We characterise the complex measures μ on the open unit disk D such that for all f in the Hardy space H2. The characterisation involves Carleson measures, the duality between H1 and BMOA, and Hankel operators.

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.

Chase has given several characterizations of a right coherent ring, among which are: every direct product of copies of the ring is left-flat; and every finitely generated submodule of a free right module is finitely related. We extend his results to obtain conditions for the ring of quotients of a ring with respect to a torsion theory to be coherent.

In the study of the theory of rings, matrix rings, group rings, algebras, and so on, play a very important role. However, the analogous systems may not exist in the theory of near-rings. Recently Ligh obtained a necessary and sufficient condition for the set of n × n matrices with entries from a near-ring to be a near-ring. This opens the door for the study of other structures such as group near-rings, algebras, and so on. In this paper we initiate a study of the basic properties of pseudo-distributive near-rings, which is exactly the class of near-rings needed to carry out the construction of matrix near-rings, group near-rings, polynomials with near-ring coefficients, and so on.

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.

We give a simple proof of the identity The proof uses only a few well-known properties of the cubic theta functions a(q), b(q) and c(q). We show this identity implies the interesting definite integral .

In this article, the existence of travelling wave solutions for premixed laminar flames in a model of slow, “constant density” combustion is studied. The model is governed by a simple system of an exothermic chemical reaction in a gas, via the reaction rate function, which is very natural, as we do not impose the assumption of its continuity. The existence of travelling waves is demonstrated and they are shown to be specific heteroclinic orbits of a three dimensional system of ordinary differential equations, connecting the unburned state points to a burned state point. The existence of these solutions is based on some general topological arguments in ordinary differential equations.

We prove a DDVV inequality for submanifolds of warped products of the form $I\times _{a}\mathbb{M}^{n}(c)$ , where $I$ is an interval and $\mathbb{M}^{n}(c)$ is a real space form of curvature $c$ . As an application, we give a rigidity result for submanifolds of $\mathbb{R}\times _{e^{\unicode[STIX]{x1D706}t}}\mathbb{H}^{n}(c)$ .

It is well-known that warped products play some important roles in differential geometry as well as in physics. In this article we extend the notion of warped product to the notion of convolution of Riemannian manifolds. We study the basic properties of convolutions of Riemannian manifolds. We also apply the notion of convolution to establish and characterise the Euclidean version of Segre embedding.

Recently Calegari and Emerton made a conjecture about the 3-class groups of certain pure cubic fields and their normal closures. This paper proves their conjecture and provides additional insight into the structure of the 3-class groups of pure cubic fields and their normal closures.

We show that, in an inner product space $H$, the inequality

$$\begin{eqnarray}{\textstyle \frac{1}{2}}[\Vert x\Vert \,\Vert y\Vert +|\langle x,y\rangle |]\geq |\langle Px,y\rangle |\end{eqnarray}$$

$x,y$

$P:H\rightarrow H$

In the present paper a theorem on the spectral radius of the sum of linear operators is established. The application of this theorem to a functional differential equation of neutral type is also given.

A continuous form of Hölder's inequality is established and used to extend the inequality of Chuan on the arithmetic-geometric mean inequality.

Let G be a group. A subset N of G is a set of pairwise noncommuting elements if xy⁄=yx for any two distinct elements x and y in N. If ∣N∣≥∣M∣ for any other set of pairwise noncommuting elements M in G, then N is said to be a maximal subset of pairwise noncommuting elements. In this paper we determine the cardinality of a maximal subset of pairwise noncommuting elements in a three-dimensional general linear group. Moreover, we show how to modify a given maximal subset of pairwise noncommuting elements into another maximal subset of pairwise noncommuting elements that contains a given ‘generating element’ from each maximal torus.

In this paper, we characterise the n-dimensional (n ≥ 3) complete spacelike hypersurfaces Mn in a de Sitter space with constant scalar curvature and with two distinct principal curvatures. We show that if the multiplicities of such principal curvatures are greater than 1, then Mn is isometric to Hk (sinh r) × Sn−k (cosh r), 1 < k < n − 1. In particular, when Mn is the complete spacelike hypersurfaces in with the scalar curvature and the mean curvature being linearly related, we also obtain a characteristic Theorem of such hypersurfaces.

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.

The purpose of this note is to establish results of a technical nature concerning a stochastic process that appears to be useful in the study of certain problems in statistical inference. These problems concern a test for symmetry, a method for obtaining an adaptive estimator of the centre of symmetry, and the detection of outliers with respect to the normal distribution. Details of the applications will be presented elsewhere.

Let ℒ be an atomic Boolean subspace lattice on a Banach space X. In this paper, we prove that if ℳ is an ideal of Alg ℒ then every derivation δ from Alg ℒ into ℳ is necessarily quasi-spatial, that is, there exists a densely defined closed linear operator T: 𝒟(T) ⊆ X → X with its domain 𝒟(T) invariant under every element of Alg ℒ, such that δ(A) x = (TA – AT) x for every A ∈ Alg ℒ and every x ∈ 𝒟(T). Also, if ℳ ⊆ ℬ(X) is an Alg ℒ-module then it is shown that every local derivation from Alg ℒ into ℳ is necessary a derivation. In particular, every local derivation from Alg ℒ into ℬ(X) is a derivation and every local derivation from Alg ℒ into itself is a quasi-spatial derivation.

Modifying the concept underlying Daneš' drop theorem, Rolewicz introduced the notion of the drop property of a norm which was later generalised to the weak drop property of a norm. Kutzarova extended the discussion to consider the drop property for closed bounded convex sets. Here we characterise the drop and weak drop properties for such sets by upper semi-continuous and compact valued subdifferential mappings.

A continuous analogue is derived for Radó's comparison formulæ. The analogue is then employed to provide a result which continues Radó's result and interpolates an inequality of Pittenger.