Density functional theory calculations (DFT), as well as hybrid methods (B3LYP) for Bi8N18-[CoF6]3- complexhave been carried out to study the non-bonded interaction. The geometry of the 1313N18 has been optimized atB3LYP method with EPR-II basis set and geometry of the [CoF6]3 have been optimized at B3LYP method withDe12-TZVP basis set and Stuttgart RSC 1997 Effective Core Potential. The electr...

Let A ⊂ R be a set-germ at 0 ∈ R such that 0 ∈ A. We say that r ∈ S is a direction of A at 0 ∈ R if there is a sequence of points {xi} ⊂ A\{0} tending to 0 ∈ R such that xi ‖xi‖ → r as i → ∞. Let D(A) denote the set of all directions of A at 0 ∈ R. Let A, B ⊂ R be subanalytic set-germs at 0 ∈ R such that 0 ∈ A ∩ B. We study the problem of whether the dimension of the common direction set, dim(D...

Mixtures of Truncated Basis Functions (MoTBFs) have recently been proposed for modelling univariate and joint distributions in hybrid Bayesian networks. In this paper we analyse the problem of learning conditional MoTBF distributions from data. Our approach utilizes a new technique for learning joint MoTBF densities, then propose a method for using these to generate the conditional distribution...

For a non-commutative domain R and a multiplicatively closed set S the (left) Ore localization of R at S exists if and only if S satisfies the (left) Ore property. Since the concept has been introduced by Ore back in the 1930’s, Ore localizations have been widely used in theory and in applications. We investigate the arithmetics of the localized ring SR from both theoretical and practical point...

to investigate the electromagnetic interaction of molecules inside the nanotubes, first, the structure of nanotubes b16n16 was optimized with hybrid density functional theory (b3lyp) using the epr-ii basis set, then cu, cu+, cu++ were located in nanotube and we studied the total energy, band gap energy, electrical potential, changes of band gap energy in terms of total energy and dipole moment ...

The aim of a multi-mode resource-constrained project scheduling problem (MRCPSP) is to assign resource(s) with the restricted capacity to an execution mode of activities by considering relationship constraints, to achieve pre-determined objective(s). These goals vary with managers or decision makers of any organization who should determine suitable objective(s) considering organization strategi...

The three-loop vacuum polarization function Π(q 2) induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the O(α 2 s) result for the production of heavy quarks R(s) = σ(e + e − → hadrons)/σ(e + e − → µ + µ −) can be extracted. Explicit formulae separated into the different colour factors are given.

1. Introduction. Let 6 be a class of real valued functions defined on an interval [a, b]. A set E is called stationary for Q provided any member of C which is constant on E must be constant on all of [a, b]. Several recent articles have been concerned with the problem of determining the stationary sets for various classes of functions [l], [2],

The two most commonly used topologies on R are the ordinary topology and the density topology. The ordinary topology is, of course, more widely known, and has the open intervals as its basic sets. The density topology, on the other hand, appears naturally in deeper studies of the structure of measurable sets. Its open sets are all measurable sets S ⊂ R which have the property that if x ∈ S, the...