U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Mathematics & Statistics

Search Publications

Search Title, Abstract, Conference, Citation, Keyword or Author
  • Published Date
Displaying 451 - 475 of 872

Class Numbers via 3-Isogenies and Elliptic Surfaces

November 6, 2012
Author(s)
Cam McLeman, Dustin Moody
We show that a character sum attached to a family of 3-isogenies defi ned on the fibers of a certain elliptic surface over Fp relates to the class number of the quadratic imaginary number field Q(\sqrtp}). In this sense, this provides a higher-dimensional

Reduction Formulae for Products of Theta Functions

November 6, 2012
Author(s)
Peter L. Walker
In four cases it is already known that the product of two distinct Jacobian theta functions having the same variable z and the same nome q is a multiple of a single Jacobian theta function, with the multiple independent of z. The main purpose of the

Definite integrals using orthogonality and integral transforms

October 19, 2012
Author(s)
Howard S. Cohl, Hans Volkmer
We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

The TriTon Transformation

August 27, 2012
Author(s)
Daniel C. Smith-Tone
Many new systems have been proposed which hide an easily invertible multivariate quadratic map in a larger structure by adding more variables and introducing some mixing of a random component to the structured system. While many systems which have been

Transient Convection-Diffusion Modelling of Peak Temperature in Orthogonal Cutting

August 19, 2012
Author(s)
Timothy J. Burns, Steven P. Mates, Richard L. Rhorer, Eric P. Whitenton, Debasis Basak
Numerical finite-difference simulations of a two-dimensional transient fast convection-slow diffusion model of the temperature field in orthogonal cutting, due to Tlusty, have been shown to provide better predictions of the peak temperature during

Variable Projection for Nonlinear Least Squares Problems

August 2, 2012
Author(s)
Dianne M. O'Leary, Bert W. Rust
The variable projection algorithm of Golub and Pereyra (1973) has proven to be quite valuable in the solution of nonlinear least squares problems in which a substantial number of the parameters are linear. Its advantages are efficiency and, more

Arithmetic Progressions on Huff Curves

July 23, 2012
Author(s)
Dustin Moody
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous

Evolutionary Construction of de Bruijn Sequences

July 20, 2012
Author(s)
Meltem Sonmez Turan
A binary de Bruijn sequence of order n is a cyclic sequence of period 2^n, in which each n-bit pattern appears exactly once. These sequences are commonly used in applications such as stream cipher design, pseudo-random number generation, 3-D pattern