Additive constant

Assume that there are two distinct potentials (aside from an additive constant that simply shifts the zero of total energy) V r) and V r) which, when used in //and //, respectively, to solve for a ground... 

Comparing this equation with Eq. (75), it is seen that the mixing angle p is, up to an additive constant, identical to the relevant adiabatic-to-diabatic transformation—angle y ... 

The Hildebrand Solubility Parameter. This parameter, 4 can be estimated (10) based on data for a set of additive constants, E, for the more common groups ia organic molecules to account for the observed magnitude of the solubiHty parameter d = EE/V where Erepresents molar volume. SolubiHty parameters can be used to classify plasticizers of a given family ia terms of their compatibihty with PVC, but they are of limited use for comparing plasticizers of differeat families, eg, phthalates with adipates. 

For higher (0 > 0.05) concentrations where particle—particle interactions are noticeable, the viscosity is higher than predicted by the Einstein equation. The viscosity—concentration equation becomes equation 10, where b and c are additional constants (87). 

The equation developed by the Design Institute for Physical Property Data (DIPPR) is another successful correlating tool for vapor pressure (4). It is an empirical extension of the Antoine equation and has two additional constants, D and E ... 

E° is the standard potential of the reaction 2Y = Y, -I- 2e . The additive constants set Hu and n equal to zero for H2O. The quantities a and b are parameters measuring susceptibility to the corresponding nucleophilic parameters. Evidently /7n describes... 

Taking t] = 2 and dropping any additive constant, the likelihood penalty 0Gauss(x) writes ... 

Since H and N differ only by the factor hco and an additive constant, they commute and, therefore, have the same eigenfunctions. 

As a consequence of the Hohenberg-Kohn theorem [14], a non-degenerate ground state electron density p(r) determines the Hamiltonian H of the system within an additive constant, implying that the electron density p(r) also determines all ground state and all excited state properties of the system. 

This potential is related to the electrode potential, E (apart from an additive constant depending on the definition of the reference potential). The first term in Eq. (4.5.6), Af(j> characterizes the band bending... 

Noordsij and Rotte (N10) studied mass transfer at a vibrating sphere. The oscillating motion was achieved by means of an attached rod, held by a spring against an eccentric wheel. The results, showing considerable scatter, are represented approximately by a Pe1/2 dependence, with an additive constant term accounting for pure diffusion. 

Some additional comments regarding Equation 4 are in order. The factor 143.88 converts the units to kcal/mol. There are two additional constants. The first is ks, which is the stretching force constant parameter in units of md A 1. The second constant is cs, which is the cubic term with a unitless value of 2.55. When a Morse potential is expanded in a power series, the factor 7/12 is obtained. 

Conversely it can be shown that v r) is a unique functional of p(r), apart from a trivial additive constant. Assume that another potential v (r), with ground state F gives rise to the same density p(r). This F that satisfies a different Schrodinger equation, cannot be equal to F, unless v (r) — v(r) =constant. From the minimal property of the ground state it follows immediately that... 

The procedure is similar to that for one reactant, although there is an additional constant to determine. From equation 3.4-3,... 

Since the absolute and the conventional electrode potentials differ only by an additive constant, the absolute potential depends on the concentration of the reactants through the familiar Nernst s equation. This dependence is implicitly contained in Eq. (2.6) the real Gibbs energies of solvation contain an entropic term, which depends on the concentration of the species in the solution. 

Theorem 1. The external potential v(r) is determined, within a trivial additive constant, by the electron density p(r). (The implication of this existence theorem is that p(r) determines the wave function and therefore all electronic properties in the ground state see also Equation 4.6.)... 

Fourth, initial conditions are needed for 4>, v, A and A. For the first two they are free additive constants and for A and A we can proceed as in 4 dimensions. Anyway, it is clear that even if we choose such initial conditions that 42 (r = 0) = 0, then it does not remain zero out of the center. 

The portion of surplus value destined for accumulation as additional constant capital... increases so rapidly that it devours a progressively larger share of surplus value. It devours the portion reserved for... 

In contrast, Samuelson and Wolfson (1986) exclude variable capital in their calculation of investment. Examination of Table 7.1 shows their calculation to be incorrect. In year 1, for example, total savings of 25,000 are equal to 20,000 investment in additional constant capital plus 5,000 investment in additional variable capital. This approach to modelling investment in Marx s reproduction schema has been introduced in Chapter 3. 

Lagrange multiplier assuring global electroneutrality (additive constant to the electrostatic potential) normalization constant assuring 2af (ct) = 1... 

In addition, constant turbulent parameters and constant mixture com-... 

Methods and Analyses for the Additional Constant Rate Tests... 

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