Sentence examples for derived rigorously from inspiring English sources

The posterior probability density function (PDF) of the modal parameters is derived rigorously from modeling assumptions and Bayesian probability logic.

The governing partial differential equations (PDEs) and constitution relations are derived rigorously from an asymptotically correct, geometrically nonlinear theory.

The thermal boundary conditions are derived rigorously and are verified by the identical numerical results obtained by the two unit cells.

One is the general type derived rigorously from a free-energy formulation, and another is the antisymmetric type where only dual interface interaction is taken into account.

The equations of motion are derived rigorously by means of the Appell Gibbs equations for constant longitudinal velocity of the vehicle.

An analytical model describing liquid droplet and dendrite arm migration due to temperature gradient zone melting (TGZM) is derived rigorously for both static and dynamic conditions.

An approach based on the theory of dynamical systems is used to derive rigorously effective or pseudohomogeneous type models for catalytic reactors.

In Section 3 we derive rigorously the amplitude equation with error term and state the main theorem of this paper.

Our approach is distinct in that it aims at deriving rigorously and without approximations the mean-field equations of populations of neurons whose individual neurons are described by biological, if not correct at least plausible, representations.

Our aim of this paper is to derive rigorously this amplitude equation with the quintic nonlinearity for the SGSH equation (1) with (nu _{varepsilon}=varepsilon^{4}nu), (mu_{varepsilon}=varepsilon^{2}) and (gamma^{2}=frac{27}{38}).

The ssLNA can also be derived more rigorously using the projection operator formalism as shown in [ 57].