On diagonal resolvable spheres

In this paper we give the complete answer to a question posed by A. Arhangel?skii and prove that the sphere Sⁿ$S^n$ is diagonal resolvable if and only if Sⁿ$S^n$ is an H  -space if and only if n∈{0,1,3,7}$n\in \{0,1,3,7\}$. Moreover, we prove that any upper half even dimensional Q$\mathbb{Q}$-sphere cannot be diagonal resolvable.     

Successive computation of some efficient locations of the Weber problem with barriers

We transform a continuous Weber problem with barriers to a discrete problem by computing some efficient locations, which are considered as promising locations for a new facility. A theorem determining conditions for a location to be efficient is introduced. A method for constructing the weighted coefficients and travel costs modeled by some distance metrics, is derived. This method provides successive computation of some efficient locations. Also, we propose an algorithm for the verification of location’s efficiency. Numerical examples are provided using squared Euclidean and Manhattan distance metrics, as well as the implementation details in programming package MATHEMATICA.     

Mass moment vector applications to the multi body dynamics with coupled rotations about no intersecting axes

Multi body system contains finite number of rigid bodies that are placed on each axis, which do not intersect each other. Derivatives of the linear momentum and angular momentum with respect to time by use mass moment vectors and vector rotators for pole and axis, are determined. A number of theorems are defined. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A kinetic model for polytropic gases with internal energy

We consider a mixture of N ideal, polytropic gases. Each species is described by a distribution function f_i(t, x, v, I) ≥ 0, 1 ≤ i ≤ N, defined on , and its evolution is governed by a Boltzmann-type equation. In order to recover the energy law of polytropic gases, the authors of [4] proposed a kinetic model in the framework of a weighted L¹ space. Another approach has been developed in [3] in the context of polyatomic gases. Following this previous lead, our model provides a L² framework in both variables v and I, to eventually perform a mathematical study of the diffusion asymptotics, as it was done in [2] for a model without energy exchange. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Convergence of a finite difference method for the time-fractional diffusion equation with concentrated capacity

We investigate the convergence of difference scheme for the time-fractional differential equation with fractional derivative of an order with the coefficient at the time derivative containing Dirac delta distribution. Convergence order of is proved. A numerical example demonstrates the theoretical results. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some Fixed Point Results for a Sequence of Mappings on G-Metric Space

In the setting of generalized metric spaces, so called G-metric spaced introduced by Z. Mustafa and B. Sims in 2006, some fixed point results for mappings with contractive iterate at a point and common fixed point results for infinite family of self mappings will be presented. The results are generalizations of well known results in the metric space. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Explicit Formulas and Combinatorial Identities for Generalized Stirling Numbers

In this paper, a modified approach to the multiparameter non-central Stirling numbers via differential operators, introduced by El-Desouky, and new explicit formulae of both kinds of these numbers are given. Also, some relations between these numbers and the generalized Hermite and Truesdel polynomials are obtained. Moreover, we investigate some new results for the generalized Stirling-type pair of Hsu and Shiue. Furthermore some interesting special cases, new combinatorial identities and a matrix representation are deduced.     

On efficient two-parameter methods for solving nonlinear equations

Derivative free methods for solving nonlinear equations of Steffensen’s type are presented. Using two self-correcting parameters, calculated by Newton’s interpolatory polynomials of second and third degree, the order of convergence is increased from 2 to 3.56. This method is used as a corrector for a family of biparametric two-step derivative free methods with and without memory with the accelerated convergence rate up to order 7. Significant acceleration of convergence is attained without any additional function calculations, which provides very high computational efficiency of the proposed methods. Another advantage is a convenient fact that the proposed methods do not use derivatives. Numerical examples are given to demonstrate excellent convergence behavior of the proposed methods and good coincidence with theoretical results.