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One Equation (one + equation)
Selected AbstractsModification of upwind finite difference fractional step methods by the transient state of the semiconductor deviceNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008Yirang Yuan Abstract The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasi-linear partial differential equations for initial boundary value problem. One equation of elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Upwind finite difference fractional step methods are put forward. Some techniques, such as calculus of variations, energy method multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates and techniques are adopted. Optimal order estimates in L2 norm are derived to determine the error in the approximate solution.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source] Estimation of height in elderly Japanese using region-specific knee height equationsAMERICAN JOURNAL OF HUMAN BIOLOGY, Issue 3 2002Barbara Lohse Knous Two knee height equations to predict standing height of Japanese elderly were cross-validated with Joetsu City elders. One equation was derived with Hawaiian residents of Japanese ancestry and the other with elders from the Kumamoto Prefecture in Japan. Subjects included 40 men and 39 women free-dwelling, healthy elders with mean ages of 68.0 ± 2.2 years and 68.0 ± 2.7 years, respectively. Heights of the subjects were representative of Japanese elderly. Experienced nurses, trained to measure knee height, also measured standing height with an automatic stadiometer. A pilot study refined measurement skills. Differences between actual and predicted heights for both equations were significant. Multiple linear regression was used to derive knee height equations specific for elderly males and females living in Joetsu City: women, 63.06 + (2.38 × knee height in cm) ,(0.34 × age in years); men, 71.16 + (2.61 × knee height in cm) - (0.56 × age in years). Geographic-specific knee height equations for Japanese elderly and cross-validation with other locations are suggested to facilitate the accurate use of knee height in nutritional assessment of Japanese elders. Am. J. Hum. Biol. 14:300,307, 2002. © 2002 Wiley-Liss, Inc. [source] Characterization of differential ebulliometers for measuring activity coefficientsAICHE JOURNAL, Issue 1 2000J. David Raal Differential ebulliometry is a powerful and rapid procedure for obtaining infinitely dilute activity coefficients with potentially very good accuracy. Tedious degassing procedures are not necessary, as in a static method, and from only a few measurements full system phase behavior can be evaluated. The principal problem, precise evaluation of the equilibrium liquid composition from the known composition of a prepared solution charged to the apparatus, is well known but has so far defied adequate resolution. A system of exact self-consistent equations was developed for the characterization of an ebulliometer through a dimensionless ebulliometer constant. Evaluation of this constant from typical data and its subsequent use are illustrated for a system of known phase equilibrium behavior. Remarkably, the equations permit evaluation of the effective "static" holdups in various parts of the equipment without any volume measurements. Since one equation is redundant to the main purpose, it can be used for a consistency check of measured and calculated data. The equations also furnish a guide for the operation of ebulliometers. [source] Prediction of experimentally unknown re distances of organic molecules from Dunning basis set extrapolations for ab initio post-HF calculationsJOURNAL OF PHYSICAL ORGANIC CHEMISTRY, Issue 3 2006Alexander Neugebauer Abstract An approach to estimate equilibrium re bond lengths of organic molecules which contain standard bonding situations for CC, CH, CO and CN distances from only one equation is presented. For this, optimizations of molecular geometries using correlated post-Hartree,Fock and density functional methods have been performed. A selection scheme was developed to determine the most reliable methodology for prediction of equilibrium re distances of covalent bonds from a set of investigated theoretical methods. Consequently, distances computed in the CCSD(T) procedure via exponential extrapolation from a consecutive set of Dunning cc-pVXZ basis sets by use of Eqn (2) are accurate up to ±,0.0005,Å in comparison to experimentally available re distances. Applications for predictions of the experimentally unknown re distances of methanol, methylamine and methylenimine are presented. Additionally the estimation of re distances of larger, chemically more interesting molecules is possible by lower order calculations (e.g. DFT B3LYP/cc-pVDZ) via linear correlation statistics using the results from our re reference model system via Eqn (3). Copyright © 2006 John Wiley & Sons, Ltd. [source] | ||||||||||