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We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
We give a new proof of the existence of designs, which is much shorter and gives better bounds.
The assumptions needed to prove Cox's Theorem are discussed and examined. Various sets of assumptions under which a Cox-style theorem can be proved are provided, although all are rather strong and, arguably, not natural.
The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…
In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].
We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.
In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.
We describe two distinct simple, short and self contained proofs of the composition lemma.
In this short paper we review and extract some features of the Fredholm Alternative problem .
We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them…
Many versions of the Stokes theorem are known. More advanced of them require complicated mathematical machinery to be formulated which discourages the users. Our theorem is sufficiently simple to suit the handbooks and yet it is pretty…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.
We give a new proof of the decidability of reachability in alternating pushdown systems, showing that it is a simple consequence of a cut-elimination theorem for some natural-deduction style inference systems. Then, we show how this result…
An technically interesting proof of a known theorem.
In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.
The purpose of the paper is to present an short proof of the Chuang's inequality.
Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.
We give a q-analogue of Gauss' divisibility theorem