# International Journal of Mathematical Models and Methods in Applied Sciences

**ISSN: 1998-0140
Volume 10, 2016**

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of NAUN Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

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**Volume 10, 2016**

Title of the Paper: **Multidimensional Comparisons of Health Systems Functioning in OECD Countries**

Authors: **V. Pacáková, M. Papoušková**

Pages: **388-394**

Abstract: Objective of the article is comparison of health care status and functioning of health systems in OECD countries, depending on risk factors, health expenditures, and health care resources and activities using appropriate multidimensional statistical methods. There are significant differences in health and healthcare results between and within OECD countries and regions. Article aims to present the results of application of multivariate statistical methods, namely factor analysis, cluster analysis and multidimensional comparative methods which provide an overview of the health care status and public health systems expenditures, various causal relations and differences or similarities of the OECD countries. This information is essential to the development of national and international health policies for treatment and financial budget of public health systems.

Title of the Paper: **Long Sine Wave Transformation in the Framework of Gardner Equation: Spectral and Statistical Analysis**

Authors: **O. Kurkina, E. Rouvinskaya, A. Giniyatullin, A. Kurkin, T. Talipova, E. Pelinovsky**

Pages: **381-387**

Abstract: The main stages of the process of tidal wave evolution can be described within a weakly nonlinear model based on the Gardner equation (extended version of the Korteweg – de Vries equation with both quadratic and cubic nonlinear terms), which is actively applied in physical oceanography. These stages include nonlinear steepening, and then generation and development of undular bore. We carried out numerical modeling of long sine wave evolution in the framework of the Gardner model for different signs of its cubic nonlinear term and for different initial amplitudes to demonstrate the principal features of the process. The present study is focused on spectral and statistical characteristics of the generated wave field. If amplitude of sine wave is large enough, soliton-like impulses of different polarities depending on the sign of cubic nonlinearity are generated and their interactions may result in the formation of extreme amplitude waves. Statistical analysis of the wave field in time shows almost permanent substantial exceedance of the level of the significant wave height in some position in spatial coordinate. Spectrum behavior after a long time of initial wave evolution demonstrate the power asymptotic for small wave numbers and exponential asymptotics – for large wave numbers.

Title of the Paper: **Global Interval Sensitivity Analysis of Hermite Probability Density Function Percentiles**

Authors: **Zdeněk Kala**

Pages: **373-380**

Abstract: The derivation of a Hermite probability density function whose parameters are mean value, standard deviation, skewness and kurtosis is presented in the article. Global interval sensitivity analysis capable of evaluating the effects of all combinations of the intervals of input parameters on the model output is presented. Global interval sensitivity analysis was used to identify the effects of uncertainties of the parameters of Hermite probability density function on its 5 percentile. A strong influence of the interaction between skewness and kurtosis, which would not have been identified using local sensitivity analysis, was identified. The global interval sensitivity analysis and Hermite probability density function presented here provide in combination with Monte Carlo simulation methods a very powerful tool for the probabilistic evaluation of structural reliability.

Title of the Paper: **Numerical Modeling of T-Cell Dynamics by Reaction-Diffusion Problems**

Authors: **Raffaele D’Ambrosio, Beatrice Paternoster, Carmela Scalone**

Pages: **367-372**

Abstract: The paper proposes a numerical model for T-cell dynamics, based on a reaction-diffusion problem originated by adding a diffusion term in the model introduced in [1] and based on ordinary differential equations. The model here introduced is specifically intended to provide a mathematical description of the homeostasis of T-cells, mainly due to a quorum-sensing mechanism. The introduced reaction-diffusion problem is then discretized by means of a finite difference numerical scheme. Numerical experiments supporting the approach are provided.

Title of the Paper: **Study of the Lattices with CFC with Varying Temperature**

Authors: **Fulvio Frisone**

Pages: **361-366**

Abstract: In this theoretical study, it is underlined that the presence of micro-cracks in the lattice structure increases the probability of tunneling effect between two deuterons by some orders of magnitude with respect to non-deformed lattices. We have derived an expression to compute the tunneling probability within a micro-crack, and hypothesized a D+2-D+2 binding mechanism Finally, the overall indications provided by these theoretical simulations appear to suggest that the deformation of the crystalline lattice, at varying temperature, seems able to influence the process of tunneling between the deuterons in the metal, while the forced loading with D2 has, in general, no evident positive effects in pure metals, but in some cases could, on the contrary, condition the phenomenon negatively.

Title of the Paper: **Generalized Least-Powers Regressions I: Bivariate Regressions**

Authors: **Nataniel Greene**

Pages: **352-360**

Abstract: The bivariate theory of generalized least-squares is extended here to least-powers. The bivariate generalized least-powers problem of order p seeks a line which minimizes the average generalized mean of the absolute pth power deviations between the data and the line. Least-squares regressions utilize second order moments of the data to construct the regression line whereas least-powers regressions use moments of order p to construct the line. The focus is on even values of p, since this case admits analytic solution methods for the regression coefficients. A numerical example shows generalized least-powers methods performing comparably to generalized least-squares methods, but with a wider range of slope values.

Title of the Paper: **Theoretical Foundation of Collective Decision Making Procecess in Society Based on Airtificial Society Model**

Authors: **Satoru Ozawa**

Pages: **347-351**

Abstract: The order-disorder phase transition is an interesting topic in modern physics. The phase transition phenomena in physical systems and decision making processes in society have some similarities; they are based on nonlinear multibody interactions. The theoretical foundation of the physical phenomena is given by statistical physics. The same method will also apply to decision making process in society. This paper deals with the study of theoretical foundation of collective decision making processes in society with referring the method of statistical physics. The mathematical description is based on Artificial Society Model (ASM). Peoples who have similar knowledge and similar character in society are classified into one agent and society is composed of several agents. It has been shown that social decision making occurs as result of nonlinear interactions between agents via message transfers. The fruits of this study provide frameworks of computer simulations of decision making processes for particular problems in actual society.

Title of the Paper: **Simulation and Experimental Validation of Fatigue Endurance Limit of Copper Alloy for Industrial Applications**

Authors: **M. Viscardi, P. Napolitano, M. Arena**

Pages: **340-346**

Abstract: Fatigue resistance performance represents one of the main characteristic for flexible structures as those used in aerospace and other means of transport. For this reason, particular attentions are dedicated during the design stage to the evaluation of the lifetime resistance parameters. Many numerical and analytical approaches are actually available for this purpose, as well-standardized experimental test procedures have been assessed. With reference to a copper bar of an electric motor, the paper presents a survey of the main analytical and numerical methodologies for the prediction of the fatigue peculiarities. The estimation data have been than validated by an experimental campaign in simulated operating conditions, revealing advantage and drawbacks of different models.

Title of the Paper: **Magnetohydrodynamic Convection of Cu-Water Nanofluid in a Square Cavity with a Circular Cylinder**

Authors: **Canan Bozkaya**

Pages: **332-339**

Abstract: The hydromagnetic free convection of a Cu-water nanofluid in a square cavity involving an adiabatic circular cylinder is numerically investigated in the presence of an inclined uniform magnetic field. The left and right walls of the cavity are kept at constant hot and cold temperatures, respectively, while the horizontal walls are assumed to be adiabatic. The coupled nonlinear equations of mass, momentum and energy governing the present problem are discretized using the dual reciprocity boundary element method which is a boundary only nature technique treating the nonlinear terms by the use of radial basis functions. The flow and thermal fields are analyzed through streamline, isotherm, and average Nusselt number plots for a wide range of controlling parameters, such as Rayleigh and Hartmann numbers, the nanoparticle volume fraction and the inclination angle of the magnetic field. The results reveal that heat transfer and fluid flow are strongly affected by the presence of the circular cylinder and the inclined magnetic field.

Title of the Paper: **Modified Collocation Techniques for Evolutionary Problems**

Authors: **Angelamaria Cardone, Dajana Conte, Raffaele D'Ambrosio, Beatrice Paternoster**

Pages: **321-331**

Abstract: We present some modified collocation based numerical methods for the numerical integration of Ordinary Differential Equations (ODEs) and Volterra Integral Equations (VIEs). The treatise is framed into the existing literature on classical collocation methods and shows how this idea can evolve into a multistep setting, also in case of basis of functions other than polynomials.

Title of the Paper: **The Use of Navier-Stokes Equations in Modeling Water Quality in River-Type Systems**

Authors: **Galina Marusic, Calin Ciufudean**

Pages: **317-320**

Abstract: This paper addresses the problem of water quality in river-type systems. The actuality of water quality modeling based on mathematical and numerical modeling is discussed. The water motion in river-type systems is presented on the basis of Navier-Stokes equations.

Title of the Paper: **Sensitivity Analysis of the Accident Rate of a Plant by the Generalized Perturbation Theory**

Authors: **E. F. Lima, D. G. Teixeira, P. F. Frutuoso e Melo, F. C. Silva, A. C. M. Alvim**

Pages: **307-316**

Abstract: We discuss the application of the Generalized Perturbation Theory (GPT) to the reliability of a system of three equal protection channels of an industrial plant. The influence of parameters such as the demand rate and the failure rate over the plant accident rate is discussed. Traditional methods have been used to study the influence of these parameters on the plant accident rate in which the system of differential equations derived from the Markov approach adopted is solved for each value of the demand rate. From the solution of this system of equations, curves for the accident frequency depending on the demand rate (direct calculation) are obtained. However, it is possible to obtain these curves by GPT in a faster way, wherein the calculation effort may be reduced by a factor of up to 10. It was found that for demand rates lower than 1000 / year, GPT calculations with 3rd and 5th orders of approximations of gave better results than those with 1st order approximation when compared to direct calculation. However, for demand rates equal or greater than 1000 / year, the 1st order approach presented better results than the 3rd and 5th orders.

Title of the Paper: **Scheduling Jobs with Two Release Times and Tails on a Single Machine**

Authors: **Elisa Chinos, Nodari Vakhania**

Pages: **302-306**

Abstract: We consider a basic single-machine scheduling problem when jobs have release and delivery times and the objective is to minimize maximum job lateness. This problem is known to be strongly NP-hard and its special case when there are only two allowable release times remains to be NP-hard. In this paper we study the latter problem and derive conditions when it can be efficiently solved.

Title of the Paper: **Numerical Simulation of Particle Transport in Supersonic Mixing Layer**

Authors: **Altyn Makasheva, Altynshash Naimanova**

Pages: **297-301**

Abstract: Direct numerical simulations of the flowfield structures and the properties of the particle dispersion in the quasi-2D turbulent mixing layer (hydrogen-air) are performed by solving the time-dependent, compressible Euler equations. The 3D numerical code using the high-order essentially non-oscillatory (ENO) scheme is developed. The dispersion of the particles is studied by following their trajectories in the mixing layer with the Lagrangian method. In detail, the effect of the initial mass fraction of hydrogen and the number of particles on the growth of vortices and their thickness are studied. The simulation reveals that the capturing of the particles by the vortices essentially depend on the density of particles.

Title of the Paper: **About the Linear Complexity of Binary Sequences with Optimal Autocorrelation Value/Magnitude and Length 4p**

Authors: **Vladimir Edemskiy**

Pages: **292-296**

Abstract: We derive the linear complexity and the minimal polynomial over the finite fields of order two and p of series of binary sequences with a period 4p and optimal autocorrelation value/magnitude. These sequences are constructed by cyclotomic classes of order two, four and six by methods proposed by K.T. Arasu et al. and Y. Sun et al. We define the parameters of sequences with optimal autocorrelation and high linear complexity.

Title of the Paper: **A Computational Fluid Dynamics Simulation of Anthrax Diffusion in a Subway Station**

Authors: **Jean-François Ciparisse, Orlando Cenciarelli, Sandro Mancinelli, Gian Marco Ludovici, Andrea Malizia, Mariachiara Carestia, Daniele Di Giovanni, Carlo Bellecci, Leonardo Palombi Pasquale Gaudio**

Pages: **286-291**

Abstract: Anthrax endospores were used in the past to attempt to the life of civilians, just think about the failed attack in Tokyo in 1993 or the 22 cases, including five deaths, occurred in USA in 2001. Because of the high case-fatality rate (CFR around 50% for respiratory form of anthrax), to the strong resistance to environmental adverse conditions and to their high mobility in the air, anthrax endospores represent the ideal agent to perpetrate a spread with offensive purposes. Subway stations are densely frequented places, and are therefore a highly worthy objective for terrorists. The aim of this work is to determine, by means of Computational Fluid Dynamics simulations of the airflow blowing anthrax endospores dropped on the platform of a subway station, the temporal evolution of their concentration, and to estimate the related health risk. COMSOL Multiphysics™ software was used to simulate the so-produced multiphase flow.

Title of the Paper: **Using of Generalized Cyclotomy for Sequence Design over the Finite Field of Order Four with High Linear Complexity**

Authors: **Vladimir Edemskiy**

Pages: **281-285**

Abstract: We consider the use of generalized Ding-Helleseth cyclotomy to design sequences over the finite field of order four. Using generalized cyclotomic classes of order four we obtain the family of balanced sequences of odd period with high linear complexity. Also we present a method of constructing sequences with high linear complexity and arbitrary even period over the finite field of order four. These sequences are obtained with generalized Ding-Helleseth cyclotomy of order two . We generalize design of the sequences over the finite field of order four proposed by P. Ke et al. and D. Li et al.

Title of the Paper: **Verification of Hypotheses to the Selected Indicators from the Annual Report of the Prague Public Transit Company and Ostrava Transport Company**

Authors: **Michal Krajňák**

Pages: **274-280**

Abstract: The paper deals with testing of hypotheses and development of selected indicators from the annual reports of two companies in the Czech Republic - the Prague Public Transit Company and Ostrava Transport Company. The annual report is an important document presenting the summary of the profit or loss of an accounting unit during the reference period. In case of the Prague Public Transit Company it holds that the number of passengers is increasing slightly, the similar case is with the time accuracy of transport. It is, on the contrary, higher in Ostrava, but here there is a decline in the number of transported passengers. In both analyzed cities is increased the accuracy of urban public transport and the speed of circulation of vehicles. As indicated, for passenger it is also important the price of ticket, which in Ostrava Transport Company in comparison with the Prague Public Transit Company increases more frequently and on a larger amount. This fact has subsequently influence on reducing the number of passengers in Ostrava.

Title of the Paper: **Manipulating Intervals of Probability Density Function in Autoregression Model for Simulating Strictly Stationary Random Sequences**

Authors: **Sergey Garbar**

Pages: **270-273**

Abstract: We consider a problem of simulating strictly stationary random sequences. A modification of an autoregression algorithm of first order is proposed. It allows to simulate of stationary random sequences with uniform distribution. Correlation properties of resulting random sequences are examined. Value R(1) of autocorrelation function must be in [-0.625, 0.625]. As the uniform distribution is the base for the inverse random sampling, simulated sequence can be further transformed to get the random sequence with specified distribution.

Title of the Paper: **Integration of ARIMA and Software Models for Wind Speed Forecast and Noise Map Prediction in a Wind Farm**

Authors: **Claudio Guarnaccia, Joseph Quartieri, Carmine Tepedino**

Pages: **259-269**

Abstract: Wind turbine installation for electricity production is growing all around the world. The large energy demand, in fact, together with the environmental issue, leads to the promotion of renewable energy sources, with low (or zero) polluting impact. Wind turbines represent a sustainable solution, especially in areas with strong wind speeds and low density of obstacles. Anyway, there is a problem of annoyance related basically to noise production and landscape degradation. Regarding noise, it is almost evident that the greater is the wind speed, the larger is the noise emission, because of higher rotation speed of the blades and higher aerodynamic noise. Of course higher wind speed corresponds also to larger electricity production, thus a compromise must be found between energy and noise. For this reason, models able to exploit the relation between wind speed and noise map in the surrounding area of any wind farm, represent a strong tool to help policy makers in monitoring operating wind farms and in designing turbines placements. In this paper, the wind turbine noise issue is faced by different point of view. After presenting the noise maps in a wind farm in Italy, produced in the framework of a predictive software, in different wind speed and directivity conditions, a seasonal ARIMA model is presented. This model is used to predict wind speeds, to be given as input of the software for noise map drawing. This method will show that, starting from the time series of wind speeds in the wind farm area, strong information about the noise levels map can be obtained by means of accurate modelling of the area under investigation.

Title of the Paper: **Lattice Paths Approach for Transient Solutions of Queues Using Coxian 2-Phase Distribution**

Authors: **Isnandar Slamet, Ritu Gupta, Narasimaha R. Achuthan, Roger Collinson**

Pages: **251-258**

Abstract: The paper aims at deriving transient solutions of non-Markovian queuing system M/G/1 starting from to remaining below the barrier and does not include any idle time of server through lattice path approach. The explicit form of the density and other measures of the system performance are not known. Our approach is to approximate general service time with Coxian 2-phase distribution, C2 and represent the queuing process as a lattice path by recording the state of the system at the point of transitions. We use the lattice path combinatorics to count the feasible number of paths and corresponding probabilities. The above leads to the required density that has simple probabilistic structure and can be computed using .The investigation of the influence of taking different values of a parameter on the behavior of the graphs of the density is also presented.

Title of the Paper: **Wiener-Hammerstein Models Identification**

Authors: **A. Brouri**

Pages: **244-250**

Abstract: This work discusses the identification of nonlinear systems structured in blocks. Presently, the proposed method is addressed to Wiener-Hammerstein models. Hammerstein and Wiener models are nonlinear representations of systems composed by connecting of a nonlinearity element f(.) and a linear subsystem G(s) in the form f(.)-G(s) and G(s)-f(.) respectively. The identification of nonlinearity blocks and linear subsystems is not a trivial problem, and has attracted a lot of research interest. The linear subsystems Gi(s) and Go(s) are allowed to be nonparametric and of unknown structure. Presently, the system nonlinearity is static and may be noninvertible. Moreover, this latter is of unknown structure and is only supposed to be well approximated, within any subinterval belonging to the working interval, with a polynomial of unknown order and parameters. Then, using a frequency identification method, a two-phase algorithm is presented for identifying the linear subsystems Gi(s) and Go(s) (the frequency complex gains) and the nonlinearity element f(.). The procedure is illustrated with simulated and experimental data. The proposed strategy involves simples input signals.

Title of the Paper: **Visualization Algorithms for the Steady State Sets of a Class of Singularly Disturbed Nonlinear Control Dynamical Systems**

Authors: **Byungik Kahng, Mathew Gomez, Eduardo Padilla**

Pages: **237-243**

Abstract: It is known that a multiple valued iterative dynamical system (MVIDS) can be used to model a nonlinear disturbed control dynamical systems (DCDS). When the system is subject to large sudden disturbance, which we call the singular disturbance, its maximal invariant set often exhibits a fractal structure. This paper focuses upon the visualization algorithm of the resulting invariant fractal. It discusses the nature of the multiple valuedness of the iterative dynamics in an algorithmic viewpoint. The relevant source codes of our visualization programs will be analyzed.

Title of the Paper: **Pricing in the Real Estate Market as a Stochastic Limit. Log Normal Approximation**

Authors: **Oleg V. Rusakov, Michael B. Laskin, Olga I. Jaksumbaeva**

Pages: **229-236**

Abstract: We construct a stochastic model of real estate pricing. The method of the pricing construction is based on a sequential comparison of the supply prices. We proof that under standard assumptions imposed upon the comparison coefficients there exists an unique non-degenerated limit in distribution and this limit has the Log Normal law of distribution. The accordance of empirical distributions of prices to the theoretically obtained Log Normal distribution we verify by numerous statistical data of real estate prices from Saint-Petersburg (Russia). For establishing this accordance we essentially apply the efficient and sensitive test of fit of Kolmogorov-Smirnov. Basing on the world admitted standard of estimation prices in real estate market, we conclude that the most probable price, i.e. mode of distribution, is correctly and uniquely determined under the Log Normal approximation. Since the mean value of Log Normal distribution exceeds the mode ? most probable value, it follows that the prices valued by the mathematical expectation are systematically overstated.

Title of the Paper: **Numerical Simulation of the Disturbances Development in a Supersonic Boundary Layer**

Authors: **S. A. Gaponov, A. N. Semenov**

Pages: **220-228**

Abstract: For solution of hydrodynamic stability problems the evolutionary method is offered. The essence of this method consists that an arbitrary initial disturbance is described by one wave with the greatest increment on large times, which varies according to the law exp(-iωτ) . In order to verify the new method and to work out the numerical scheme the stability calculations were carried out also on the base of the classical theory. The evolutionary method is used to study the effects of the gas injection direction through a porous surface on stability of a supersonic boundary layer at the Mach number M=2. Results of the evolutionary method coincide with data of the classical theory very well. The boundary layer receptivity process due to the interaction of three-dimensional slow acoustic disturbances is numerically investigated at a free stream Mach number of 2.0. Problem is solved in the linear approximation relatively excited disturbances by an acoustic wave. Numerical simulations were conducted with using the program complex Ansys. In general, matching the results of the approximate method (based on stability equations for low-frequency fluctuations) with direct numerical simulation data is satisfactory. Normalized solutions on the corresponding maxima of the velocity perturbations amplitudes are coincided well enough about a wall. The greatest discrepancy occurs in the area of the boundary layer edge where the approximation theory is inapplicable.

Title of the Paper: **A Dual Method to Model IoT Systems**

Authors: **Sunghyeon Lee, Yeongbok Choe, Moonkun Lee**

Pages: **210-219**

Abstract: This paper presents a dual method: 1) to specify both dynamic properties, such as operational requirements, and static properties, such as safety requirements, of IoT systems, whose services are distributed over a geographical space and are mobile over the space in time, and 2) verify the validation of the static properties over the dynamic properties. Firstly, the dynamic properties are specified with a process algebra, called δ-Calculus, and the static properties are specified a first-order logic, called GTS Logic. Secondly, once specifications are done, the static properties are verified for its validity over the dynamic properties. For example, safety requirements are verified to see its validity over operational requirements by checking whether or not the safety requirements are satisfied for all the possible simulation cases of the operational requirements. In order to demonstrate the feasibility of the method, a tool, namely SAVE, is developed on a meta-modeling platform, namely ADOxx. The method and the tool can be considered one of the most innovative approaches to model the IoT systems.

Title of the Paper: **A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE – 1973 CE**

Authors: **Andrey V. Korotayev, Artemy Y. Malkov**

Pages: **200-209**

Abstract: Extremely simple mathematical models are shown to be able to account for 99.2–99.91 per cent of all the variation in economic and demographic macrodynamics of the world for almost two millennia of its history. In this article we show that it is in no way coincidental that the world GDP dynamics in 1–1973 is approximated so well with a quadratic hyperbola, whereas the world population one does with a simple hyperbola. This appears to suggest a novel approach to the formation of the general theory of social macroevolution.

Title of the Paper: **On Approximations by Polynomial and Trigonometrical Integro-Differential Splines**

Authors: **I. G. Burova, S. V. Poluyanov**

Pages: **190-199**

Abstract: Here we construct continuously differentiable approximation using middle and left basis integro-differential splines of fifth order. The goal of this work is the presentation of some new formulas which are useful for the approximation of the functions with one and two variables. Here we construct the basic one-dimensional polynomial and trigonometrical integro-differential splines of the fifth order approximation. For each interval we construct the approximation separately. In order to construct the approximation in each interval we need the values of the function, its first derivative in the points of interpolation, and the value of the integral of the function over the interval. If we don’t know the values of the first derivative of the function in the points of interpolation and/or the value of the integral of the function over the interval then we use the expressions which were obtained for this instance and the error of the approximation will be of the fifth order. The one-dimensional case can be extended to multiple dimensions through the use of the tensor product spline constructs. The examples of the approximations functions of two variables are included. The spline approximation schemes discussed in this paper allow us to control the effect of knot placement on the accuracy of spline approximation. Numerical examples are presented.

Title of the Paper: **Dual Methods for Optimal Allocation of Total Network Resources**

Authors: **I. V. Konnov, A. Yu. Kashuba, E. Laitinen**

Pages: **185-189**

Abstract: We consider a general problem of optimal allocation of a homogeneous resource (bandwidth) in a wireless communication network, which is decomposed into several zones (clusters). The network manager must satisfy different users requirements. However, they may vary essentially from time to time. This makes the fixed allocation rules inefficient and requires certain adjustment procedure for each selected time period. Besides, sometimes users requirements may exceed the local network capacity in some zones, hence the network manager can buy additional volumes of this resource. This approach leads to a constrained convex optimization problem. We discuss several ways to find a solution of this problem, which exploit its special features. We suggest the dual Lagrangian method to be applied to selected constraints. This in particular enables us to replace the initial problem with one-dimensional dual one. We consider the case of the affine cost (utility) functions, when each calculation of the value of the dual function requires solution of a special linear programming problem. We can also utilize the zonal resource decomposition approach, which leads to a sequence of onedimensional optimization problems. The results of the numerical experiments confirm the preferences of the first method.

Title of the Paper: **Deformation of a Rotating Two-Lobed Droplet**

Authors: **Tadashi Watanabe**

Pages: **179-184**

Abstract: Deformation of a rotating two-lobed liquid droplet was simulated numerically by solving the three-dimensional Navier-Stokes equations using the level set method. The two-lobed droplet was formed by rotating a spherical droplet; the droplet changed its shape from the sphere to the rotating ellipsoid, and to the two-lobed shape. It was found that the time histories of the deformation of two-lobed droplet were almost the same for the cases with different initial rotation rate. The relationship between the deformation and the rotation rate was shown to agree qualitatively with the experimental data, and the preservation of rotation energy was confirmed.

Title of the Paper: **Modelling of Extreme Losses in Natural Disasters**

Authors: **P. Jindrová, V. Pacáková**

Pages: **171-178**

Abstract: The aim of this paper is to describe parametric curve-fitting methods for modelling extreme historical losses of natural catastrophes in the world. Article summarizes relevant theoretical results Extreme value theory (EVT) and Excess over Threshold Method (EOT) and results of their application to the data about amounts of damages in world catastrophe events in time period 2010-2014, published by Swiss Re studies Sigma. We aim to develop the models for extreme catastrophic losses by selecting a particular probability distributions through statistical analysis of empirical data with the best possible estimate of the upper tail area.

Title of the Paper: **A Preemptive Goal Programming for Allocating Students into Academic Departments of a Faculty**

Authors: **Nasruddin Hassan**

Pages: **166-170**

Abstract: A goal programming model is built to optimize the allocation of students into academic departmentss of a faculty. The goal programming model takes into account the limits of space capacity, financial allocation, the number of instructors and affirmative action quotas as goal constraints that are required to be fulfilled. Each constraint has a priority level and a weight attached. This goal programming model is then applied to the Faculty of Science and Technology, Universiti Kebangsaan Malaysia. The results of the preemptive goal programming model are then compared to that of the current allocation using the weighted mean absolute percentage error. The successful application demonstrates the ability of the goal programming model to comply with the student intake requirement and goal constraints of the academic departments.

Title of the Paper: **Intelligent Technology of Nonlinear Dynamics Diagnostics Using Volterra Kernels Moments**

Authors: **Oleksandr Fomin, Mohanad Masri, Vitaliy Pavlenko**

Pages: **158-165**

Abstract: The paper presents the technology of intelligent diagnostic systems construction for improving a reliability of nonlinear dynamic objects fault diagnosing. There genesis of the problem, goals and motivation are presented. It’s proposed improving method of model-based diagnostics based on nonparametric identification of systems and parameterization of diagnostic models with using Volterra kernels moments. Effective algorithms of diagnostic models parameterization are offered. Effectiveness of the proposed diagnostic model is investigated on example of switched reluctance motor. The recommendations of using considered technology in the tasks of diagnosing of various parameters of the electric motor are given.

Title of the Paper: **A Nonlinear Curve Equation for an Object Moving with Constant Acceleration Components**

Authors: **Mehmet Pakdemirli, İhsan Timuçin Dolapci**

Pages: **152-157**

Abstract: An ordinary differential equation describing a curve for which the tangential and normal acceleration components of the object remains constant is derived. The equation and initial conditions are expressed in dimensionless form. In its dimensionless form, the curves are effected only by a parameter which represents the ratio of the tangential acceleration to the normal acceleration. For constant velocity case, the equation can be solved analytically yielding a circular arc solution as expected. For nonzero tangential acceleration, closed form solutions are not available. Using a series solution, the curve is approximated by polynomials of arbitrary order. The general recursion relation for the polynomial coefficients are given. Two different perturbation solutions are also presented. In the first perturbation approach, the curve parameter is selected as the perturbation parameter. In the second approach, the depending variable is assumed to be small by introducing an alternative perturbation parameter. It is found that the second perturbation solution yields identical results with the series solutions. The approximate solutions and the numerical solutions are contrasted and within the range of validity, the curves can be successfully approximated by the analytical solutions. Potential application areas can be the design of highway curves, highway exits, railroads, route selection for ships and aircrafts. A practical application to highway exits is considered as an example.

Title of the Paper: **Energy Aspects at High Power Wounded Rotor Motors Startup**

Authors: **Ion Vlad , Sorin Enache, Monica Adela Enache, Ionut D. Smarandescu**

Pages: **143-151**

Abstract: The actual demand is to optimize the design of the high power three-phase induction motors with wounded rotor, so that power losses be minimized during the start. The paper analyzes the energetic aspects at the rheostatic startup of the existing three-phase induction motors with wounded rotor, used in conveyor belts actuation, characterized by hard starting. The higher moment of inertia of the system significantly increases the startup time, so it results a higher power consumption and a higher operating cost. A startup improvement can be made, in terms of investment and operating costs, using the main constructive sizes and the electromagnetic data sheet requirements of the induction motor. The study was made on customer request, which proposes a modernization of the start by using an electronically controlled rheostat at the rotor and a three-phase bridge. The paper makes a technical and an economical comparison between the known classic rheostatic starting and the version proposed by the beneficiary. Presented simulations aimed the electricity losses analysis for the wounded rotor induction motors startup. The proposed modernization of the induction motor with wounded rotor that exists at the conveyor, means a controlled starting with lower current shocks, but it results an increased electricity consumption by 10.7% during the start.

Title of the Paper: **A Novel Software Application for Interactive Affine Transformations of Fractals**

Authors: **Elena Hadzievay, Jovan Petkoski**

Pages: **134-142**

Abstract: The paper presents a novel interactive application created in the C# programming language under the Microsoft Visual Studio environment: its introduction, theoretical grounds and application. The application allows generating two-dimensional fractals defined by iterated function systems and performing their arbitrary affine transformation. Most importantly, this transformations are easily controllable and visible, done by dragging and dropping three predefined non-collinear points, exploiting the full potential of high quality fractal rendering in real-time. The affine transformations are enabled by assigning barycentric coordinates to the points that represent the image of the fractal attractor with respect to the three above mentioned points and thus relating the fractal to the points. Besides this main purpose of our application, many other features are offered: modifying specific parameters in the IFS code, gradually changing one or more parameters in the IFS code to follow the continuous transformation of the fractal attractor as a form of animation, coloring fractals, saving files in different image formats for post-processing, exporting and importing IFS parameter files and performing fast basic transformations to the fractals with the hotkeys option. Also, the application allows finding vertices of a kind of triangle with minimal area that contains the fractal, which form an affine basis. The practical use of such affine basis in modeling particular fractal is that the fractal is in the convex hull of the last affine basis, which makes the modeling more governable.

Title of the Paper: **On Hamiltonian Decomposition of Direct Graph Bundle**

Authors: **Irena Hrastnik Ladinek, Janez Žerovnik**

Pages: **120-133**

Abstract: Hamiltonian decomposition of direct graph bundles is studied. Based on the recent proof of hamiltonicity of all connected direct graph bundles over hamiltonian base and hamiltonian fibres, we conjecture that all direct graph bundles with fibres and base graphs being hamiltonian decomposable also admit a hamiltonian decomposition. The conjecture is proved for direct bundles over cycles when the nontrivial automorphism is any reflection. We also prove that direct graph bundles with a a cyclic shift when the base cycle is even admit a hamiltonian decomposition. In the case of odd base cycle we look at one partical situation where we can construct a hamiltonian decomposition.

Title of the Paper: **The Effectiveness of Horizontally Integrated Hospitals in the Czech Republic**

Authors: **Š. Papadaki, P. Staňková, and P. Klímek**

Pages: **110-119**

Abstract: In the Czech Republic, hospital costs are close to half of the total health care costs. This ratio is quite high compared to other V4 countries. It is therefore essential to concern ourselves with whether these expenses are spent effectively. Regarding the fact that in recent years hospitals continue to unite into various holdings, it is desirable to look into whether this form of horizontal integration leads to the desired effect, that is, to lowering expenses, raising effectiveness and to higher quality health care. This article is focussed on the effectiveness of two chosen holdings and it will analyse 6 indicators before and after integration.

Title of the Paper: **A New Block Method of Order Nine for Solving Fourth Order Ordinary Differential Equations Directly**

Authors: **Z. Omar, Kuboye J. O.**

Pages: **102-109**

Abstract: This paper considers the derivation of a new block method of order nine for the solution of fourth order ordinary differential equations directly. The multistep collocation approach is adopted in developing the new method where the use of power series approximate solution as an interpolation polynomial and its fourth derivative as a collocation equation are considered. The properties of the new developed method which include zero-stability, order, error constant, consistency, convergence and region of absolute stability are verified. Furthermore, the accuracy of the method is tested by solving some fourth order initial value problems which confirmed the superiority of the method over the existing methods.

Title of the Paper: **Estimation of the Maximum Error Induced by the Uncertainties of the Model of a Process in the Determination of a Control Law**

Authors: **A. Gharbi, M. Benrejeb, P. Borne**

Pages: **94-101**

Abstract: This paper presents an approach which enables to check the quality of the control law for a process whose evolution is described in the state space and the control is made from accessible information about the process and its desired evolution. For that it deals with the definition of the attractors characterizing the precision of control laws for a nonlinear process in presence of uncertainties and/or bounded perturbations This approach is based on aggregation techniques for stability study and on the choice of the state representations of the process.

Title of the Paper: **Mathematical Model and Finite-Volume Solution of a Three-Dimensional Fluid Flow Between an Eccentric Cylinder and a Cone**

Authors: **E. Kornaeva, L. Savin, A. Kornaev, V. Arkhipov**

Pages: **87-93**

Abstract: The goal of this paper is to detect and to justify the basic parameters and operational conditions in hydrodynamic seals with thin layer fluid flow when three–dimensionality of space, influence of inertia and viscous forces in consistent cannot be neglected. The mathematical model of three-dimensional enforced and shear fluid flow in an eccentric channel between a stationary outer cone and a rotating inner cylinder is based on the Navier-Stokes equation and the continuity equation. Such flows occur in the hydrodynamic seals and fluid–film bearings. On the basis of similarity theory and dimensional analysis the significance of the terms in the Navier–Stokes equation and the continuity equation were considered with the values of similarity criteria, such as Reynolds number, Euler number and others and geometry parameters, such as the eccentricity and conicity parameters. The numerical solution and simulation program are based on the finite-volume method with the calculation schemes, represented in this paper. The results represent velocity and pressure fields together with some integral characteristics e.g. leakage as a function of conicity and eccentricity. The results of numerical solutions were compared with results of widely known analytical solutions and with the results calculated by other numerical methods.

Title of the Paper: **A Methodological Approach for Managing Rail Disruptions with Different Perspectives**

Authors: **Luca D’Acierno, Antonio Placido, Marilisa Botte, Bruno Montella**

Pages: **80-86**

Abstract: Public transport systems represent a potentially effective tool for managing mobility in urban and metropolitan areas. In particular, especially in high density contexts, rail systems can be adopted as the backbone of transportation services. However, rail systems are also somewhat vulnerable to system failure since, for instance, a faulty train cannot be easily removed or overtaken. Hence, our proposal is to develop an off-line procedure based on a microsimulation approach for analysing the most frequent breakdown conditions and suggesting the adoption of optimal intervention strategies. Finally, different perspectives (i.e. requirements of passengers and rail operators) are proposed and applied in the case of a real metro line in the south of Italy.

Title of the Paper: **Fitting Anisochronic Models by Method of Moments for Anisochronic Control of Time Delay Systems**

Authors: **Milan Hofreiter**

Pages: **71-79**

Abstract: The paper introduces an original approach to parameter estimation of anisochronic models describing systems, which are conventionally described by a serial combination of a rational transfer function and a transportation delay. The method of moments is used for this purpose. Since the method of moments uses step responses, the paper also introduces an original formula for the derivation of step responses from relay feedback control. At the end of this paper, the anisochronic controller using the anisochronic model and the Desired Model Method will be derived. The applicability of the suggested methodology is presented examples in the Matlab/Simulink environment.

Title of the Paper: **Deterministic, Stochastic and Fractional Technology Diffusion Model with Distributed Time Delay**

Authors: **Mihaela Neamţu, Nicoleta Sîrghi, Gabriela Mircea, Petru C. Străin**

Pages: **62-70**

Abstract: In this paper, we analyze a technology diffusion model with distributed time delays. In the process of adoption a technology, a firm takes into account the advertising effectiveness, government policy and production costs. The average time for making the final decision is introduced. The mathematical model is described by a system with three nonlinear differential equations with distributed time delays. Two types of kernels are taken into account: Dirac and weak. When the distributions are Dirac, the cases, with one delay and two different delays, are considered. The conditions for the existence of a Hopf bifurcation are given. The stochastic and fractional technology diffusion models are introduced and their orbits are displayed. The last part of the paper includes numerical simulations and conclusions.

Title of the Paper: **Aircraft Flap Control System: Proposal of a Simulink Test Bench for Evaluating Innovative Asymmetry Monitoring and Control Techniques**

Authors: **Dario Belmonte, Matteo D. L. Dalla Vedova, Paolo Maggiore**

Pages: **51-61**

Abstract: One of the most important requirements in the design of secondary flight control actuation system is the proper limitation of the asymmetry between left and right wing flap surfaces; these asymmetries, that are typically due to mechanical transmission failures, must be timely detected and neutralized in order to guarantee the aircraft safety (especially during takeoff and landing flight phase in which the effects of these asymmetries could generates uncontrollable aircraft attitudes). In particular, when the angular asymmetry exceeds a defined critical value, the flap control system must detect and identify the incoming failure and actuate proper stopping procedures in order to limit this increasing asymmetry; to this purpose, it is necessary to conceive effective control algorithms able to perform an early fault detection avoiding false alarms. In recent applications, the most commonly used architectures employ the reversible actuators with wingtip brakes and centrally located PDU (of a dual motor type for operational reliability) because it is cheaper and more efficient, nevertheless, especially in severe fault conditions (torque shaft break under very high aerodynamic load) could generate unacceptable asymmetries. Therefore the development of enhanced flap actuation systems based on innovative layout or enhanced monitoring and control techniques can improve significantly the operating performances of the secondary flight control systems. In order to evaluate the behaviors of a real flap actuation system, simulating with a proper accuracy its dynamic responses and testing the performances of different monitoring and control algorithms, the authors propose a robust simulation developed in Matlab-Simulink numerical environment. By means the proposed numerical simulation model it is also possible to simulate a wide range of operating conditions (variable aerodynamic load, different mechanical layouts and several hydraulic and mechanical failures), to test new flap control system solutions (alternative architectures, new no-back devices or damping systems) and to evaluate the robustness of the aforesaid asymmetry monitoring techniques.

Title of the Paper: **A Package of Fast Tools for Genomic Sequence Analysis**

Authors: **Boris J. Steinberg, Jumana M. Abu-Khalil, Mikhail G. Adigeyev, Andrey A. Bout, Anton V. Kermanov, Evgeny A. Pshenichnyy, Galina V. Ramanchauskayte, Alena P. Kroshkina, Alexandr V. Gutnikov, Natalia S. Ponomareva, Anatoliy E. Panich, Tatiana P. Shkurat**

Pages: **42-50**

Abstract: Here we present a current progress towards the develepment of nucleotide sequence analysis software package produced as a result of bioinformatics initiative at SFedU. Different modules included in the package allow to perform wide range of sophisticated operations including sequence alignment, motif search and de novo discovery, primer design etc. The particular advantage of the package modules is the reduced time of task performing coupled with optimization for memory usage both leading to improved performance. The latter was reached due to using special data structures, parallel running, etc. Widely used in bioinformatics pairwise alignments are represented by two pairwise alignment algorithms (parallel block and parallel block with optimal memory usage) adjusted to running on multi-core processors and accelerators. The performance tests have confirmed that the former one is faster than Needleman-Wunsch algorithm by ~60% and EMBOSS tool by ~30% . The latter one aligns long sequences faster than EMBOSS Stretcher by 40%. The motif discovery time was decreased tenfold for some conditions when Gibbs sampling method with truncated generalized suffix trees was introduced into algortihm. A VP-tree based approach offered for locating of genome origins of replications allowed to lower time complexity comparing with the na?ve algorithm.

Title of the Paper: **Combination of Evolutionary and Gradient Optimization Techniques in Model Predictive Control**

Authors: **Jan Antos, Marek Kubalcik**

Pages: **34-41**

Abstract: Model predictive control (MPC) designates a control method based on the model. This method is suitable for controlling of various kinds of systems. The basic principle is to calculate the future behaviour of a system and to use this prediction for the optimization of a control process. The optimization problem must be then solved in each sampling period. One of the advantages of MPC is its ability to do online constraints handling systematically. These constraints may, however, cause that the optimization problem is more complex. In this case, some iterative algorithms must be applied in order to solve this problem effectively. This paper is focus on the combination of the optimization techniques. The basic idea is to combine the advantages of gradient and evolutionary algorithms.

Title of the Paper: **Stabilization of Convective Instability in Micropolar Fluid Model by Feedback Control Strategy Subjected to Internal Heat Source**

Authors: **N. F. M. Mokhtar, I. K. Khalid**

Pages: **27-33**

Abstract: This investigation reports on a stability analysis of Rayleigh-Benard convection in a horizontal of micropolar fluid layer heated from below. The effect of a feedback control strategy on the onset of steady convection in the presence of internal heat source is investigated theoretically using Galerkin technique. The eigenvalues are obtained for free-free, rigid-rigid, free-rigid boundary combination with isothermal temperature boundary condition. The influence of various micropolar parameters on the onset of convection has also been analyzed. The onset of motion is found to depend on the feedback control parameter, K and internal heat source, Q and the micropolar parameter Ni.

Title of the Paper: **CBSMAP-Model. Optimization and Control**

Authors: **Kondrashova E. V.**

Pages: **18-26**

Abstract: The present paper is devoted to the research of new controlled queuing model at control of Controlled Batch Semi-Markov Arrival Process (CBSMAP). Note that it is very reasonable to change the characteristics of arrival flows in various queuing models for optimization of its functioning. The control is based on the theory of controlled semi-markov processes for system optimization. The control is carried out using a type of the next batch, the moments of batch arrivals and the quantity of queries in the batch. CBSMAP-flow (new type flow) is constructed and research queuing model using the controlled flow is investigated. Several control measures for the model are used. Two theorems about the income functional for the model are formulated.

Title of the Paper: **Optimal Control Law for the Concentration of Carbon Dioxide in a Tomato Greenhouse and Optimal-Tuning PI Control as LQR for the Automatic Device**

Authors: **J. E. Moisés Gutierrez Arias, Nubia Ilia Ponce de León Puig, Gabriela Pérez Osorio, Eladio Flores Mena, Josefina Castaneda Camacho**

Pages: **7-17**

Abstract: The tomato model-space has been developed and it is called a big leaf-big fruit model, this model is formed by the mass balances: the non-structural biomass (nutrients) and the structural biomass of fruits and leaves. Also, a model that describes the behaviour on carbon dioxide concentration inside greenhouse is obtained. From the two models we get a new complete cropgreenhouse model. This model allows to get an optimal control for the carbon dioxide enrichment in a tomato greenhouse which gives benefits, because it is possible to achieve a saving for energy consumption and more tomato production. The optimal control theory is applied to the crop-greenhouse integrated system, which is based on four state variables: the consumption of nutrients, the fruits and leafs growth and the carbon dioxide concentration. This work contributes with the optimal control law that gives the desired CO2 concentration behaviour during the growth time for the crop. This behaviour will be a reference signal for the controller implementation in the electronic device that will be made in a future work. The simulations for the crop-greenhouse system are presented for a two weeks period. This paper also contributes at optimal-tuning PI control as Linear Quadratic Regulator of the electronic device. The simulation of the optimal control PI are showed here.

Title of the Paper: **Stability Enhancement of Hydroelectric Multi-Machines Power System Using Hybrid PSS-FACTS Devices**

Authors: **Abdessamad Horch, Abdelatif Naceri**

Pages: **1-6**

Abstract: This paper investigates comparison of SVC and STACOM performance for the transient stability improvement of a two area hydroelectric multi machines power system. The improvement of transient stability of a two- area multi- machine power system, using SVC (Static VAR Compensator) STATCOM (Static Synchronous Compensator) which is an effective FACTS (Flexible AC Transmission System) device capable of controlling the active and reactive power flows in a transmission line by controlling appropriately parameters. Simulations are carried out under Matlab/Simulink environment for the two- area multi- machine power system model with SVC & STATCOM to analyze the effects of SVC & STATCOM on transient stability performance of the system under two types of contingency (3-phase-to-ground fault and sudden load changes). The performance of SVC and STATCOM is compared from each other. In comparative result, STACOM gives the better result than SVC. So for the improvement of transient stability STATCOM is better than SVC. The simulation results showed the effectiveness and robustness of the proposed STATCOM and SVC on transient stability improvement of the system.