34,046 research outputs found
Analysis of thermal stress and metal movement during welding
Objectives of study were: investigation of temperature changes caused by welding arc with analysis of temperature distribution; development of system of mathematical statements describing thermal stresses and plastic strains during welding; and development of system of mathematical solutions and computer programs for one-dimensional analysis
Difference equation of the colored Jones polynomial for torus knot
We prove that the N-colored Jones polynomial for the torus knot T_{s,t}
satisfies the second order difference equation, which reduces to the first
order difference equation for a case of T_{2,2m+1}. We show that the
A-polynomial of the torus knot can be derived from this difference equation.
Also constructed is a q-hypergeometric type expression of the colored Jones
polynomial for T_{2,2m+1}.Comment: 7 page
Maximum Likelihood Estimation and Uniform Inference with Sporadic Identification Failure
This paper analyzes the properties of a class of estimators, tests, and confidence sets (CS's) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter theta. This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine the asymptotic distributions of estimators under lack of identification and under weak, semi-strong, and strong identification. We determine the asymptotic size (in a uniform sense) of standard t and quasi-likelihood ratio (QLR) tests and CS's. We provide methods of constructing QLR tests and CS's that are robust to the strength of identification. The results are applied to two examples: a nonlinear binary choice model and the smooth transition threshold autoregressive (STAR) model.Asymptotic size, Binary choice, Confidence set, Estimator, Identification, Likelihood, Nonlinear models, Test, Smooth transition threshold autoregression, Weak identification
Optical-radar imaging of scale models for studies in asteroid astronomy
During the past five years, delay-Doppler radar has become the primary technique for studying the structure of Earth-crossing asteroids. None of these objects has yet been visited by spacecraft, so ground-truth test cases are lacking. A laboratory system is described that provides optical-radar images at 0.1-mm resolution. These data are analogous to the highest-resolution asteroid radar images currently available and provided realistic test cases for developing signal-processing techniques. The system can be thought of as a 1/188,000 scale model of the Arecibo radar, or a 1/52,800 scale model of the Goldstone radar
Summary of XB-70 airplane cockpit environmental data
Thermal, acoustical, and acceleration environments of XB-70 airplane crew compartment in airworthiness test
Uncovering Ramanujan's "Lost" Notebook: An Oral History
Here we weave together interviews conducted by the author with three
prominent figures in the world of Ramanujan's mathematics, George Andrews,
Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the
"lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's
notes, and recent breakthroughs by Ono and others carrying certain important
aspects of the Indian mathematician's work into the future. Also presented are
historical details related to Ramanujan and his mathematics, perspectives on
the impact of his work in contemporary mathematics, and a number of interesting
personal anecdotes from Andrews, Berndt and Ono
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