Related papers: A short proof of the irreflexivity conjecture
We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.
The Kervaire conjecture asserts that adding a generator and then a relator to a nontrivial group always results in a nontrivial group. We introduce new methods from stable commutator length to study this type of problems about nontriviality…
Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.
Although scalar curvature is the simplest curvature invariant, our understanding of scalar curvature has not matured to the same level as Ricci or sectional curvature. Despite this fact, many rigidity phenomenon have been established which…
In this paper, we present a new argument (see Lemma 3.4) that allows us to simplify the proof of stability of peakons established in Lin and Liu (2009) (Theorem 1.1).
We give a simple new proof for the straightening law of Doubilet, Rota, and Stein using a generalization of the Laplace expansion of a determinant.
All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…
In their recent paper [Phys. Rev. Lett. 98, 094101 (2007)], A. Porporato et al. studied the irreversibility and fluctuation theorem for stationary time series. In this comment, we point out that the fluctuation theorem is in fact the…
In this note, we give short inductive proofs of two known results on $k$-extendible graphs based on a property proved in [Qinglin Yu, A note on $n$-extendable graphs. Journal of Graph Theory, 16:349-353, 1992].
A weak version of Birkhoff's generalization of the Perron-Frobenius theorem states that every endomorphism of a finite-dimensional real vector that leaves invariant a non-degenerate closed convex cone has an eigenvector in that cone. Here,…
We give an undergraduate short and simple proof for Zariski's lemma.
The purpose of this short note is to provide a new and very short proof of a result by Sudakov, offering an important improvement of the classical result by Kolmogorov-Riesz on compact subsets of Lebesgue spaces.
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
This paper has been withdrawn by the author due to an error in the main proof (thanks to Carlos D'Andrea)
A selection of basic results on Borel reducibility of ideals and equivalence relations, especially those with comparably short proofs. This is an unfinished text as yet. Some proofs have missing parts and loose ends. [email protected] and…
We settle in the affirmative the Graham-Sloane conjecture.
Relativistic length contraction is revisited and a simple but new thought experiment is proposed in which an apparent asymmetric situation is developed between two different inertial frames regarding detection of light that comes from a…
A one-line proof of a minimax theorem due to Steinerberger is given.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
An technically interesting proof of a known theorem.