Search results for: mathematical problems

Authors: Risti Suryantari, Flaviana

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The aim of this research is to design calibration method of Thermochromic Liquid Crystal for temperature distribution measurement based on mathematical morphology of hue image A glass of water is placed on the surface of sample TLC R25C5W at certain temperature. We use scanner for image acquisition. The true images in RGB format is converted to HSV (hue, saturation, value) by taking of hue without saturation and value. Then the hue images is processed based on mathematical morphology using Matlab2013a software to get better images. There are differences on the final images after processing at each temperature variation based on visualization observation and the statistic value. The value of maximum and mean increase with rising temperature. It could be parameter to identify the temperature of the human body surface like hand or foot surface.

Keywords: thermochromic liquid crystal, TLC, mathematical morphology, hue image

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Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Ebru Dural, M. Zulfu Asık

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Laminated glass is a kind of safety glass, which is made by 'sandwiching' two glass sheets and a polyvinyl butyral (PVB) interlayer in between them. When the glass is broken, the interlayer in between the glass sheets can stick them together. Because of this property, the hazards of sharp projectiles during natural and man-made disasters reduces. They can be widely applied in building, architecture, automotive, transport industries. Laminated glass can easily undergo large displacements even under their own weight. In order to explain their true behavior, they should be analyzed by using large deflection theory to represent nonlinear behavior. In this study, a nonlinear mathematical model is developed for the analysis of laminated glass cylindrical shell which is free in radial directions and restrained in axial directions. The results will be verified by using the results of the experiment, carried out on laminated glass cylindrical shells. The behavior of laminated composite cylindrical shell can be represented by five partial differential equations. Four of the five equations are used to represent axial displacements and radial displacements and the fifth one for the transverse deflection of the unit. Governing partial differential equations are derived by employing variational principles and minimum potential energy concept. Finite difference method is employed to solve the coupled differential equations. First, they are converted into a system of matrix equations and then iterative procedure is employed. Iterative procedure is necessary since equations are coupled. Problems occurred in getting convergent sequence generated by the employed procedure are overcome by employing variable underrelaxation factor. The procedure developed to solve the differential equations provides not only less storage but also less calculation time, which is a substantial advantage in computational mechanics problems.

Keywords: laminated glass, mathematical model, nonlinear behavior, PVB

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Authors: Miriam Sosa-Díaz, Faustino Sánchez-Garduño

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In population dynamics the study of both, the abundance and the spatial distribution of the populations in a given habitat, is a fundamental issue a From ecological point of view, the determination of the factors influencing such changes involves important problems. In this paper a mathematical model to describe the temporal dynamic and the spatiotemporal dynamic of the interaction of three populations (pollinators, plants and herbivores) is presented. The study we present is carried out by stages: 1. The temporal dynamics and 2. The spatio-temporal dynamics. In turn, each of these stages is developed by considering three cases which correspond to the dynamics of each type of interaction. For instance, for stage 1, we consider three ODE nonlinear systems describing the pollinator-plant, plant-herbivore and plant-pollinator-herbivore, interactions, respectively. In each of these systems different types of dynamical behaviors are reported. Namely, transcritical and pitchfork bifurcations, existence of a limit cycle, existence of a heteroclinic orbit, etc. For the spatiotemporal dynamics of the two mathematical models a novel factor are introduced. This consists in considering that both, the pollinators and the herbivores, move towards those places of the habitat where the plant population density is high. In mathematical terms, this means that the diffusive part of the pollinators and herbivores equations depend on the plant population density. The analysis of this part is presented by considering pairs of populations, i. e., the pollinator-plant and plant-herbivore interactions and at the end the two mathematical model is presented, these models consist of two coupled nonlinear partial differential equations of reaction-diffusion type. These are defined on a rectangular domain with the homogeneous Neumann boundary conditions. We focused in the role played by the density dependent diffusion term into the coexistence of the populations. For both, the temporal and spatio-temporal dynamics, a several of numerical simulations are included.

Keywords: bifurcation, heteroclinic orbits, steady state, traveling wave

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Hanbey Hazar, Hakan Gul

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In this study; piston, exhaust, and suction valves of a diesel engine were coated in 300 mm thickness with Tungsten Carbide (WC) by using the HVOF coating method. Mathematical modeling of a coated and uncoated (standardized) engine was performed by using ANN (Artificial Neural Networks). The purpose was to decrease the number of repetitions of tests and reduce the test cost through mathematical modeling of engines by using ANN. The results obtained from the tests were entered in ANN and therefore engines' values at all speeds were estimated. Results obtained from the tests were compared with those obtained from ANN and they were observed to be compatible. It was also observed that, with thermal barrier coating, hydrocarbon (HC), carbon monoxide (CO), and smoke density values of the diesel engine decreased; but nitrogen oxides (NOx) increased. Furthermore, it was determined that results obtained through mathematical modeling by means of ANN reduced the number of test repetitions. Therefore, it was understood that time, fuel and labor could be saved in this way.

Keywords: Artificial Neural Network, Diesel Engine, Mathematical Modelling, Thermal Barrier Coating

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Authors: Michael G. Pantelyat

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Fundamental basics of pure and applied research in the area of magneto-thermo-mechanical numerical analysis and design of innovative electromagnetic devices (modern induction heaters, novel thermoelastic actuators, rotating electrical machines, induction cookers, electrophysical devices) are elaborated. Thus, mathematical models of magneto-thermo-mechanical processes in electromagnetic devices taking into account main interactions of interrelated phenomena are developed. In addition, graphical representation of coupled (multiphysics) phenomena under consideration is proposed. Besides, numerical techniques for nonlinear problems solution are developed. On this base, effective numerical algorithms for solution of actual problems of practical interest are proposed, validated and implemented in applied 2D and 3D computer codes developed. Many applied problems of practical interest regarding modern electrical engineering devices are numerically solved. Investigations of the influences of various interrelated physical phenomena (temperature dependences of material properties, thermal radiation, conditions of convective heat transfer, contact phenomena, etc.) on the accuracy of the electromagnetic, thermal and structural analyses are conducted. Important practical recommendations on the choice of rational structures, materials and operation modes of electromagnetic devices under consideration are proposed and implemented in industry.

Keywords: electromagnetic devices, multiphysics, numerical analysis, simulation and design

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Authors: Alexander N. Savostyanov, Tatiana A. Dolgorukova, Elena A. Esipenko, Mikhail S. Zaleshin, Margherita Malanchini, Anna V. Budakova, Alexander E. Saprygin, Tatiana A. Golovko, Yulia V. Kovas

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EEG correlates of mathematical and trait anxiety level were studied in 52 healthy Russian-speakers during execution of error-recognition tasks with lexical, arithmetic and algebraic conditions. Event-related spectral perturbations were used as a measure of brain activity. The ERSP plots revealed alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchronization within an interval of 150-350 ms. Amplitudes of these intervals reflected the accuracy of error recognition, and were differently associated with the three conditions. The correlates of anxiety were found in theta (4-8 Hz) and beta2 (16-20 Hz) frequency bands. In theta band the effects of mathematical anxiety were stronger expressed in lexical, than in arithmetic and algebraic condition. The mathematical anxiety effects in theta band were associated with differences between anterior and posterior cortical areas, whereas the effects of trait anxiety were associated with inter-hemispherical differences. In beta1 and beta2 bands effects of trait and mathematical anxiety were directed oppositely. The trait anxiety was associated with increase of amplitude of desynchronization, whereas the mathematical anxiety was associated with decrease of this amplitude. The effect of mathematical anxiety in beta2 band was insignificant for lexical condition but was the strongest in algebraic condition. EEG correlates of anxiety in theta band could be interpreted as indexes of task emotionality, whereas the reaction in beta2 band is related to tension of intellectual resources.

Keywords: EEG, brain activity, lexical and numerical error-recognition tasks, mathematical and trait anxiety

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Authors: P. Thepnarintra

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Frozen shrimp industry plays an important role in the development of production industry of the country. There has been a continuing development to response the increasing demand; however, there have been some problems in running the enterprises. The purposes of this study are to: 1) investigate problems related to basic factors in operating frozen shrimp industry based on the entrepreneurs’ points of view. The enterprises involved in this study were small and medium industry receiving Thai Frozen Foods Association. 2) Compare the problems of the frozen shrimp industry according to their sizes of operation in 3 provinces of the central region Thailand. Population in this study consisted of 148 managers from 148 frozen shrimp enterprises Thai Frozen Foods Association, of which 77 were small size and 71 were medium size. The data were analyzed to find percentage, arithmetic mean, standard deviation, and independent sample T-test with the significant hypothesis at .05. The results revealed that the problems of the frozen shrimp industries of both size were in high level. The needs for government supporting were in high level. The comparison of the problems and the basic factors between the small and medium size enterprises showed no statistically significant level. The problems that they mentioned included raw materials, labors, production, marketing, and the need for academic supporting from the government sector.

Keywords: frozen shrimp industry, problems, related to the enterprise, operation

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Authors: Zahid Ullah, Atlas Khan

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The rapid growth of data in diverse domains has created an urgent need for effective utilization of mathematical and statistical sciences in data analytics. This abstract explores the journey from theory to practice, emphasizing the importance of harnessing mathematical and statistical innovations to unlock the full potential of data analytics. Drawing on a comprehensive review of existing literature and research, this study investigates the fundamental theories and principles underpinning mathematical and statistical sciences in the context of data analytics. It delves into key mathematical concepts such as optimization, probability theory, statistical modeling, and machine learning algorithms, highlighting their significance in analyzing and extracting insights from complex datasets. Moreover, this abstract sheds light on the practical applications of mathematical and statistical sciences in real-world data analytics scenarios. Through case studies and examples, it showcases how mathematical and statistical innovations are being applied to tackle challenges in various fields such as finance, healthcare, marketing, and social sciences. These applications demonstrate the transformative power of mathematical and statistical sciences in data-driven decision-making. The abstract also emphasizes the importance of interdisciplinary collaboration, as it recognizes the synergy between mathematical and statistical sciences and other domains such as computer science, information technology, and domain-specific knowledge. Collaborative efforts enable the development of innovative methodologies and tools that bridge the gap between theory and practice, ultimately enhancing the effectiveness of data analytics. Furthermore, ethical considerations surrounding data analytics, including privacy, bias, and fairness, are addressed within the abstract. It underscores the need for responsible and transparent practices in data analytics, and highlights the role of mathematical and statistical sciences in ensuring ethical data handling and analysis. In conclusion, this abstract highlights the journey from theory to practice in harnessing mathematical and statistical sciences in data analytics. It showcases the practical applications of these sciences, the importance of interdisciplinary collaboration, and the need for ethical considerations. By bridging the gap between theory and practice, mathematical and statistical sciences contribute to unlocking the full potential of data analytics, empowering organizations and decision-makers with valuable insights for informed decision-making.

Keywords: data analytics, mathematical sciences, optimization, machine learning, interdisciplinary collaboration, practical applications

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Authors: Francis O. Nwawuru

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The convergence analysis of split monotone inclusion problems and fixed point problems of certain nonlinear mappings are investigated in the setting of real Hilbert spaces. Inertial extrapolation term in the spirit of Polyak is incorporated to speed up the rate of convergence. Under standard assumptions, a strong convergence of the proposed algorithm is established without computing the resolvent operator or involving Yosida approximation method. The stepsize involved in the algorithm does not depend on the spectral radius of the linear operator. Furthermore, applications of the proposed algorithm in solving some related optimization problems are also considered. Our result complements and extends numerous results in the literature.

Keywords: fixedpoint, hilbertspace, monotonemapping, resolventoperators

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Authors: Omar Alhamad, Waleed Eid

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Reinforced concrete is a concrete lined with steel so that the materials work together in the resistance forces. Reinforcement rods or mesh are used for tensile, shear, and sometimes intense pressure in a concrete structure. Reinforced concrete is subject to many natural problems or industrial errors. The result of these problems is that it reduces the efficiency of the reinforced concrete or its usefulness. Some of these problems are cracks, earthquakes, high temperatures or fires, as well as corrosion of reinforced iron inside reinforced concrete. There are also factors of ancient buildings or monuments that require some techniques to preserve them. This research presents some general information about reinforced concrete, the pros and cons of reinforced concrete, and then presents a series of literary studies of some of the late published researches on the subject of reinforced concrete and how to preserve it, propose solutions or treatments for the treatment of reinforced concrete problems, raise efficiency and quality for a longer period. These studies have provided advanced and modern methods and techniques in the field of reinforced concrete.

Keywords: reinforced concrete, treatment, concrete, corrosion, seismic, cracks

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Authors: Manana Chumburidze

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We have considered a non-classical model of dynamical problems for a conjugated system of differential equations arising in thermo-piezoelectricity, which was formulated by Toupin – Mindlin. The basic concepts and the general theory of solvability for isotropic homogeneous elastic media is considered. They are worked by using the methods the Laplace integral transform, potential method and singular integral equations. Approximate solutions of mixed boundary value problems for finite domain, bounded by the some closed surface are constructed. They are solved in explicitly by using the generalized Fourier's series method.

Keywords: thermo-piezoelectricity, boundary value problems, Fourier's series, isotropic homogeneous elastic media

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Authors: Chonlawit Yuwajitaa, Suttipong Pruangkab

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Existing situation on labour use, health management and problems, and ancillary work done along with buffalo farming in Thailand was studied, There were 52 farms had been interviewed during August to September 2014. The study revealed that 100 percent of labor use was family labors themselves and all of farmers reared their buffaloes and grew rice simultaneously. The farmers valued veterinary service and advice as the most important problem (40.40%) and buffalo farming health problems was found 7.69% of dystocia, retain placenta and abortion. The major problem that should be taken into account was officials involved and buffalo farming should be continually promoted by government sectors to help solving economic problems as a whole.

Keywords: buffalo, labor use, health management, Thailand

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Authors: Mohieddine Benghersallah, Lakhdar Boulanouar, Salim Belhadi

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Currently, higher production rate with required quality and low cost is the basic principle in the competitive manufacturing industry. This is mainly achieved by using high cutting speed and feed rates. Elevated temperatures in the cutting zone under these conditions shorten tool life and adversely affect the dimensional accuracy and surface integrity of component. Thus it is necessary to find optimum cutting conditions (cutting speed, feed rate, machining environment, tool material and geometry) that can produce components in accordance with the project and having a relatively high production rate. Response surface methodology is a collection of mathematical and statistical techniques that are useful for modelling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response. The work presented in this paper examines the effects of cutting parameters (cutting speed, feed rate and depth of cut) on to the surface roughness through the mathematical model developed by using the data gathered from a series of milling experiments performed.

Keywords: Statistical analysis (RSM), Bearing steel, Coating inserts, Tool life, Surface Roughness, End milling.

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Authors: A. Chateauneuf, M. Mostoufi, D. Vyncke

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Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo, comonotonicity, option pricing, scientific computing

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Authors: Imen Debbabi, Hédi BelHadjSalah

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The Improved Element Free Galerkin (IEFG) method is presented to treat the steady states and the transient heat transfer problems. As a result of a combination between the Improved Moving Least Square (IMLS) approximation and the Element Free Galerkin (EFG) method, the IEFG's shape functions don't have the Kronecker delta property and the penalty method is used to impose the Dirichlet boundary conditions. In this paper, two heat transfer problems, transient and steady states, are studied to improve the efficiency of this meshfree method for 2D heat transfer problems. The performance of the IEFG method is shown using the comparison between numerical and analytic results.

Keywords: meshfree methods, the Improved Moving Least Square approximation (IMLS), the Improved Element Free Galerkin method (IEFG), heat transfer problems

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Authors: Ghorbanali Mohammadi

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Background: Due to the widespread outbreak of the COVID-19 virus, a large number of people become infected with the disease every day and go to hospitals. The acute condition of this disease has caused the death of many people. Since all the stages of treatment for these people happen in the hospitals, nurses are at the forefront of the fight against this virus. This causes nurses to suffer from physical and mental health problems. Methods: Physical and mental problems in nurses were assessed using the Depression, Anxiety and Stress Scale (DASS-42) of Lovibond (1995) and the Nordic Questionnaire. Results: 90 nurses from emergency, intensive care, and coronary care units were examined, and a total of 180 questionnaires were collected and evaluated. It was found that 37.78%, 47.78%, and 21.11% of nurses have symptoms of depression, anxiety, and stress, respectively. 40% of the nurses had physical problems. In total, 65.17% of them were involved in one or more mental or physical illnesses. Conclusions: Of the three units surveyed, the nurses in intensive care, emergency room, and coronary care units worked more than ten hours a day. Examining the interaction of physical and mental health problems indicated that physical problems can aggravate mental problems.

Keywords: depression anxiety and stress scale of Lovibond, nordic questionnaire, mental health of nurses, physical health problems in nurses

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Authors: Theddeus T. Akano, Omotayo A. Fakinlede

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The modelling of physical phenomena, such as the earth’s free oscillations, the vibration of strings, the interaction of atomic particles, or the steady state flow in a bar give rise to Sturm-Liouville (SL) eigenvalue problems. The boundary applications of some systems like the convection-diffusion equation, electromagnetic and heat transfer problems requires the combination of Dirichlet and Neumann boundary conditions. Hence, the incorporation of Robin boundary condition in the analyses of Sturm-Liouville problem. This paper deals with the computation of the eigenvalues and eigenfunction of generalized Sturm-Liouville problems with Robin boundary condition using the finite element method. Numerical solutions of classical Sturm–Liouville problems are presented. The results show an agreement with the exact solution. High results precision is achieved with higher number of elements.

Keywords: Sturm-Liouville problem, Robin boundary condition, finite element method, eigenvalue problems

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Authors: Zahid Ullah, Atlas Khan

Abstract:

The rapid growth of data in various domains has created a pressing need for effective methods to transform this data into meaningful knowledge. In this era of big data, mathematical and statistical innovations play a crucial role in unlocking insights and facilitating informed decision-making in data analytics. This abstract aims to explore the transformative potential of these innovations and their impact on converting raw data into actionable knowledge. Drawing upon a comprehensive review of existing literature, this research investigates the cutting-edge mathematical and statistical techniques that enable the conversion of data into knowledge. By evaluating their underlying principles, strengths, and limitations, we aim to identify the most promising innovations in data analytics. To demonstrate the practical applications of these innovations, real-world datasets will be utilized through case studies or simulations. This empirical approach will showcase how mathematical and statistical innovations can extract patterns, trends, and insights from complex data, enabling evidence-based decision-making across diverse domains. Furthermore, a comparative analysis will be conducted to assess the performance, scalability, interpretability, and adaptability of different innovations. By benchmarking against established techniques, we aim to validate the effectiveness and superiority of the proposed mathematical and statistical innovations in data analytics. Ethical considerations surrounding data analytics, such as privacy, security, bias, and fairness, will be addressed throughout the research. Guidelines and best practices will be developed to ensure the responsible and ethical use of mathematical and statistical innovations in data analytics. The expected contributions of this research include advancements in mathematical and statistical sciences, improved data analysis techniques, enhanced decision-making processes, and practical implications for industries and policymakers. The outcomes will guide the adoption and implementation of mathematical and statistical innovations, empowering stakeholders to transform data into actionable knowledge and drive meaningful outcomes.

Keywords: data analytics, mathematical innovations, knowledge extraction, decision-making

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Authors: Lela Mirtskhulava, Mariam Khunjgurua, Nino Lomineishvili, Koba Bakuria

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Software reliability prediction gives a great opportunity to measure the software failure rate at any point throughout system test. A software reliability prediction model provides with the technique for improving reliability. Software reliability is very important factor for estimating overall system reliability, which depends on the individual component reliabilities. It differs from hardware reliability in that it reflects the design perfection. Main reason of software reliability problems is high complexity of software. Various approaches can be used to improve the reliability of software. We focus on software reliability model in this article, assuming that there is a time redundancy, the value of which (the number of repeated transmission of basic blocks) can be an optimization parameter. We consider given mathematical model in the assumption that in the system may occur not only irreversible failures, but also a failure that can be taken as self-repairing failures that significantly affect the reliability and accuracy of information transfer. Main task of the given paper is to find a time distribution function (DF) of instructions sequence transmission, which consists of random number of basic blocks. We consider the system software unreliable; the time between adjacent failures has exponential distribution.

Keywords: exponential distribution, conditional mean time to failure, distribution function, mathematical model, software reliability

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Authors: Nükhet Konuk, N. Gamze Turan, Yüksel Ardalı

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Cities play a vital role in the social fabric of countries and in national and regional economic growth worldwide; however, the environmental effects of such growth need to be assessed and managed better. The critical and most immediate problems faced by cities of developing countries are the health impacts of urban pollution that derive from inadequate water, sanitation, drainage and solid waste services, poor urban and industrial waste management, and air pollution. As globalization continues, earth's natural processes transform local problems into international issues. The aim of this study is to provide a broad overview of the pollution from urban wastes and emissions in Turkey which is a developing country. It is aimed to underline the significance of reorganizing the institutional tools in a worldwide perspective in order to generate coherent solutions to urban problems, and to enhance urban quality.

Keywords: environmental pollution, developing countries, environmental degradation, urban environmental problems

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Authors: V. S. Klimash, Ye Min Thu

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Thyristor rectifiers, inverters grid-tied, and AC voltage regulators are widely used in industry, and on electrified transport, they have a lot in common both in the power circuit and in the control system. They have a common mathematical structure and switching processes. At the same time, the rectifier, but the inverter units and thyristor regulators of alternating voltage are considered separately both theoretically and practically. They are written about in different books as completely different devices. The aim of this work is to combine them into one class based on the unity of the equations describing electromagnetic processes, and then, to show this unity on the mathematical model and experimental setup. Based on research from mathematics to the product, a conclusion is made about the methodology for the rapid conduct of research and experimental design work, preparation for production and serial production of converters with a unified bundle. In recent years, there has been a transition from thyristor circuits and transistor in modular design. Showing the example of thyristor rectifiers and AC voltage regulators, we can conclude that there is a unity of mathematical structures and grid-tied thyristor converters.

Keywords: direct current, alternating current, rectifier, AC voltage regulator, generalized mathematical model

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Authors: Aymen Laadhari

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The cardiovascular system is centered on the heart and is characterized by a very complex structure with different physical scales in space (e.g. micrometers for erythrocytes and centimeters for organs) and time (e.g. milliseconds for human brain activity and several years for development of some pathologies). The development and numerical implementation of mathematical models of the cardiovascular system is a tremendously challenging topic at the theoretical and computational levels, inducing consequently a growing interest over the past decade. The accurate computational investigations in both healthy and pathological cases of processes related to the functioning of the human cardiovascular system can be of great potential in tackling several problems of clinical relevance and in improving the diagnosis of specific diseases. In this talk, we focus on the specific task of simulating three particular phenomena related to the cardiovascular system on the macroscopic, mesoscopic and microscopic scales, respectively. Namely, we develop numerical methodologies tailored for the simulation of (i) the haemodynamics (i.e., fluid mechanics of blood) in the aorta and sinus of Valsalva interacting with highly deformable thin leaflets, (ii) the hyperelastic anisotropic behaviour of cardiomyocytes and the influence of calcium concentrations on the contraction of single cells, and (iii) the dynamics of red blood cells in microvasculature. For each problem, we present an appropriate fully Eulerian finite element methodology. We report several numerical examples to address in detail the relevance of the mathematical models in terms of physiological meaning and to illustrate the accuracy and efficiency of the numerical methods.

Keywords: finite element method, cardiovascular system, Eulerian framework, haemodynamics, heart valve, cardiomyocyte, red blood cell

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Authors: Alexander N. Savostyanov, Tatyana A. Dolgorukova, Elena A. Esipenko, Mikhail S. Zaleshin, Margherita Malanchini, Anna V. Budakova, Alexander E. Saprygin, Yulia V. Kovas

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The present study compared spectral-power indexes and cortical topography of brain activity in a sample characterized by different levels of trait and mathematical anxiety. 52 healthy Russian-speakers (age 17-32; 30 males) participated in the study. Participants solved an error recognition task under 3 conditions: A lexical condition (simple sentences in Russian), and two numerical conditions (simple arithmetic and complicated algebraic problems). Trait and mathematical anxiety were measured using self-repot questionnaires. EEG activity was recorded simultaneously during task execution. Event-related spectral perturbations (ERSP) were used to analyze spectral-power changes in brain activity. Additionally, sLORETA was applied in order to localize the sources of brain activity. When exploring EEG activity recorded after tasks onset during lexical conditions, sLORETA revealed increased activation in frontal and left temporal cortical areas, mainly in the alpha/beta frequency ranges. When examining the EEG activity recorded after task onset during arithmetic and algebraic conditions, additional activation in delta/theta band in the right parietal cortex was observed. The ERSP plots reveled alpha/beta desynchronizations within a 500-3000 ms interval after task onset and slow-wave synchronization within an interval of 150-350 ms. Amplitudes of these intervals reflected the accuracy of error recognition, and were differently associated with the three (lexical, arithmetic and algebraic) conditions. The level of trait anxiety was positively correlated with the amplitude of alpha/beta desynchronization. The level of mathematical anxiety was negatively correlated with the amplitude of theta synchronization and of alpha/beta desynchronization. Overall, trait anxiety was related with an increase in brain activation during task execution, whereas mathematical anxiety was associated with increased inhibitory-related activity. We gratefully acknowledge the support from the №11.G34.31.0043 grant from the Government of the Russian Federation.

Keywords: anxiety, EEG, lexical and numerical error-recognition tasks, alpha/beta desynchronization

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Refik Uyanöz, Sadife Güngör, Sevilay Konya

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The aim of this study is to show the employing ability of vocational students. And also, the employment problems of these students are emphasized in this study.The rapid development in technology and information and increased qualified labor is widely affects labor market. On the other hand, labor market will look for educated, qualified, talented and young people. Because of this reason, qualified staff should be educated at vocational high schools. Vocational high schools are one of the best institutions to educate qualified staff. In this research, the conditions of vocational high schools are studied. The difference between the employment policies and current employment problems are researched.

Keywords: vocational high school, employment, employment problems, vocational students

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Authors: Sulmaz Mozaffari, Zahra Mozaffari, Saman Mozaffari

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Man has always tried to find the Ideal place for life and he has experienced a lot of problems. So many internal and external limits has been on his way. Today man is threatened by so many crisis because of his specific look to the world. Literature as a universal science has not ignored this problem either. Children's literature has tried to present the social, cultural, religious and economical problems in tales and novels. This research tries to analyse social and cultural problems related to 10th century children from social point of criticism.

Keywords: social criticism, crisis, children's literature, tale

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Authors: Abdullah Ali H. Ahmadini, Firoz Ahmad, Intekhab Alam

Abstract:

Geometric programming problem (GPP) is a well-known non-linear optimization problem having a wide range of applications in many engineering problems. The structure of GPP is quite dynamic and easily fit to the various decision-making processes. The aim of this paper is to highlight the bounded solution method for GPP with special reference to variation among right-hand side parameters. Thus this paper is taken the advantage of two-level mathematical programming problems and determines the solution of the objective function in a specified interval called lower and upper bounds. The beauty of the proposed bounded solution method is that it does not require sensitivity analyses of the obtained optimal solution. The value of the objective function is directly calculated under varying parameters. To show the validity and applicability of the proposed method, a numerical example is presented. The system reliability optimization problem is also illustrated and found that the value of the objective function lies between the range of lower and upper bounds, respectively. At last, conclusions and future research are depicted based on the discussed work.

Keywords: varying parameters, geometric programming problem, bounded solution method, system reliability optimization

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