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

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.

We present a short and self-contained proof of the choosability version of Brooks' theorem.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

We prove several extensions of the Erdos-Fuchs theorem.

We prove a local version of the Mazur-Ulam theorem.

We give a direct proof of the Ohsawa-Takegoshi by solving directly the d-bar equation.

In this paper, we give a simple counter example to the famous Hodge conjecture.

We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

We expose here a short proof of Cramer's theorem in R based on convex duality.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

We give a new proof of Lucas' Theorem in elementary number theory.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.