Sentence examples for proved in the third from inspiring English sources

Our main results regarding boundedness of Hausdorff operators on weighted central Morrey spaces are stated and proved in the third section.

The existence and uniqueness theorem of the solution with regard to weaker conditions such as the local Lipschitz and Linear growth conditions is proved in the third section, and finally in the last and the most important section, the stability of FFDEs in weaker conditions is elaborated.

On that wicket, as we proved in the second innings, runs were there to be had.

These are tropes about "the other" whose capacity to galvanize mobs, and wreak havoc, was proved in the first half of the 20th century.

In the first part of the argument, the existence of a necessary being is proved; in the second part of the argument, the essence of that necessary being is identified with what men call God.

One of the desirable mathematical features of this method (the stereographic projection) is that it converts circles into circles or straight lines, a property proved in the first pages of Apollonius's Conics.

These figures illustrate the result proved in the first example.

The above theory was proved in the ninth chapter of the book by Neapolitan and Naimipour.

As proved in the first part, we conclude that S and T are orbitally continuous.

Many had predicted a final where attritional forward play would hold sway over creativity and flair, and so it proved in the first half.

The first subsection is devoted to the statement of the main results which is going to be proved in the second subsection.