Sentence examples for describes an arbitrary from inspiring English sources

The result is a linear model which describes an arbitrary shape s based on its shape parameters b s, the shape eigenvectors P s, and the mean shape s ¯ of all samples via s = s ¯ + P s b s. (1).

Of the five parameters that describe an arbitrary grain boundary, only those describing the inclination are crucial for the scalar stiffness.

The coefficients g n describe an arbitrary conservative nonlinearity of degree N and f 0 and Q are the characteristic frequency and quality factor of the linear resonator.

Equations for the anisotropic hyperfine interaction matrix, T, of a nucleus that undergoes through-space dipolar interactions to two spin-coupled metal ions were generalized to describe an arbitrary [M1 H M2] fragment of a spin-coupled cluster.

The model is developed such that it can describe any arbitrary deformation history because it uses the time-dependent strain as an input.

These equations are described in an arbitrary Lagrangian Eulerian finite volume framework.

"We can only imagine the anguish that John and Tarek feel after realizing that their detention could be extended for so long in what can only be described as an arbitrary process that lacks any credibility," she said.

Alternatively, the parameters can be described using an arbitrary expression.

The metapopulation structure is characterized by a random connectivity pattern described by an arbitrary degree distribution P(k).

The formulation is based on the exact general solution of the governing differential equation, which provides complete flexibility to describe any arbitrary boundary conditions.

Then we describe a general, arbitrary-order, continuous spatial finite-element approach that is applied to each of the three equations in conjunction with backward-Euler differencing in time.