# International Journal of Mathematical Models and Methods in Applied Sciences

**ISSN: 1998-0140
Volume 12, 2018**

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.

Submit a paper | Submission terms | Paper format

**Volume 12, 2018**

Title of the Paper: **On A New Symbolic Method for Initial Value Problems for Systems of Higher-Order Linear Differential Equations**

Authors: **Srinivasarao Thota**

Pages: **194-202**

Abstract: This paper presents a symbolic method for solving an initial value problem (IVP) for the system of higher-order linear differential equations (HLDEs) with constant coefficients. In the proposed symbolic method, we apply the algebra of integrodifferential operators for computing the Green’s operator and Green’s function of a fully-inhomogeneous IVP on the level of operators. The algorithm of the proposed method will help to implement the manual calculations in commercial packages such as Mathematica, Matlab, Singular, Scilab etc. Maple implementation of the proposed method is discussed and provided sample computations. Certain examples are presented to illustrate the proposed method.

Title of the Paper: **A New Improved Technique for Frequency Band Implementation of Fractional Order Functions**

Authors: **Nitisha Shrivastava, Pragya Varshney**

Pages: **185-193**

Abstract: In this paper, a new approach for polynomial approximation of fractional order functions based on Carlson’s method is presented. This novel technique allows the user to choose the frequency range (low, medium or high), in which the approximation is to be developed. In order, to obtain a numerical solution using any iterative formulae, the initial conditions play a very important role. The Newton iterative formula used by Carlson starts with an initial estimate of one. With this initial guess, the frequency versus magnitude characteristics of the approximation obtained always has 1 rad/s as the centre frequency. Moreover, the choice of frequency range is not possible in the Carlson’s method. In this paper, we propose a new formula for the starting (initial) value of the approximation. The advantage of the formula is that it can be directly used for frequency band implementation of fractional order functions i.e. the approximation can be obtained in any desired frequency range with centre frequency not necessarily being one. The consistency of the novel approach has been verified for three fractional order functions. Comparisons with existing techniques have been presented and it is validated that the technique proposed in the paper shows better performance in all the frequency ranges.

Title of the Paper: **Denoising of Image Corrupted by Additive-Impulsive Noise Using Sparse Representation**

Authors: **Volodymyr Ponomaryov, Alfredo Palacios-Enriquez**

Pages: **177-184**

Abstract: In this paper, a novel framework is presented for suppression of noise in a color image contaminated by a mixture of additive and impulsive noise. This method consists of three principal stages: in the first stage, the suppression of impulsive noise is performed where the corrupted by impulsive noise pixels should be detected and filtered by a variant of median filter. In the second stage, novel additive noise suppression filter is used on Wavelet domain applying the sparse representation and 3D-filtering. Finally, the image obtained on the previous filtering stages is processed to correct non-desirable effects such as fine details blurring and texture distortions. Evaluation of novel approach in suppressing complex noise has been performed using objective criteria (PSNR and SSIM) and subjective perception via human visual system confirming their better performance in comparison with state-of-the-art techniques.

Title of the Paper: **How the Sirolimous-Releasing Dynamics Change when Adventitia Layer and Drug Metabolism are Taken into Account?**

Authors: **S. M. Vahedi, M. Valipour**

Pages: **167-176**

Abstract: Nowadays, the drug-eluting stent application has boomed as an effective treatment for coronary artery blockage. Experimental determination of the spatio-temporal variation of drug concentration in the arterial wall as well as the polymeric coating is very expensive and even impossible for many cases. In this paper, the volume-averaged porous media equations were developed to solve for transport through the porous arterial layers. The established equations are solved numerically by using the finite-volume method. The effects of adding adventitia layer and the drug consumption at the surface of Vasa vasorum cells in the mathematical modeling were considered as two important factors on drug pharmacokinetics. These models have been presented in two types of interface conditions, real porosity, and equal porosity, for the coating-media and media-adventitia interfaces, respectively. It was assumed that the injuries due to the angioplasty procedure penetrate to the depth of the media layer to have a more realistic simulation. The results showed that drug-containing polymer is diffusion-dominated and the porosity difference of the layers is the most effective factor for drug release dynamics in comparison to adding the adventitia layer and considering the sink condition there. Neglecting the adventitia layer causes a faster drug depletion during release action. While considering the drug reaction and washing out via Vasa vasorum cells have an inverse effect. The results show that although these two factors have a significant impact on the arterial drug uptake, the polymer does not change due to its low porosity. Utilizing the real porosities results in a considerable increase in concentration level. Therefore, dome shape of temporal variation of the normalized drug concentration profile in the media layer becomes more tapered when the difference of porosities not taken into account. Altogether, the results imply on the noticeable effect of interface condition on drug dynamics.

Title of the Paper: **Compressible Subsonic Flow in Gas Turbine Annular Diffusers**

Authors: **Meiriele A. Alvarenga, Cláudia R. Andrade**

Pages: **159-166**

Abstract: This work focuses on a numerical study of compressible subsonic flow in gas turbine annular diffusers. A diffuser is a diverging passage in which the flow is decelerated and the reduction in velocity head is converted to a rise in static pressure. Usually, for aircraft engines, and also many industrial engines, the length is a crucial restriction, resulting that diffuser shape should be the shortest possible distance. However, with an increase in divergence angle, stall losses arising from boundary-layer separation become more significant and the pressure recovery coefficient is affected. Hence, it is important to study the divergence angle as a function of the airflow behavior. In the numerical solution, mass, momentum and energy equations are discretized and solved employing the finite volume method, and the turbulence effects are taken into account using the realizable k- model with an enhanced wall treatment. Results showed that the annular diffuser performance is insensitive to Mach number for the divergence angle equal to 9°. On the other hand, the pressure recovery coefficient elevates as the Mach number increases for the divergence angle equal to 6°. The opposite phenomenon occurred for 12° diffuser due to the intense recirculation zones as the divergence angle increases.

Title of the Paper: **A New Approach Spider's Web Initial Solution and Data Envelopment Analysis for Solving an X-bar Control Chart**

Authors: **Kourosh Ranjbar, Hamid Khaloozadeh, Aghileh Heydari**

Pages: **141-158**

Abstract: X-bar control charts are widely used to monitor and control business and manufacturing processes. Design of control charts refers to the selection of parameters, including sample size, control-limit width, and sampling frequency. Many researchers have worked on this issue and also offered ways, however due to the many advantages acceptable the proposed methods have problems as well. The biggest challenge is the complexity of solving these issues. Due to the fact that optimal design of control charts can be formulated as a multi objective optimization problem, in this paper to solve this problem, we used initial solution Spider's web data envelopment analysis method. In previous methods used multiple algorithms to resolve the issue. But in the proposed method once using Data Envelopment Analysis method and without any other algorithm can solve multi objective problem and this method can yield desirable efficient. Finally, we compare the proposed method with other methods and an industrial application is presented to illustrate the solution procedure.

Title of the Paper: **A Simple Construction of Incoherent Finite Frames**

Authors: **Ghanshyam Bhatt**

Pages: **133-140**

Abstract: The frames with low mutual coherence are known to have several applications in compressed sensing. Householder matrices are used in this paper to construct matrices that form finite tight frames and have low mutual coherence. The algorithm also produces finite equiangular tight frames. In cases when the equiangular frames do not exit, it produces tight frames of approximately unit norm. A pair of orthogonal tight frames can be constructed from the resulting frames very easily.

Title of the Paper: **Adomian Decomposition Method to Generalized Thermoelastic Infinite Medium with Cylindrical Cavity under Three Theorems**

Authors: **Hamdy M. Youssef, Eman A. N. Al-Lehaibi**

Pages: **126-132**

Abstract: In this paper, a mathematical model of thermoelastic an infinite body with cylindrical cavity has been improved. A unified system of governing equations has been formulated in the context of three different models of thermoelasticity; Biot model, Lord-Shulman model, and Green-Lindsay model. Adomian decomposition method has been applied to get the solution of the model. The boundary surface of the cavity is subjected to harmonic thermal loading with zero heat flux and strain. The first components of the iteration have been calculated and used to get the rest components of the iteration formulas by using MAPLE 17 and by applying a certain Algorithm. The numerical results for the temperature, radial stress, strain, and displacement have been represented graphically. The angular thermal load and the relaxation times have significant effects on all the studied fields in the context of the three applied thermoelastic models. The results show that, Lord-Shulman model is much closed to Green-Lindsay model.

Title of the Paper: **3D Modelling of the Earth Crust and Upper Mantle by Geometrical Features of Bi-Characteristic Curves**

Authors: **Georgi Boyadzhiev**

Pages: **120-125**

Abstract: The aim of this paper is the introduction of a new approach to the 3D modelling of elastic piecewise homogeneous media, for instance Earth crust and upper mantle. The method is based on the principle of tomography with a point-force (singlet) as a source of the signal and a set of observations (records) at the surface. For the sake of simplicity of the exposition in this article we consider solid media only. The wave propagation in solid media is described by a system of three strongly coupled hyperbolic equations with piecewise constant coefficients. The characteristic set and bi-characteristic curves of this system are computed in a piecewise homogeneous half-space with free boundary and the formulae of reflection and diffraction of the bi-characteristics on the internal boundaries of the media. Applications of the characteristic set and bi-characteristic curves for the inverse problem in geophysics and Earth modelling are given.

Title of the Paper: **Design and Control of an Altazimuth Liquid Mirror Telescope**

Authors: **Juan Cristobal Alcaraz Tapia, Carlos E. Castaneda, Hector Vargas-Rodrıguez**

Pages: **112-119**

Abstract: In this paper, it is considered the design of a telescope in an altazimuth configuration. Its primary objective is a rotating liquid mirror made of mercury (any rotating liquid naturally adopts a perfect paraboloidal shape). This liquid mirror cannot be oriented. Hence, a mechanical and optical system is needed to conduct the light of a celestial body to it. The latter system is composed of two plane mirrors which, rotate around a horizontal and a vertical axis, two motors are employed to fulfill this purpose. The non-linear-block-control method is used to control these motors. A third motor keeps-up rotating a container filled with mercury to form the liquid mirror, the focal length of the rotating mirror depends on the angular velocity of this last motor. Hence, its rotation rate also needs to be controlled. The Methodology’s part A describes the design of a 2-links mechanical and optical system. The Methodology’s part B introduces the gravitational potential and the kinetic energy for each link in the mechanical and optical system. Then, using the Euler-Lagrange formalism, the equations governing this mechanical and optical system are obtained. Next, in the Methodology’s part C, a nonlinear block control strategy is used to synthesize the control algorithm for the mechanical and optical guide system. Finally, a stability analysis is performed, using the

Title of the Paper: **A Sub-Domain Meshless Method Based on Combination of Weak and Strong Forms**

Authors: **Yong-Ming Guo, Tatuya Hamada, Genki Yagawa, Shunpei Kamitani**

Pages: **106-111**

Abstract: A sub-domain method is often used in computational mechanics. The conforming sub-domains are often used, while the nonconforming sub-domains could be employed if needed. In the latter cases, the integrations of the sub-domains may be performed easily by choosing a simple configuration. Then, the meshless method with nonconforming sub-domains is considered one of the reasonable choices. We have proposed the sub-domain meshless method (SDMM). In this work, a nonlinear problem is analyzed by using the proposed SDMM. The numerical solutions show that the relative errors by using the SDMM are small and that the proposed method possesses a good convergence.

Title of the Paper: **Minimax Extrapolation of Multidimensional Stationary Processes with Missing Observations**

Authors: **Mikhail Moklyachuk, Oleksandr Masyutka, Maria Sidei**

Pages: **94-105**

Abstract: The problem of the mean-square optimal linear estimation of linear functionals which depend on the unknown values of a stochastic stationary stochastic process , , from observations of the process at points is considered. Formulas for calculating the mean-square errors and the spectral characteristics of the optimal linear estimates of the functionals are proposed under the condition of spectral certainty, where spectral densities of the processes and are exactly known. The minimax (robust) method of estimation is applied in the case of spectral uncertainty, where spectral densities are not known exactly, while sets of admissible spectral densities are given. Formulas that determine the least favorable spectral densities and minimax spectral characteristics are proposed for some special sets of admissible densities.

Title of the Paper: **An Enhanced LMI Approach for Observer-Based Control Design**

Authors: **D. Krokavec, A. Filasova**

Pages: **88-93**

Abstract: Enhanced linear matrix inequality form of design conditions for the observer-based state control of the continuous-time linear systems is presented in the paper. The design conditions are formulated in an enhanced bounded real lemma structure, documenting that the controller and observer parameter separation does not limit the design for systems with unknown disturbance. It is shown that the proposed design conditions provide better results considering the closed-loop system performances.

Title of the Paper: **An Approach to the Mathematical Modelling of the Multiphase Flow as of a Random Process**

Authors: **Іvan V. Kazachkov**

Pages: **79-87**

Abstract: The basic system of differential equations for a multiphase flow with the introduction of the probability of each phase in the flow is considered. The main analysis is focused on the case of a heterogeneous two-phase flow. The conservation equations for mass, momentum and energy are obtained under the assumption that parameters of the interacting phases are players of the statistical process. In parallel, dynamical system by the Kolmogorov's theorem for two states of a statistical system (phases of a two-phase mixture) is considered. Probability of phases in a flow is taken further for comparison with the probability and parameters of a two-phase flow from the equations of flow dynamics. Analysis of the parameters of a two-phase flow is performed as relating to available flow regimes from a statistical point of view on the basis of achievable parameter values and, first of all, on the condition that the probability is strictly in the range from 0 to 1. Correspondence of parameters by the equation array for flow dynamics and by solution of the dynamical system of two phases (two interacting statistical states) revealed the values of the coefficients for dynamical system, expressed in terms of the flow parameters. The results obtained are intended for further discussion, research, comparison with experimental data and with results of other researchers of the multiphase flows.

Title of the Paper: **Performance of ANN Classifier Using HRV Analysis for ECG Database**

Authors: **Desh Deepak Gautam, V. K. Giri, K. G. Upadhyay**

Pages: **73-78**

Abstract: Arrhythmias are the abnormal heartbeats inn which Ventricular arrhythmias are a fatal type of them. The timely prediction and classification of this irregularity can help in saving life or human health. In this paper, Artificial Neural Network (ANN) classifier has been tested on MIT-BIH database to predict and to classify the ventricular arrhythmias using HRV analysis. HRV or heart rate variability is a low frequency signal showing variations in heart beats, and can be efficiently utilized in the analysis of ECG signals. First, the preprocessing of the available database is done by de-noising and finding the peaks, then the HRV signal is built. ANN is used as a classifier to predict and classify the HRV signals into various arrhythmias.

Title of the Paper: **Modelling of Biological Purification Process Taking into Account the Temperature Mode**

Authors: **Andrii Safonyk**

Pages: **67-72**

Abstract: A mathematical model of the biological purification process is developed, taking into account the interaction of bacteria, organic and biologically non-oxidising substance in the conditions of diffusion, mass exchange disturbances and different temperature modes. An algorithm for solving the nonlinearly perturbed task "convection-diffusion-heat-mass-exchange" was elaborated. A computer experiment on the basis of the received algorithm was conducted. The influence of the concentration of oxygen and active sludge on the quality of the purification process as well as the mutual influence among heat and mass processes is shown. The possibility of automated control of the process for efficient purification of a biological filter taking into account the initial data of the wastewater is expected within the framework of this model.

Title of the Paper: **Analysis on Influence of Bottom Sediment Types on Side-Scan Sonar Imaging Properties**

Authors: **Zhang Kaihan, Yuan Fei, Cheng En**

Pages: **60-66**

Abstract: Side-scan sonar is widely used in the field of most kinds of detection, due to the imaging prooerties side-scan sonar generates corresponding noise. The different bottom sediment types causing different effects on seabed reverberation effects. After considering the seabed reverberation statistical model, four typical probability distribution models are compared by experiments to get the conclusion that Gamma distribution model is superior from the fitting effect and fastest calculation speed. On the basis of this, model can adjusts parameters of Gamma distribution with different types of bottom sediment to simulate the noise. Using the image gray scale mean and the gray level entropy, the image distribution parameters of the image are analyzed by multiple regression analysis, and the corresponding model is obtained. According to the model, it is possible to simulate noise caused by the reverberation of different bottom sediment types. This result provides an important basis for the separation of the subsurface image and the subsequent de-noising.

Title of the Paper: **Dual Solutions in the Stagnation-Point Flow Over a Shrinking Sheet**

Authors: **A. Ishak**

Pages: **56-59**

Abstract: In the present study, we consider a stagnation point flow over a stretching or shrinking sheet with slip effect at the boundary. The external flow and the stretching/shrinking velocities are assumed to vary linearly from the stagnation point. Different from the previous studies, we consider both stretching and shrinking cases, as well as the slip effect at the boundary. The numerical results show that the solution is unique for the stretching case, while dual solutions are possible for the shrinking case. A stability analysis is performed for the case where dual solutions exist to determine the stability of the solutions. Applying the slip condition increases the range of solutions for the shrinking case.

Title of the Paper: **Adaptive Compression Method of Underwater Image Based on Perceived Quality Estimation**

Authors: **Cai Yaqiong, Zou Haixia, Yuan Fei**

Pages: **43-55**

Abstract: Underwater image compression is one of the most important and essential part in underwater image transmission system, the effective image quality assessment and estimation of the compressed image can make the system adjust the compression ratio better in the compression process, improve the efficiency of image transmission system. This paper respectively estimate the underwater image compression perceived quality based on the strategy of coding compression and the compression strategy of compressive sensing, built model base on the mapping between image activity measurement(IAM) and BPP-SSIM curve, and obtain model parameters, then predict the perceived quality of image compression based on image activity measurement, compression ratio and compression strategy. The experimental results show that the model can effectively fit the quality curve of underwater image compression, according to the rules of the parameters in this model, the perceived quality of underwater compressed image can be estimated in the small error range. The presented method can effectively estimate the perceived quality of underwater compressed image , and effectively balance the relationship between the compression ratio and compression quality, reduce the pressure of the data cache, and improve the efficiency of underwater image communication system.

Title of the Paper: **Predicting Lactobacillus sp. (LAB) Population in a Functional Yoghurt**

Authors: **Elena Hadjimbei, George Botsaris, Vassilis Gekas**

Pages: **37-42**

Abstract: Lactic Acid Bacteria (LAB) are technologically necessary to manufacture yoghurt. Functional yoghurts contain not only Lactobacillus bulgaricus and Streptococcus thermophilus, but also probiotic LAB strains which are associated with certain human health benefits. Therefore, total LAB population is an essential quality criterion, as their viability should be retained at the highest level possible, throughout the commercial life of the yoghurt. The aim of the present study was the modeling of the survival of LAB in a functional goats’ milk yoghurt, enriched with Pistacia resin extracts and Saccharomyces boulardii. Novel modeling approaches were adopted, by the authors, which coined the concept of “thermal action” (Temperature x logarithm of Time). The modeling results provided a very promising approach not only in death kinetics but also in the case of moderate and low microbial population reductions as in the case of LAB survival in functional yoghurts. A modification of Bayes approach was also applied, which could provide an alternative way of modeling LAB growth and survival.

Title of the Paper: **Markov Chain Modeling for Reliability Estimation of the Self-Excited Induction Generator**

Authors: **Y. Naoui, H. Meglouli, S. Abudura**

Pages: **26-36**

Abstract: A new approach to the prediction of the reliability of Self-excited induction generator is presented in this paper. In this approach, a reliability analysis based on the Markov chain is used to diagnose the parameters that influence on the quality of the produced electrical energy. For this, we have designed mathematical models to the vacuum self-excited induction generator and load. These models are simulated by the MATLAB software to determine the parameters that affect the voltage supplied by the generator .After allowing us to study the influence of failures of devices on the system operation, we perform an analysis of the Failure Modes and their Effects which is a method commonly used in the first step of a reliability study. Then a model of Markov chain of the installation is applied to the system for studying the reliability and determines the failure probability of the installation components.

Title of the Paper: **Unsteady Flow of a Newtonian Fluid in a Contracting and Expanding Pipe**

Authors: **T. S. L. Radhika, M. B. Srinivas, T. Raja Rani, A. Karthik**

Pages: **21-25**

Abstract: In this paper, we considered the unsteady flow of Newtonian fluid in a contracting and expanding pipe. Flow is considered to be in a circular pipe whose radius is a function of time. Further, the flow is taken to be under the influence of a negative pressure gradient that is expressed as a separable function of spatial variable and time. The function in the spatial variable is taken in two forms: linear and exponential (both decreasing) and a sinusoidal function has been assumed in terms of the time variable. Fluid flow equations have been derived under the assumptions that the fluid is incompressible and the flow is axi-symmetric. The resulting coupled system of partial differential equation in terms of the radial and axial velocity components have been solved using Homotopy perturbation method. The effect of the parameters related to the contraction and expansion of the pipe and the frequency of oscillations, on the wall shear stress and volumetric flux has been studied for the two models developed in this work and the results are presented and discussed.

Title of the Paper: **Influence of Flooding Compartment on the Ship’s Safety Mironiuk Waldemar**

Authors: **Mironiuk Waldemar**

Pages: **16-20**

Abstract: Every damage to a ship results in certain effects, ie flooding water over one or more watertight compartments, which affects changes in stability and position of the ship. Determination of these changes is the basis for the sub-capacity calculations related to the operation of a damaged ship. During the ship's operation, unusual damage not anticipated in the stability documentation may occur, so it is necessary to know the methods of calculating the subdivision. During the ship's operation at sea a significant threat to his safety is a fire. Rarely causes sinking of the ship, however, the damage that it leaves is usually very serious and as always, depending on the level of crew training in the area of emergency response. The main extinguishing agent used on ships is usually sea water, which in large quantities poses a threat to the stability and submarine of the ship. Therefore, the main focus of the work was to determine the impact of flooding of high-stability compartments of the ship. The results of the calculations presented in the work include information on the amount of water in the range causing deterioration of the stability of the ship.

Title of the Paper: **Iterative Solution in Adaptive Model Predictive Control by Using Fixed-Point Transformation Method**

Authors: **Hamza Khan, Jozsef K. Tar, Imre J. Rudas, Gyorgy Eigner**

Pages: **7-15**

Abstract: In this paper the application of a recently introduced simple iterative solution of the Nonlinear Programming approach is investigated for the Adaptive Model Predictive Control of a strongly nonlinear dynamic paradigm, the Duffing oscillator. The main idea is to replace the numerically much more complex Reduced Gradient method in the optimization task under constraints when the cost function has relatively simple structure, but it does not allow the use of the traditional LQR controller. The suggested iterative solution is based on Banach’s Fixed Point Theorem that has twofold utilization: in approaching the solution of the optimization task, and in the realization of the adaptive behavior of the controller. In the presented, Julia language-based numerical simulations certain numerical tricks are also applied that were used to stabilize the run of the numerical simulations. The numerical examples illustrate the applicability of the suggested method for a wide class of cost function structures.

Title of the Paper: **Event-Triggered Global Robust Adaptive Stabilization for a Class of Nonlinear Systems**

Authors: **Wei Liu, Jie Huang**

Pages: **1-6**

Abstract: In this paper, we study the event-triggered global robust adaptive stabilization problem for a class of nonlinear systems with unity relative degree, which contain not only disturbances, but also static parameter uncertainties and dynamic uncertainties. By combining the robust control technique and the adaptive control technique, we design a digital control law, a digital adaptive law, and an event-triggered mechanism to stabilize the system in the sense that the state of the closed-loop system is globally ultimately bounded. What’s more, we show that the Zeno behavior does not happen. Finally, we illustrate our approach by applying it to the controlled Lorenz system.