The well-known approximation of the difference between the arithmetic average and geometric average returns as one-half of the variance of the underlying returns is reexamined using Jensen’s Inequality. The ”defect” in Jensen’s Indequality, is given an exlicit formula in terms of the variance following some ideas put forward by Holder. A new form of the AM-GM Inequality follows and is is applie...

Desertification in arid, semi-arid and dry sub-humid regions is a global environmental problem. Considering theincreasing importance of desertification and its complexity, the necessity of giving attention to desertification criteria andindices is essential. Models and methods such as MEDALUS, UNEP-FAO, and others have been proposed on local andnational scales. In this research, IMDPA was selec...

We consider a scenario where a population of customers is spatially distributed in a region which is served by two wireless service providers that offer Internet Access via two noninterfering technologies: one having a uniform coverage over the region (e.g. WAN), and the other, a limited coverage (e.g. WiFi “hotspots”). We assume that customers are equipped with “dual mode” wireless communicati...

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [5] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

We construct a martingale which has the same marginals as the arithmetic average of geometric Brownian motion. This provides a short proof of the recent result due to P. Carr et al [7] that the arithmetic average of geometric Brownian motion is increasing in the convex order. The Brownian sheet plays an essential role in the construction. Our method may also be applied when the Brownian motion ...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

Computing a bijective spherical parametrization of a genus-0 surface with low distortion is a fundamental task in geometric modeling and processing. Current methods for spherical parametrization cannot, in general, control the worst case distortion of all triangles nor guarantee bijectivity. Given an initial bijective spherical parametrization, with high distortion, we develop a non-linear cons...

Consider the Delaunay triangulation T of a set P of points in the plane as a Euclidean graph, in which the weight of every edge is its length. It has long been conjectured that the dilation in T of any pair p, p′ ∈ P , which is the ratio of the length of the shortest path from p to p′ in T over the Euclidean distance ‖pp′‖, can be at most π/2 ≈ 1.5708. In this paper, we show how to construct po...