Laver and set theory

In this commemorative article, the work of Richard Laver is surveyed in its full range and extent.Accepted manuscrip

On The Periodic Solutions of Certain Fifth Order Nonlinear Vector Differential Equations

The purpose of this paper is tonbsp show that under some sufficient conditions of equation (1.1) have no periodic solution other than the trivial solution

The x−x-coordinates of Pell equations and sums of two Fibonacci numbers II

International audienceLet $\{F_{n}\}_{n\geq 0}$ be the sequence of Fibonacci numbers defined by $F_0=0$, $F_1 =1$ and $F_{n+2}= F_{n+1} +F_n$ for all $n\geq 0$. In this paper, for an integer $d\ge 2$ which is square-free, we show that there is at most one value of the positive integer $x$ participating in the Pell equation $x^2-dy^2=\pm 4$ which is a sum of two Fibonacci numbers, with a few exceptions that we completely characterize

On Sequences of J. P. King-Type Operators

This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King's approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators