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The two-dimensional half-plane problem is formulated using the Fourier integral transform method and the analytical formulation of the contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure.
In this paper we propose an analytical formulation of the dynamical behaviour of complex and open physical systems which is formulated on the total thermodynamic phase space using the contact form associated with Gibbs' relation.
Analytical formulation of deterministic location has been well developed.
This leads to an analytical formulation of the reliability problem.
The analytical formulation of the ECR is based on a mathematical derivation with high accuracy.
This paper presents the analytical formulation of the proposed approach, whose validation follows in part II.
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Analytical formulations of interaction tensors are presented for ellipsoidal inclusions.
Approximate analytical formulations of the fundamental frequency for such plates with core are obtained.
Analytical formulations of intensity factors and distributions of dual variables are obtained by the symplectic expansion method.
Furthermore, comprehensive analytical formulations of the design parameters associated with MCML circuits are presented to provide guidelines for MCML designers.
Analytical formulations of cost functions are derived for three types of operating modes: uncoordinated operation, departure punctual control and departure delayed control.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com