Consider a unit sphere on which are placed N random spherical caps of area 4rip(N). We prove that if lim (p(N).N/log N) < 1, then the probabil i ty that the sphere is completely covered by N caps tends to 0 as N--" 0% and if lim (p(N).N/ log N) > 1, then for any integer n > 0 the probabili ty that each point of the sphere is covered more than n times tends to 1 as N--* oo.

In this article, we consider ‘N ’spherical caps of area 4πp were uniformly distributed over the surface of a unit sphere. We are giving the strong threshold function for the size of random caps to cover the surface of a unit sphere. We have shown that for large N, if Np log N > 1/2 the surface of sphere is completely covered by the N caps almost surely , and if Np log N ≤ 1/2 a partition of the...

An important part of understanding women's and men's attitudes and behaviors is considering their ideas and opinions. Based on gender stereotyping of view women and men have different types of behavior, manner and characteristics. Both genders do their jobs differently. Stereotyping  process focuses on ability and characteristics of women, and men are lack of them. On the other hand, it also f...

A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distributio...

Let V be a set of distinct points in the Euclidean plane. For each point x 2 V , let sx be the ball centered at x with radius equal to the distance from x to its nearest neighbour. We refer to these balls as the spheres of in uence of the set V . The sphere of in uence graph on V is de ned as the graph where (x; y) is an edge if and only if sx and sy intersect. In this extended abstract, we dem...

The structure of polydisperse hard sphere fluids, in the presence of a wall, is studied by the Rosenfeld density functional theory. Within this approach, the local excess free energy depends on only four combinations of the full set of density fields. The case of continuous polydispersity thereby becomes tractable. We predict, generically, an oscillatory size segregation close to the wall, and ...

We studied the accuracy of volume integral equation simulations of internal fields in small particles illuminated by a monochromatic plane wave as well as the accuracy of the scattered fields. We obtained this accuracy by considering scattering by spheres and comparing the simulated internal and scattered fields with those obtained by Mie theory. The accuracy was measured in several error norms...

A quantitative description of the configurational part of the total energy of metallic alloys with substantial atomic size difference cannot be achieved in the atomic sphere approximation: It needs to be corrected at least for the multipole moment interactions in the Madelung part of the one-electron potential and energy. In the case of a random alloy such interactions can be accounted for only...