Sentence examples for by the arbitrary function from inspiring English sources

In the following, we theoretically derive the solution in the time domain for the sea-bottom deformation given by the arbitrary function of χ (t).

The main difficulty with respect to the integration is that the residue theorem is not applicable to the sea-bottom deformation given by the arbitrary function χ (t) or χ (t) = δ (t).

Within these analyses the effect of the aberration is described by the arbitrary function ϕ.

For this case that the arbitrary function is given by the smoothed ramp function with sine function, the dynamic and quasi-static behaviors of the stresses are examined by numerical calculations.

Notice that the weight of an edge is evaluated by an arbitrary function, which is denoted by the d and is normalized to the range [0, 1].

It is assumed that a transient magnetic field which is defined by an arbitrary function of time acts on the surface of the solid cylinder in the direction parallel to its surface.

Motivated by the works in [22 24], in this paper, we establish some new generalized Volterra-Fredholm type discrete inequalities involving four iterated infinite sums with the right-hand side denoted by an arbitrary function ϕ ( u ), which are of more general forms.

Even if p0 y) were Gaussian, the very act of multiplying it by an arbitrary function makes p w y), and hence p1 y) non-Gaussian.

The state feedback is given by the composition of an arbitrary function and the control contact Hamiltonian function.

This study considers the buckling of an elastic truncated conical shell having a meridional thickness expressed by an arbitrary function, subject to a uniform external pressure, which is a power function of time.

To obtain two dimensional images, expanding spiral scanning patterns are imposed on the fiber cantilever by using sinusoidal driving voltages with linearly varying amplitudes, which are generated by an arbitrary function generator (AFG3022B, Tektronics) and amplified by piezo driver modules (E-835, Physik Instrumente).