Sentence examples for proof can be extended from inspiring English sources

The proof can be extended, however, to the full elementary logic in a fairly direct manner.

Alternatively, the proof can be extended for channel matrix of any rank L. As an example, if A is a diagonalizable matrix of size N × N with rank L.

The proof can be extended to the case where by observing the fact that the maximum of the inner problem is independent of the BS which is selected by user in step (3) (however, it clearly matters for complying with the feasible rate region constraints); from (26) it follows that (34). is necessary and sufficient for the maximization of the inner problem and that by (21) holds.

We expect that the proof can be extended for a second moment that does not converge in the scale given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f$$\end{document} f, but is bounded.

The array receives one signal from a known direction and one interferer (this proof can be extended similarly).

The proofs can be extended to handle any smoothly bounded domain in C in place of the unit disk.

Presenting the basic system at a high level of generality and non-determinism allows transparent correctness proofs that can be extended in a modular fashion when new features are introduced in the system.

This proof-of-concept can be extended in order to design more complex patterns through the intelligent design of the counter electrodes.

Since PA signal intensity is proportional to the concentration and absorption coefficient of nanoparticles [ 19], this proof-of-concept method can be extended to detect and monitor other types of nanoparticles (such as carbon nanotubes, gold nanorods and organic dyes) in vivo.

The proof of the Lawson conjecture can be extended to give a classification of all Alexandrov immersed minimal tori in (S^3): (Brendle [10]) Let (F: Sigma rightarrow S^3) be an immersed minimal surface in (S^3) of genus (1).

However, we also provide proof of principle that this approach can be extended to other experimental models and modes of administration.