Milan Merkle

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We consider the ratio T(x,y) = r(~)r(y)/r2((~ + y)/2) and its properties related to convexity, logarithmic convexity, Schur-convexity, and complete monotonicity. Several new bounds and asymptotic expansions for T are derived. Sharp bounds for the function x ~-~ x/(1-e-~) are presented, as well as bounds for the trigamma function. The results axe applied to(More)
The first part of the paper deals with general features of weak star convergence from a topological point of view. We present basic facts about weak and weak star topologies, dual spaces and representations of linear functionals as Radon measures. A special attention is payed to finitely additive measures and some results regarding the Baire sets. We prove(More)
The Barnes' G-function G(x) = 1/Γ2, satisfies the functional equation log G(x + 1) − log G(x) = log Γ(x). We complement W. Krull's work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = ϕ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on(More)
A new near term operational concept for arrival and departure airspace in major metropolitan areas has been developed and validated that will require increased surveillance accuracy in an expanded area of arrival/departure airspace. This paper details the proposed concept, concept validation results, estimated benefits, and the operational and technical(More)
This is the last issue of the journal Publikacije Elektrotehničkog Fakulteta-serija Matematika (PEF), or with the English title, Publications of the Faculty of Electrical Engineering-series Mathematics. Founded in the year 1956 as Serija Matematika i Fizika, the journal will continue its life under the name Applicable Analysis and Discrete Mathematics(More)