Differentiation quotient

The dimensionless groups can be replaced by the corresponding differential quotient expressions for the derivatives as ... 

The buffering ability of a buffer solution is characterized by its buffering capacity / , which is a differential quotient indicating the change of... 

The quantity dyl3 In a2 at the potential of the electrocapillary maximum is of basic importance. As the surface charge of the electrode is here equal to zero, the electrostatic effect of the electrode on the ions ceases. Thus, if no specific ion adsorption occurs, this differential quotient is equal to zero and no surface excess of ions is formed at the electrode. This is especially true for ions of the alkali metals and alkaline earths and, of the anions, fluoride at low concentrations and hydroxide. Sulphate, nitrate and perchlorate ions are very weakly surface active. The remaining ions decrease the surface tension at the maximum on the electrocapillary curve to a greater or lesser degree. 

Dependence of the measured value (signal intensity), y, from other constituents than the analyte A, present in the measuring sample, quantitatively expressed by the respective partial differential quotient. 

Change in the response of a measuring instrument divided by the corresponding change in the stimulus . In analytical measurements is this, in fact, the differential quotient of the measured value to the analytical value. 

The theory of the thermodynamics of irreversible systems (Prigogine, 1979 Prigogine and Stengers, 1986) shows that the differential quotient of entropy with time (the change of entropy with time) can be expressed as the sum of products, the terms of which contain a force factor and a flow factor. In chemical systems, the... 

If S remains constant during the pumping process, then one can use the difference quotient instead of the differential quotient ... 

However, in view of the boundary condition eqn. (93c), the value of B has to be zero. The quantity A can be found by calculating the differential quotient appearing in eqn. (93d) evidently... 

The quantity, h, in Equation 5 is not likely to be greatly different from its value in a plane adiabatic combustion wave. Taking x as the coordinate normal to such wave, h becomes the integral of the excess enthalpy per unit volume along the x-axis, so that the differential quotient, dh/dx, represents the excess enthalpy per unit volume in any layer, dx. Assuming the layer to be fixed with respect to a reference point on the x-axis, the mass flow passes through the layer in the direction from the unbumed, w, to the burned, 6, side at a velocity, S, transporting enthalpy at the rate Sdh/dx. Because the wave is in the steady state, heat flows by conduction at the same rate in the opposite direction, so that... 

The curve describing the time behavior of a certain F(Z) is always a step function.127 The time differential quotient therefore can assume only the following three values ... 

The normal Auger spectrometer bombards metallic samples with an intense beam of (not necessarily monoenergetic) electrons, and the position of the signals is usually found by a device recording the differential quotient of the number of Auger electrons as a function of their Tin- Wagner (185) pointed out that they can also be observed in favourable cases with a photo-electron spectrometer like... 

For (3u / 3f) p the Henry equation may be used because for o O there is negligible polarization. Again assuming that xa is large, this differential quotient becomes e elt]. (3f/3v ) is the extent by which f lags behind yr because of the vlscoelectrlc effect at the zero point the difference between f and Vr is negligible (flg. 4.12), so the differential quotient is unity. Further, dyf /da = -l/C and 3o /3o° = -1. Hence,... 

To obtain the energy from the force, as required by [2.5.4], [2.5.15] must be integrated with respect to z, from 0 to z. After integration the first differential quotient in [2.5.15] becomes (Pj tz) - pjj) (because the zero point is in the bulk of the liquid) the second becomes... 

The next step is to derive a relation between, J and K. It is a matter of taste, or convenience, which of these variables to take as the independent variable. For adsorption from dilute solutions it is customary to take the concentration (i.e. g ) as independent. On the other hand, for many theoretical analyses it is easier to assume a certain spatial geometry and then And out the g of the solvent with which the curved interface is at equilibrium. Let us foUow the second route, i.e. we want to establish dg / 3J rmd dg / 8K. These differential quotients can be obtained from [4.7.11 by changing variables and cross-differentiation. For instance. 

These differential quotients may now be identified with those in [4.7.5], considering that ]4.7.5 and 7] both give the same, complete, information. The results are... 

The reaction to be demonstrated should be a simple one, and it should be based on a simple kinetic expression. Moreover, it should proceed with a constant velocity. In such a case the reaction velocity need not be expressed as a differential quotient, but rather as the straightforward quotient ... 

Figure 30. Amount retained / as a function of time r, the differential quotient of this function d/ /dz, and the cut size x, associated with the corresponding retained amount...

For a decaying concentration-time function SER(f) is obtained from (Eq. 1) by transition to differential quotients according to Eq. (2) ... 

The reason for the suppression of coalescence was sought in the repulsive electrical forces, which resulted from the electric potential difference at the G/L interface and resulted from the difference in ion concentrations there. Here Gibbs s absorption isotherm applies, which related the surface excess or deficiency to the differential quotient dcr/do ... 

Because of the relations Me = ricM and h = Mh = nh, the differential quotients in the last term in (B.12) can be rewritten in terms of partial molar quantities ... 

In order to do so, we first evaluate the partial differential quotients yn,i <)yn,ca cl <>ai where n identifies the particular data pair, i.e., 1 < < N, while i specifies a given parameter a,-. The numerical differentiation uses the method explained in sections 2.3 and 2.4, and already implemented in the propagation macro of section 10.3. We then compute the matrix... 

In this simple case the differential quotient is found... 

In contrast to a chemical reaction, dynamic surface processes are mainly characterised as "incomplete". This means that one or more parameters, necessary for the equilibrium state, are required to describe the distance of the instantaneous state of the entire system from equilibrium. A chemical reaction can be described by a degree of advancement e. The same procedure is possible for surface chemical reaction including mass transfer and processes of formation and dissolution of associates, e varies between +1 and -1 and depends on the equilibriiun state and affinity A. The differential quotient of affinity to the degree of advancement was defined by Yao (1981) as the ordering coefficient... 

The general idea of the finite difference method is to replace differential quotients by a difference quotient. For example, the derivative of c with respect to time t is approximated by ... 

Of course, if a differential quotient is replaced by a difference quotient with respect to one of the coordinates, the remaining coordinates have to be kept constant. There are for example... 

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