Sentence examples for principles and proved from inspiring English sources

He has gone back to basic principles and proved that Shakespeare works best with an ensemble.

Branciari [2] gave an integral version of the Banach contraction principles and proved fixed point theorem for a single-valued contractive mapping of integral type in metric space.

Tom Miller Oakland, Calif., April 23 , 2009• To the Editor: "My Tortured Decision," by Ali Soufan (Op-Ed, April 23), sheds welcome light and credibility on one more instance where the previous administration ignored fundamental American principles and proven bodies of knowledge to justify imprudent actions detrimental to our country's best interests (going to war with Iraq being another instance).

However, Kalichman et al. [ 19] have noted that HIV prevention programs that are based on social cognitive principles and proven to be effective in the scientific literature have not been widely utilized because of their reliance on expert interventionists for implementation in face-to-face formats, making them difficult to transfer to community-based organizations [ 19].

He established a nice integral version of the Banach contraction principle and proved the following fixed point theorem.

It is well known that the contraction mapping principle, formulated and proved in the Ph.D. dissertation of Banach in 1920, which was published in 1922 [1], is one of the most important theorems in classical functional analysis.

In Section 2, we recall the maximum principle and prove the main stability result.

This paper solves such problems for discrete fuzzy variables via maximum entropy principle and proves some maximum entropy theorems with certain constraints.

Meanwhile, LTR principles are analyzed and proved theoretically by adopting the matrix inversion lemma.

At a technical level, the paper presents an expressive concurrent programming language with recursive functions for modeling interfaces and a logic of programs in which compositional reasoning principles are formalized and proved sound with respect to trace semantics.

The weak comparison principle is stated and proved in the Appendix.