Related papers: Sieving and the Erd{\H o}s-Kac theorem
This note reviews the Peano-Baker series and its use to solve the general linear system of ODEs. The account is elementary and self-contained, and is meant as a pedagogic introduction to this approach, which is well known but usually…
This work studies existence and regularity questions for attracting invariant tori in three dimensional dissipative systems of ordinary differential equations. Our main result is a constructive method of computer assisted proof which…
We characterize the points that satisfy Birkhoff's ergodic theorem under certain computability conditions in terms of algorithmic randomness. First, we use the method of cutting and stacking to show that if an element x of the Cantor space…
Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract…
We prove the Erdos-Turan equidistribution inequality, using a construction due to Chebyshev, Markov, and Stieltjes. The method is applicable in a more general setting. As an example, we state another inequality that can be proved using this…
Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…
In this paper we prove the following result, useful and often needed in the study of the ergodic properties of hard ball systems: In any such system, for any phase point x with a non-singular forward trajectory and infinitely many connected…
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
This paper develops ideas from a previous paper described as `an appetizer for non-linear Wiener--Hopf theory', but is completely independent of that paper. It again considers only the simplest possible case in which the underlying motion…
We compare the values associated with (traditional) community based proof verification to those associated with computer proof verification. We propose ways that computer proofs might incorporate successful strategies from human…
We prove laws of large numbers as well as central and non-central limit theorems for the Curie-Weiss model of magnetism. The rather elementary proofs are based on the method of moments.
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
In this paper we introduce and study a certain type of sub semi-group of $\mathbb{R}/\mathbb{Z}$ which turns out to be closely related to \sz's theorem on arithmetic progressions.
Two aspects of the physical side of the Church-Turing thesis are discussed. The first issue is a variant of the Eleatic argument against motion, dealing with Zeno squeezed time cycles of computers. The second argument reviews the issue of…
We prove Euler's theorem of number theory developing an argument based on quandles. A quandle is an algebraic structure whose axioms mimic the three Reidemeister moves of knot theory.
This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…
Leonid Levin (arxiv.org/abs/cs/0503039v14, p.7) published a new (and very nice) proof of G\'acs-Ku\v{c}era's theorem that occupies only a few lines when presented in his style. We try to explain more details and discuss the connection of…
We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.
In this paper, we formulate and prove several variants of the Erd\H{o}s-Tur\'{a}n additive bases conjecture.
We prove pointwise in time decay estimates via an abstract conjugate operator method. This is then applied to a large class of dispersive equations.