Let f be a real function defined on [0, 1] × R3 and let η ∈ (0, 1). Very recently, C.P. Gupta and V. Lakshimikantham, making use of the Leray-Schauder continuation theorem and Wirtinger-type inequalities, established an existence result for the problem

(Theorem 1 and Remark 4 of [Nonlinear Anal. 16 (1991), 949–957]).

The aim of the present paper is simply to point out how, bu means of a completely different approach, it is possible to improve that result not only by requiring much general on f, but also by giving a precise pointwise estimate on x″′

We give explicit optimal curvature pinching constants for the Riemannian (p, q)- football orbifolds under the assumption that they are realised as surfaces of revolution in ℝ3. We show that sufficiently pinched sectional curvature assumptions imply that a (p, q)-football must be good.

Unitary representations of the braid group and corresponding link polynomials are constructed corresponding to each irreducible representation of a quantum double finite group algebra. Moreover the diagonal form of the braid generator is derived from which a general closed formula is obtained for link polynomials. As an example, link polynomials corresponding to certain induced representations of the symmetric group and its subgroups are determined explicitly.

The uniqueness of limit cycles is proved for quadratic systems with an invariant parabola and for cubic systems with four real line invariants. Also a new, simple proof is given of the uniqueness of limit cycles occurring in unfoldings of certain vector fields with codimension two singularities.

A ring R is called right FSG if every finitely generated right R-subgenerator is a generator. In this note we consider the question of when a ring extension of a given right FSG ring is right FSG and the converse. As a consequence we obtain some results about right FSG group rings.

In this paper we prove that the equivalence of anisotropic principal series of a free group Г related to different generator sets induces a Г-isomorphism between the related Cayley-graphs. As a consequence we obtain that a nontrivial change of generators for Г leads to inequivalent anisotropic principal series.

For an ideal I in a commutative ring R we consider the ideal In = ({in | i ∈I}). We show that if n! is a unit in R, then In = In. We give an example of a doubly generated ideal I with Is not finitely generated.

We consider the classifying set, denoted ℂ/˜ below, introduced by Mahler and we show that it can be endowed with non-discrete, Hausdorff topologies (even local distances) based on diophantine approximation properties of (complex) numbers. We then establish several results on the pointed topological space obtained, which could be dubbed Mahler's space (of first degree). We recover an analogue of Mahler's original classification by considering local distances to the special point (that is the class of all algebraic numbers). The main ingredients used here are diophantine properties in dimension zero over ℚ and non-standard analysis.

It is shown that the well-known theorem of Kadec for the HГ renorming of separable Banach spaces, when Г is a norming subspace in the dual, cannot be extended to the class of nonseparable Banach spaces.

In this paper we show that for a compact connected abelian group G the near-ring [G, G] of all homotopy classes of continuous selfmaps of G is an abstract affine near-ring, and investigate the ideal structure of these near-rings.

We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficiency test for invertibility for twice differentiable local diffeomorphisms defined on a ball.

We determine explicitly the space of invariant Hermitian and Kähler metrics on the flag manifold. In particular, we show that a Killing metric is not Kähler. The Chern forms are also computed in terms of the Maurer–Cartan form, and this calculation is used to prove that the flag manifold is projective algebraic. An explicit projective embedding of the flag manifold is also given.

We introduce in this paper the space of bounded holomorphic functions on the open unit ball of a Banach space endowed with the strict topology. Some good properties of this topology are obtained. As applications, we prove some results on approximation by polynomials and a description of the continuous homomorphisms.

Let R be a right Noetherian ring with right global dimension bounded by 2, which is integral over its centre, and let a be a regular non-unit element in R. Then R/a; R is right hereditary if and only if a; is not in the square of any maximal ideal of R. More generally, we compare for a right Noetherian ring R which is integral over its center, the global dimension of R with the global dimension of R/(a1R + a2R + … + arR) for a regular R-sequence {ai}, which will allow us to give a considerable extension of a result of Hillman.

Modules whose nonzero endomorphisms are epimorphisms and modules whose nonzero endomorphisms are monomorphisms are considered in this paper. We prove that these two classes of modules are dual to each other via Morita duality. We also prove that a left artinian ring R with Jacobson radical J has a Morita duality if either (1) J/J2 is a central bimodule; or (2) R is artinian right duo and R/J is commutative.

In this paper, we prove that there exist three finite sets Sj (j = 1, 2, 3) such that any two non-constant meromorphic functions f and g satisfying Ef(Sj) = Eg(Sj) for j = 1,2,3 must be identical. As a particular case of the above result, we obtain that there exist two finite sets Sj (j = 1, 2) such that any two non-constant entire functions f and g satisfying Ej(Sj) = Eg(Sj) for j = 1, 2 must be identical, which answers a question posed by Gross.

The purpose of this note is to give a general existence theorem for maximal elements for a new type of preference correspondences which are u-majorised. As an application, an existence theorem of equilibria for a qualitative game is obtained in which the preferences are u-majorised with an arbitrary (countable or uncountable) set of players and without compactness assumption on their domains in Hausdorff locally convex topological vector spaces.

Mendelsohn triple system of order ν which can be extended to a tetrahedral quadruple system of order ν + 1 we call a derived Mendelsohn triple system. We consider some properties of derived Mendelsohn triple systems and give some results on their existence.

Suppose the qth derivative of a function f is Hölder continuous of index α, where 0 < α ≤ 1, on the interval [-1,1]. Suppose further that pn is any polynomial of degree at most n such that |τn(x)| = |f(x) - pn(x)| ≤ c {max ((1 - x2)½/n, 1/n2) } q+a [-1,1]. If

then it is shown that

‖τn‖β ≤ cn−q−α+β, 0 < β ≤ 1.

It is proved that the upper radical determined by the class of prime essential rings is an N-radical.