Sentence examples for be extended to functions from inspiring English sources

The above results can be extended to functions on ({mathbb R}).

(3.2) The projection (P_{h}) can be extended to functions of x, y and t in an (L^{2}) sense.

We assume that the boundary values and for Problem 1 can be extended to functions defined on such that.

These generalized trigonometric functions may be extended to functions on the whole real line with period 2π.

Note that (A_{h}) can also be extended to functions in (L^{2}(0,T;L^{2}(Omega))) in the (L^{2}) sense.

In this section, we shall prove that the notion of q-convolution product can be extended to functions in L q p ( R q, +, x d q x ) space.

(P) We have (lim_{nto+infty}|F_{R^{ntau}theta _{1}^{(f)} vartheta_{1},cdot)}-F_{R^{alpha}f}|=0) where the uniform norm (|cdot|) is extended to functions on (mathbb {T}).

We have (lim_{nto+infty}|F_{R^{ntau}theta _{1}^{(f)} vartheta_{1},cdot)}-F_{R^{alpha}f}|=0) where the uniform norm (|cdot|) is extended to functions on (mathbb {T}).

Recently, it has been extended to functions mapping from the family of nonempty subsets of Y to (mathbb{R}), and whether the extended Gerstewitz functions can characterize the generalized convex set-valued mappings is also an interesting question; for more details related to the extended Gerstewitz functions, we refer to [19 22].

Third, federal officials will generally have a "qualified immunity" from such suits; absolute immunity will be extended to certain functions only on the basis of a showing that exposure to liability is inconsistent with the proper performance of the official's duties and responsibilities.

The following result shows that the polynomial coefficients in Theorem A can be extended to rational functions.