The Scattering of a Plane Electromagnetic Wave by a Finite Cone

This paper treats the solution of the -vector Helmholtz equation for the case of a plane electromagnetic wave at ’nose-on\u27 incidence, on a perfectly-conducting cone of finite size* The solution presented is exact and in the form of an infinite series of spherical harmonics. The expansion coefficients of the series are determined by a set of an infinite number of equations involving an infinite number of unknowns. A discussion and numerical investigation of the field singularities at the tip and edge of the cone are included* as well as graphs of the associated Legendre functions of non-integral degree, P1(cos θ), and their first derivative

Darboux transformation with dihedral reduction group

We construct the Darboux transformation with Dihedral reduction group for the 2-dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix, we obtain local conservation laws of the system

New Gynandromorph Records for Chirocephalus diaphanus (Branchiopoda, Anostraca, Chirocephalidae)

We report and describe new Chirocephalus diaphanus Pr\ue9vost, 1803 gynandromorphs from Tunisia and review the literature of anostracan gynandromorphy and other, possibly associated, somatic aberrations, with comments on their evolutionary significance. Our material has three specimens that are specifi cally deformed on the left side of the head

Care-less spaces and identity construction: transition to secondary school for disabled children

There is a growing body of literature which marks out a feminist ethics of care and it is within this framework we understand transitions from primary to secondary school education can be challenging and care-less, especially for disabled children. By exploring the narratives of parents and professionals we investigate transitions and self-identity, as a meaningful transition depends on the care-full spaces pupils inhabit. These education narratives are all in the context of privileging academic attainment and a culture of testing and examinations. Parents and professionals, as well as children are also surveyed. Notably, until there are care-full education processes, marginalisation will remain, impacting on children’s transition to secondary school and healthy identity construction. Moreover, if educational challenges not addressed, their life chances are increasingly limited. Interdependent caring work enables engagement in a meaningful education and positive identity formation. In school and at home, care-full spaces are key in this process

Nonlinear self-adjointness and conservation laws

The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced earlier by the author. It is shown that the equations possessing the nonlinear self-adjointness can be written equivalently in a strictly self-adjoint form by using appropriate multipliers. All linear equations possess the property of nonlinear self-adjointness, and hence can be rewritten in a nonlinear strictly self-adjoint. For example, the heat equation $u_t - \Delta u = 0$ becomes strictly self-adjoint after multiplying by $u^{-1}.$ Conservation laws associated with symmetries can be constructed for all differential equations and systems having the property of nonlinear self-adjointness

Implementation of the Backlund transformations for the Ablowitz-Ladik hierarchy

The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by several authors. The main aim of this work is to solve these equations. This can be done in the framework of the so-called functional representation of the ALH, when an infinite number of the evolutionary equations are replaced, using the Miwa's shifts, with a few equations linking tau-functions with different arguments. It is shown that starting from these equations it is possible to obtain explicit solutions of the BT equations. In other words, the main result of this work is a presentation of the discrete BTs as a superposition of an infinite number of evolutionary flows of the hierarchy. These results are used to derive the superposition formulae for the BTs as well as pure soliton solutions.Comment: 20 page

Coherent Vector Meson Photo-Production from Deuterium at Intermediate Energies

We analyze the cross section for vector meson photo-production off a deuteron for the intermediate range of photon energies starting at a few GeVs above the threshold and higher. We reproduce the steps in the derivation of the conventional non-relativistic Glauber expression based on an effective diagrammatic method while making corrections for Fermi motion and intermediate energy kinematic effects. We show that, for intermediate energy vector meson production, the usual Glauber factorization breaks down and we derive corrections to the usual Glauber method to linear order in longitudinal nucleon momentum. The purpose of our analysis is to establish methods for probing interesting physics in the production mechanism for phi-mesons and heavier vector mesons. We demonstrate how neglecting the breakdown of Glauber factorization can lead to errors in measurements of basic cross sections extracted from nuclear data.Comment: 41 pages, 13 figures, figure 9 is compressed from previous version, typos fixe

On the Hamiltonian structure of Ermakov systems

A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by several different frequency functions. This class of systems comprises all known cases of Hamiltonian Ermakov systems and can always be reduced to quadratures. The Hamiltonian structure is explored to find exact solutions for the Calogero system and for a noncentral potential with dynamic symmetry. Some generalizations of these systems possessing exact solutions are also identified and solved

Invariant description of solutions of hydrodynamic type systems in hodograph space: hydrodynamic surfaces

Hydrodynamic surfaces are solutions of hydrodynamic type systems viewed as non-parametrized submanifolds of the hodograph space. We propose an invariant differential-geometric characterization of hydrodynamic surfaces by expressing the curvature form of the characteristic web in terms of the reciprocal invariants.Comment: 12 page