Related papers: A simple case within Nash-Moser-Ekeland theory
We prove that, for simple modules $M$ and $N$ over a quantum affine algebra, their tensor product $M \otimes N$ has a simple head and a simple socle if $M \otimes M$ is simple. A similar result is proved for the convolution product of…
Here we give a short survey of our new results. References to the complete proofs can be found in the text of this article and in the litterature.
A theorem of Mirsky provides necessary and sufficient conditions for the existence of an N-square complex matrix with prescribed diagonal entries and prescribed eigenvalues. We give a simple inductive proof of this theorem.
We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…
We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.
In this paper, we prove a conjecture of Schnell in the surface case.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
An complete exposition of Matthias Gunther's elementary proof of Nash's isometric embedding theorem.
This paper presents a simple proof of Dekel (1986)'s representation theorem for betweenness preferences. The proof is based on the separation theorem.
We formulate and prove a version of the celebrated Coifman-Rochberg-Weiss commutator theorem for the real method of interpolation
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
This paper provides a new simple proof of Hesse's theorem in projective geometry for any dimension.
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We consider the classical Inverse Function Theorem of Nash and Moser from the angle of some recent development by Ekeland and the authors. Geometrisation of tame estimates coupled with certain ideas coming from Variational Analysis when…
We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.
A very simple and short proof of the polynomial matrix spectral factorization theorem (on the unit circle as well as on the real line) is presented, which relies on elementary complex analysis and linear algebra.
We give a simple proof of the Birkhoff theorem about existence of a faithful representation for any finite-dimensional nilpotent Lie algebra of characteristic zero.
This short note present a "proof" of $P\neq NP$. The "proof" with double quotation marks is to indicate that we do not know whether the proof is correct or not (We're confused because we do know in which we make the mistakes).
We prove a Noether-Deuring theorem for the derived category of bounded complexes of modules over a Noetherian algebra.
This is just a short proof of Kruskal's theorem regarding uniqueness of expressions for tensors, phrased in geometric language.