We extend our previous method to determine globular cluster ages using the luminosity function (Jimenez & Padoan 1996). We show that the luminosity function depends on both age and distance modulus and that it is possible to distinguish between the two. This method provides at the same time independent determinations of distance and age of a GC by simply counting the number of stars found insid...

For minimizers u ∈W 1,p(x)(Ω) of quasiconvex integral functionals of the type F [u] := ∫ Ω f(x,Du(x)) dx with p(x) growth in the class K := {u ∈ W 1,p(x)(Ω) : u ≥ ψ}, where ψ ∈ W 1,p(x)(Ω) is a given obstacle function, we show estimates of Calderón-Zygmund type, i.e. |Dψ|p(·) ∈ L =⇒ |Du|p(·) ∈ L , for any q > 1, provided that the modulus of continuity ω of the exponent function p satisfies the ...

In this paper we consider subharmonic functions »gl in the unit disk whose minimum modulus and maximum modulus satisfy a certain inequality. We show the existence of an extremal member of this class with largest maximum modulus. We then obtain an upper bound for the maximum modulus of this function in terms of the logarithmic measure of a certain set. We use this upper bound to prove theorems a...

The RSA is based on a trapdoor one-way function which is easy to compute but is most hard to revert without knowing the trapdoor. A cryptanalysis, presented in this paper, consists in finding a new decrypt key which plays the same role of the original trapdoor. To find this new decrypt key we must seek the maximum degree of ciphering function composition in a given modulus N. The maximum degree...

We generalize a well-known result of L. Caffarelli on Lipschitz estimates for optimal transportation T between uniformly log-concave probability measures. Let T : R → R be an optimal transportation pushing forward μ = e dx to ν = e dx. Assume that 1) the second differential quotient of V can be estimated from above by a power function, 2) modulus of convexity of W can be estimated from below by...

We investigate two greedy strategies for finding an approximation to the minimum of a convex function E defined on a Hilbert space H. We prove convergence rates for these algorithms under suitable conditions on the objective function E. These conditions involve the behavior of the modulus of smoothness and the modulus of uniform convexity of E.

In this study, the mechanical and thermal behavior of the nano-reinforced polymer composite reinforced by Montmorillonite (MMT) nanoparticles is investigated. Due to low cost of computations, the 3D representative volume elements (RVE) method is utilized using ABAQUS finite element commercial software. Low density poly ethylene (LDPE) and MMT are used as matrix and nanoparticle material, respec...