# Publications Portal

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Topic Area: Math

Displaying records 31 to 40 of 234 records.

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31.

**Class Numbers via 3-Isogenies and Elliptic Surfaces**
**Topic:** Math

**Published:** 11/6/2012

**Authors:** Cam McLeman, Dustin Moody

**Abstract:** We show that a character sum attached to a family of 3-isogenies defined on the fibers of
a certain elliptic surface over Fp relates to the class number of the quadratic imaginary
number field Q(\sqrt{p}). In this sense, this provides a higher-d

...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911885
32.

**Reduction Formulae for Products of Theta Functions**
**Series:** Journal of Research (NIST JRES)

**Report Number:** 117.017

**Topic:** Math

**Published:** 11/6/2012

**Author:** Peter L. Walker

**Abstract:** 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 t

...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911334
33.

**Definite integrals using orthogonality and integral transforms**
**Topic:** Math

**Published:** 10/19/2012

**Authors:** Howard S Cohl, Hans Volkmer

**Abstract:** 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.

http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911945
34.

**Counting on Today's Students**
**Topic:** Math

**Published:** 9/3/2012

**Author:** Isabel M Beichl

http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911915
35.

**The TriTon Transformation**
**Topic:** Math

**Published:** 8/27/2012

**Author:** Daniel C Smith-Tone

**Abstract:** 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 b

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=911681
36.

**Transient Convection-Diffusion Modelling of Peak Temperature in Orthogonal Cutting**
**Topic:** Math

**Published:** 8/19/2012

**Authors:** Timothy J Burns, Steven P Mates, Richard L. Rhorer, Eric Paul Whitenton, Debasis Basak

**Abstract:** 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 or

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=910514
37.

**Variable Projection for Nonlinear Least Squares Problems**
**Topic:** Math

**Published:** 8/2/2012

**Authors:** Dianne M O'Leary, Bert W Rust

**Abstract:** 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 imp

...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=906612
38.

**Arithmetic Progressions on Huff Curves**
**Topic:** Math

**Published:** 7/23/2012

**Author:** Dustin Moody

**Abstract:** 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.

...
http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908329
39.

**Evolutionary Construction of de Bruijn Sequences**
**Topic:** Math

**Published:** 7/20/2012

**Author:** Meltem Sonmez Turan

**Abstract:** 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

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=909087
40.

**Reconstructing the past from imprecise knowledge of the present: Some examples of non uniqueness
in solving parabolic equations backward in time.**
**Topic:** Math

**Published:** 5/24/2012

**Author:** Alfred S Carasso

**Abstract:** Identifying sources of ground water pollution, and deblurring astronomical galaxy images, are two important applications generating growing interest in the numerical computation of parabolic equations backward in time. However, while backward uniquen

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http://www.nist.gov/manuscript-publication-search.cfm?pub_id=908242