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

Bodies of Revolution Having Minimum Drag at High Supersonic Airspeeds

Approximate shapes of nonlifting bodies having minimum pressure foredrag at high supersonic airspeeds are calculated. With the aid of Newton's law of resistance, the investigation is carried out for various combinations of the conditions of given body length, base diameter, surface area, and volume. In general, it is found that when body length is fixed, the body has a blunt nose; whereas, when the length is not fixed, the body has a sharp nose. The additional effect of curvature of the flow over the surface is investigated to determine its influence on the shapes for minimum drag. The effect is to increase the bluntness of the shapes in the region of the nose and the curvature in the region downstream of the nose. These shape modifications have, according to calculation, only a slight tendency to reduce drag. Several bodies of revolution of fineness ratios 3 and 5, including the calculated shapes of minimum drag for given length and base diameter and for given base diameter and surface area, were tested at Mach numbers from 2.73 to 6.28. A comparison of theoretical and experimental foredrag coefficients indicates that the calculated minimum-drag bodies are reasonable approximations to the correct shape

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

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