Sentence examples for a proof based on from inspiring English sources

Thomson himself never gave a proof for the formula; but a proof based on Differential Geometry was suggested by Jackson [Classical Electrodynamics, Wiley, New York, NY, 1962, p. 51] and later published by Pappas [Differential geometric solution of a problem in electrostatics, SIAM Rev. 28 (1986) 225].

Here we give a proof based on the ideas developed in [25].

Despite its fundamental importance, it is probably true that Peano's proof of his theorem is even more important than the result itself, which nowadays we know can be deduced quickly from standard fixed point theorems (see [1, Theorem ] for a proof based on the Schauder's theorem).

Remark 2 A proof based on similar arguments to those in the previous theorem allows us to represent p-convex Banach lattices (with p-convexity constant equal to 1) having the σ-Fatou property and such that E a is super order dense in E. In this case, E is order isometric to [ L p ] σ -F for some vector measure ν defined on a δ-ring.

We used a constructive proof based on a min-cut strategy, which has been largely considered in the context of supertrees [ 25- 27].

We give some sufficient conditions for the existence of a unique bounded solution to the difference equation and present an elegant proof based on a combination of theory of linear difference equations and the Banach fixed point theorem.

We prove the existence of a weak solution to this class of problems by designing a constructive proof based on the time discretization via operator splitting.

Only a mathematical proof, based on logic, can handle questions of the infinite.

We give a short proof based on properties of the row sum vectors of submatrices in an incidence matrix.

A unified representation of HAC limit theory for untruncated kernels is provided using a new proof based on Mercer's theorem that allows for kernels which may or may not be differentiable at the origin.

We also present a short proof, based on Pierrot's argument, of the core issue in both of the two papers namely a result on the separation of a point from a closed submodule.