Carson transformation

McLaughlin and Rozett (23) have recently described a method for Carson transform and gives results identical with ours. 

Let f(t) be a function of t, with the same properties than before, the Carson transform is then defined as... 

The graph obtained is solved by the method described above to give the Laplace-Carson transformation function of the reaction rate ... 

An elegant method has been described by Vinh 2 for converting (7 and tan 5 as functions of co to G(t), by Laplace and Carson transforms. The data are processed numerically with the aid of graphical devices, and the result is obtained in the form of an analytic function. 

In the case of the mixed kineticsthe diffusion mass transfer in the solid and liquid phases occur with comparable rates) on an ideally flat electrode with = 0 in the presence of a solid phase adsorption effect the diffusion problem (2)-(12) is reduced to the onedimensional task. Its solution is obtained using the method of the integral Laplace-Carson transformation in the form of concentration profiles and voltammogram ... 

The measurable linear viscoelastic functions are defined either in the time domain or in the frequency domain. The interrelations between functions in the firequenpy domain are pxirely algebraic. The interrelations between functions in the time domain are convolution integrals. The interrelations between functions in the time and frequency domain are Carson-Laplace or inverse Carson-Laplace transforms. Some of these interrelations will be given below, and a general scheme of these interrelations may be found in [1]. These interrelations derive directly from the mathematical theory of linear viscoelasticity and do not imply any molecular or continuum mechanics modelling. 

The relaxation modulus G(t) is the value of the transient stress per unit strain in a step-strain experiment. This type of experiment may be achieved with modem rotary rheometers with a limited resolution in time (roughly 10 2 s). If one wishes to evaluate G(t) at shorter times, it is necessary to derive G(t) from the high frequency G (co) data by an inverse Carson-Laplace transform. 

Let the integral transformation of Laplace-Carson be applied to system (50). The functions of time x t) can then be substituted by the x (q) transformation functions, and the time derivatives by the qx (g) — f/xlO) values, where q represents reciprocal time and the x(0) are the initial concentrations of the intermediates. The Laplace-Carson procedure transforms the system of differential equations (50) into a system of algebric equations with respect to X (q) thus ... 

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