Sentence examples for an arbitrary condition from inspiring English sources

Not only has Pluto set an arbitrary condition that states Orfeo cannot turn round to see if Euridice is following him, there's also a strong suggestion that the noises off that trick Orfeo into doing so were well planned.

Free flexural vibrations of homogeneous, thin, orthotropic plates of an arbitrary shape with mixed boundary conditions are studied using the R-function method.

Making use of the variables separation method and of the superposition principle, the general solution is obtained by the sum of two solutions: one is derived for null boundary conditions and an arbitrary initial condition; the other is derived for a null initial condition and two arbitrary boundary conditions.

One of the exact solutions is used to validate numerical solution obtained from an arbitrary initial condition.

Most classical beam theories assume that the beam cross section remains a rigid surface under an arbitrary loading condition.

Here, (tau_{1}) denotes the achieved spike time, and (bar{tau}_{1}) is the solution of P1 for an arbitrary initial condition (mathbf{v}(0)).

Below, we shall show that all the above-mentioned solutions converge to the trivial solution u = 0 as t → ∞ for an arbitrary initial condition ϕ.

Specifically, we aim to identify an actuator which requires the least amount of control energy to drive the system from an arbitrary initial condition to the origin in the worst case.

It is easy to see that (u(cdot, omega)=sum_{j=1} ^{l}d_{j}u_{j} (l=2, 3, ldots, 2m) ) is also an eigenfunction of (lambda omega)) which satisfies an arbitrary initial condition at (a_{0}).

where all the system matrices are as in (4), and τ i in (7) is the supremum of τ i (t) in (4), as shown in (5), τ is defined by (6), and ϕ : [ - τ, 0 ] ∩ T 0 → ℝ 0, + n is an arbitrary initial condition.

Given an arbitrary initial condition ([v_{1} v_{2}]^{T}), the time-optimal solution of the first part without any terminal cost (i.e., (varphi v_{2} tau_{1})) equiv0), given by Proposition 1) has the property that, among all admissible controls, it leads to the smallest possible value for the terminal state (v_{2}({tau_{1}})).