Ramanujan's harmonic number expansion into negative powers of a triangular number.
Ramsey, Lebesgue, and Marczewski sets and the Baire property
We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented. THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets. THEOREM. In the Ellentuck topology on , is a proper subset of the hereditary ideal associated with (s). We construct an example in the Ellentuck topology of a set which is...
Random theorems in topology
Ranks for baire multifunctions
Various ordinal ranks for Baire-1 real-valued functions, which have been used in the literature, are adapted to provide ranks for Baire-1 multifunctions. A new rank is also introduced which, roughly speaking, gives an estimate of how far a Baire-1 multifunction is from being upper semicontinuous.
Ratio vectors of polynomial-like functions.
Real functions as traces of Infinte polynomials.
Real functions having graphs connected and dense in the plane
Recent applications of fractional calculus to science and engineering.
Recherches sur les fonctions ayant une infinité d'oscillations et sur les fonctions discontinues
Recherches sur les fractions continues
Reconciliation of discrete and continuous versions of some dynamic inequalities synthesized on time scale calculus
The aim of this paper is to synthesize discrete and continuous versions of some dynamic inequalities such as Radon's Inequality, Bergström's Inequality, Schlömilch's Inequality and Rogers-Hölder's Inequality on time scales in comprehensive form.
Reconnaître si un polynôme à plusieurs variables peut être décomposé en facteurs entiers
Recueil d'exercices sur le calcul infinitésimal [Book]
Recurring mean inequality of random variables.
Redheffer type inequality for Bessel functions.
Refined multidimensional Hardy-type inequalities via superquadracity.
Refinement of the Jensen integral inequality
In this paper we give a refinement of Jensen’s integral inequality and its generalization for linear functionals. We also present some applications in Information Theory.
Refinements and sharpenings of some double inequalities for bounding the gamma function.
Refinements, generalizations, and applications of Jordan's inequality and related problems.
Refinements of Carleman's inequality.