# International Journal of Mathematical Models and Methods in Applied Sciences

**E-**ISSN: 1998-0140

Volume 11, 2017

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 11, 2017**

Title of the Paper: **Nonlinear Dynamics in Computer Design of Growth "Areas" for Regular and Irregular Schwartz’s Cylinder**

Authors: **Eugeny I. Smirnov, Artem D. Uvarov, Sergey A. Tikhomirov**

Pages: **320-327**

Abstract: In this article problems of students’ development of surface area concept by means of computer and mathematical modeling are discussed. The difficult mathematical concept is investigated on the example of lateral surface "area" of Schwartz's cylinder or Schwartz’s "boot" with use of the Qt Creator environment. The directions and basic constructs of computer and mathematical modeling in the conditions of triangulations crushing of the cylinder lateral surface and the identification of dynamics growth of the areas of the corresponding many-sided complexes in case of regular (equal) and irregular (unequal) splitting of cylinder’s height in research activity of students setting in small groups are revealed. Logistic mapping is reviewed as the basic instrument of regular triangulations crushing of lateral surface of the cylinder, which based on ideas of T. Malthus and generating compliance to the scenario of P. Verhulst of chaotic dynamics of nontrivial growth of many-sided complexes of the areas. Some of the new regularities similar to expansion of a tree of M. Feigenbaum via the cascade of bifurcation transitions of doubling of the period are received. It is concern of the synergy research of growth of the areas of many-sided of the operating parameters of the area’s growth. Growth rates of area difference of regular and irregular Schwartz’s cylinder is researched. The independence of areas growth dynamics at regular and irregular height splittings as functional variable at change of equal breakdowns of cylinder foundation is shown. The connection of research activity of students with increase of mathematical competence and creative activity processes of self-organization and educational motivation is established.

Title of the Paper: **Computational Mathematics in Algebra Teaching Process**

Authors: **Paola A. Szekieta, Alicia M. Tinnirello, Eduardo A. Gago**

Pages: **313-319**

Abstract: In this work the authors present a mathematic laboratory experience where the concepts of discrete dynamic systems are introduced in Algebra and Analytical Geometry subject with the purpose of using computer packages to familiarize students with recent developments at an early stage, in this case cellular automaton models are used as a dynamical system with discrete values in space, time and state. In this experience, computer scientists and mathematicians work together to carry out interdisciplinary projects which present discrete data management to first-year engineering students. Starting from the theoretical concepts, different cellular automata have being presented with interesting applications for connecting and integrating the computational mathematics in engineering teaching process.

Title of the Paper: **Acoustic Devices for Breathing Investigations**

Authors: **Semyon Shkundin, Valentina Rumyantseva**

Pages: **308-312**

Abstract: The problem of spirometry control in medicine and medical engineering still remains urgent. The necessity of getting more and more information from spirometry investigations imposes more and more stringent requirements for spirometers, volumeters and bodypletizmographs, first of all, to the primary spiroflow transdusers. Practice shows that these requirements can not be met by improving devices which use conventional spirometric principles. The new acoustic means for pulsating air-gas flow rate measurement has been created in Russia and is described in the paper. The main feature - special air-metric channel, supplied with ceramics electro-acoustic transducers. The principle of its operation is based on the dependence of the velocity of the acoustic vibrations arriving at the receiver upon the air-gas velocity. The device does not disturb the air dynamic structure of the flow, has no inertia or moving elements and unsurpassed sensitivity and precision.

Title of the Paper: **A Study of the Problem-Solving Process Using Fuzzy Relation Equations**

Authors: **Michael Gr. Voskoglou**

Pages: **303-307**

Abstract: Fuzzy relation equations are associated with the composition of binary fuzzy relations. In the present paper fuzzy relation equations are used as a tool for studying student problem-solving skills. A classroom application and other suitable examples connected to student problem-solving are also presented illustrating our results and useful conclusions are obtained.

Title of the Paper: **Determining Minimum Loading Margin of Power System Using Boundary Equations for Saddle Node Bifurcation**

Authors: **Tao Yi, Yanje Wang**

Pages: **296-302**

Abstract: Obtaining the minimum loading margin is the critical factor to determine the boundary of the voltage stability of power system. The paper formulates the electric power network equation with the status variables being nodal voltages and branch currents. The boundary characteristic equation for the saddle node bifurcation, which represents the boundary of voltage stability, is built based on the derived expression of power flow equilibrium curve in branch currents. The steady state boundary conditions for voltage on critical voltage circle are given. The equation for the distance between the loading point and the bifurcation boundary is found by geometrical analysis. This equation represents the shortest distance of the loading variation. The distance equation along with the boundary characteristic equation serves as an additional set of equations for analyzing the minimum loading margin. These equations are solved by Newton method which replaces the critical points to avoid the sigularity around saddle node bifurcation points. Simulation results demonstrate the method’s correctness and effectiveness.

Title of the Paper: **Designing of Wind Farm Layout by Using of Multi-Objective Optimization**

Authors: **Daniela I. Borissova, Ivan C. Mustakerov**

Pages: **290-295**

Abstract: The article deals with designing of wind farm layout using multi-objective combinatorial optimization modeling approach. This approach is implemented in a proposed algorithm for design and assessment of wind farm layout design. The described multi-objective model and algorithm are numerically tested for a real-life problem. The testing results show their applicability for designing of wind farm layout (determination of Pareto-optimal layouts of turbines) taking into account wind site area, wind conditions, wake effect and decision-maker preferences.

Title of the Paper: **A Novel Way of Treating the Finite-Buffer Queue GI/M/c/N Using Roots**

Authors: **James J. Kim, Mohan L. Chaudhry**

Pages: **286-289**

Abstract: We present a new way of solving the model using roots. By deriving and then solving the model’s characteristic equation we are able to achieve this. The roots of the characteristic equation are quickly found and the solution is computed efficiently since it is entirely in terms of roots. The method presented embarks on the first application of the roots method in the finite-buffer multi-server queues and it remains robust even if the inter-arrival times follow heavy-tailed distributions. Some numerical results are provided.

Title of the Paper: **Mathematical Description of the Resonance Effect in the Problem of Oscillations of Rotating Stratified Fluid**

Authors: **A. Giniatoulline**

Pages: **279-285**

Abstract: For various models of three-dimensional fluid which describe the flows in the Atmosphere and the Ocean, we find a relation between the essential spectrum of normal vibrations of internal waves and non-uniqueness of the limit amplitude of vibrations induced by external mass forces. We consider the both cases of incompressible and compressible and fluid and find a new mathematical description of the resonance of the internal waves. Since all the considered models correspond to of the stratified density in a homogeneous gravitational field, the obtained results may find their application in the study of the Atmosphere and the Ocean.

Title of the Paper: **Robust H∞ Controller of a Nonlinear Unstable System: Robotics Wrist**

Authors: **Youcef Zennir, Mohand Said Larabi**

Pages: **273-278**

Abstract: The paper presents a new multi-controllers approach with Hµ control applied to control a manipulator robot wrist (Staubli RX-90). A brief description of process and linear mathematical modeling of the process. Principle of multicontrollers approach of control is briefly presented. Our new proposals concerning the type of the controllers used in the multicontroller approach of control and which are one controller based on Hµ control for nonlinear system and linear local models around each operating points. The principal of Hµ control has been described and finally the simulation results obtained approve the efficiency of our design control followed by a conclusion and some perspectives for future work.

Title of the Paper: **Optimization of Fluid Flow Apportionment in a Manifold for a Skewed Flow Distribution**

Authors: **Bura Sreenivas**

Pages: **266-272**

Abstract: Fluid flow optimization of an 8-parameter flow manifold for skewed flow distribution is dealt in this paper. We deal with a one-by-four manifold. We have to optimally locate the guide plates. The objective of the work is to minimize the standard deviation of the actual flow rates from the set points by controlling 8 parameters four of which are lengths and four of which are angles of deflection. The set points are flows in ratios of 40:30:20:10. We take the input as the 60 data points generated by the process of CFD. Using the combination of ordinary least squares and genetic algorithms we develop the minimization algorithm for the objective function. We have successfully evaluated the objective and 8 parameters for skewed flow distribution. Since we needed to achieve skewed distribution, the guide vanes were found to have greater role in offering resistances in flow apportionment as compared to the case of equal flow distribution, thus serving as high value resistors in the manifold circuit.

Title of the Paper: **Research on Position Servo Control Based on Improved MFAC**

Authors: **Chen Huang, Aiping Xiao, Lei Zhao, Hua Qian**

Pages: **260-265**

Abstract: An improved model-free adaptive control algorithm in motor position control is designed, and use genetic algorithm for parameter optimization model-free adaptive control algorithm. Through the MATLAB software simulation and experimental tests, verify parameters of model-free adaptive control algorithms and improvement of model-free adaptive control algorithms for motor position control have good results.

Title of the Paper: **Unit Commitment and Dispatch with Coordination of Wind and Pumped Storage Hydro Units by using Cuckoo Search Algorithm**

Authors: **R. Jayashree, R. Soundarapandian**

Pages: **250-259**

Abstract: This paper proposes a multi objective model for Advanced Unit Commitment (AUC) with wind power and Pumped Storage (PS) units using Cuckoo Search (CS) algorithm. The novelty of the proposed method is improved levy flight searching ability, random reduction and ability to adapt complex optimization problems. Here, the CS algorithm to accommodate wind output uncertainty, with the multi-objective of providing an optimal AUC schedule for the thermal generators in the day-ahead market that minimizes the total cost under the different wind power output scenario. The proposed method is more reliable for AUC because it considering the wind power uncertainty using the Artificial Neural Network (ANN) and PS units, which are significantly reduces the total cost. Then the proposed method is implemented in the MATLAB/simulink platform and tested under IEEE standard bench mark system. The proposed method performance has been verified through the comparison analysis with the existing techniques. The comparison results were proved the superiority of the proposed method.

Title of the Paper: **On the Existence of Weak Solutions for a Nonlinear System of Atmosphere Dynamics Counting with Humidity and Heat Transfer**

Authors: **A. Giniatoulline**

Pages: **246-249**

Abstract: A nonlinear model of the mathematical fluid dynamics of the Atmosphere is considered. The model is a generalization of the nonlinear Navier-Stokes system with the addition of the equations for changeable density, humidity, moisture content in the clouds and heat transfer. An explicit algorithm for a weak solution is constructed by Galerkin method, the “a priori” estimates for the weak solution are obtained and the proof of the existence of the weak solution is given.

Title of the Paper: **Modeling and Control for Vertical Rail Vehicle Dynamic Vibration with Comfort Evaluation**

Authors: **Mortadha Graa**

Pages: **240-245**

Abstract: Investigation of control vibration is an important topic for the purposes of ride comfort in railway engineering. The vibration of rail vehicles becomes very complex because it is affected by the condition of vehicles, including suspensions and wheel profile, condition of track sections, including rail profile, rail irregularities, cant and curvature. The present study deals with the modeling and control for vertical active suspension rail vehicle by PID-ZN controller. A model of 17 degrees of freedom is adopted which consists of one car body 2 bogies and 4 wheel-sets. A Sperling ride index (ISO2631) is calculated using filtered RMS accelerations in order to evaluate the ride comfort. It should be noticed that the control model was carried out to improve Wz index about 41% at speed of 60 m/s.

Title of the Paper: **A Weight Restriction Approach for Evaluating Two-Stage Decision Making Units**

Authors: **A. Payan, A. R. Hajihosseini**

Pages: **233-239**

Abstract: In this paper, the relative efficiency of two-stage decision making units (DMUs) is estimated by modifying the product model proposed by Kao and Hwang (2008) and the additive model by Chen et al. (2009). Articles that have so far addressed the evaluation of two-stage units have been mainly unable to calculate relative efficiency. When no calculation of relative efficiency is available, it is not possible to form efficiency frontier, determine benchmark units, estimate returns to scale and so on. Based on the nature of two-stage models, we propose to consider them as data envelopment analysis models with the assurance region type II. In this direction, the relative efficiency of two-stage DMUs is estimated. The validity of the method is also proved. An example is presented to explain the method and draw a comparison between this method and other available methods of two-stage units.

Title of the Paper: **Numerical Investigation of the Couette Flow in a Duct with an Embedded Cavity**

Authors: **E. Rossi di Schio, S. Guidozzi**

Pages: **229-232**

Abstract: In the present paper a numerical solution of the Couette flow is presented. The considered channes displays a cavity, shortly after the inlet section, that enhances the vortex formation. The governing equations are written in a dimensionless form and solved by employing Comsol Multiphysics, a software package based on a Galerkin finite element procedure. Visualizations of vortex, for different values of the Reylonds number, are provided.

Title of the Paper: **A Penalty Based Filters method in Direct Search Optimization**

Authors: **Aldina Correia, Joao Matias, Pedro Mestre, Carlos Serodio**

Pages: **221-228**

Abstract: Constrained nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving unconstrained problems obtained form the original problem, has shown to be effective, particularly when used with direct search methods. An alternative to solve the above mentioned problems is the filters method. The filters method, introduced by Fletcher and Leyffer in 2002, has been widely used to solve constrained problems. These methods use a different strategy when compared with penalty or barrier functions. The previous functions define a new one that combine the objective function and the constraints, while the filters method treat optimization problems as bi-objective problems where the objective function and a function that aggregates the constraints are optimized. Based on the work of Audet and Dennis, using filters method with derivative-free algorithms, the authors developed some works where other direct search methods were used, combining their potential with the filters method. More recently, a new variant of these methods was presented, where some alternative aggregation restrictions for the construction of filters were proposed. This paper presents a variant of the filters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are linked together and are not treated as completely independently.

Title of the Paper: **Adaptive Sampling for QoS Traffic Parameters Using Fuzzy System and Regression Model**

Authors: **A. Salama, R. Saatchi**

Pages: **212-220**

Abstract: Quality of service evaluation of wired and wireless networks for multimedia communication requires transmission parameters of packets making up the traffic through the medium to be analysed. Sampling methods play an important role in this process. Sampling provides a representative subset of the traffic thus reducing the time and resources needed for packet analysis. In an adaptive sampling, unlike fixed rate sampling, the sample rate changes over time in accordance with transmission rate or other traffic characteristics and thus could be more optimal than fixed parameter sampling. In this study an adaptive sampling technique that combined regression modelling and a fuzzy inference system was developed. The method adaptively determined the optimum number of packets to be selected by considering the changes in the traffic transmission characteristics. The method's operation was assessed using a computer network simulated in the NS-2 package. The adaptive sampling evaluated against a number of non-adaptive sampling methods gave an improved performance.

Title of the Paper: **Derivation of Boundary Conditions for Homogeneous Reservoir with Fractures**

Authors: **Elena Andriyanova, Vladimir Tyan**

Pages: **206-211**

Abstract: In this paper the new boundary conditions are presented for the understanding of flow behavior in a reservoir with fractures. As can be seen from the current seismic researches, most of the reservoirs in the world have faults with different permeability. The derived boundary conditions allow us to model filtration process for cases of tectonic faults and for hydraulic fracturing. It is achieved throw the complex potential and mathematical analyze technique.

Title of the Paper: **The Construction the New Way for the Solving of the Volterra Integral Equations with the Symmetric Boundaries**

Authors: **Mehdiyeva Galina, Ibrahimov Vagif, Imanova Mehriban**

Pages: **201-205**

Abstract: One of the priorities directions in modern computational mathematics is to define certain criteria for comparison of existing methods, which are applied to the solving of the different certain problems of natural science. In this connection here we will try to give some criteria for the comparison, of the onestep and multistep methods, which have applied to solving of the Volterra integral equation with the symmetric boundaries. By these comparison we are constructed more accurate methods and prove the advantages of the proposed methods have constructed at the junction of the forward jumping and hybrid methods. For the illustration the results obtained here, we used the model equation to solving of which here, have constructed the specific effective methods having certain accuracy.

Title of the Paper: **Full Path Trajectory Optimization for Different Constraints**

Authors: **AbdelMageed Mahmoud**

Pages: **183-200**

Abstract: Most of previous work discussed about trajectory optimization for one phase either ascent or gliding. This paper introduced the full trajectory optimization for different vehicle dynamics, and how be linked these two dynamics in one optimal trajectory. The full path optimal trajectory is important for many applications like aerospace industry, computing rocket and missile launch trajectories. Another goal in the paper how to set the final constraints for the ascent phase to meet the initial requirements for gliding phase. Finally, full analysis for different final constraints at gliding phase was done to improve the algorithm and to be sure, it is suitable for different constraint problems.

Title of the Paper: **Capitulation of the 2-Ideal Class Group of the Fields K = Q(sqrt(q1q2), sqrt(pq1q3)) where p, q1, q2 and q3 are distinct primes such that p≡ -q1 ≡ -q2 ≡-q3 ≡1 (mod 4)**

Authors: **A. Elmahi, A. Azizi, A. Mouhib, M. Ziane**

Pages: **178-182**

Title of the Paper: **A Fractional Order Mathematical Model for Enzymatic Biodiesel Synthesis and its Optimization**

Authors: **Fahad Al Basir, Priti Kmar Roy, Santanu Ray**

Pages: **170-177**

Abstract: Biodiesel, themost possible alternative of diesel fuel, is produced through transesterification of vegetable oil using chemical or enzyme catalytic methods. In this study, a mathematical model for enzymatic transesterification is proposed using fractional order differential equation. Optimal control approach on the system dynamics is adopted to maximize biodiesel yield. Necessary conditions for the optimality of the system are derived using Hamiltonian. The optimal control problem is solved numerically by developing iterative schemes through Matlab. Results obtained from simulating the proposed model, are compared to the existing results and found to be satisfactory.

Title of the Paper: **Learning to Strike Accurately with DQN-Based Algorithms**

Authors: **Ayal Taitler, Nahum Shimkin**

Pages: **158-169**

Abstract: We consider in this paper the application of deep reinforcement learning techniques to learning closed loop control and goal-oriented trajectory planning in a robotic application. We employ an end-to-end (from the motor input the required task) model free approach using a deep Q-learning framework to learn a motoric skill. We propose several improvements to the naive deep Q-learning algorithm which otherwise fails. First we use some rough prior knowledge we have on the goal of the task to heuristically explore the environment. Second we manage to prevent the so-called catastrophic forgetting of neural networks. We present our simulation results for accurate striking task in air hockey, and show the success and stability of our learning algorithm due to the proposed modifications. We also present simulations that further support our claim of successfully mitigating the problem of catastrophic forgetting.

Title of the Paper: **Control of the Molten Metal Crystallization Process in the Foundry Mold**

Authors: **A. Albu, V. Zubov**

Pages: **144-157**

Abstract: The optimal control problem of the metal solidification in casting is considered. The process is modeled by a three-dimensional two-phase initial-boundary value problem of the Stefan type. The mathematical formulation of the optimal control problem for the solidification process is presented. This problem was solved numerically using gradient optimization methods. The gradient of the cost function was computed by applying the fast automatic differentiation technique, which yields the exact value of the cost function gradient for the chosen discrete version of the optimal control problem.

Title of the Paper: **Planar Swarming Motion Under Single Leader as Nash Equilibrium**

Authors: **Aykut Yıldız, A. Bulent Ozguler**

Pages: **139-143**

Abstract: Two dimensional foraging swarms are modeled as a dynamic noncooperative game played by swarm members, each one of which minimizes its total effort during the journey by controlling its velocity. It is assumed that each member monitors its distance only to the member that starts the journey up front, called the leader. The leader is only concerned with minimizing its total control effort. The foraging location is assumed to be known by all members. It is shown that a unique Nash equilibrium exists under certain assumptions on the nature of relative weighing between the motions along the two coordinates in the plane. The Nash equilibrium displays a number of observed characteristics of biological swarms; for instance, a V-shape formation is preserved during the whole journey.

Title of the Paper: **Effect of Mass Transfer and Reaction Kinetics in Transesterification of Jatropha Curcas Oil**

Authors: **Jahangir Chowdhury, Xianbing Cao, Fahad Al Basir, Priti Kumar Roy**

Pages: **130-138**

Abstract: This paper presents the formulation and analysis of a mathematical model for biodiesel production through transesterification of vegetable oil such as Jatropha oil using alkaline catalysts in industrial scale. Previous works indicates that the transesterification reaction is mass transfer limited and it can be resolved with small changes in the kinetic properties exprimentally. With this view, our main focus is to develope the mathematical model for discussing the effect of parameters such as catalyst loading, stirring, temperature on mass transfer and reaction kinetics in different phases of transesterification process. Optimal control theoretic approach is applied on catalyst loading to administer the said dynamics for the maximum production of biodiesel. Validity of the mathematical model is established by experimental results.

Title of the Paper: **Mathematical Model of Temperature Mode for Protected Ground**

Authors: **I. Vladykin, N. Kondrateva, O. Riabova**

Pages: **124-129**

Abstract: Electro technology for protected ground is currently being developed as an energy-efficient and science-based branch of an agricultural sector. World tendencies of vegetable cultivation development for protected ground show almost universal switch to intensive energy-saving technologies for vegetable growing. The reduction of energy consumption is particularly topical as energy usage takes a significant percentage of the cost of vegetable output from greenhouses. The analysis of scientific publications, reports from greenhouse complexes and our own studies has shown that expenditure of energy on vegetable production in greenhouse complexes is around 40%. The analysis of specialist literature reveals that vegetable production in protected ground cannot always be profitable due to the influence of various economical, technological and also natural factors. So the reduction of costs on fuel-and power resources in the cost of output from protected ground is of current interest. Increased production in protected ground is connected with maintenance of required microclimate parameters by various electrical facilities for greenhouses. The operation of technological electrical facility that provides required microclimate parameters is impossible without programmable logic controllers which need the development of special operating model and program. With reference to the above mentioned the research task is to work outa mathematical model of temperature field which describes temperature change in the working volume of structures for protected ground according to external environmental conditions and allows managing the operation of installed equipment effectively in energy saving mode to maintain the required parameters of microclimate. Development of the mathematical model describing the change of temperature mode in greenhouses will allow to work out a program for electrical equipment operation under conditions of protected ground and reduce the consumption of fuel -and -energy resources by means of a system of microclimate maintenance.

Title of the Paper: **Enterprise Safe Management. Quantitative Modeling Aspects**

Authors: **Valery G. Matveykin, Boris S. Dmitrievsky, Vladimir I. Mednikov**

Pages: **117-123**

Abstract: Primitive community safety based on some its representatives’ strength and endurance. Later during the industrial age manufacturing processes complexity increased and needed not only named human qualities, but wide knowledge. Enterprises’ safe management became increasingly important. Their safety was determined by the amount of capital accumulated, relationships with raw materials or other resources providers and market customers. K. Marx created enterprise capital math model in terms of value-added. Later Kobb and Douglas created enterprise math models which included capital and labor for its safety. Never the less enterprises’ system has addiction crisis. J.M. Keynes suggested the state model of money flows and its control as a tool of overcoming crisis. In order to reduce uncertainty in enterprise safe management R Kaplan and D. Norton created model of enterprise strategic management system, which based on aggregation of four heterogeneous components such as finance (capital), internal processes, marketing, personnel education and growth. Thus, the capital accumulation remains the only way to form enterprise safety. Unlike predecessors we devised enterprise’s math model, i.e. their function, which uses seven complementary resource components and obligatorily comprise enterprise external environment. Based on the model we proved incompletion and inaccuracy of enterprise activity descriptions, which inherent to modern directions of its safety. Our devised models made it possible to create commodity market math models, including crisis, to create math models of environment influence on enterprise resources, including force majeure, and finally determine the enterprise resource protection sufficiency in these interactions. These models describe the other way for enterprises’ safety.

Title of the Paper: **Mathematical Models and Simulations of Glioblastoma Invasion**

Authors: **A. Kisato Kubo, Yuto Miyata, Hidetoshi Kobayashi, Naoki Hayashi**

Pages: **107-116**

Abstract: Stein and coworkers have in vitro experiments of U87MG glioblastoma invasion on the patterns of growth and dispersion of U87MG tumour spheroids in a three-dimensional collagen-I gel. They identify and characterise discrete cellular mechanisms underlying invasive cell motility from the experimental data and propose a continuum mathematical model describing the behaviour of invasive cells observed in their experiments. However in their experiments it is seen that the U87MG invasive cells often exhibit more complicated and irregular behaviour than their simulations. We propose a mathematical model, which generalises the radially biased motility term of their model, based on some kind of taxis govering the behaviour of U87MG cells in the experiment. We show a mathematical analysis of our model and give more realistic computer simulations of the behaviour of invasive cells by using our mathematical model.

Title of the Paper: **Modelling the Effect of Evaporation or Infiltration on the Free Surface of Groundwater in Certain Problems of Underground Hydromechanics**

Authors: **E. N. Bereslavskii**

Pages: **102-106**

Abstract: Within the framework of the theory of plane steady filtration of an incompressible fluid according to Darcy’s law, two limiting schemes modeling the filtration flows under the Joukowski tongue through a soil massive spread over an impermeable foundation or strongly permeable confined water bearing horizon are considered.

Title of the Paper: **Asymptotic Solutions of Integral Boundary Problem**

Authors: **Kalimoldayev Maksat, Kalizhanova Аliya, Kozbakova Ainur, Kartbayev Timur, Aitkulov Zhalau, Abdildayeva Assel, Akhmetzhanov Maxat, Kopbosyn Leila**

Pages: **94-101**

Abstract: This work is devoted to the asymptotic solutions of integral boundary value problem for the Inter-linear second order differential equation of Fredholm type. Studying an integral boundary value task, obtaining solution assessment of the set singular perturbed integral boundary value problem and difference estimate between the solutions of singular perturbed and unperturbed tasks; determination of singular perturbed integral boundary value problem solution behavior mode and its derivatives in discontinuity (jump) of the considered section and determination of the solution initial jumps values at discontinuity and of an integral member of the equation, as well, creation of asymptotic solution expansion assessing a residual member with any range of accuracy according to a small parameter by means of Cauchy task with an initial jump, at that selection of initial conditions due to singular perturbed boundary value problem solution behavior mode and its derivatives in the jump point. In the paper there applied methods of differential and integral equations theories, boundary function method, method of successive approximations and method of mathematical induction.

Title of the Paper: **Global Practical Tracking by Output Feedback for Uncertain Nonlinear Systems Under a Weaker Condition**

Authors: **Keylan Alimhan, Naohisa Otsuka, Orken J. Mamyrbayev**

Pages: **88-93**

Abstract: This paper considers the problem of global practical tracking via output feedback control for a class of more general uncertain high-order nonlinear systems. Under a weaker growth condition, by introducing sign function and necessarily modifying the homogeneous domination approach, this paper proposes a new control scheme to achieve the global practical tracking. It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.

Title of the Paper: **Numerical Strategies for Fluid-Dynamic and Heat Transfer Simulation for Regenerative Chambers in Glass Production Plants**

Authors: **C. Cravero, D. Marsano, A. Spoladore**

Pages: **82-87**

Abstract: The thermal regeneration systems are vital components for the energy performance of a glass furnace. The heat transfer in a conventional regenerative process is a complex phenomenon: mixed convection during the cold period (air flux) and combined presence of radiation ad forced convection during the hot period (exhaust gases flux). In a past work, the authors studied the regeneration chambers using CFD techniques assuming the checkers zone as a porous domain. The developed non-equilibrium porous model has confirmed to be a suitable tool for the design of regenerative chambers. In this work, a lower order 1-D model is presented as an additional tool to simulate the regenerative chamber during the design phase. The lower order model is tuned using the CFD 3D approach. A gases emissivity model, developed by the authors, is implemented into the 1D model in order to simulate the thermal effects of a waste gas injection in the air phase as a strategy to reduce NOx production during the following combustion process.

Title of the Paper: **Investigation and Rothe’s Type Scheme for Nonlinear Integro-Differential Multi-Dimensional Equations Associated with the Penetration of a Magnetic Field in a Substance**

Authors: **Temur Jangveladze, Zurab Kiguradze**

Pages: **75-81**

Abstract: The paper is devoted to the construction and study of the additive average semi-discrete scheme for two nonlinear multidimensional integro-differential equations of parabolic type. The studied equation is based on well-known Maxwell’s system arising in mathematical simulation of electromagnetic field penetration into a substance. Existence, uniqueness and long-time behavior of solutions of initial-boundary value problems for nonlinear systems of parabolic integro-differential equations are fixed too.

Title of the Paper: **Stochastic Simulation of Advection-Diffusion Equation Considering Uncertainty in Input Variables**

Authors: **Hossein Khorshidi, Gholamreza Rakhshandehroo, Nasser Talebbeydokhti**

Pages: **68-74**

Abstract: Due to the lack of understanding of the flow parameters including roughness coefficient, bed slope, and initial conditions, governing equations may be considered in the stochastic form. Karhunen–Loeve expansion (KLE) approach as a perturbative expansion method is applied to explore uncertainty and its propagation based on the Advection-Diffusion equation (ADE). To assess the uncertainty in the present work, input variables (including initial condition, boundary condition, and diffusion coefficient), as source of uncertainty, is imposed in the framework of one-dimensional open channel flow. Our investigation is aimed at obtaining higher-order solutions to the statistical moments of the flow depth as random field. KLE approach is adopted to decompose the uncertain parameter in terms of infinite series containing a set of orthogonal Gaussian random variables. Eigenvalues and eigenfunctions of the covariance function associated with the random initial condition play a key role in computing the coefficients of the series and extracted from Fredholm’s equation. The flow depth, as random dependent variable, is also represented as an infinite series which are obtained through decomposing by polynomial expansions in terms of the products of Gaussian random variables. The coefficients of the last series are governed by a set of recursive equations that are derived from the ADE. Monte Carlo simulation (MCS), as a reliable approach, is carried out for about 1000 realizations and compared with the KLE. The present results highlight statistical properties of input variables including initial condition, boundary condition and diffusion coefficient, then, flow depth variance is achieved based on the variance of the input random variable. It was found that when higher-order approximations are used to represent initial condition, KLE results (mean flow depth and the flow depth variance) would be as accurate as MCS, however, with much less computational time and effort.

Title of the Paper: **Comparison Between Available Assessment Methods of Historical Masonry Arches**

Authors: **Lucio Nobile, Veronica Bartolomeo**

Pages: **61-67**

Abstract: The aim of this paper is to compare each other the main analytical and numerical methods for the assessment of masonry arch bridges, highlighting strengths and weaknesses. The methods are mainly three: i) the Thrust Line Analysis Method; ii) the Mechanism Method; iii) the Finite Element Method. In addition a particular closed-form approach has been recently developed, the Elastio-Plastic Method. The Thrust Line Analysis Method and the Mechanism Method are analytical methods and are based on two of the fundamental theorems of the Plastic Analysis, while the Finite Element Method is a numerical method that uses different strategies of discretization to analyze these structures.

Title of the Paper: **Robust Carrier Tracking Approach for High Dynamic GNSS Signals based on Gaussian Particle Filtering**

Authors: **Pang Jing, Ni Shaojie, Ou Gang**

Pages: **55-60**

Abstract: For high dynamic applications of GNSS receivers, the tracking sensitivity is heavily affected by the large unpredictable motion dynamics. The stability of the traditional tracking approaches is poor when outlier occurs among observations. In this paper, a novel Gaussian Particle Filtering-based carrier tracking algorithm is proposed for high dynamic GNSS signals. The proposed algorithm can work stable when the received signal is weak. To deal with the outliers in the observations, a robust carrier tracking algorithm based on Gaussian Particle Filtering is also proposed. Finally, the performance of the proposed algorithms is evaluated by simulation, compared with two typical approaches.

Title of the Paper: **Wannier-Stark Ladders and the “Resonance” Technique**

Authors: **C. D. Papageorgiou, T. E. Raptis, A. C. Boucouvalas**

Pages: **47-54**

Abstract: The method of Resonant Transmission Lines (RTL) is introduced for the generic Sturm-Liouville problem. This is then used to derive a fast, non-perturbative algorithm for obtaining eigenvalues and eigenfunctions of the Schrödinger operator. Solutions are obtained via a special recursion from a fine tuning condition equivalent with a functional Continued Fraction Expansion or an equivalent set of Möbius transforms. We apply this technique in the case of an external electric field excitation into a long thin wire modeled as a 1D quantum trap for the electron gas. Some associations with previously reported experimental results in exploding wires under high power, high voltage but low energy exploding wires is discussed.

Title of the Paper: **Differential and Average Approaches to Rose and Mei Dropwise Condensation Models**

Authors: **Solmaz Boroomandi Barati, Jean-Charls Pinoli, Stéphane Valette, Yann Gavet**

Pages: **40-46**

Abstract: Two well-known models for drop-size distribution function during dropwise condensation -called Rose model and Mei model- were examined in two different aspects, average and differential point of view. It has been proved that these two models are able to describe the relation between droplets size and distribution function at each time step. The goal of this research is to investigate how these models can predict the relation between average distribution function (Nave) and average radius (rave) of droplets during a complete procedure of dropwise condensation and the relation between differential distribution function (dN dr ) and drops radius (r) at each time step. The empirical parameters are drop size distribution exponent (n) and fractal dimension (df) in Rose model and Mei model respectively. At first these two parameters were calculated based on the experimental data and then the validity of these calculations for our computer simulation was investigated. It was concluded that Rose method fits the results of differential distribution function with exponent n between 0.33 and 0.35, and average distribution function with n of around 0.38. The Mei model also can describe both differential and average results of simulation and experiments with fractal dimension of 1.79

Title of the Paper: **An Appraisal Model for Residential Construction: the Italian Case**

Authors: **Rubina Canesi, Giuliano Marella**

Pages: **33-39**

Abstract: The aim of this paper is to analyse the concept of production cost in a contemporary developing city in order to investigate and interpret the actual Italian real estate construction scenario. This study aims at shedding light on how construction costs have been affected by the new Italian sustainable and densification policies, analysing features such as the increase of the overall built volume and of the height of new buildings projects. In this paper we implement a statistical model able to interpret several and different variables influencing residential urban developments in order to define best practices in public policy and private urban development. In order to do this, the present study implements a regression model on 70 property development projects collected in the North of Italy between 2007 and 2015.

Title of the Paper: **Bayesian Estimations in the Generalized Lindley Model**

Authors: **Fairouz Aouf, Assia Chadli**

Pages: **26-32**

Abstract: The generalized Lindley distribution offers an important and a reliable tool for modelling and testing lifetime data. In this paper, the Bayesian analysis of generalized Lindley distribution model is considered under type II censured data. Bayes estimator and corresponding risks were derived using different loss functions such us squared error loss (SELF), Linex loss (LF) and entropy loss function (EF). We define two criteria which are the Pitman closeness criterion and the integrated mean square error (IMSE) to compare the Bayesian and the maximum likelihood estimators (MLE). A real data example is given for illustration.

Title of the Paper: **Performance of Macrodiversity System in the Presence of Gamma Long Term Fading and Different Short Term Fading**

Authors: **Dragana Krstić, Siniša Minić, Suad Suljović, Miloš Perić, Vladimir Veličković, Mihajlo Stefanović**

Pages: **16-25**

Abstract: In this paper, the performance of macrodiversity system with macrodiversity selection reception and two microdiversity maximum ratio combining (MRC) receivers are derived. In the first microdiversity receiver, received signal suffers correlated Gamma long term fading and Rayleigh short term fading, and in the second microdiversity receiver, received signal experiences correlated Gamma long term fading and κ-μ short term fading. Macrodiversity (MAD) receiver is of selection combining (SC) type and it mitigates Gamma long term fading effects; the first microdiversity (MID) MRC receiver reduces Rayleigh short term fading effects and the second one eliminates κ-μ short term fading effects on system performance. Cumulative distribution functions (CDF) and level crossing rates of signals at outputs of MID receivers are determined. Based on them, the level crossing rate (LCR) of MAD Selection Combining (SC) receiver output signal is calculated. Some figures are presented to show the influence of severity parameter of Nakagami-m short term fading, Rician factor of Rician fading, Rician factor of κ-μ fading, severity parameter and correlation coefficient of Gamma long term fading on LCR.

Title of the Paper: **Comparison of Different FEM Simulations of a Modular Wooden Arch Made with Hollow Blocks**

Authors: **Dora Foti, Giovanni Arrè, Salvatore Carbone**

Pages: **9-15**

Abstract: The paper proposes a comparison of different numerical simulations by Finite Element Models (FEM) of an arch made of modular wooden blocks with a hollow shape. Experimental tests have been realized on a prototype of the arch and the results have been compared with the results obtained from the numerical simulations. Three different numerical modeling of the blocks have been assumed in three different models, that is beam elements, plate elements and block elements. They distinguish for the level of accuracy and the level of calculus. Results are interesting to evaluate the better compromise between accuracy and cumbersome calculus to get a reliable modeling of these kind of structures. In particular, the investigations carried out considering different levels of detail allowed to clarify the potential use of wood for structural purposes. The weakest points results to be the connections as the arch collapsed not for failure of the material, but because of its connections and the joints between the various blocks; they have to be improved and modified, especially to face wind and earthquake actions, different from the loads utilized in the present study and dangerous for lightweight structures.

Title of the Paper: **3D Models of Cultural Heritage**

Authors: **V. Barrile, G. Bilotta, D. Lamari**

Pages: **1-8**

Abstract: Recent advances in the techniques of laser scanning and the increase in computing power in last years have enabled astonishing experiments of virtual reality. The three-dimensional digitizing of cultural heritage and its modeling are so becoming increasingly widespread. This work shows a comparison between the consolidated operating mode of the laser scanner with the techniques of image capture and generation of 3D models based on photographs made with ordinary digital cameras. Thanks to a special software exploiting appropriate photogrammetric techniques and algorithms defined as "Structure from Motion" (SfM), we can reconstruct high-resolution DEMs (Digital Elevation Model) of high quality. We studied a masonry tower in the south of Italy (Marina di Gioiosa Jonica, Reggio Calabria), dating back to the fifteenth and sixteenth century.