Sentence examples for derivation of the generalized from inspiring English sources

Next, the universal form of the resulting surface susceptibility matrix is employed for the derivation of the generalized Fresnel coefficients for such surfaces, which enable the comprehensive interpretation of several significant, yet relatively unexamined, physical interactions.

Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

The derivation of the generalized Goertzel algorithm is analog to the technique presented in Section 2. Compared to that, however, we extend formula (22) at the very beginning by unity in the form of e j2 π k N N ⋅ e - j 2 π k N N = 1 for  k ∈ ℝ, (23).

Since the sum in (26) is identical to (3), the derivation of the generalized algorithm can proceed using the same steps as in Section 2.1, with one noteworthy change: the equation that characterizes the output using state variables (17) will now be of the form y k [ n ] = s [ n ] - e - j 2 π k N s [ n - 1 ] ⋅ e - j 2 π k. (27).

This approach has been used also in derivation of the family of generalized PImDn-1controllers.

We deduced its generating function, recurrence relations and q-difference equation, which gives us the differential equation of each of the Bessel function and the modified Bessel function when q tends to 1. Finally, the quantum algebra E 2 ( q ) and its representations presented an algebraic derivation for the generating function of the generalized q-Bessel function.

The non-dimensionalization enabled the analytical derivation of a generalized non-propagating fatigue crack length, which can be utilized for fatigue designs.

Detailed derivation of a generalized matrix equation is given.

The paper deals with a derivation of a time domain variant of the generalized telegrapher's equations for transient electromagnetic field coupling to buried wires.

For specific such applications we refer to the geometric derivation of generalized Student and Fisher distributions.

The theoretical derivation of the joint acquisition is detailed in the principle of the generalized likelihood ratio test (GLRT) to evaluate detection performance.