We prove among others results that the harmonic mean of ?q(x) and ?q(1/x) is greater than or equal to 1 for arbitrary x > 0, q ? J where a subset [0,+?). Also, we there unique real number p0 (1, 9/2), such (0, p0), ?q(1) minimum q(1/x) 0 (p0,+?), maximum. Our generalize some known inequalities due Alzer Gautschi.

A necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

Charge movements were measured in frog intact fibers with the three-microelectrode technique and in cut fibers with the double Vaseline gap technique. At 13-14 degrees C, the ON segments of charge movement records from both preparations showed an early I beta component and a late I gamma hump component. When an intact fiber was cooled to 4-7 degrees C, the time-to-peak of I gamma (tp,gamma) was...

Convexity properties are often useful in characterizing and nding bounds for special function and their zeros as well as in questions concerning the existence and uniqueness of zeros in certain intervals In this survey paper we describe some work related to the gamma function the q gamma function Bessel and cylinder functions and the Hermite function Introduction Many inequalities for special f...

The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the flow between these sectors. In most functions, expansion Hubble considered and sometimes it argued that, as a local property, inclusion may influence overall dynamics. This starting point present article where we consider very simple cosmic scenario vacuum cold matter...

We suggest a new strategy for proving large N duality by interpreting GromovWitten, Donaldson-Thomas and Chern-Simons invariants of a Calabi-Yau threefold as different characterizations of the same holomorphic function. For the resolved conifold this function turns out to be the quantum Barnes function, a natural qdeformation of the classical one that in its turn generalizes Euler’s gamma funct...