Related papers: The Ostrowski Expansions Revealed
We investigate global continuation of periodic orbits of a differential equation depending on a parameter, assuming that a closed 1-form satisfying certain properties exists. We begin by extending the global continuation theory of…
A cluster expansion is proposed, that applies to both continuous and discrete systems. The assumption for its convergence involves an extension of the neat Kotecky-Preiss criterion. Expressions and estimates for correlation functions are…
We show that the first-order theory of Sturmian words over Presburger arithmetic is decidable. Using a general adder recognizing addition in Ostrowski numeration systems by Baranwal, Schaeffer and Shallit, we prove that the first-order…
We study a family of generalized continued fractions, which are defined by a pair of substitution sequences in a finite alphabet. We prove that they are stammering sequences, in the sense of Adamczewski and Bugeaud. We also prove that this…
In this paper we prove that the condition one-to-one of continuous open-resolvable mapping is necessary in the Ostrovsky's Theorem. Also we get that the Ostrovsky's Problem (Is every open-LCn function between Polish spaces piecewise open…
We intend to contribute to the Collatz dynamics problem by seeking to analyze the Collatz conjecture from the tree of numbers sequences. First, we show numerically that the distribution of odd numbers has an initial transient, and proceeds…
We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…
Maximal estimates for Schr\"odinger means and convergence almost everywhere of sequences of Schr\"odinger means are studied.
We investigate the first-order correction in the homogenization of linear parabolic equations with random coefficients. In dimension $3$ and higher and for coefficients having a finite range of dependence, we prove a pointwise version of…
A generalization of the law of total covariance is presented and proved.
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
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 consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.
We prove here essentially sharp linear and bilinear Strichartz type estimates for the wave equations on Minkowski space, where we assume the initial data possesses additional regularity with respect to fractional powers of the usual angular…
We briefly indicate some implications of [1] for the second Lie algebra cohomology of equivariant map algebras and (twisted multi) loop algebras.
The explicit formulas expressing harmonic sums via alternating Euler sums (colored multiple zeta values) are given, and some explicit evaluations are given as applications.
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
We utilize operational methods to generalize the Chernoff inequality and prove a new result that relates the moment bound to strictly absolute monotonic functions. We show that the Chernoff bound is part of a continuum of probability…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
We present an extension theorem for a separately holomorphic function which is polynomial/rational in some variables.