Equation. . 48 imposed

There has been fierce debate (see Refs. 232, 235-237) over the usefulness of the preceding methods and the matter is far from resolved. On the one hand, the use of algebraic models such as modified DR equations imposes artificial constraints, while on the other hand, the assumption of the validity of the /-plot in the MP method is least tenable just in the relatively low region where micropore filling should occur. 

This result, known as the Gibbs-Duhem equation, imposes a constraint on how the partial molar properties of any phase may vary with temperature, pressure, and composition. In particular, at constant T and P it represents a simple relation among the Af/ to which measured values of partial properties must conform. 

Nearly two years ago, studying electrodynamics in curved space-time I found1 that Maxwell s equations impose on space-time a restriction which can be formulated by saying that a certain vector q determined by the curvature field must be the gradient of a scalar function, or... 

An iterative procedure using the solid film linear driving force model has been used with a steric mass action isotherm to model displacement chromatography on ion exchange materials and the procedure applied to the separation of horse and bovine cytochrome c using neomycin sulfate as the displacer.4 The solid film linear driving force model is a set of two differential equations imposing mass transfer limitations. 

This equation imposes limitations on kinetic model parameters. Whence... 

The Schrodinger wave equation imposes certain mathematical restrictions on the quantum numbers. They are as follows ... 

The Gibbs/Duhem equation imposes a constraint on activity coefficients that may not be satisfied by experimental values containing systematic error. If tliis is the case, the experimental values of In yx and lnj/2 used for calculation of G lRThy Eq. (12.6), which does not depend... 

When represents a metal cation not in the background electrolyte, the intrinsic constants are determined by fitting the triple layer model to adsorption edge data. This fitting entails a surface speciation calculation with previously measured values of the intrinsic constants in Eq. 5.61, the capacitance parameters Ci and C2, and the parameter Af. The computation includes Eqs. 5.58, 5.59, and 5.69, as well as surface charge and mole balance equations imposed as constraints. " ... 

This equation imposes a constraint among the various first order tangential force constants. The parameters the second order derivatives of the potential, are defined by ... 

The disappearance of gas-water interfaces in macroscopic equations imposes some difficulties in describing the neuston which represents a pore-scale object. This means that the movement of neuston in macroscopic equations can be obtained by homogenization of its pore-scale motion. 

These equations impose constraints on the singles and doubles cluster amplitudes in the spin-orbital basis. 

To aid with the design of the CRS, a study on the repaired riser pipe subjected to complex loadings is required. Theoretical equations impose the use of a deteriorating factor... 

If the m Equations (7-1) are considered independent, additional restrictions must be imposed as... 

The modification of the surface force apparatus (see Fig. VI-4) to measure viscosities between crossed mica cylinders has alleviated concerns about surface roughness. In dynamic mode, a slow, small-amplitude periodic oscillation was imposed on one of the cylinders such that the separation x varied by approximately 10% or less. In the limit of low shear rates, a simple equation defines the viscosity as a function of separation... 

The alternative simulation approaches are based on molecular dynamics calculations. This is conceptually simpler that the Monte Carlo method the equations of motion are solved for a system of A molecules, and periodic boundary conditions are again imposed. This method pennits both the equilibrium and transport properties of the system to be evaluated, essentially by numerically solvmg the equations of motion... 

Flere, A and B are regarded as pool chemicals , with concentrations regarded as imposed constants. The concentrations of the intemiediate species X and Y are the variables, with D and E being product species whose concentrations do not influence the reaction rates. The reaction rate equations for [X] and [Y] can be written in the following dimensionless fomi ... 

For example, the SHAKE algorithm [17] freezes out particular motions, such as bond stretching, using holonomic constraints. One of the differences between SHAKE and the present approach is that in SHAKE we have to know in advance the identity of the fast modes. No such restriction is imposed in the present investigation. Another related algorithm is the Backward Euler approach [18], in which a Langevin equation is solved and the slow modes are constantly cooled down. However, the Backward Euler scheme employs an initial value solver of the differential equation and therefore the increase in step size is limited. 

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