-sequence and applications.
Racines de fonctions différentiables
Nous précisons la classe de différentiabilité de où désigne une fonction positive de classe , -plate sur l’ensemble de ses zéros, et un réel, ; de plus, nous étudions l’existence locale d’une racine -ième de classe , pour une fonction de classe admettant une racine -ième formelle en chaque point.
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...
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.
Real functions having graphs connected and dense in the plane
Recent applications of fractional calculus to science and engineering.
Refined multidimensional Hardy-type inequalities via superquadracity.
Refinements of the Hermite-Hadamard inequality for convex functions.
Regarding arc-wise accessibility in the plane
Regular fractional iteration of convex functions
The existence of a unique solution φ of equation (1) is proved under the condition that f: I → I is convex or concave and of class in I, 0 < f(x) < x in I*, and f’(x) > 0 in I. Here I = [0, a] or [0, a), 0 < a ≤ ∞, and I* = I 0.
Regular fractional iterations.
Regular Iteration in the Case of Multiplier Zero
Regular Variation In Probability Theory
Regular variation on homogeneous cones
Regularity, nonoscillation and asymptotic behaviour of solutions of second order linear equations.
Regularity of Lipschitz minima
Regularly Varying Distributions
Regularly Varying Sequences and Entire Functions of Finite Order
Regularly varying solutions of generalized Thomas-Fermi equations
Regulární variace: od škálové invariance ke konvergenčním testům
Článek se snaží přiblížit některé aspekty teorie regulární variace. Jde o pojem z klasické analýzy, který má bohatou historii a četné aplikace v teorii pravděpodobnosti, teorii čísel, integrálních transformacích, komplexní analýze, diferenciálních rovnicích, teorii her či teorii grafů. Regulárně měnící se funkce mají souvislost s mnoha matematickými pojmy, včetně škálové invariance, kterou náš výklad začíná, či konvergenčními testy pro nekonečné řady, kterými náš výklad končí. V průběhu výkladu...