Related papers: A generalization of Pappus chain theorem

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

The focus of this paper is on the study of specific circle formations known as orthogonal Pappus chains and the related incidence results that involve points of tangency between the circles in the construction. These chains give rise to new…

In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.

We present a proof of a multidimensional version of Peres-Schlag's theorem on Diophantine approximations with lacunary sequences.

We give a counterexample to a recently conjectured variant of the Penrose inequality.

We exhibit a family of linear operators related to the almost-periodic approach for the generalized Riemann hypothesis.

We show a classification method for finite groupoids and discuss the cardinality of cosets and its relation with the index. We prove a generalization of the Lagrange's Theorem and establish a Sylow theory for groupoids.

We present a generalization of a formula of higher order derivatives and give a short proof.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

We introduce and discuss the dual of a chain geometry. Each chain geometry is canonically isomorphic to its dual. This allows us to show that there are isomorphisms of chain geometries that arise from antiisomorphisms of the underlying…

We present a generalization of Descartes' theorem for the family of polytopal sphere packings arising from uniform polytopes. The corresponding quadratic equation is expressed in terms of geometric invariants of uniform polytopes which are…

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

We prove a general duality theorem for tangle-like dense objects in combinatorial structures such as graphs and matroids. This paper continues, and assumes familiarity with, the theory developed in [6]

In this paper we prove the theorem on freedom for free products with a single relation (analogous with the well-known result of Magnus) and a generalized Freiheitssatz for free products (analogous with the well-known result of Romanovski)

The strong recurrence is equivalent to the Riemann hypothesis. In the present paper, we give a simple proof of the generalized strong recurrence for all non-zero parameters.

We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.

We extend the inequality of Audenaert et al to general von Neumann algebras.

Consider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing…

A short proof of the classic Hardy inequality is presented for $p$-norms with $p>1$. Along the lines of this proof a sharpened version is proved of a recent generalization of Hardy's inequality in the terminology of probability theory. A…

We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a…