Sentence examples for given functions of from inspiring English sources

The governing equations for designing non-geodesics on a toroid are formulated using the given functions of slippage coefficients.

In this approach, locally optimal design points and weights are studied as implicitly given functions of the nonlinear parameters included in the model.

Both p and e are given functions of ρ and s, satisfying the thermodynamical constraint T, mathrm{d} s =mathrm{d} e + p, mathrm{d} frac{1}{rho}, (1.2) where (T=T(rho, s)) is the temperature.

We consider the boundary value problem Delta u=0 quadtext{on } Pi,quadquad u=varphi_{j}(s) quadtext{on } gamma _{j}, j=1,2,3,4, (1) where (Deltaequivpartial^{2}/partial x^{2}+partial^{2}/partial y^{2}), (varphi_{j}) are given functions of s.

where n ≥ 1 ( n ∈ N ), W n is unknown function of n, A n and B n are arbitrary given functions of n, and W 0 = C 0, W 1 = C 1 are initial conditions (we assume not to have the trivial case when C 1 = C 0 = 0 and W n ≡ 0 ).

Here p in and p out are given functions of two variables ( r, t ) for 0 ≤ r ≤ R − and 0 ≤ r ≤ R +, respectively, 0 ≤ t ≤ T. The aim of this paper is to extend the existence result of [1] concerning the two-dimensional fluid-structure interaction problem to the radially symmetric case expressed in terms of the cylindrical coordinate system.

Pressure errors are prevented by solving an additional transport equation for a given function of the ratio of specific heats.

The magnetic reconnection process is initiated by variation of a local resistivity assumed to be a given function of time and spatial coordinates.

This paper is concerned with the numerical solution for linear scalar advection problems, the velocity field of which may be uniform or a given function of the space variable.

Output end is open, v n + 1 = 0. Input voltage u 0 ( t ) is a given function of t.

where L and N are the linear and non-linear components, respectively, and H is a given function of η.