A graph that contains a Hamiltonian cycle is called a Hamiltonian graph. In this paper we compute the first and the second geometric – arithmetic indices of Hamiltonian graphs. Then we apply our results to obtain some bounds for fullerene.

Many classical inequalities are just statements about the convexity or concavity of certain (hidden) underlying functions. This is nicely illustrated by Hardy, Littlewood, and Pólya [5] whose Chapter III deals with “Mean values with an arbitrary function and the theory of convex functions,” and by Steele [12] whose Chapter 6 is called “Convexity—The third pillar.” Yet another illustration is th...

in this study, geometrical, gravimetrical and frictional properties of four common varieties of iranian canola seeds (namely: slm, hyola, okapi, orient), containing the mean moisture value of 6.5% (w.b.) were investigated. geometrical and gravimetrical properties included length, diameter, geometric mean diameter, sphericity, thousand seed mass, volume, true density, bulk density and porosity. ...

physical properties of four common iranian varieties of canola seeds (hyola, okapi, orient and slm) were evaluated as a function of their moisture contents. the average seed length and thousand seed mass varied linearly from 1.925 to 2.262 mm and from 3.06 to 4.84 g, respectively. the average diameter, geometric mean diameter, and sphericity varied non-linearly from 1.475 to 1.911 mm, 1.625 to ...

Given matrices of the same size, A = a ij ] and B = b ij ], we deene their Hadamard Product to be A B = a ij b ij ]. We show that if x i > 0 and q p 0 then the n n matrices q j # are positive deenite and relate these facts to some matrix valued arithmetic-geometric-harmonic mean inequalities-some of which involve Hadamard products and others unitarily invariant norms. It is known that if A is p...

In this paper we obtain a best upper bound for the ratio of the extreme values of positive numbers in terms of the arithmetic-geometric means ratio. This has immediate consequences for condition numbers of matrices and the standard deviation of equiprobable events. It also allows for a refinement of Schwarz’s vector inequality.