Related papers: Certain results on uniform circle random covering …
We employ an extension of ergodic theory to the random setting to investigate the existence of random periodic solutions of random dynamical systems. Given that a random dynamical system has a dissipative structure, we proved that a random…
We build upon previous work on the densities of uniform random walks in higher dimensions, exploring some properties of the even moments of these densities and extending a result about their modularity.
The fundamental theorem in the theory of the uniform convergence of sine series is due to Chaundy and Jolliffe from 1916 (see [1]). Several authors gave conditions for this problem supposing that coefficients are monotone, non-negative or…
We show that a number of conditions on oriented graphs, all of which are satisfied with high probability by randomly oriented graphs, are equivalent. These equivalences are similar to those given by Chung, Graham and Wilson in the case of…
In this note, we compute the probability that a $k\times n$ matrix can be extended to an $n\times n$ invertible matrix over $\F_q[x]$, which turns out to be $(1-q^{k-n})(1-q^{k-1-n})...(1-q^{1-n})$. Connections with Dirichlet's density…
We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.
In ``Rips complexes and covers in the uniform category'' the authors define, following James, covering maps of uniform spaces and introduce the concept of generalized uniform covering maps. Conditions for the existence of universal uniform…
In this note, we prove a theorem covering Chartrand, Kaigars, and Lick's theorem in [Proc. Amer. Math. Soc. 32 (1972), 63-68]. As an application, we give a simpler proof of theorem proved by Mader [J. Graph Theory 65 (2010), 61-69. (Theorem…
In this note we refine the alternativity in some bifurcation theorems of Rabinowitz type, and then improve a few of results in Lu (2022) [17].
A very simple but useful almost sure convergence theorem of probability is given.
We show that equidistribution of irrational orbits on the unit circle implies Furstenberg's conjecture.
We give a short proof of Ahlfors' theorem on covering surfaces.
This paper is a sequel to [3]. We formulate a natural algebraic geometry conjecture, give some of its number theoretic and analytical consequences, and show that those can be used to get further advances in wave turbulence theory.
We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…
In this paper, we continue the study of almost squares and extend the result of the author's fourth paper of the series to almost squares with closer factors.
In this note we introduce a notion of a generically (strongly generically) NP-complete problem and show that the randomized bounded version of the halting problem is strongly generically NP-complete.
This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].
We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…
We introduce a variable radius form of the extended exterior sphere condition of [16], and then, we prove that the complement of a closed set satisfying this new property is nothing but the union of closed balls with lower semicontinous…
In this paper, we prove some foundational results on the deformation theory of E-infinity ring spectra.