Sentence examples for upper equation from inspiring English sources

Now, from condition (1.3), the right hand of the upper equation is just, so ; Lemma 1.1 is proved.

This assumption simplifies upper equation for each steady-state element as follow: G 0 × ∂ n ∂ L n u = ∑ n o · Q o V - ∑ n i · Q i V. (35).

The labour supply and rationing equations (upper pane) and programme participation equations (lower pane) are estimated simultaneously.

Since minimization of τ is the same as finding the least upper bound of Equation 25, the first equivalence relationship holds.

Thus, we further consider the Taylor expansion of this term at 0 and get (11) To achieve further convenience in the local search, we minimize an upper bound of Equation (10), where we replace the exponential term using Equation (11) and also substitute the total curve length (which is larger than 1) with the sum of squared piece-wise distances of control points.

The next result is about upper solutions to equation (6).

This implies that (U_{t}) is the upper solution of equation (3.17).

and the function w is an upper solution of equation (1) if the reversed inequalities hold.

s o and s e are the new lower and upper limits of Equation 15.

Thus, we know that the coupled lower and upper solutions for equation (15) are also natural lower and upper solutions.

Let v, w∈C 1[J, R] be the lower and upper solutions of equation (1) such that v( t)≤ w( t) on J and F∈ C[ Ω, R].