-surjective semigroups are semigroups such that all idempotent congruence classes contain idempotents; eventually regular semigroups are idempotent-surjective. Many results for regular semigroups also hold for eventually regular semigroups or even for idempotent-surjective semigroups and so in particular are also valid for group-bound semigroups. Lallement's lemma is generalized to eventually regular semigroups and the maximum idempotent-separating congruence on such a semigroup is found. Other congruences are considered and the results obtained are applied to yield results on biordered sets.

The energy functional for a pendent drop in a capillary tube is neither convex nor bounded from below. We obtain local minima of the energy by making the physically reasonable assumption that the gravitation or the prescribed volume of the drop is small.

For the Hermite-Fejér interpolation operator of higher order constructed on the roots , 1 ≤ k ≤ m, of the Jacobi-polynomial it is shown that is positive for all m ∈ N, if (α, β) ∈ [−¾, −¼]2. Further there is given an bound, which implies for arbitrary f ∈ C(I) and (α, β) ∈ [−¾, −¼]2.

We treat necessary and sufficient conditions for the classical solvability of the Dirichlet problem for the equation of prescribed Gauss curvature in uniformly convex domains in Euclidean n space. Our methods simultaneously embrace more general equations of Monge-Ampère type and we establish conditions which ensure that solutions have globally bounded second derivatives.

The classification of the finite simple groups has had far-reaching consequences for many branches of algebra. This paper is a discussion of several problems about primitive permutation groups which have been solved using the simple group classification.

Sufficient conditions are obtained for a homogeneous scalar integrodifferential system to have solutions all of which either converge to zero or oscillate or at least one of which can be nonoscillatory asymptotically.

We give a class C of continuous functions from [0, 1] onto itself which are chaotic in the sense of Li and Yorke, but with the property that almost all (in the sense of Lebesgue) points of [0, 1] are eventually fixed. For some continuous functions from [0, 1] onto itself which are not in C, We also show that their non-wandering sets are all equal to the interval [0, 1].