Sentence examples for are proven for from inspiring English sources

Lp to Lpβ boundedness results are proven for translation invariant averaging operators over hypersurfaces in Euclidean space.

Necessary and sufficient conditions are proven for the existence of nodal approximations to the first derivative with the SBP property.

Some mathematical properties of the language are proven, for instance, that the proposed semantics is equivalent to that given earlier for the portion of the language without concurrency.

Different implementation techniques are discussed, theories analogous to scalar cases are proven for linear systems, and numerical results are given illustrating the method on nonlinear systems.

Existence and convergence from this mathematical model are proven for a finite element discrete numerical solution in the framework of a fractal geometry theory.

In the end the controlling effect of the retrofitting system and the applicability of the optimal parameters analytical expressions are proven for a wide range of circulating velocities.

Conditional stability and error estimates are proved for the scheme.

Analogous results are proved for the stochastic Burgers equation.

Various separation theorems are proved for the chain event graph.

Numerical stability and error estimate are proved for both schemes.

So I'm sort of fortunate that these formulas are proved for any function including this function.