Sentence examples for a complete proof of from inspiring English sources

By the end of the following week, the title of Zhu and Cao's paper on the A.J.M.'s Web site had changed, to "A Complete Proof of the Poincaré and Geometrization Conjectures: Application of the Hamilton-Perelman Theory of the Ricci Flow".

A complete proof of this behavior appears in [2].

This includes Iohvidov's theorem, a complete proof of which we could not find in print.

We also give a complete proof of the correctness of this construction making use of the crucial "property A".

Via the method of convex geometric analysis, a complete proof of inequality (26) with equality condition is given in [9].

For the implicit operator we develop boundary conditions and give a complete proof of strong stability using the Laplace transform technique.

Now, we will provide a complete proof for some of results obtained in this and the following sections so that the reader may be familiar with the ways the proofs are constructed and written.

In [29], Azaïs and Wschebor gave a mathematically complete statement of a Kac Rice-type formula, and recently Azaïs, Wschebor and León used it (following Berry and Dennis) to give a mathematically complete proof of the above theorem, though they wrote down the details only in case z is monochromatic [37].

We adopt the notion of process refinement to formalise the substitutivity of components, and provide a complete proof method based on the notion of simulations.

We will give the complete proof of the second part.

This paper contains a solution with complete proofs of the main problems of the inverse scattering at fixed energy E for the Schrödinger two-dimensional operator with decreasing coefficients (uniqueness of the reconstruction, a reconstruction procedure, characterization of the scattering data).