Identities for hyperelliptic P-functions of genus one, two and three in covariant form

We give a covariant treatment of the quadratic differential identities satisfied by the P-functions on the Jacobian of smooth hyperelliptic curves of genera 1, 2 and 3

An evaluation of potentially useful separator materials for nickel-cadmium (Ni-Cd] satellite batteries

An evaluation intended to determine the potential suitability and probable efficacy of a group of separator materials for use in nickel-cadmium (Ni-Cd) satellite batteries was carried out. These results were obtained using test procedures established in an earlier evaluation of other separator materials, some of which were used in experimental battery cells subjected to simulated use conditions. The properties that appear to be most important are: high electrolyte absorptivity, good electrolyte retention, low specific resistivity, rapid wettability and low resistance to air permeation. Wicking characteristics and wet-out time seem to be more important with respect to the initial filling of the battery with the electrolyte

On a generalization of Jacobi's elliptic functions and the Double Sine-Gordon kink chain

A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical application we show that periodic kink solutions (kink chains) of the double sine-Gordon model can be described in a canonical form in terms of generalized Jacobi functions.Comment: 18 pages, 9 figures, 3 table

Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions

Explicit function forms of hyperelliptic solutions of Korteweg-de Vries (KdV) and \break Kadomtsev-Petviashvili (KP) equations were constructed for a given curve $y^2 = f(x)$ whose genus is three. This study was based upon the fact that about one hundred years ago (Acta Math. (1903) {\bf{27}}, 135-156), H. F. Baker essentially derived KdV hierarchy and KP equation by using bilinear differential operator ${\bold{D}}$, identities of Pfaffians, symmetric functions, hyperelliptic $\sigma$-function and $\wp$-functions; $\wp_{\mu \nu} = -\partial_\mu \partial_\nu \log \sigma$ $= - ({\bold{D}}_\mu {\bold{D}}_\nu \sigma \sigma)/2\sigma^2$. The connection between his theory and the modern soliton theory was also discussed.Comment: AMS-Tex, 12 page

Exact solutions for a class of integrable Henon-Heiles-type systems

We study the exact solutions of a class of integrable Henon-Heiles-type systems (according to the analysis of Bountis et al. (1982)). These solutions are expressed in terms of two-dimensional Kleinian functions. Special periodic solutions are expressed in terms of the well-known Weierstrass function. We extend some of our results to a generalized Henon-Heiles-type system with n+1 degrees of freedom.Comment: RevTeX4-1, 13 pages, Submitted to J. Math. Phy

Rodrigues Formula for the Nonsymmetric Multivariable Laguerre Polynomial

Extending a method developed by Takamura and Takano, we present the Rodrigues formula for the nonsymmetric multivariable Laguerre polynomials which form the orthogonal basis for the $B_{N}$-type Calogero model with distinguishable particles. Our construction makes it possible for the first time to algebraically generate all the nonsymmetric multivariable Laguerre polynomials with different parities for each variable.Comment: 6 pages, LaTe

Eigenvalue correlations on Hyperelliptic Riemann surfaces

In this note we compute the functional derivative of the induced charge density, on a thin conductor, consisting of the union of g+1 disjoint intervals, $J:=\cup_{j=1}^{g+1}(a_j,b_j),$ with respect to an external potential. In the context of random matrix theory this object gives the eigenvalue fluctuations of Hermitian random matrix ensembles where the eigenvalue density is supported on J.Comment: latex 2e, seven pages, one figure. To appear in Journal of Physics

A qualitative investigation into patients' views on visual field testing for glaucoma monitoring

Objectives: To investigate the views and experiences of patients regarding their glaucoma follow-up, particularly towards the type and frequency of visual field (VF) testing. Design: A qualitative investigation using focus groups. The group discussion used broad open questions around the topics in a prompt guide relating to experiences of glaucoma follow-up, and in particular, VF monitoring. All the groups were taped, transcribed and coded using manual and computer-aided methods. Setting: Three National Health Service (NHS) hospitals in England; two focus groups took place at each hospital. Participants: 28 patients (mean (SD) age: 74 (9) years; 54% women) diagnosed with glaucoma for at least 2 years. Each focus group consisted of 3–6 patients. Primary and secondary outcomes: (1) Attitudes and experiences of patients with glaucoma regarding VF testing. (2) Patients’ opinions about successful follow-up in glaucoma. Results: These patients did not enjoy the VF test but they recognised the importance of regular monitoring for preserving their vision. These patients would agree to more frequent VF testing on their clinician's recommendation. A number of themes recurred throughout the focus groups representing perceived barriers to follow-up care. The testing environment, waiting times, efficiency of appointment booking and travel to the clinic were all perceived to influence the general clinical experience and the quality of assessment data. Patients were also concerned about aspects of patient–doctor communication, and often received little to no feedback about their results. Conclusions: Patients trust the clinician to make the best decisions for their glaucoma follow-up. However, patients highlighted a number of issues that could compromise the effectiveness of VF testing. Addressing patient-perceived barriers could be an important step for devising optimal strategies for follow-up care