Related papers: A Simple Proof of Sharkovsky's Theorem Rerevisited
In this paper, we study the stability result of a well-known theorem of Bondy. We prove that for any 2-connected non-hamiltonian graph, if every vertex except for at most one vertex has degree at least $k$, then it contains a cycle of…
In this paper we first obtain a formula of averaged Lyapunov exponents for ergodic Szego cocycles via the Herman-Avila-Bochi formula. Then using acceleration, we construct a class of analytic quasi-periodic Szego cocycles with uniformly…
A theory of cyclic elements in semisimple Lie algebras is developed. It is applied to an explicit construction of regular elements in Weyl groups.
Consider the graph that has as vertices all bitstrings of length $2n+1$ with exactly $n$ or $n+1$ entries equal to 1, and an edge between any two bitstrings that differ in exactly one bit. The well-known middle levels conjecture asserts…
We present an alternative cyclic proof system for Peano arithmetic that could be simpler than the existing ones and well-adapted both for proof analysis and for automatizing inductive proof search. In addition, we will show how various…
A short proof of the equivalence of the recurrence of non-backtracking random walk and that of simple random walk on regular infinite graphs is given. It is then shown how this proof can be extended in certain cases where the graph in…
We prove a Korovkin type approximation theorem via power series methods of summability for continuous $2\pi$-periodic functions of two variables and verify the convergence of approximating double sequences of positive linear operators by…
In directed graphs, a cycle can be seen as a structure that allows its vertices to loop back to themselves, or as a structure that allows pairs of vertices to reach each other through distinct paths. We extend these concepts to temporal…
We prove the existence of infinitely many periodic orbits of symplectomorphisms isotopic to the identity if they admit at least one hyperbolic periodic orbit and satisfy some condition on the flux. Our result is proved for a certain class…
A universal cycle is a compact listing of a class of combinatorial objects. In this paper, we prove the existence of universal cycles of classes of labeled graphs, including simple graphs, trees, graphs with m edges, graphs with loops,…
This short note studies $C^{\infty}$-smooth cocycles in $\mathbb{T}\times SO(3)$ that have $0$ degree and are non-homotopic to constants. The study picks up from where the author's PhD thesis left the subject, and shows that, under a…
The goal of this very short note is to give a new proof of Faber's formula for the socle intersection numbers in the tautological ring of $\mathcal{M}_g$. This new proof exhibits a new beautiful tautological relation that stems from the…
In this paper, we study a general Syracuse problem. We give some necessary conditions concerning the existence of eventual non trivial cycles. Some properties based on linear logarithmic forms are established. New general conjectures are…
We prove a noncommutative variant of Saskin's classical theorem -- on the connection between Choquet boundaries for function spaces and Korovkin sets -- for operator systems generating separable Type I C*-algebras. The main result implies…
We offer a new structural basis for the theory of 3-connected graphs, providing a unique decomposition of every such graph into parts that are either quasi 4-connected, wheels, or thickened $K_{3,m}$'s. Our construction is explicit,…
Many of the strengthenings and extensions of the topological Tverberg theorem can be derived with surprising ease directly from the original theorem: For this we introduce a proof technique that combines a concept of "Tverberg unavoidable…
We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new…
In this note we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.
We know that a continuous function on a closed interval satisfies the Intermediate Value Property. Likewise, the derivative function of a differentiable function on a closed interval satisfies the IVP property which is known as the Darboux…
In this article we develop intersection theory in terms of the $\mathcal{B}$-group of a reduced analytic space. This group was introduced in a previous work as an analogue of the Chow group; it is generated by currents that are direct…