The packing density and the coordination number of regular spherical packing

The article shows the receiving of density equation of regular spherical packing functioning as an effective coordination number and dimension of space on the basis of six-dimensional physical space determinatio

Mathematical model of coordination number of spherical packing

The article considers a mathematical model of the coordination number, which allows obtaining an equation for multi component spherical packing in the entire range of its change. The resulting model can be used in both 2-d and 3-d spaces. The concept of the coordination index is introduced as a function of the inter-particle distance related to a single particle located near the central particle. The model provides unambiguous compliance between the simulated and calculated data on the coordination numbers of the spherical packin

Simulation of the coordination number of random sphere packing

Given article presents a generalized equation for calculating the average coordination number from the density of a random sphere packing, supplemented by a dependence on the threshold value of the interparticle distance in two- and three-dimensional spaces. It is shown that the calculation of the average coordination numbers according to the proposed equation gives an unambiguous correspondence between the simulated, calculated and experimental data for threshold values of more than 1.02 particle diameters. An explanation of the weak dependence of the average coordinate number on the packing density for small threshold values of the interparticle distance is given in this wor

Computer modeling of parameters of the electronic shell of the atom

In work results of computer modeling of parameters of an electron shell of atom such as orbital radiuses and constants of shielding are presented. It is shown that for atoms with completely filled electronic subshells, the dependence of the orbital radii from the nuclear charge (atomic number) can be described by application of a computing experiment, and to consider the received equations as a basis for extrapolation of data on orbital radiuses on all range of atomic numbers of elements what gives the chance of creation of the full scheme of dependence of orbital radii on charging number of the nucleus and calculation of the average size of ato

Finding the set of k-additive dominating measures viewed as a flow problem

n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it

Proportionate flow shop games

htmlabstractIn a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines. By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face two problems: the first one is how to obtain an optimal order that minimizes the total processing cost, the second one is how to allocate the cost savings obtained by ordering the jobs optimally. In this paper we focus on the allocation problem. PFS games are defined as cooperative games associated to proportionate flow shop problems. It is seen that PFS games have a nonempty core. Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency. For this case an explicit game independent expression for the Shapley value is provid