Sentence examples for by an explicit expression from inspiring English sources

Replacing the force in the slender body integral equation by an explicit expression that uses Euler Bernoulli theory to model bending and tensile forces yields an integral expression for the velocity of the filament centerlines, coupled to auxiliary integro-differential equations for the filament tensions.

3, we prove the existence of TW by establishing an explicit expression of their shape.

The Cauchy distribution was used by Stigler (1989) to obtain an explicit expression for P(Z 1 ≤ 0, Z 2 ≤ 0) where (Z 1, Z 2) T follows the standard bivariate normal distribution.

The variability of a displacement can be evaluated by a Monte Carlo Simulation (MCS) using an explicit expression.

With such approximations, the directional integration was achieved by means of tensor multiplication, leading to an explicit expression of the stress tensor in terms of the direction tensors.

By introducing a novel multivariable curve fitting approach, an explicit expression for the DI is developed which shows effect of all important parameters clearly.

First, we obtain an explicit expression (at the continuous level) of the expected compliance and its variance, then we consider a numerical discretization (by using a finite element method) of this expression and finally we use an optimization algorithm.

The model incorporates finite-size effects and an explicit expression for the relative permittivity.

Then, an explicit expression for the topological derivative of the approximate shape functional is given.

We next need an explicit expression for γ Y ( t ).

This motivates us to find an explicit expression for a class of functions satisfying (1.18).