On the Distribution of Atkin and Elkies Primes

Given an elliptic curve E over a finite field F_q of q elements, we say that an odd prime ell not dividing q is an Elkies prime for E if t_E^2 - 4q is a square modulo ell, where t_E = q+1 - #E(F_q) and #E(F_q) is the number of F_q-rational points on E; otherwise ell is called an Atkin prime. We show that there are asymptotically the same number of Atkin and Elkies primes ell < L on average over all curves E over F_q, provided that L >= (log q)^e for any fixed e > 0 and a sufficiently large q. We use this result to design and analyse a fast algorithm to generate random elliptic curves with #E(F_p) prime, where p varies uniformly over primes in a given interval [x,2x].Comment: 17 pages, minor edit

On the distribution of Atkin and Elkies primes for reductions of elliptic curves on average

For an elliptic curve E/Q without complex multiplication we study the distribution of Atkin and Elkies primes l, on average, over all good reductions of E modulo primes p. We show that, under the Generalised Riemann Hypothesis, for almost all primes p there are enough small Elkies primes l to ensure that the Schoof-Elkies-Atkin point-counting algorithm runs in (log p)^(4+o(1)) expected time.Comment: 20 pages, to appear in LMS J. Comput. Mat

Preliminary criteria for internal acoustic environments of orbiting space stations

Maximum noise levels for manned orbiting space station

A theoretical study of heterojunction and graded band gap type solar cells

The theory of heterojunction and graded bandgap solar cells was studied to help determine the material compositions and device dimensions needed for high efficiency solar cells. Because of the involved analysis of the fundamental equations describing solar cell operation, a general numerical device analysis program was used. A major part of the initial work was involved in modifying an existing silicon solar cell analysis program to account for the unique features of graded bandgap and heterojunction solar cells. The most successful III-V solar cells have so far been constructed in the GaAs and Gal-xAlxAs material systems; this project was concerned with such solar cells. The most efficient solar cell so far evaluated is an abrupt heterojunction cell with a pure AlAs layer at the surface with a GaAs substrate. The predicted efficiency for this cell is slightly larger than that of a graded bandgap Gal-xAlxAs solar cell

A theoretical study of heterojunction and graded band gap type solar cells

A computer program was designed for the analysis of variable composition solar cells and applied to several proposed solar cell structures using appropriate semiconductor materials. The program simulates solar cells made of a ternary alloy of two binary semiconductors with an arbitrary composition profile, and an abrupt or Gaussian doping profile of polarity n-on-p or p-on-n with arbitrary doping levels. Once the device structure is specified, the program numerically solves a complete set of differential equations and calculates electrostatic potential, quasi-Fermi levels, carrier concentrations and current densities, total current density and efficiency as functions of terminal voltage and position within the cell. These results are then recorded by computer in tabulated or plotted form for interpretation by the user

A theoretical study of heterojunction and graded band gap type solar cells

Heterojunction and graded band gap type solar cells are theoretically investigated. A computer program is developed to account for energy band gap variations and the resulting built-in electric fields which result from heterojunctions and graded energy band gaps. This program is used in studying solar cell operation under various optical irradiation conditions. Results are summarized

OBSERVATIONS OF PROPERTIES OF SINTERED WROUGHT TUNGSTEN SHEET AT VERY HIGH TEMPERATURES

Examination of mechanical properties of tungsten sheet at very high temperature

An equivalence relation of boundary/initial conditions, and the infinite limit properties

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex model is classified through the density of left/down arrows on the boundary. The free energy becomes identical to that obtained by Lieb and Sutherland with the periodic boundary condition, if the density of the arrows is equal to 1/2. The relation to the structure of the transfer matrix and a relation to stochastic processes are noted.Comment: 6 pages with a figure, no change but the omitted figure is adde