Amply boundedness of collections of analytic mappings is proved to be equivalent to equicontinuity of the corresponding collections of adjoints, for certain classes of locally convex spaces which have good analytic properties.

In this paper we prove a coincidence theorem in not necessarily locally convex topological vector spaces, which contains, as a special case, a coincidence theorem proved by Felix Browder. As an application, a result about the existence of maximal elements is obtained.

In this paper a single server preemptive priority queueing system, consisting of two types of units, with unlimited Poisson inputs and exponential service time distributions, is studied. The higher priority units are served in batches according to a general bulk service rule and they have preemptive priority over lower priority units. Steady state queue length distributions, stability condition and the mean queue lengths are obtained.

It is shown that in the Fitting class of all finite p-by-q groups, where p and q are different primes, there is among the sub-direct product closed sub-Fitting classes a unique maximal one: it consists of the groups whose minimal normal subgroups are central.

We study real hypersurfaces M of a complex projective space and show that a condition on the derivative of the Ricci Tensor of M implies M is locally homogeneous with two or three principal curvatures.

Let L = L(X) be the free Lie ring of countable rank and let p be prime. Then L(Vp) = L/[(L')p, L] is the relatively free ring for the variety of Lie rings Vp = [Np−1A, E] and Vp is defined by the identity

The purpose of this note is to establish that there exist elements of order p in the additive group of L(Vp). Previously, the existence of p-torsion was proved by Kuz'min for p = 2 only. Similar results were obtained for varieties of groups by Gupta when p = 2 and by Stöhr when p = 3.

It is proved that the simple group PSL (2,q) satisfies a law [x,3y] = [x, sy], s > 3, if and only if q = 4, 5, 8.

For 0 < P,q < ∞, α> −1, Ap,q,α denotes the space of all holomorphic functions in the unit disc satisfying

where

In this paper, we find a sufficient condition for the multipliers from AP,q,α into ls, 1 ≤ s ≤ ∞, 1 ≤ q ≤ 2, which interpolates the results of Patrick Ahern and Miroljub Jevtic. As a corollary, we can calculate

for q′ ≤ s ≤ ∞, 1/q + 1/q′ = 1. Also, we can find a sharp coefficient condition for HP functions.

In this paper quasi-codivisible covers are defined and investigated relative to a torsion theory (T, F) on Mod R. It is shown that if (T, F) is cohereditary, then a right R-module M has a quasi-codivisible cover whenever it has a codivisible cover. Moreover, it is shown that if (T, F) is cohereditary, then the universal existence of quasi-codivisible covers implies that the ring R/T (R) must be right perfect. The converse holds when (T, F) is pseudo-hereditary.

Every hermitian hypergroup structure on the set of nonnegative integers can be generated by a family of real-valued continuous functions defined on a compact interval. we characterise such structures in terms of properties of the generating functions.

It is shown that any sequential subgroup of a free topological group is either sequential of order ω1 or discrete. Hence any metrizable subgroup of a free topological group is discrete.

An Atsuji space is a metric space X such that each continuous function form X to an arbitrary metric space Y is uniformly continuous. We here present (i) characterizations of metric spaces with Atsuji completions; (ii) Cantor-type theorems for Atsuji spaces; (iii) a fixed point theorem for self-maps of an Atsuji space.

It is shown that a semidirect product of an inverse semigroup and a group, in that order, contains an inverse subsemigroup that is a retract and that, together with the retraction mapping, forms free inverse morphic image of the semidirect product. The congruence determined by the retraction mapping is shown to be determined by the semigroup of idempotents of the semidirect product.

We consider the Cauchy problem x (t) = f (t,x (t)), x (0) = x0 in a nonreflexive Banach space X and for f: T × X → X a weakly continuous vector field. Using a compactness hypothesis involving a weak measure of noncompactness we prove an existence result that generalizes earlier theorems by Chow-Shur, Kato and Cramer-Lakshmikantham-Mitchell.

Let Δ denote the Banach algebra of all conservative triangular matrics, M the maximal group of invertible elements of Δ, B the boundary of M and . In this note little Nörlund means are located with respect to the disjoint decomposition M u B u N of Δ in terms of the zeros of the generating power series. Further, corridor matrices of finite type, that is, conservative methods with finitely many convergent diagonals, are located with respect to M u B u N.

Our main concern is the existence of maximal compact subgroups in a locally compact topological group. If G is a locally compact group such that P(G/G o), the set of periodic points of G/Go, is a compact subgroup of G/Go, than G has maximal compact subgroups K such that G/N is a Lie group where N = ∩K, the intersection of the collection K of all maximal compact subgroups of G. Also every compact subgroup of G is contained in a maximal compact subgroup. We given an example of a discrete group which has maximal finite subgroup and has finite subgroups not contained in maximal finite subgroups. We note that the above result on P(G/Go) is an extension of the well-known corresponding result for almost connected groups.

We consider the Cauchy problem x (t) = f (t,x (t)), x (O) = xO defined in a nonreflexive Banach space and with the vector field f: T × X → X being weakly uniformly continuous. Using a compactness hypothesis that involves the weak measure of noncompactness, we prove that the solution set of the above Cauchy problem is nonempty, connected and compact in .

In this paper a new family of quotients of the triangle group < x, y, z | x2 = y3 = z7 = xyz = 1 > is obtained. It is shown that for every positive integer m divisible by 3 there is a Hurwitz group of order 504m6 having a centre of size 3, and as a consequence there is a Riemann surface of genus 6m6 + 1 with the maximum possible number of automorphisms.

Two new types of containment of operators on Hilbert space, namely partial containment and semi-containment are introduced. We show in Proposition 11 that A is semi-contained in B if and only if the map P(B) → P(A) for polynomials P extends to be an ultra-weakly continuous completely positive map from all bounded operators on the underlying Hilbert space of B. We show in Theorem 15 that if an isometry is semi-contained in a contraction T, then T has a non-zero invariant subspace on which T is isometric. The semi-equivalence class of the simple unilateral shift is characterized in Theorem 18, and we show that a unilateral positive-weighted shift semi-contains the unilateral shift if and only the weights are eventually 1.

We sharpen a result of Byers on the existence of periodic points for some continuous expanding maps of the interval and generalize it to some classes of continuous maps of the interval which are not necessarily expanding. We then use these results to construct one-parameter families of continuous maps of the interval which have a bifurcation form fixed points directly to period 3 points together with a series of reverse bifurcations from period 3 points back to fixed points. Consequently, our results also provide examples of one-parameter families of continuous maps of the interval whose topological entropy jumps form zero to some positive number and then changes back to zero as the parameter varies.