Singular Kummer Surfaces and Hilbert Modular Forms

Paper by H. L. Resnikof

Generating Some Rings of Modular Forms in Several Complex Variables By One Element

Paper by H. L. Resnikof

Non Trivial Cusp Forms in Several Complex Variables

Paper by H. L. Resnikof

On the Analysis of Library Growth

Paper by H. L. Resnikoff and J. L. Dolb

Time scales in nuclear giant resonances

We propose a general approach to characterise fluctuations of measured cross sections of nuclear giant resonances. Simulated cross sections are obtained from a particular, yet representative self-energy which contains all information about fragmentations. Using a wavelet analysis, we demonstrate the extraction of time scales of cascading decays into configurations of different complexity of the resonance. We argue that the spreading widths of collective excitations in nuclei are determined by the number of fragmentations as seen in the power spectrum. An analytic treatment of the wavelet analysis using a Fourier expansion of the cross section confirms this principle. A simple rule for the relative life times of states associated with hierarchies of different complexity is given.Comment: 5 pages, 4 figure

Wavelet Methods in the Relativistic Three-Body Problem

In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean, interaction independent treatment of the scattering singularities which does not require any subtractions.Comment: 14 pages, 3 figures, corrected referenc

Rapid assessment of visual impairment (RAVI) in marine fishing communities in South India - study protocol and main findings

<p>Abstract</p> <p>Background</p> <p>Reliable data are a pre-requisite for planning eye care services. Though conventional cross sectional studies provide reliable information, they are resource intensive. A novel rapid assessment method was used to investigate the prevalence and causes of visual impairment and presbyopia in subjects aged 40 years and older. This paper describes the detailed methodology and study procedures of Rapid Assessment of Visual Impairment (RAVI) project.</p> <p>Methods</p> <p>A population-based cross-sectional study was conducted using cluster random sampling in the coastal region of Prakasam district of Andhra Pradesh in India, predominantly inhabited by fishing communities. Unaided, aided and pinhole visual acuity (VA) was assessed using a Snellen chart at a distance of 6 meters. The VA was re-assessed using a pinhole, if VA was < 6/12 in either eye. Near vision was assessed using N notation chart binocularly. Visual impairment was defined as presenting VA < 6/18 in the better eye. Presbyopia is defined as binocular near vision worse than N8 in subjects with binocular distance VA of 6/18 or better.</p> <p>Results</p> <p>The data collection was completed in <12 weeks using two teams each consisting of one paramedical ophthalmic personnel and two community eye health workers. The prevalence of visual impairment was 30% (95% CI, 27.6-32.2). This included 111 (7.1%; 95% CI, 5.8-8.4) individuals with blindness. Cataract was the leading cause of visual impairment followed by uncorrected refractive errors. The prevalence of blindness according to WHO definition (presenting VA < 3/60 in the better eye) was 2.7% (95% CI, 1.9-3.5).</p> <p>Conclusion</p> <p>There is a high prevalence of visual impairment in marine fishing communities in Prakasam district in India. The data from this rapid assessment survey can now be used as a baseline to start eye care services in this region. The rapid assessment methodology (RAVI) reported in this paper is robust, quick and has the potential to be replicated in other areas.</p

Nonlinear Differential Equations Satisfied by Certain Classical Modular Forms

A unified treatment is given of low-weight modular forms on \Gamma_0(N), N=2,3,4, that have Eisenstein series representations. For each N, certain weight-1 forms are shown to satisfy a coupled system of nonlinear differential equations, which yields a single nonlinear third-order equation, called a generalized Chazy equation. As byproducts, a table of divisor function and theta identities is generated by means of q-expansions, and a transformation law under \Gamma_0(4) for the second complete elliptic integral is derived. More generally, it is shown how Picard-Fuchs equations of triangle subgroups of PSL(2,R) which are hypergeometric equations, yield systems of nonlinear equations for weight-1 forms, and generalized Chazy equations. Each triangle group commensurable with \Gamma(1) is treated.Comment: 40 pages, final version, accepted by Manuscripta Mathematic

A Rapid Assessment of Avoidable Blindness in Southern Zambia

INTRODUCTION: A rapid assessment of avoidable blindness (RAAB) was conducted in Southern Zambia to establish the prevalence and causes of blindness in order to plan effective services and advocate for support for eye care to achieve the goals of VISION 2020: the right to sight. METHODS: Cluster randomisation was used to select villages in the survey area. These were further subdivided into segments. One segment was selected randomly and a survey team moved from house to house examining everyone over the age of 50 years. Each individual received a visual acuity assessment and simple ocular examination. Data was recorded on a standard proforma and entered into an established software programme for analysis. RESULTS: 2.29% of people over the age of 50 were found to be blind (VA <3/60 in the better eye with available correction). The major cause of blindness was cataract (47.2%) with posterior segment disease being the next main cause (18.8%). 113 eyes had received cataract surgery with 30.1% having a poor outcome (VA <6/60) following surgery. Cataract surgical coverage showed that men (72%) received more surgery than women (65%). DISCUSSION: The results from the RAAB survey in Zambia were very similar to the results from a similar survey in Malawi, where the main cause of blindness was cataract but posterior segment disease was also a significant contributor. Blindness in this part of Zambia is mainly avoidable and there is a need for comprehensive eye care services that can address both cataract and posterior segment disease in the population if the aim of VISION 2020 is to be achieved. Services should focus on quality and gender equity of cataract surgery