Some Kurzweil-Henstock-type integrals and the wide Denjoy integral
Kurzweil-Henstock integrals related to local systems and the wide Denjoy integral are discussed in the frame of their comparability and compatibility.
Some mean value theorems as consequences of the Darboux property
The aim of the paper is to present some mean value theorems obtained as consequences of the intermediate value property. First, we will prove that any nonextremum value of a Darboux function can be represented as an arithmetic, geometric or harmonic mean of some different values of this function. Then, we will present some extensions of the Cauchy or Lagrange Theorem in classical or integral form. Also, we include similar results involving divided differences. The paper was motivated by some problems...
Some Results on Maps That Factor through a Tree
We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps can be characterized by the vanishing of some integrals over winding number functions. This in particular shows that if the target is the Heisenberg group equipped with the Carnot-Carathéodory metric and the Hölder exponent of the map is bigger than...
Stability criteria of linear neutral systems with distributed delays
In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...
Sur la constante d'Euler et la fonction de Binet.
Sur la détermination de quelques intégrales indéfinies
Sur la méthode de Gauss pour le calcul approché des intégrales.
Sur les fractions continues algébriques
Sur les intégrales définies uniformément convergentes
Sur les intégrales eulériennes de seconde espèce
Sur les quadratures.
Sur les quadratures
Sur les valeurs limites des intégrales.
Sur l’intégrale
Sur l’intégrale
Sur l’intégrale
Sur l'intégration de l'équation différentielles de Lamé.
Sur l'intégration des différentielles rationnelles
Sur l'intégration des fractions rationnelles
Sur une formule générale des intégrales définies