Sentence examples for straightforward proof that from inspiring English sources

The present paper is concerned with expounding an altogether new method specifically designed to provide a straightforward proof that there is no possible solution for some family of systems of Diophantine linear equations which share the same dependent terms while differing in its independent terms.

We omit the straightforward proofs that the MWVR and MWER problems are in NP.

Long's natural-law theology, which often decried "the gay agenda," was relatively straightforward: penises are proof that God has created men to have sex with women, and vaginas are evidence that God wants women to have sex with men.

In this work, a straightforward proof is presented to demonstrate that, for an isotropic hyperelastic solid, the just-mentioned stress strain pair τ and h are derivable from two dual scalar potentials with respect to each other.

Furthermore, we give some bounds on total restrained domination number of graphs with diameter 3. Finally, we present some bounds for total restrained domination number of some planar graphs with diameter 2 and γ-set of cardinality 2. We begin with the following result that has a straightforward proof.

The proof that this common fixed point of, and is unique is straightforward.

The straightforward proof of this result is omitted.

Finally Dedekind indicates how, along such lines, explicit and straightforward proofs of various facts about the real numbers can be given, including ones that had been accepted without satisfactory proof so far.

Proof A straightforward calculation shows that the mapping U is ρ-nonexpansive.

The proof consists from a straightforward verification that the conditions (Equation 52) are satisfied for [ K ] D = { [ K ] G AB E } Open image in new window and g AB = g a ' b ', h ab Open image in new window.

Then (as proved in [3]), Theorem 1.1 holds (once again, the LS condition amounts to proper ellipticity plus complementing condition and proper ellipticity is equivalent to ellipticity if and ) and it is straightforward to check that the proof of Theorem 1.2 carries over to this case if If so, Corollary 2.1 is also valid, with a similar proof and an obvious modification of the function spaces.