Sentence examples for began by proving from inspiring English sources

7 began by proving himself to the Abwehr with a report on Pierre Laval? 8 nearly blew it when he mistakenly confused Glass and Sand? 9 was known as Leonhard by his German paymasters? 10 later dug up artefacts in Corsica? 1 What does the Bard credit with subtlety? 2 Where does Kitchener have an Elephantine companion?

It began by proving that cartoon characters don't have to be caricatures; they can be invested with real emotions.

We begin by proving a lower bound showing that adapting to both the size of the gradients and distance to optimal model simultaneously is fundamentally much harder than adapting to either individually, and proceed to develop the first algorithm to meet this lower bound, obtaining optimal adaptivity to both parameters at once.

Hamilton's first published mathematical paper, "Theory of Systems of Rays," begins by proving that a system of light rays filling a region of space can be focused down to a single point by a suitably curved mirror if and only if those light rays are orthogonal to some series of surfaces.

We begin by proving that (2.12).

We begin by proving the following result.

We first begin by proving the following useful results.

We begin by proving the following technical proposition.

We begin by proving the inequality when (Omega ) is a convex polytope.

We begin by proving that ((x_{n})_{ninmathbb{N}}) is bounded.

We begin by proving a local existence result for a fractional Caputo nonlocal thermistor problem.