A Stieltjes-Volterra integral equation system

is firstly considered. Pointwise estimates and boundedness of its solutions are obtained under various conditions on the function K. To do this, the well-known Gronwall-Bellman integral inequality is generalized. For a particular choice of u, it is shown that the integral equation reduces to a difference equation. The problem of existence (and non-existence), uniqueness (and non-uniqueness) of the difference equation is discussed. Gronwall-Bellman inequality is further generalized to n linear terms and is subsequently applied to obtain sufficient conditions in order that a certain stability of the unperturbed Volterra system

implies the corresponding local stability of the (discontinuously) perturbed system

The natural completion functor on the category of cλ-embedded Cauchy spaces induces a completion functor on a category of sequential Cauchy spaces which preserves sequential regularity.

Explicit expressions for the Green's functions due to a point force in one of two half space fluids are presented for the case when inertial effects of the fluid are negligible (Stokes flow) and the interface between the two fluids is considered to be flat due to the action of surface tension. The analytic expressions are discussed in terms of singularity diagrams. For the case of a force parallel to the interface a first approximation to the interface displacement is made.

This article contains one method of fully embedding a symmetric closed category into a symmetric monoidal closed category. Such an embedding is very useful in the study of coherence problems. Also we give an example of a non-symmetric closed category for which, under the embedding discussed in this article, the resultant monoidal closed structure has associativity not an isomorphism.

Let X be a set and G a group which acts on X and is generated by two elements α and b. Motivated by a geometric problem of L. Fejes Tóth, we define a subset S ⊂ X to have [α, b]-symmetry if its images under α and b satisfy Sα ∩ Sb = S. The problem of finding all sets with [α, b]- symmetry when an arbitrary 2-generator group G acts on an arbitrary space X is shown to be equivalent to the same problem in the special case when the 2-generator free group acts on itself by right translation. This action is modelled in the hyperbolic plane in a way that helps to reveal the [α, b]- symmetric subsets of the free group.

An oscillation criterion is established for a class of functional differential equations including the generalized Emden-Fowler equation

as a special case. The deviating arguments involved may be retarded or advanced or otherwise. The result extends and improves known fundamental oscillation criteria for superlinear differential equations with retarded arguments.

Let K be a closed convex set in the plane containing no nonzero point of the integral lattice. We show that if the area A(K) of K is equally distributed amongst the four principal quadrants of the plane, then A(K) < 4.

In this paper we present further properties of the kth variation of a function, and obtain an integral representation for a function having bounded kth variation and an absolutely continuous (k-l)th derivative. The absolute continuity-requirement replaces a previous stronger condition that required the kth derivative of a function to be continuous except on a set of Lebesgue measure zero.

A classical theorem of Camille Jordan concerning finite linear groups is used to give two structural characterisations of profinite groups which have only finitely many pairwise inequivalent, continuous, irreducible, unitary representations of each degree. Our characterisations of such groups involve properties of their open normal subgroups.

This paper characterizes topological spaces which have an Abian structure - a uniform-like structure of the covering type.

A study of centered composition operators on l2 is made in this paper. Also the spectrum of surjective composition operators is computed. A necessary and sufficient condition is obtained for the closed unit disc to be the spectrum of a surjective composition operator.

In 1929 Rolf Nevanlinna posed a problem attributed to Bloch which has since been known as the Bloch-Nevanlinna conjecture. It can be stated as follows: Is the derivative of a function of bounded characteristic of bounded characteristic? A variety of different counterexamples have provided negative answers to this question. The purpose of the paper is to survey these counterexamples and then give a truly elementary proof of the following theorem.

Two nonlinear ordinary differential systems, one of which contains impulses are considered in this note, and assuming the existence of bounded solutions, some results on asymptotic equivalence type correspondence between them are obtained. At the end an open question is posed.

We show that there exists a conjugate Banach space E = B* with a basis, such that the distance from E to the collection of all conjugate Banach spaces can be made arbitrarily large, by suitable renorming of E. This solves a problem raised by B.V. Godun, Dokl. Akad. Nauk SSSR. 236 (1977), 18–20.

Suppose that G is a doubly transitive permutation group on a finite set Ω and that for α in ω the stabilizer Gα of αhas a set σ = {B1, …, Bt} of nontrivial blocks of imprimitivity in Ω – {α}. If Gα is 3-transitive on σ it is shown that either G is a collineation group of a desarguesian projective or affine plane or no nonidentity element of Gα fixes B pointwise.

Aspects of duality relating to compact totally disconnected universal algebras are considered. It is shown that if P is a ““basic“ set of injectives in a variety of compact totally disconnected algebras then the category P of P-copresentable objects is in duality with the class of all G-copresentable algebras on P, where G: P → Ens is the forgetful functor and an algebra is taken to mean a finite-product-preserving functor from P to Ens.