Sentence examples for be arbitrary functions of from inspiring English sources

The elastic moduli are allowed to be arbitrary functions of the radius r.

Variations in the material properties such as Young's modulus and Poisson's ratio may be arbitrary functions of the radial coordinate.

This paper addresses an axisymmetric quasi-static contact problem on both thermal and mechanical interactions of a circular punch and a nonhomogeneous elastic half-space whose mechanical and thermophysical properties are assumed to be arbitrary functions of the depth coordinate.

Metabolite uptake and export rate limits can be arbitrary functions of metabolite concentrations or environmental variables.

Birth and migration rates may be arbitrary functions of the state of the system and time.

(10)D'Alembert showed that the general solution to (10) isy x, t) = f(x + ct) + g(x − ct) (11 where f and g are arbitrary functions (of one variable).

(10) D'Alembert showed that the general solution to (10) is y x, t) = f(x + ct) + g(x − ct) (11) where f and g are arbitrary functions (of one variable).

We present a numerical algorithm for the rapid solution of the time-dependent diffusion equation in a semi-infinite inhomogeneous medium whose scattering and absorption coefficients are arbitrary functions of depth, given a point source impulsive excitation.

where, and are arbitrary functions of while, and are arbitrary functions of and.

where, and are arbitrary functions of their arguments.

with the similarity variable ξ = x − x0t, where F j and G j (j = 0,1,.) are arbitrary functions of ξ.