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For a graph G = (V(G),E(G)) having no isolated vertex, a function ƒ : E(G)→{0;1} is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex be such that the number of edges with label 0 and the number of edges with label 1 differ by at the most 1 and the number of vertices with label 0 and the number...
To solve the problem of determining the volume of memory of information systems (IS), it was suggested to use a stochastic model based on the use of HM (Howard-Matalytski) - a queueing network with revenues. This model allows you to take into account the dependencies of the processing times of messages (claims) on their volumes, the possibility of changing the volume of messages over time, and also...
In this paper, the characteristics of the flow and forced heat transfer of power law non-Newtonian fluids that flow around a quadrilateral and rectangular cylinder that are located in a 2D channel are investigated by use of the finite volume method (FVM) in a steady state flow regime. To this accomplishment, in the constant temperature, the effects of a different obstruction ratio, aspect ratio and...
Rotations are an integral part of various computational techniques and mechanics. The objective in this paper is twofold: first to have a classical insight into the history of quaternions, a problem that Hamilton faced for over a decade and secondly to look at into its applications from computer graphics perspective. Thorough revision of quaternion algebra and its use case as a rotation operator has...
The climb is the steep fragment of the road. In road cycling, climbs should be categorized by the effort necessary to overcome it. Two values have the greatest influence on a difficulty of the climb: its average slope (rise/run ratio) and length. A simple approach to describing a climb's difficulty is multiplication slope squared and run. In this paper, the beginning of the climb is mathematically...
In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential...
Corrosion or contamination of flexible joints of a telescopic hydraulic cylinder may cause an increase of movement resistance in these places. In this work the influence of mounting rigidity on the strength of a telescopic hydraulic cylinder is under consideration. Buckling criterion and the strength of cylinder barrels (material effort) were included due to analysis. Boundary value problem concerning...
In this paper we extend the method of obtaining symmetries of ordinary differential equations to first order non-homogeneous neutral differential equations with variable coefficients. The existing method for delay differential equations uses a Lie-Bäcklund operator and an Invariant Manifold Theorem to define the operators which are used to obtain the infinitesimal generators of the Lie group. In this...
Thin plates of three different forms with different physical-mechanical characteristics and free edges are examined in this work. Modeling of geometry and numerical calculation of frequencies and forms of free oscillation of plates is accomplished by the finite element method, which is realized using the licensed computer program FEMAP with the NASTRAN solver. A comparative analysis of the calculated...
The main goal of the work is to support the marketing strategy using the characteristics created on the base of the game theory and uncertain knowledge. We want to elaborate algorithm, which does not require game-playing investigation. The additional aim consists in adaptating the game strategy to the concrete e.g. economic situation, described by selected, specific parameters. The next aim consists...
This article proposes an analysis of the results of the application of hyperexponential approximations with parameters of the paradoxical and complex type for calculating the steady-state probabilities of the G/G/n/m queueing systems with the number of channels n = 1, 2 and 3. The steady-state probabilities are solutions of a system of linear algebraic equations obtained by the method of fictitious...
In the present research analysis, linear fractional order ordinary differential equations with some defined condition (s) have been solved under the Caputo differential operator having order α > 0 via the Shehu integral transform technique. In this regard, we have presented the proof of finding the Shehu transform for a classical nth order integral of a piecewise continuous with an exponential...
In the present paper, the Generalized Differential Transform Method (GDTM) is used for obtaining the approximate analytic solutions of a free vibration linear differential equation of a single-degree-of-freedom (SDOF) system with fractional derivative damping. The fractional derivatives are described in the Caputo sense.
In this paper, the analytical solution of natural convective heat transfer of a non-Newtonian fluid flow between two vertical infinite plates using the Homotopy Perturbation Method (HPM) and Daftardar-Gejiji & Jafari Method (DJM) is presented. The heat transfer problem of natural convection is observed in many engineering fields including geothermal systems, heat exchangers, petroleum reservoirs,...
In this research, our purpose is to investigate some types of solutions to a simplified modified form of the Camassa-Holm equation. The Jacobi elliptic function expansion method is applied to this equation. Then, a lot of travelling wave solutions are obtained. The derived solutions are in the form of Jacobi elliptic functions, hyperbolic functions, and trigonometric functions. Graphics of solutions...
An analytical solution is presented for entropy generation on MHD Walter’s liquid B fluid over a stretching sheet with elastic deformation. The governing expressions of PDEs are converted into ODEs by suitable transformation which is solved by a hypergeometric function. Plots for velocity, heat transfer, entropy generation and a Bejan number are examined and their behavior is deliberated for several...
A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the...
This article discusses the question of restarting the script, when restart is used by many users of the information network, which can be modelled as a G-network. Negative claims simulate the crash of the script and the re-sending of the request. Investigation of an open queuing network (QN) with several types of positive customers with the phase type of distribution of their service time and one...
The article is aimed at the development of the analytical approach for evaluating the parameters of the Basset force acting on a particle in two-dimensional fluid flow induced by the oscillating wall. By applying regression analysis, analytical expressions to determine complementary functions were established for evaluating the Basset force. The obtained dependencies were generalized using the infinite...
In the present work, a solution to the problem of viscous flow in a rectangular region with two moving parallel walls is obtained by using a hybrid finite volume scheme. The discretized governing equations are solved iteratively, and thereby the flow variables are computed numerically. The results for velocity and pressure in horizontal and vertical directions through the centre of a rectangular region...
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