Sentence examples for and the functions are from inspiring English sources

The other derivatives (and the functions) are obtained through integrations.

The conditions for Clarke's generalized gradient and the functions are the same as in (j1)–(j1).

Let be a compact metric space, selfmaps of set-valued functions with and Suppose that the pairs, are weakly compatible and the functions, are continuous.

In case that is a compact metric space and the functions are contractions, using some fixed point theorems for contractions from to, we prove the existence of the attractor of such a GIFS and its continuous dependence in the 's.

where (i) the functions are continuous and ;   (ii) the functions, are measurable, for all and (5.5)  . the functions are continuous and ; the functions, are measurable, for all and (5.5).

Based on the above result, the geometry and kinematics of workpiece in this method is described, and the functions are proved valid by an experiment in which the rolling speed of roller is observed in video.

And some of the functions are pretty esoteric.

(H3) The functions are continuous and.

We prove that the complete elementary symmetric function and the function are Schur-convex functions in, where are nonnegative integers,,.

where the operator and the function are defined by the equalities (2.6).

Interviews with customers and others suggest that the functions were available, although some in more rudimentary form than others.