Related papers: A simple case within Nash-Moser-Ekeland theory
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
I present a simple derivation of the de Gennes narrowing phenomenon.
We prove the Aharoni Berger Conjecture
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We proove a Bloch's theorem in an almost complex projective plane.
We present a streamlined and simplified proof of the Kakeya set conjecture in $\mathbb{R}^3$.
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
We provide a short proof of the 1-dimensional flat chain conjecture.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We prove a second main theorem for elliptic projective planes.
We present a short proof of Reisner's Theorem, characterizing which simplicial complexes have a Cohen-Macaulay face ring. In some cases, we can also express some homological invariants of the face ring in terms of the reduced homology of…
In this paper we present a short and elementary proof for the error in Simpson's rule.
Recently we have obtained two simple proofs of Sharkovsky's theorem, one with directed graphs [7] and the other without [8]. In this note, we present yet more simple proofs of Sharkovsky's theorem.
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
We prove De Giorgi-Nash-Moser Theory using a geometric approach.
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
A simple proof of Egorov's theorem for infinite measure is given