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Topic Area: Math
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Displaying records 191 to 200 of 230 records.
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191. Estimating Critical Hopf Bifurcation Parameters for a Second Order DelayDifferential Equation with Application to Machine Tool Chatter
Topic: Math
Published: 5/1/2002
Author: David E. Gilsinn
Abstract: Nonlinear time delay differential equations are well known to have arisen in models in physiology, biology and population dynamics. They have also arisen in models of metal cutting processes. Machine tool chatter, from a process called regenerative c ...

192. The Role of Rendering in the Competence Project in Measurement Science for Optical Reflection and Scattering
Series: Journal of Research (NIST JRES)
Topic: Math
Published: 5/1/2002
Authors: H B Westlund, G W Meyer, Fern Y Hunt
Abstract: Rendering is the process of producing a synthetic image using a computer. The best known application is animation and simulation of scenes for the entertainment industry but recognition of its value as a tool for product design in other areas is incr ...

193. Lattice Symmetry and Identification--The Fundamental Role of Reduced Cells in Materials Characterization
Series: Journal of Research (NIST JRES)
Topic: Math
Published: 2/1/2002
Author: Alan D. Mighell
Abstract: In theory, physical crystals can be represented by idealized mathematical lattices. Under appropriate conditions, these representations can be used for a variety of purposes such as identifying, classifying, and understanding the physical properties ...

194. The Relegation Algorithm
Topic: Math
Published: 3/3/2001
Authors: A Deprit, E Deprit, Jesúus Palacián
Abstract: Given a perturbed Hamiltonian system, normalization yields a Lie transformation which converts the main part of the Hamiltonian into an integral of the transformed system. An extension of the normalization method--the relegation algorithm--does the s ...

195. Constructing Sibson Elements for a Rectangular Mesh
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 6718
Topic: Math
Published: 2/1/2001
Author: David E. Gilsinn
Abstract: This paper documents the construction of a finite element, called the Sibson element. The shape function of this element is formed on rectangular grids by C^u1^ splines defined on a triangulation of each subrectangle by dividing it into four subtri ...

196. Analytic Continuation, Singular Value Expansions, and Kramers-Kronig Analysis
Topic: Math
Published: 1/17/2001
Authors: Andrew M Dienstfrey, L Greengard
Abstract: We describe a systematic approach to the recovery of a function analytic in the upper half plane, ${\bfC:^+$, from measurements over a finite interval on the real axis, $D\subset {\bfR}$. Analytic continuation problems of this type are well-known to ...

197. Lattice Sums and the Two-dimensional, Periodic Green s Function for the Helmholtz Equation
Topic: Math
Published: 1/16/2001
Authors: Andrew M Dienstfrey, Fengbo Hang, Jingfang Huang
Abstract: Many algorithms that are currently used for the solution of the Helmholtz equation in periodic domains require the evaluation of the Green s function, G(x, x0). The fact that the natural representation of G via the method of images gives rise to a co ...

198. Multiresolution Representation of Urban Terrain By L^1^ Splines, L^2^ Splines, and Piecewise Planar Surfaces
Topic: Math
Published: 12/11/2000
Authors: J E Lavery, David E. Gilsinn
Abstract: Cubic L^d1^ and L^d2^ interpolating splines based on C^u1^ smooth piecewise cubic Sibson elements on a tensor-product grid are investigated. Computational tests were carried out for a 102.4 km area of Fort Hood, Texas represented by a 1025 x 1025 set ...

199. Direct Blind Deconvolution II. Substitute Images and the Beak Method
Series: NIST Interagency/Internal Report (NISTIR)
Report Number: 6570
Topic: Math
Published: 11/1/2000
Author: Alfred S Carasso
Abstract: The BEAK method is an FFT-based direct blind deconvolution technique previously introduced by the author, and applied to a limited but significant class of blurs that can be expressed as convolutions of 2-D symmetric L vy probability density function ...

200. Attractors, Chain Transitive Sets and Invariant Measures
Topic: Math
Published: 9/15/2000
Author: Fern Y Hunt
Abstract: This paper discusses an easy to implement procedure for approximating the long time behavior of iterates of maps. Applications include to finding the roots of a complex polynomial and approximating attractors. The method uses the theory of Markov ch ...

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