相关论文: A Simple Proof of Sharkovsky's Theorem

Salikhov has proved a conjecture of Kontsevich and Shoikhet by reducing it to the consideration of three families of graphs, a consideration which was left to the reader for two of those families. We show, that the conjecture is just a very…

We introduce a homotopy theory of digraphs (directed graphs) and prove its basic properties, including the relations to the homology theory of digraphs constructed by the authors in previous papers. In particular, we prove the homotopy…

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow's rigidity theorem for hyperbolic manifolds. This…

Parikh's theorem is a fundamental result of the formal language's theory. There had been published many proofs and many papers claimed to provide a simplified proof, but most of them are long and still complicated. We provide the proof that…

In this paper, we present a simplified proof of Kharitonov's Theorem, an important result on determining the Hurwitz stability of interval polynomials. Our new approach to the proof, which is based on the Wronskian of a pair of polynomials,…

In this paper we present a short and elementary proof for the error in Simpson's rule.

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.

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.

A new shortest proof of Kotzig's Theorem about graphs with unique perfect matching is presented in this paper. It is well known that Kotzig's theorem is a consequence of Yeo's Theorem about edge-colored graph without alternating cycle. We…

A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.

This note presents a simple proof of the characteristic function of Student's $t$-distribution. The method of proof, which involves finding a differential equation satisfied by the characteristic function, is applicable to many other…

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

In this paper we give a generalization of a result of Wei.

A short, fairly self-contained proof is given of the Poincar\'e Conjecture. In the previous version there was an error on Page 8. This gap has now been filled.

We give a short, topological proof that all graphs admit tree-decompositions displaying their topological ends.

We give a sharp spectral condition for the existence of odd cycles in a graph of given order. We also prove a related stability result.

We prove several extensions of the Erdos-Fuchs theorem.

A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.