Related papers: Simple Proofs of two Dirac-type Theorems Involving…
Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.
The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…
We provide a simple proof of Kamp's theorem.
We introduce the notion of doubling and r-tupling for simplicial complexes, a notion reminiscent to that of matching complexes in graph theory. We prove a connectivity result for such complexes and relate r-tupling to stabilizing r times…
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
We prove Barth-type connectedness results for low-codimension smooth subvarieties with good numerical properties inside certain "easy" ambient spaces (such as homogeneous varieties, or spherical varieties). The argument employs some basics…
Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided
We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for Differential Linear Logic…
In the first part of the paper we give a tensor version of the Dirac equation. In the second part we formulate and analyse a simple model equation which for weak external fields appears to have properties similar to those of the…
We give a shorter and simpler proof of the result of [2], which gives a necessary and sufficient condition for when a lattice diagram is the projection of a lattice link.
This paper presents simple, syntactic strong normalization proofs for the simply-typed lambda-calculus and the polymorphic lambda-calculus (system F) with the full set of logical connectives, and all the permutative reductions. The…
Beben and Theriault proved a theorem on the homotopy fiber of an extension of a map with respect to a cone attachment, which has produced several applications. We give a short and elementary proof of this theorem.
We produce a new, shorter construction of a minor-universal planar graph.
A famous theorem of Dirac states that any graph on $n$ vertices with minimum degree at least $n/2$ has a Hamilton cycle. Such graphs are called Dirac graphs. Strengthening this result, we show the existence of rainbow Hamilton cycles in…
We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.
We give a purely algebraic treatment of reduction theory for connections over the formal punctured disc. Our proofs apply to arbitrary connected linear algebraic groups over an algebraically closed field of characteristic 0. We also state…
A very short proof of the Fej\'er-Riesz lemma is presented in the matrix case
Let T be a countable, small simple theory. In this paper, we prove for such T, the notion of Lascar Strong type coincides with the notion of a strong type,over an arbitrary set.