Related papers: The Sharkovsky Theorem

As a first application of a very old theorem, known as Herschel's theorem, we provide direct elementary proofs of several explicit expressions for some numbers and polynomials that are known in combinatorics. The second application deals…

We present an adaptation of a relatively simple topological argument to show the existence of many periodic orbits in an infinite dimensional dynamical system, provided that the system is close to a one-dimensional map in a certain sense.…

We survey the classical results of the Dirichlet Approximation Theorem.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

This note is intended primarily for college calculus students right after the introduction of the Intermediate Value Theorem, to show them how the Intermediate Value Theorem is used repeatedly and straightforwardly to prove the celebrated…

We give a new independent proof of a generalised version of the theorem by Rashevskii, which appeared in [Uch. Zapiski Ped. Inst. K. 2 (1938), 83 -- 94] and from which the classical Chow-Rashevskii Theorem follows as a corollary. The proof…

Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof.…

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

We present a proof of the Chevalley-Weil Theorem that is somewhat different from the proofs appearing in the literature and with somewhat weaker hypotheses, of purely topological type. We also provide a discussion of the assumptions, and an…

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…

A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…

The purpose of the current paper is twofold: to some extent it is intended as a review of the recent optimal result in [4] concerning the unique continuation property of solutions to the two-dimensional Zakharov-Kuznetsov equation. On the…

The Chernoff bound is one of the most widely used tools in theoretical computer science. It's rare to find a randomized algorithm that doesn't employ a Chernoff bound in its analysis. The standard proofs of Chernoff bounds are beautiful but…

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

We clarify and extend insights from Lavrentiev's seminal paper. We examine the original theorem dealing with the absence of the Lavrentiev phenomenon, a cornerstone issue in the calculus of variations. We point out some inconsistencies in…

We generalize Iskovskih's theorem about surfaces without irregularity and bigenus from the smooth case to regular surfaces over arbitrary fields, with special focus on the case of imperfect fields. This includes surfaces that are…

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

Question when rectangle can be tiled with similar copies of rectangles witch quetient of sides quadratic irrationalities. New proof of one part F. Sharov's theorem. Other close result.