Related papers: A more reasonable proof of Cobham's theorem
We give an alternative proof of Kov\'acs' vanishing theorem. Our proof is based on the standard arguments of the minimal model theory. We do not need the notion of Du Bois pairs. We reduce Kov\'acs' vanishing theorem to the well-known…
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
This note contains a complete proof of the Abhyankar-Moh-Suzuki theorem (in characteristic zero case).
By any account, the 1998 proof of the Kepler conjecture is complex. The thesis underlying this article is that the proof is complex because it is highly under-automated. Throughout that proof, manual procedures are used where automated ones…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
We give a short proof of the most general version of the Nullstellensatz without using the Axiom of Choice.
In this note, we give a simple, counting based proof of Fisher's Inequality that does not use any tools from linear algebra.
We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…
Lov\'asz gave a short proof of Brooks' theorem by coloring greedily in a good order. We give a different short proof by reducing to the cubic case. Then we show how to extend the result to (online) list coloring via the Kernel Lemma.
The goal of this article is to prove the comparison theorem between algebraic and topological nearby cycles of a morphism without slopes. We prove in particular that for a family of holomorphic functions without slopes, if we iterate…
This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.
The basic adiabatic theorems of classical and quantum mechanics are over-viewed and an adiabatic theorem in quantum mechanics without a gap condition is described.
We present here a simple proof of Brown's diagonalizability theorem for certain elements of the algebra of a left regular band, including probability measures.
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
We give a new proof of Quillen's conjecture for solvable groups via a geometric and explicit method. For p-solvable groups, we provide both a new proof using the Classification of Finite Simple Groups and an asymptotic version without…
We present a simple proof of monotonicity for cooperative systems of linear ordinary differential equations, without having recourse to approximation by strongly cooperative systems.
It is shown that the restrictions of what can be inferred from classically-recorded observational outcomes that are imposed by the no-cloning theorem, the Kochen-Specker theorem and Bell's theorem also follow from restrictions on inferences…
We describe how the use of a different degeneration from that considered by Eisenbud and Harris leads to a simple and characteristic-independent proof of the Brill-Noether theorem using limit linear series. As suggested by the degeneration,…
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.