For fixed s 1 and t1,t2 ∈ (0,1/2) we prove that the inequalities G(t1a + (1− t1)b,t1b+(1− t1)a)A1−s(a,b) > AG(a,b) and G(t2a+(1− t2)b,t2b+(1− t2)a)A1−s(a,b) > L(a,b) hold for all a,b > 0 with a = b if and only if t1 1/2− √ 2s/(4s) and t2 1/2− √ 6s/(6s) . Here G(a,b) , L(a,b) , A(a,b) and AG(a,b) are the geometric, logarithmic, arithmetic and arithmetic-geometric means of a and b , respectively....

Background: Total Body Irradiation (TBI) is different from standard radiotherapy in many aspects, so it is not easy to predict the delivered dose to the patient under TBI treatment. Diode dosimetry procedures for surface dose reading can help to define variations of the actually delivered dose from the prescribed one. The aim of this study was to describe the measurements made to calib...

background: total body irradiation (tbi) is different from standard radiotherapy in many aspects, so it is not easy to predict the delivered dose to the patient under tbi treatment. diode dosimetry procedures for surface dose reading can help to define variations of the actually delivered dose from the prescribed one. the aim of this study was to describe the measurements made to calibrate diod...

Copulas represent the dependence structure of multivariate distributions in a natural way. In order to generate new copulas from given ones, several proposals found its way into statistical literature. One simple approach is to consider convex-combinations (i.e. weighted arithmetic means) of two or more copulas. Similarly, one might consider weighted geometric means. Consider, for instance, the...

Abstract The main purpose of this work is to present essential extensions results in [7] and [8], apply them some special situations. Of particular interest the refinement integral Jensen inequality for vector valued integrable functions. applications related four topics, namely f -divergences information theory (an interesting weighted geometric mean–arithmetic mean obtained as a consequence),...

background and objectives: scolymus is one of most abundant plants of mountain areas iran, because of role in the digestion of food auxiliary is located the focus of attention consumers. in iran, more than 17 percent of crops in various stages of the supply becomes losses, which requires knowledge of physical properties, mechanical and hydrodynamic agricultural products. the existence of the in...

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

The article shows how two choices are possible whenever computing the geometric mean, and repetition of this process can in general yield 2-to-the power N different values when compounded first steps evaluation arithmetic-geometric mean. This happens not only simple AGM involved computation complete elliptic integral kind, but also analogous methods for incomplete integrals second kind.

The Analytic Hierarchy Process (AHP) is a popular methodology for group decision making. Individual judgments can be aggregated in several ways, with the most effective approach being the aggregation of individual judgments (AIJ) and Individual priorities (AIP). When the judgments are aggregated, regardless of whether AIJ or AIP are used, arithmetic and geometric means are selected by decision ...