Cyclic behaviour of Volterra composition operators

We determine the cyclic behaviour of Volterra composition operators, which are defined as $(V_\phif)(x) =\int_0^{\phi(x)}f(t) dt$, $f ? L^p[0, 1]$, 1\leq p <\infty$,
where $?$ is a measurable self-map of [0, 1]. The cyclic behaviour of $V_\phi$ is essentially determined by the behaviour of the inducing symbol $\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas.

Nearshore oscillating wave surge converters and the development of Oyster

Oscillating wave surge converters (OWSCs) are a class of wave power technology that exploits the enhanced horizontal fluid particle movement of waves in the nearshore coastal zone with water depths of 10–20 m. OWSCs predominantly oscillate horizontally in surge as opposed to the majority of wave devices, which oscillate vertically in heave and usually are deployed in deeper water. The characteristics of the nearshore wave resource are described along with the hydrodynamics of OWSCs. The variables in the OWSC design space are discussed together with a presentation of some of their effects on capture width, frequency bandwidth response and power take-off characteristics. There are notable differences between the different OWSCs under development worldwide, and these are highlighted. The final section of the paper describes Aquamarine Power’s 315kW Oyster 1 prototype, which was deployed at the European Marine Energy Centre in August 2009. Its place in the OWSC design space is described along with the practical experience gained. This has led to the design of Oyster 2, which was deployed in August 2011. It is concluded that nearshore OWSCs are serious contenders in the mix of wave power technologies. The nearshore wave climate has a narrower directional spread than the offshore, the largest waves are filtered out and the exploitable resource is typically only 10–20% less in 10m depth compared with 50m depth. Regarding the devices, a key conclusion is that OWSCs such as Oyster primarily respond in the working frequency range to the horizontal fluid acceleration; Oyster is not a drag device responding to horizontal fluid velocity. The hydrodynamics of Oyster is dominated by inertia with added inertia being a very significant contributor. It is unlikely that individual flap modules will exceed 1MW in installed capacity owing to wave resource, hydrodynamic and economic constraints. Generating stations will be made up of line arrays of flaps with communal secondary power conversion every 5–10 units.

Switching ferroelectric domain configurations using both electric and magnetic fields in Pb(Zr,Ti)O3–Pb(Fe,Ta)O3 single-crystal lamellae

Thin single-crystal lamellae cut from Pb(Zr,Ti)O3–Pb(Fe,Ta)O3 ceramic samples have been integrated into simple coplanar capacitor devices. The influence of applied electric and magnetic fields on ferroelectric domain configurations has been mapped, using piezoresponse force microscopy. The extent to which magnetic fields alter the ferroelectric domains was found to be strongly history dependent: after switching had been induced by applying electric fields, the susceptibility of the domains to change under a magnetic field (the effective magnetoelectric coupling parameter) was large. Such large, magnetic field-induced changes resulted in a remanent domain state very similar to the remanent state induced by an electric field. Subsequent magnetic field reversal induced more modest ferroelectric switching.

Norms of basic elementary operators on algebras of regular operators

We show that if E is an atomic Banach lattice with an ordercontinuous norm, A, B ∈ L^r(E) and M_A,_B is the operator on L^r(E) defined by M_A,_B(T) = AT B then ||M_A,_B||r = ||A||_r||B||_r but that there is no real α > 0 such that ||MA,B || ≥ α ||A||r||B ||r.

Two dimensional unital Riesz algebras, their representations and norms

We describe all two dimensional unital Riesz algebras and study representations of them in Riesz algebras of regular operators. Although our results are not complete, we do demonstrate that very varied behaviour can occur even though all these algebras can be given a Banach lattice algebra norm.

Is proof dead in the age of computers?

Some knowledge of what it means to construct a proof is an extremely important part of mathematics. All mathematics teachers and students should have some exposure to the ideas of proof and proving. This paper deals with the issue of creating proofs in mathematics problems.

The contexts of mathematics tasks and the context of the classroom: are we including all students?

Mathematics teachers are encouraged to use realistic contexts in order to make mathematics more meaningful and accessible for all students. However, the focus group research reported in this article shows that decisions on the suitability of contexts are complex and multidimensional. Similarly, the way the task contexts are presented, and the way the tasks are incorporated into classroom routines have potential to alienate some groups of students. We suggest that teachers and researchers should be sensitive to difficulties that students might experience as a result of both the task and classroom contexts, and take specific steps to avoid or overcome the difficulties.

Mathematics for the practical man explaining simply and quickly all the elements of algebra, geometry, trigonometry, logarithms, coördinate geometry, calculus,

Mode of access: Internet.

Welded pipe fabrication; a course of instruction explaining all common cuts and layouts made on pipe, with explanations of short methods, the mathematics needed, and the tools used in developing patterns for, calculating, and fabricating any welded piping system.

Mode of access: Internet.

A new system of practical astronomy : made plain and easy to those who have not studied mathematics : containing the elementary principles of the science, all the rules and tables necessary for making all the calculations for an almanac ... /

Includes index.

DML and RusDML – Virtual Library Initiatives for Covering All Mathematics Electronically

With the rapidly growing activities in electronic publishing ideas came up to install global repositories which deal with three mainstreams in this enterprise: storing the electronic material currently available, pursuing projects to solve the archiving problem for this material with the ambition to preserve the content in readable form for future generations, and to capture the printed literature in digital versions providing good access and search facilities for the readers. Long-term availability of published research articles in mathematics and easy access to them is a strong need for researchers working with mathematics. Hence in this domain some pioneering projects have been established addressing the above mentioned problems.