Sentence examples for constructive existence from inspiring English sources

Martin-Löf (1982) advocated the use of constructive mathematics as a means of deriving programs from (constructive) existence proofs.

This technique coupled with the method of upper and lower solutions [26] manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by the lower and upper solutions.

The aim of the present work is to provide some constructive existence and uniqueness theorems for problem (1.1 - 1.2 1.1 - 1.2ame type as thofe provided by Ford and Pennline in [26] by the same assumptypes considered by them, i.e., (f (x,y(x) )) is not only aslowed those sign-changing but it also can be singular with resprovidedy.

The method of upper and lower solutions coupled with its associated monotone iteration scheme is an interesting and powerful mechanism that offers the theoretical as well constructive existence results for nonlinear problem in a closed set, generated by the lower and upper solutions (see [9 26]).

The monotone iterative technique coupled with the method of upper and lower solutions [3] manifests itself as an effective and flexible mechanism that offers theoretical as well as constructive existence results in a closed set, generated by the lower and upper solutions.

It is important to indicate that this method combined with the method of upper and lower solutions is an interesting and powerful mechanism that offers the theoretical as well as constructive existence results for nonlinear problems in a closed set, generated by the lower and upper solutions.

Dora who objected to non-constructive existence proofs could not plausibly be interpreted as just expressing a preference for constructive methods: she found the notion of non-constructive existence unintelligible not just unappealing.

It is an example of a "non-constructive" existence proof: demonstrating that one or another alternative must hold without providing a means for ascertaining which one does hold.

We formulate the problem as a combinatorial design problem on cyclic superimposed codes and give a constructive proof of existence along with a delay bound.

As a first step, we present a constructive proof of the existence and uniqueness of solution.

First, we give a short summary to the constructive approach on the existence theory for the VI.