Sentence examples for new proof for from inspiring English sources

We give a new proof for the existence of a Ck-center manifold at a nonhyperbolic equilibrium point of a finite-dimensional vector field of class Ck.

As a by-product, we obtain a new proof for the existence of multi-window Gabor frames and extend the structure theory of Gabor frames.

We also give a new proof for the corresponding theorem in the curve case and treat the reparametrization problem for curves and ruled surfaces.

On the collaborative blog MathOverflow, mathematicians earn reputation points for contributing to solutions; in another math experiment dubbed the Polymath Project, mathematicians commenting on the Fields medalist Timothy Gower's blog in 2009 found a new proof for a particularly complicated theorem in just six weeks.

As a first application, we get a new proof for the fact (due to Hirai et al., 2001) that the map f C∞c(Rn)×C∞c(Rn)→C∞c(Rn), ↦γ⁎η taking a pair of test functions to their convolution is continuous.

In this paper we show that all affine buildings of type ˜A2, ˜B2 and ˜G2 have Property A. Together with results of Guentner, Higson and Weinberger, this completes a programme to show that all affine building have Property A. In passing we use our technique to obtain a new proof for groups acting on ˜An buildings.

We thus get new proofs for the classical ℓ2 rigidity theorems of Keswani obtained in [41].

In finding fast parallel algorithms, we also obtain new proofs for the theorems.

This provides new examples of hyper-reflexive algebras and new proofs for the hyper-reflexivity of the noncommutative disk algebras.

Using tools from the theory of C∗-algebras of groupoids, we also obtain new proofs for the study of b-calculus.

Recent work includes new proofs for the pigeonhole principle, Frankl's theorem, the AB=I theorem, and the Kneser-Lovasz theorem on chromatic numbers.