We note that, by energy conservation, the following equation must hold [Pg.1047]

The compressibility factors Zy are obtained after solving the following equations in for i = 1 and i = 2 [Pg.119]

These values are related to the initial wavenumber intervals by the following equations [Pg.50]

The variational derivatives of with respect to the moduli ai give the following equations [Pg.164]

The simplest way is to weight the Cp/ of each component according to the following equation [Pg.120]

The D 1160 data at 10 mmHg can be transformed to TBP at 10 mmHg by using the following equations [Pg.102]

The water pressure gradient is related to the water density (p, kg/m ) by the following equation [Pg.117]

When pure component i constitutes the solid phase, the liquid-solid equiiibrium obeys the following equation [Pg.172]

The component of the DC quadnipolar potential in the z-axis direction is described by the following equation. [Pg.1356]

Substitution of the ansatz (31) into the Schrddinger equation (1) for the full system, together with the above approximations, yields the following equations for the coefficients Co(t),djaj/0 t) of the Cl expansion (31) [Pg.371]

Here, the first factor (r, R) in the sum is one of the solutions of the electronic BO equation and its partner in the sum, Xt(R) is the solution of the following equation for the nuclear motion, with total eigenvalue [Pg.145]

Using Eqs. (29) and (30) we obtain that the coherent potential v i with elastic scattering correction is determined by the following equations [Pg.452]

If the entropy and the enthalpy for the separate mixing in each of the half-mole superlattices are calculated and then combined, the following equation is obtained [Pg.632]

Daubert has recently published a new method (Hydrocarbon Processing, September 1994, page 75) to convert D 86 data to TBP results using the following equations [Pg.100]

There are various approaches to the problem of coupling quantum degrees of freedom to classical degrees of freedom. The QCMD model is given by the following equations of motion [Pg.397]

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is [Pg.769]

In this minimal END approximation, the electronic basis functions are centered on the average nuclear positions, which are dynamical variables. In the limit of classical nuclei, these are conventional basis functions used in moleculai electronic structure theoiy, and they follow the dynamically changing nuclear positions. As can be seen from the equations of motion discussed above the evolution of the nuclear positions and momenta is governed by Newton-like equations with Hellman-Feynman forces, while the electronic dynamical variables are complex molecular orbital coefficients that follow equations that look like those of the time-dependent Hartree-Fock (TDHF) approximation [24]. The coupling terms in the dynamical metric are the well-known nonadiabatic terms due to the fact that the basis moves with the dynamically changing nuclear positions. [Pg.228]

The solubility of a solid in the liquid phase of a mixture depends on the properties of the two phases for the components that crystallize, the equilibrium is governed by the following equation [ XI [Pg.171]

Very shortly, the first one is based on the stress measurement performed using a rosetta strain gauge located in an area of sufficiently uniform stress distribution. In this case, the calibration factor Cr can be easily obtained by the following equation [Pg.410]

The general problem is to determine at given conditions of temperature and pressure, the quantities and compositions of the two phases in equilibrium starting from an initial quantity of material of known composition and to resolve the system of the following equations [Pg.152]

Eddy currents and the magnetic flux that is associated to them are proportional to the radial distance of the coil center. The magnetic flux is proportional to the probe induction and consequently to the passing current. The theoretic calculation of this induction is given by the following equation [Pg.291]

Related to the previous method, a simulation scheme was recently derived from the Onsager-Machlup action that combines atomistic simulations with a reaction path approach ([Oleander and Elber 1996]). Here, time steps up to 100 times larger than in standard molecular dynamics simulations were used to produce approximate trajectories by the following equations of motion [Pg.74]

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