Sentence examples for proof different from inspiring English sources

They could present a short and a simple proof (different of the "direct method ", initiated by Hyers in 1941) for the Hyers-Ulam stability of Jensen functional equation [13] and for quadratic functional equation [14].

In 2003, Cǎdariu and Radu applied the fixed point method and they could present a short and simple proof (different from the "direct method", initiated by Hyers in 1941) for the generalized Hyers-Ulam stability of Jensen functional equation.

They presented a short and a simple proof (different from the 'direct method,' initiated by Hyers in 1941) for the Cauchy functional equation [10] and for the quadratic functional equation [9].

They could present a short and simple proof (different from the direct method initiated by Hyers in 1941) for the generalized Hyers-Ulam stability of the Jensen functional and the quadratic functional equations.

In this note we will prove that (psi^=psi_{1}^) with (psi_{1}^(t)=sqrt{t}) is a refinement of the reverse Finsler-Hadwiger inequality, and we will also provide an alternative proof (different from the one given in [16]) of the lower bound with (psi_{1}^).

These findings constitute clear proof that different genomic regions present different genealogies.

A statement added: "The application of differing standards of proof for different individuals and organizations results in an arbitrary and confusing set of standards that seems demonstrably biased against the Middle East".

It said that Forbes had applied "differing standards of proof for different individuals".

Different proof assistants offer different capabilities measured by their power at automating reasoning tasks, supported logic, object typing, size of mathematical library, and readability of input and output.

Our proofs are different from the proofs given by Elcrat [1].

Finally, the burden of proof is different".