Sentence examples for assuring the existence from inspiring English sources

Numerous works on best proximity point theory were studied by giving sufficient conditions assuring the existence and the uniqueness of such points.

Once the ordinal number-classes are present, the representation of the alephs is not a severe problem, which means that the representation of transfinite numbers amounts to assuring the existence of sufficiently many transfinite ordinal numbers.

A sequence of standard LMI conditions assuring the existence of homogeneous polynomially parameter-dependent (HPPD) solutions to the parameter-dependent LMIs for filter design is provided in terms of the vertices of the polytope (no gridding is required), yielding parameter-dependent filters of arbitrary degree assuring quadratic stability of the error dynamics for the H2 or the H∞ cases.

Anderson ([1972]) assures the existence of a solution for r≤N/2.

In this case, the main point is to assure the existence of nontrivial solutions.

Furthermore, condition (3.28) assures the existence of a matrix function such that condition (3.18) is fulfilled.

We note that Proposition 2.2 ii) assures the existence and uniqueness of.

Energy dispersive X-ray spectroscopy (EDX) assured the existence of both iron and gold elements in the prepared nanoparticles.

Here, we assume (theta _{H} - frac {eta }{1 + eta }PDelta theta > 0) to assure the existence of an interior solution.

But, best proximity point theorems provide sufficient conditions that assure the existence of approximate solutions which are optimal as well.

The goal of best proximity point theory is to furnish sufficient conditions that assure the existence of such points.