Related papers: Another simple proof of the 1-dimensional flat cha…

Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…

This paper gives a concise proof of the Jordan curve theorem on discrete surfaces. We also embed the discrete surface in the 2D plane to prove the original version of the Jordan curve theorem. This paper is a simple version of L. Chen, Note…

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

We study flat vector bundles over complex parallelizable manifolds.

The paper presents a counterexample to the Hodge conjecture.

Based on various strategies, we obtain several simple proofs of the celebrated Sharkovsky cycle coexistence theorem.

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

We discuss the flatness property of some fiber type contractions of complex smooth projective varieties of arbitrary dimensions. We relate the flatness of some morphisms having one-dimensional fibers with their conic bundles structures,…

A one-line proof of a minimax theorem due to Steinerberger is given.

This article present a new, direct and simple formula for constructing Mignotte sequences.

We obtain simple proofs of certain inequalites for bivariate means.

We prove a result on the existence of linear forms of a given Diophantine type.

This note presents an elementary and direct proof for the convexity of the Choquet integral when the corresponding set function is submodular.

A short proof is given for the well-known Choi-Effros theorem on the structure of ranges of completely positive projections.

In this short note we give a formula for the number of chains of subgroups of a finite elementary abelian $p$-group. This completes our previous work [5].

We prove some symmetric $q$-congruences.

In this paper we give some basic results on blocking sets on minimum size for a finite chain geometry.

We present an easy proof of Polya's theorem on random walks: with the probability one a random walk on the two-dimensional lattice returns to the starting point.

In this paper, we prove a conjecture of Schnell in the surface case.

We show that there is an operator with a simple geometric significance which yields the ordinary geometry of a linear equidistant lattice via Connes' distance function.