Related papers: A simple case within Nash-Moser-Ekeland theory

In this report we describe a simple proof of Parikh's theorem a la Takahashi, based on a decomposition of derivation trees. The idea of decomposition is appeared in her master's thesis written in 1970.

We prove Sklar's theorem in infinite dimensions via a topological argument and the notion of inverse systems.

We prove an abstract Nash-Moser implicit function theorem which, when applied to control and Cauchy problems for PDEs in Sobolev class, is sharp in terms of the loss of regularity of the solution of the problem with respect to the data. The…

We prove a generalizations of the Elekes-Szab\'o theorem for relations definable in strongly minimal structures that are interpretable in distal structures.

How was this proof overlooked for 181 years? We give a simple proof of Descartes's circle theorem using Cayley-Menger determinants.

We propose a simple proof of the vertical half-space theorem for Heisenberg space.

We prove a uniformization theorem in complex algebraic geometry.

We obtain simple proofs of certain inequalites for bivariate means.

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

A proof of the Ending Laminations Theorem is given, using Teichmuller geodesics directly.

We settle in the affirmative the Graham-Sloane conjecture.

We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.

We introduce an elementary argument to the theory of distribution of sequences modulo one.

We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

We present a simpler way than usual to deduce the completeness theorem for the second-oder classical logic from the first-order one. We also extend our method to the case of second-order intuitionistic logic.

We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.

We prove the existence of a local smooth Levi decomposition for smooth Poisson structures and Lie algebroids near a singular point. In the appendix of this paper, we show an abstract Nash-Moser normal form theorem, which generalizes our…

I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.

Instantaneous derivation of the Thomas precession with only basic vector calculus.