The mathematical formulation uses the Hamilton principle and includes derivation of the governing equations along with the appropriate boundary conditions.
The mathematical formulation uses the SYNHEAT superstructure for the HEN, and ad hoc superstructures and nonlinear models to represent the utility systems.
The mathematical formulation uses the non-linear smeared crack/smeared reinforcement approach to consider plane stress states in reinforced concrete elements.
The mathematical formulation uses the ordinary unidirectional panel theory for the face-sheets and a two-dimensional elasticity approach for the core.
The mathematical formulation uses a collision model similar to that of Bhatnagar, Gross, and Krook (BGK), in a particle distribution function transport equation, in order to approximate the rates at which collisions bring about local equilibration of particle velocities and the masses, compositions, and temperatures of liquid films on bed particles.
Mathematical formulations using measured response function data under base excitation to identify mass and stiffness modeling errors, have been established.
The paper presents the mathematical formulations used in the design of the corresponding rollers which differs from the traditional Mecanum wheel rollers.
By developing a novel problem formulation using mathematical programming, we capture the essence of both routing and energy dissipation characteristics of multi-path routing.
A general transfer-matrix based mathematical formulation is used for evaluating reflection spectra of the system.
To obtain sensor fusion, a probabilistic mathematical formulation is used; in particular, the formulation of importance weight (w^{(i)}_{t},) mentioned above, is proposed to handle the GPS and LIDAR data.
