We characterise bounded and compact weighted composition operators on the Bloch space and the little Bloch space. The results generalise the known corresponding results on composition operators and pointwise multipliers on the Bloch space and the little Bloch space.

We study the asymptotic behaviour of solutions to the evolutionary Ginzburg- Landau equations in three dimensions. We show that the motion of the Ginzburg-Landau vortex curves is the flow by curvature.

We consider two aspects of the action of the extended metaplectic representation of the group G of affine, measure and orientation preserving maps of the time-frequency plane on L2 functions on the line. On the one hand, we list, up to equivalence, all possible reproducing formulas that arise by restricting the representation to connected Lie subgroups of G. On the other hand, we describe, in terms of Weyl calculus, the commutative von Neumann algebras generated by restriction to one-parameter subgroups.

In this paper we deal with the homogeneous Cauchy-Dirichlet problem for a class of parabolic equations with either Carathéodory or discontinuous nonlinear terms. We then present an application and explicitly point out an existence result for a differential inclusion, which can be applied to the classical Stefan problem.

Classes of convex lattice polygons which have minimal lp-perimeter with respect to the number of their vertices are said to be optimal in the sense of the lp-metric.

It is proved that if p and q are arbitrary integers or ∞, the asymptotic expression for the lq-perimeter of these optimal convex lattice polygons Qp(n) as a function of the number of their vertices n is . for arbitrary ɛ > 0, where . and Ap is equal to the area of the planar shape |x|p + |y|p ≤ 1.

A unit speed curve γ = γ(s) in a Riemannian manifold N is called a circle if there exists a unit vector field Y(s) along γ and a positive constant k such that ∇sγ′(s) = kY(s), ∇sY(s) = −kγ′(s). A maximal totally geodesic sphere with maximal sectional curvature in a compact irreducible symmetric space M is called a Helgason sphere. A circle which lies in a Helgason sphere of a compact symmetric space is called a Helgason circle. In this article we establish some fundamental relationships between Helgason circles, Helgason spheres of irreducible symmetric spaces of compact type and the theory of immersions of finite type.

Alternative division quasialgebras which are not associative, are characterized. Their grading groups are shown to be always Abelian and they are built from some specific graded associative algebras by means of a graded Cayley-Dickson process.

We define the concept of a special positive matrix. We use the dyadic trace to prove the result that dim for odd k ≤ 13 and that dim ≤ 4.

We give simple and almost identical proofs of several classical results in Functional Analysis by means of a single lemma concerning subseries convergence.

Arbitrary order forced difference-delay systems are considered, from which generated infinite sums of Binomial variation may be represented in closed form. It will be proved that the infinite sums may be expressed in a closed form which depends on dominant zeros of the polynomial characteristic functions. A connection between the infinite sum and generalised hypergeometric series will also be demonstrated.

Just over 60 years ago, G. Grünwald and J. Marcinkiewicz discovered a divergence phenomenon pertaining to Lagrange interpolation polynomials based on the Chebyshev nodes of the first kind. The main result of the present paper is an extension of their now classical theorem. In particular, we shall show that this divergence phenomenon occurs for odd higher order Hermite–Fejér interpolation polynomials of which Lagrange interpolation polynomials form one special case.

New and improved Poincaré-type integral inequalities involving many functions of many variables are established. These in turn can serve as generators and can generate numerous Poincaré-type integral inequalities by choosing different parameters.

Let Γ be a G-symmetric graph admitting a nontrivial G-invariant partition ℬ of block size υ. For blocks B, C of ℬ adjacent in the quotient graph Γℬ, let k be the number of vertices in B adjacent to at least one vertex in C. In this paper we classify all possibilities for (Γ Γℬ, G) in the case where k = υ − 1 ≥ 2 and ℬ(α) = ℬ(β) for adjacent vertices α β of Γ where for a vertex of Γ, say γ ∈ B, ℬ(γ) denotes the set of blocks C such that γ is the only vertex in B not adjacent to any vertex in C.

In this note we present a simple, short proof of the sum formula for subdifferentials of convex functions.

Matrices provide essential tools in many branches of mathematics, and matrix semigroups have applications in various areas. In this paper we give a complete description of all infinite matrix semigroups satisfying a certain combinatorial property defined in terms of power graphs.

In [3] the following theorem was stated.