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The variational multiscale method (VMS) is a technique used for deriving models and numerical methods for multiscale phenomena. [1] The VMS framework has been mainly applied to design stabilized finite element methods in which stability of the standard Galerkin method is not ensured both in terms of singular perturbation and of compatibility conditions with the finite element spaces.
The Differential Ability Scales (DAS) is a nationally normed (in the US), and individually administered battery of cognitive and achievement tests. Into its second edition (DAS-II), the test can be administered to children ages 2 years 6 months to 17 years 11 months across a range of developmental levels.
John Scales Avery (May 26, 1933 – January 4, 2024) was an American theoretical chemist noted for his research publications in quantum chemistry, thermodynamics, evolution, and history of science. Since the early 1990s, Avery had been an active world peace activist .
Solving Ordinary Differential Equations. I. Nonstiff Problems. Springer Series in Computational Mathematics. Vol. 8 (2nd ed.). Springer-Verlag, Berlin. ISBN 3-540-56670-8. MR 1227985. Ernst Hairer and Gerhard Wanner, Solving ordinary differential equations II: Stiff and differential-algebraic problems, second edition, Springer Verlag, Berlin, 1996.
Higher-order solutions – using the method of multiple scales – require the introduction of additional slow scales, i.e., t 2 = ε 2 t, t 3 = ε 3 t, etc. However, this introduces possible ambiguities in the perturbation series solution, which require a careful treatment (see Kevorkian & Cole 1996; Bender & Orszag 1999). [2]
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers.
The study of dynamic equations on time scales reveals such discrepancies, and helps avoid proving results twice—once for differential equations and once again for difference equations. The general idea is to prove a result for a dynamic equation where the domain of the unknown function is a so-called time scale (also known as a time-set ...
The scale includes items to measure the three components of SOC: comprehensibility (11 items), manageability (10 items), and meaningfulness (8 items). Responses are given on a semantic differential scale from 1 to 7, and after recoding reverse-scored items, they are summed to produce a total score ranging from 29 to 203. A shorter version, SOC ...