Sentence examples for suppose the functions from inspiring English sources

Now the following main result of the article is immediate from Lemmas 9 and 7. Theorem Suppose the functions f u, x) and w(x) satisfy the conditions F1, F2, F3, F4, and W1, W2.

We always study periodic or almost periodic problems assuming that the time scale (mathbb{T}) is periodic, that is, we always suppose the functions that describe the status of the object are periodic or almost periodic on periodic time scales (i.e., the status of the object is the same or almost the same after an accurately chosen interval; see [14] and its references).

Remark 3.1 Suppose the functions f 1 ( x ) and f 2 ( x ) are the solutions of the problem (1.1) with the exact data g 1 ( x ) and g 2 ( x ), respectively, then we have the estimate ∥ f 1 − f 2 ∥ ≤ e e − 1 ∥ g 1 − g 2 ∥ + E 2 p + 2 ( e e − 1 ) p p + 2 ∥ g 1 − g 2 ∥ p p + 2. (3.3).

We didn't suppose the function of the Printing Office was to tell us when to buy a book.

Suppose the function is concave,, and.

Suppose the function ϕ : I → R is C ( 2 ), i.e., twice continuously differentiable.

Lemma 1. Suppose the function f is defined by f ( x, y, z ) = x + y + z x y + y z + 1, (2.1).

That is, using the traditional names for the spectral bands, one might suppose the function maps red to violet, orange to indigo, yellow to blue, green to green, blue to yellow, indigo to orange, and violet to red.

In the sequel, suppose the modular function ρ is convex and satisfies the (Delta_{2} -type conDelta_{2} -type

Suppose the production function is Cobb-Douglas, with Q = Kα L1 − α.

Suppose, the Green's function defined by (3.14) satisfies that.