Related papers: A simple case within Nash-Moser-Ekeland theory
We prove a variation of Gronwall's lemma.
I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.
A very short proof of G\"odel's second incompleteness theorem (for set theory, second order arithmetic etc.)
In this note we give a short, direct proof of the well known Combinatorial Nullstellensatz.
In this note we give a detailed proof of a theorem of Aubin.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
A simple proof for the Shannon coding theorem, using only the Markov inequality, is presented. The technique is useful for didactic purposes, since it does not require many preliminaries and the information density and mutual information…
This is an elementary geometrical proof of Birkhoff theorem. It is hardly important, but the pictures behind are quite nice.
The paper presents a counterexample to the Hodge conjecture.
We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…
Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
We study the well-posedness of the initial value problem for a wide class of singular evolution equations. We prove a general well-posedness theorem under three assumptions easy to check: the first controls the singular part of the…
We give a new elementary proof of existence and uniqueness of a solution to the Sylvester equation $AX-XB=Y$
A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.
We report a simple rigidity theorem for certain Euler products.