An energy concerving modification of numerical methods for the integration of equations of motion

In the integration of the equations of motion of a system of particles, conventional numerical methods generate an error in the total energy of the same order as the truncation error. A simple modification of these methods is described, which results in exact conservation of the energy

Probability of Identification: A Statistical Model for the Validation of Qualitative Botanical Identification Methods

A qualitative botanical identification method (BIM) is an analytical procedure that returns a binary result (1 = Identified, 0 = Not Identified). A BIM may be used by a buyer, manufacturer, or regulator to determine whether a botanical material being tested is the same as the target (desired) material, or whether it contains excessive nontarget (undesirable) material. The report describes the development and validation of studies for a BIM based on the proportion of replicates identified, or probability of identification (POI), as the basic observed statistic. The statistical procedures proposed for data analysis follow closely those of the probability of detection, and harmonize the statistical concepts and parameters between quantitative and qualitative method validation. Use of POI statistics also harmonizes statistical concepts for botanical, microbiological, toxin, and other analyte identification methods that produce binary results. The POI statistical model provides a tool for graphical representation of response curves for qualitative methods, reporting of descriptive statistics, and application of performance requirements. Single collaborator and multicollaborative study examples are given

Energy and Momentum Conserving Methods of Arbitrary Order For the Numerical Integration of Equations of Motion. I. Motion of a Single Particle

Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these constants of the motion play a central role in mechanics, it is a great advantage to be able to conserve them exactly. A new numerical method is developed, which is a generalization to arbitrary order of the "discrete mechanics" described in earlier work, and which conserves the energy and angular momentum to all orders. This new method can be applied much like a "corrector" as a modification to conventional numerical approxirnations, such as those obtained via Taylor series, Runge-Kutta, or predictor-corrector formulae. The theory is extended to a system of particles in Part I1 of this work

Discrete Mechanics - A General Treatment

A new numerical method for use in the solution of classical equations of motion is described, accurate to third-order in the coordinates and second-order in the velocities. The method has the unique property of preserving the energy and total linear and angular momenta at their initial values in the computation. This "discrete mechanics " is derived from general symmetry properties of the equations of motion and is compared in several numerical examples with conventional predictor-corrector methods. The theory is applied to derive a general expression for the impulsive limit of motion due to a potential

An Introduction to Bootstrap Methods with Applications to R

Bootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. An Introduction to Bootstrap Methods with Applications to R explores the practicality of this approach and successfully utilizes R to illustrate applications for the bootstrap and other resampling methods. This book provides a modern introduction to bootstrap methods for readers who do not have an extensive background in advanced mathematics. Emphasis throughout is on the use of bootstrap methods as an exploratory tool, including its value in variable selection and other modeling environments… [Amazon.com]https://digitalcommons.odu.edu/mathstat_books/1009/thumbnail.jp