Related papers: A simple case within Nash-Moser-Ekeland theory
We prove a version of Hrushovski's socle lemma for rigid groups in an arbitrary simple theory.
We present a simple inductive proof of the Lagrange Inversion Formula.
We give a simple proof of the existence of a minimizer for the Sobolev inequality. Our proof is based on a representation formula via a cut-off fundamental solution.
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
We present a new, elementary, dynamical proof of the prime number theorem.
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
We point out a general argument leading from the formula for currents through an open mesoscopic system given by the theory of non-equilibrium steady states (NESS) to the Landauer-B\"uttiker formula.
This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
In this note we prove convexity, in the sense of Colding-Naber, of the regular set of solutions to some complex Monge-Ampere equations with conical singularities along simple normal crossing divisors. In particular, any two points in the…
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
Here, we give a self-contained and elementary proof of a minimax theorem due to Fan in a simplified setting that can be taught in an advanced undergraduate course. Our proof follows Nikaido's argument with some simplifications.
We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
We prove an inverse function theorem of Nash-Moser type for maps between Fr\'echet spaces satisfying tame estimates. In contrast to earlier proofs, we do not use the Newton method, that is, we do not use quadratic convergence to overcome…