Sentence examples for proving upper from inspiring English sources

We begin with three lemmas for proving upper and lower bounds of the characterization.

For differential inclusions this is sufficient for proving upper semicontinuity of the solution mapping and then to find an optimal control (cf. [49] or [[16], Chapter 6], for instance).

We also prove upper bound estimates for the spectral gap λ2−λ1 in bounded convex domains.

For a very general class of unbounded self-adjoint operator functions we prove upper bounds for eigenvalues which lie within arbitrary gaps of the essential spectrum.

We suppose that the magnetic field vanishes regularly on a hypersurface S. First, we prove upper and lower estimates for the bottom λ0(Hh) of the spectrum of the operator Hh in L2(M).

We investigate the radiative corrections to the binding energy and prove upper and lower bounds which imply that Ebin= me4Z2/8π2+c0e6+O e7lne) with explicit coefficient c0 and independent of the ultraviolet cutoff.

Most recently, Bednarczuk [12] defined weak sharp minima of order for vector-valued mappings under an assumption that the order cone is closed, convex, and pointed and used the concept to prove upper Hölderness and Hölder calmness of the solution set-valued mappings for a parametric vector optimization problem.

– Histologically/cytologically proven upper GI adenocarcinoma.

Consequently, the development of objectively proven upper limb venous thrombosis usually necessitates CVC removal.

We will later use this information to prove upper bounds on the number of edges in our hypergraphs.

For proving the upper order-preservation of Λ, take any ((omega _{1},theta_{1}), (omega_{2},theta_{2})inOmegatimesTheta) with ((omega_{1},theta_{1})succcurlyeq_{OmegatimesTheta} (omega _{2},thetand2})), and pick any (x omega_{2},theta_{2})inLambda (omega_{2},theta_{2})).