Sentence examples for required higher order from inspiring English sources

In the Knudsen limit on the other hand the details of the local microstructure became important and so an accurate prediction/correlation of the effective diffusivity required higher order information.

We assume that the functions (f x,t,u,u_{x},u_{t})), (phi(x)), (psi(x)), (a_{0}(t)) and (a_{1}(t)) are sufficiently smooth and their required higher order derivatives exist.

(1.3) We assume that the functions (A x, t, u)) and (u x, t)) are sufficiently smooth, the required higher order partial derivatives of (A x, t, u)) and (u x, t)) exist in the solution domain (Omegaequiv { (x, t)|0 < x < 1, t > 0 }), and the conditions (1.2) and (1.3) are given with sufficient smoothness to maintain the order of accuracy in the numerical method under consideration.

But the 60-somethings showed a clear, age-related advantage in solving the Martian problem, which required higher order, holistic learning about the changing relationships between choices and rewards.

This facilitates the transmission of a byte across the SDI pin since the STA013 requires higher order bytes first.

A new simplified version of this detection method is then presented, which does not require higher order statistical information.

Because of its masconian character, the gravity field of the Moon requires higher order truncations to give a realistic description of the long-term behavior of low-lunar orbits.

The present findings may be accounted by simple association mechanisms, not requiring higher order processes involving empathy.

However, some students had difficulty in answering questions that required higher-order thinking skills.

Higher-order thought (HOT) theories take the required higher-order state to be an assertoric thought-like meta-state (Rosenthal 1986 , 1993.

The initial and boundary conditions are given by begin{aligned} &u x,0) = u_{0}(x),quad 0 le x le 1, end{aligned} (1.2) begin{aligned} &u 0,t) = g_{0}(t),qquad u(1,t) = g_{1}(t),quad t > 0, end{aligned} (1.3) where we assume that the functions f, (u_{0}(x)), (g_{0}(t)) and (g_{1}(t)) are sufficiently smooth and their required higher-order derivatives exist.