Search results for: mathematical methods

Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

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Innovation in manufacturing process technologies and associated product design affects the prospects for manufacturing today and in near future. In this study some theoretical methods, useful as tools in advanced manufacturing, are considered. In particular, some basic Mathematical, Operational Research, Heuristic, and Statistical techniques are discussed. These techniques/methods are very handy in many areas of advanced manufacturing processes, including process planning optimization, modelling and analysis. Generally the production rate requires the application of Mathematical methods. The Emerging Trends Processes in Advanced Manufacturing can be enhanced by using Mathematical Modelling and Optimization techniques.

Keywords: mathematical modelling, optimization, emerging trends, advanced manufacturing

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Authors: Hanife Merve Öztürk, Sıdıka Dalgan

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In this project, a capacity analysis study is done at TAT A. Ş. Maret Plant. Production capacity of products which generate 80% of sales amount are determined. Obtained data entered the LEKIN Scheduling Program and we get production schedules by using heuristic methods. Besides heuristic methods, as mathematical model, disjunctive programming formulation is adapted to flexible job shop problems by adding a new constraint to find optimal schedule solution.

Keywords: scheduling, flexible job shop problem, shifting bottleneck heuristic, mathematical modelling

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Authors: Emhimed Saffor

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In this paper, the problem of edge detection in digital images is considered. Three methods of edge detection based on mathematical morphology algorithm were applied on two sets (Brain and Chest) CT images. 3x3 filter for first method, 5x5 filter for second method and 7x7 filter for third method under MATLAB programming environment. The results of the above-mentioned methods are subjectively evaluated. The results show these methods are more efficient and satiable for medical images, and they can be used for different other applications.

Keywords: CT images, Matlab, medical images, edge detection

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Authors: M. K. Balyan

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The main principles of X-ray Fourier interferometric holography method are discussed. The object image is reconstructed by the mathematical method of Fourier transformation. The three methods are presented – method of approximation, iteration method and step by step method. As an example the complex amplitude transmission coefficient reconstruction of a beryllium wire is considered. The results reconstructed by three presented methods are compared. The best results are obtained by means of step by step method.

Keywords: dynamical diffraction, hologram, object image, X-ray holography

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Authors: El Hassene Osmani, Mounir Haddou, Naceurdine Bensalem

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In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely, the obstacle problem. We present a relaxed formulation for the problem using smoothing functions. Since we adopt a numerical point of view, we first relax the feasible domain of the problem, then using both mathematical programming methods and penalization methods, we get optimality conditions with smooth Lagrange multipliers. Some numerical experiments using IPOPT algorithm (Interior Point Optimizer) are presented to verify the efficiency of our approach.

Keywords: complementarity problem, IPOPT, Lagrange multipliers, mathematical programming, optimal control, smoothing methods, variationally inequalities

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: S. A. Sadegh Zadeh, C. Kambhampati

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Mathematical and computational modellings are the necessary tools for reviewing, analysing, and predicting processes and events in the wide spectrum range of scientific fields. Therefore, in a field as rapidly developing as neuroscience, the combination of these two modellings can have a significant role in helping to guide the direction the field takes. The paper combined mathematical and computational modelling to prove a weakness in a very precious model in neuroscience. This paper is intended to analyse all-or-none principle in Hodgkin-Huxley mathematical model. By implementation the computational model of Hodgkin-Huxley model and applying the concept of all-or-none principle, an investigation on this mathematical model has been performed. The results clearly showed that the mathematical model of Hodgkin-Huxley does not observe this fundamental law in neurophysiology to generating action potentials. This study shows that further mathematical studies on the Hodgkin-Huxley model are needed in order to create a model without this weakness.

Keywords: all-or-none, computational modelling, mathematical model, transmembrane voltage, action potential

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Authors: Ahmed Tarek, Ahmed Alveed

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In the theory of computing, there are a wide variety of direct and indirect proof techniques. However, mathematical induction (MI) stands out to be one of the most powerful proof techniques for proving hypotheses, theorems, and new results. There are variations of mathematical induction-based proof techniques, which are broadly classified into three categories, such as structural induction (SI), weak induction (WI), and strong induction (SI). In this expository paper, several different variants of the mathematical induction techniques are explored, and the specific scenarios are discussed where a specific induction technique stands out to be more advantageous as compared to other induction strategies. Also, the essential difference among the variants of mathematical induction are explored. The points of separation among mathematical induction, recursion, and logical deduction are precisely analyzed, and the relationship among variations of recurrence relations, and mathematical induction are being explored. In this context, the application of recurrence relations, and mathematical inductions are considered together in a single framework for codewords over a given alphabet.

Keywords: alphabet, codeword, deduction, mathematical, induction, recurrence relation, strong induction, structural induction, weak induction

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Authors: Zahid Ullah, Atlas Khan

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The rapid advancements in data collection, storage, and processing capabilities have led to an explosion of data in various domains. In this era of big data, mathematical sciences play a crucial role in uncovering valuable insights and driving informed decision-making through data analytics. The purpose of this abstract is to present the latest advances in mathematical sciences and their application in harnessing the power of data analytics. This abstract highlights the interdisciplinary nature of data analytics, showcasing how mathematics intersects with statistics, computer science, and other related fields to develop cutting-edge methodologies. It explores key mathematical techniques such as optimization, mathematical modeling, network analysis, and computational algorithms that underpin effective data analysis and interpretation. The abstract emphasizes the role of mathematical sciences in addressing real-world challenges across different sectors, including finance, healthcare, engineering, social sciences, and beyond. It showcases how mathematical models and statistical methods extract meaningful insights from complex datasets, facilitating evidence-based decision-making and driving innovation. Furthermore, the abstract emphasizes the importance of collaboration and knowledge exchange among researchers, practitioners, and industry professionals. It recognizes the value of interdisciplinary collaborations and the need to bridge the gap between academia and industry to ensure the practical application of mathematical advancements in data analytics. The abstract highlights the significance of ongoing research in mathematical sciences and its impact on data analytics. It emphasizes the need for continued exploration and innovation in mathematical methodologies to tackle emerging challenges in the era of big data and digital transformation. In summary, this abstract sheds light on the advances in mathematical sciences and their pivotal role in unveiling the power of data analytics. It calls for interdisciplinary collaboration, knowledge exchange, and ongoing research to further unlock the potential of mathematical methodologies in addressing complex problems and driving data-driven decision-making in various domains.

Keywords: mathematical sciences, data analytics, advances, unveiling

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Authors: Jaroslav Masek, Juraj Camaj, Eva Nedeliakova

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The aim of optimization of store management is not only designing the situation of store management itself including its equipment, technology and operation. In optimization of store management we need to consider also synchronizing of technological, transport, store and service operations throughout the whole process of logistic chain in such a way that a natural flow of material from provider to consumer will be achieved the shortest possible way, in the shortest possible time in requested quality and quantity and with minimum costs. The paper deals with the application of the queuing theory for optimization of warehouse processes. The first part refers to common information about the problematic of warehousing and using mathematical methods for logistics chains optimization. The second part refers to preparing a model of a warehouse within queuing theory. The conclusion of the paper includes two examples of using queuing theory in praxis.

Keywords: queuing theory, logistics system, mathematical methods, warehouse optimization

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Authors: Zahid Ullah, Atlas Khan

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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: Sergey Podluzhnyy

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One of the most important tasks of investment and pension fund management is building decision support system which helps to make right decision on corporate bond portfolio formation. Today there are several basic methods of bond portfolio management. They are duration management, immunization and convexity management. Identified methods have serious disadvantage: they do not take into account credit risk or insolvency risk of issuer. So, identified methods can be applied only for management and evaluation of high-quality sovereign bonds. Applying article proposes mathematical model for building an optimal in case of risk and yield corporate bond portfolio. Proposed model takes into account the default probability in formula of assessment of bonds which results to more correct evaluation of bonds prices. Moreover, applied model provides tools for visualization of the efficient frontier of corporate bonds portfolio taking into account the exposure to credit risk, which will increase the quality of the investment decisions of portfolio managers.

Keywords: corporate bond portfolio, default probability, effective boundary, portfolio optimization task

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Authors: Vijay Kr. Yadav, Nilam Rathi

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Accurate prediction of glucose level for diabetes mellitus is required to avoid affecting the functioning of major organs of human body. This study describes the fundamental assumptions and two different methodologies of the Blood glucose prediction. First is based on the back-propagation algorithm of Artificial Neural Network (ANN), and second is based on the Neuro-Fuzzy technique, called Fuzzy Inference System (FIS). Errors between proposed methods further discussed through various statistical methods such as mean square error (MSE), normalised mean absolute error (NMAE). The main objective of present study is to develop mathematical model for blood glucose prediction before 12 hours advanced using data set of three patients for 60 days. The comparative studies of the accuracy with other existing models are also made with same data set.

Keywords: back-propagation, diabetes mellitus, fuzzy inference system, neuro-fuzzy

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Authors: Krzysztof Pomorski

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In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

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Authors: Gak-Gyu Kim, Won Il Jung

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According to a remarkable development of science and technology, function and role of the system of engineering fields has recently been diversified. The system has become increasingly more complex and precise, and thus, system designers intended to maximize reliability concentrate more effort at the design stage. This study deals with the reliability redundancy optimization problem (RROP) for k-out-of-n: G system configuration with cold standby and warm standby components. This paper further intends to present the optimal mathematical model through which the following three elements of (i) multiple components choices, (ii) redundant components quantity and (iii) the choice of redundancy strategies may be combined in order to maximize the reliability of the system. Therefore, we focus on the following three issues. First, we consider RROP that there exists warm standby state as well as cold standby state of the component. Second, as eliminating an approximation approach of the previous RROP studies, we construct a precise model for system reliability. Third, given transition time when the state of components changes, we present not simply a workable solution but the advanced method. For the wide applicability of RROPs, moreover, we use absorbing continuous time Markov chain and matrix analytic methods in the suggested mathematical model.

Keywords: RROP, matrix analytic methods, k-out-of-n: G system, MTTF, absorbing continuous time Markov Chain

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Authors: E. Koyuncu

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The problem of Order Acceptance and Scheduling (OAS) is defined as a joint decision of which orders to accept for processing and how to schedule them. Any linear programming model representing real-world situation involves the parameters defined by the decision maker in an uncertain way or by means of language statement. Fuzzy data can be used to incorporate vagueness in the real-life situation. In this study, a fuzzy mathematical model is proposed for a single machine OAS problem, where the orders are defined by their fuzzy due dates, fuzzy processing times, and fuzzy sequence dependent setup times. The signed distance method, one of the fuzzy ranking methods, is used to handle the fuzzy constraints in the model.

Keywords: fuzzy mathematical programming, fuzzy ranking, order acceptance, single machine scheduling

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Authors: Deepshikha Shukla, C. H. Solanki, Mayank K. Desai

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Amongst all the natural hazards, earthquakes have the potential for causing the greatest damages. Since the earthquake forces are random in nature and unpredictable, the quantification of the hazards becomes important in order to assess the hazards. The time and place of a future earthquake are both uncertain. Since earthquakes can neither be prevented nor be predicted, engineers have to design and construct in such a way, that the damage to life and property are minimized. Seismic hazard analysis plays an important role in earthquake design structures by providing a rational value of input parameter. In this paper, both mathematical, as well as computational methods adopted by researchers globally in the past five years, will be discussed. Some mathematical approaches involving the concepts of Poisson’s ratio, Convex Set Theory, Empirical Green’s Function, Bayesian probability estimation applied for seismic hazard and FOSM (first-order second-moment) algorithm methods will be discussed. Computational approaches and numerical model SSIFiBo developed in MATLAB to study dynamic soil-structure interaction problem is discussed in this paper. The GIS-based tool will also be discussed which is predominantly used in the assessment of seismic hazards.

Keywords: computational methods, MATLAB, seismic hazard, seismic measurements

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Authors: Nilson Barbieri, Bruno Matos Martins, Gabriel de Sant'Anna Vitor Barbieri

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In more complex systems, such as automotive gearbox, a rigorous treatment of the data is necessary because there are several moving parts (gears, bearings, shafts, etc.), and in this way, there are several possible sources of errors and also noise. The basic objective of this work is the detection of damage in automotive gearbox. The detection methods used are the wavelet method, the bispectrum; advanced filtering techniques (selective filtering) of vibrational signals and mathematical morphology. Gearbox vibration tests were performed (gearboxes in good condition and with defects) of a production line of a large vehicle assembler. The vibration signals are obtained using five accelerometers in different positions of the sample. The results obtained using the kurtosis, bispectrum, wavelet and mathematical morphology showed that it is possible to identify the existence of defects in automotive gearboxes.

Keywords: automotive gearbox, mathematical morphology, wavelet, bispectrum

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Authors: Zahid Ullah, Atlas Khan

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The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields.

Keywords: investigating smoothness, extremely degenerate elliptic equations, regularity properties, mathematical analysis, complexity solutions

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Authors: Michael Lousis

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Mathematical competence is the great aim of every mathematical teaching and learning endeavour. This can be defined as an idealised conceptualisation of the quality of cognition and the ability of implementation in practice of the mathematical subject matter, which is included in the curriculum, and is displayed only through performance of doing mathematics. The present study gives a clear definition of mathematical competence in the domains of Arithmetic and Algebra that stems from the explanation of the learners’ errors in these domains. The learners, whose errors are explained, were Greek and English participants of a large, international, longitudinal, comparative research program entitled the Kassel Project. The participants’ errors emerged as results of their work in dealing with mathematical questions and problems of the tests, which were presented to them. The construction of the tests was such as only the outcomes of the participants’ work was to be encompassed and not their course of thinking, which resulted in these outcomes. The intention was that the tests had to provide undeviating comparable results and simultaneously avoid any probable bias. Any bias could stem from obtaining results by involving so many markers from different countries and cultures, with so many different belief systems concerning the assessment of learners’ course of thinking. In this way the validity of the research was protected. This fact forced the implementation of specific research methods and theoretical prospects to take place in order the participants’ erroneous way of thinking to be disclosed. These were Methodological Pragmatism, Symbolic Interactionism, Philosophy of Mind and the ideas of Computationalism, which were used for deciding and establishing the grounds of the adequacy and legitimacy of the obtained kinds of knowledge through the explanations given by the error analysis. The employment of this methodology and of these theoretical prospects resulted in the definition of the learners’ mathematical competence, which is the thesis of the present study. Thus, learners’ mathematical competence is depending upon three key elements that should be developed in their minds: appropriate representations, appropriate meaning, and appropriate developed schemata. This definition then determined the development of appropriate teaching practices and interventions conducive to the achievement and finally the entailment of mathematical competence.

Keywords: representations, meaning, appropriate developed schemata, computationalism, error analysis, explanations for the probable causes of the errors, Kassel Project, mathematical competence

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

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This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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Authors: Rizky Oktaviana

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The main purpose of studying lies in improving students’ understanding. Teachers usually use written test to measure students’ understanding about learning material especially mathematical learning material. This common method actually has a lack point, such that in mathematics content, written test only show procedural steps to solve mathematical problems. Therefore, teachers unable to see whether students actually understand about mathematical concepts and the relation between concepts or not. One of the best tools to observe students’ understanding about the mathematical concepts is concept map. The goal of this research is to describe junior high school students understanding about mathematical concepts through Concept Maps based on the difference of mathematical ability. There were three steps in this research; the first step was choosing the research subjects by giving mathematical ability test to students. The subjects of this research are three students with difference mathematical ability, high, intermediate and low mathematical ability. The second step was giving concept mapping training to the chosen subjects. The last step was giving concept mapping task about the function to the subjects. Nodes which are the representation of concepts of function were provided in concept mapping task. The subjects had to use the nodes in concept mapping. Based on data analysis, the result of this research shows that subject with high mathematical ability has formal understanding, due to that subject could see the connection between concepts of function and arranged the concepts become concept map with valid hierarchy. Subject with intermediate mathematical ability has relational understanding, because subject could arranged all the given concepts and gave appropriate label between concepts though it did not represent the connection specifically yet. Whereas subject with low mathematical ability has poor understanding about function, it can be seen from the concept map which is only used few of the given concepts because subject could not see the connection between concepts. All subjects have instrumental understanding for the relation between linear function concept, quadratic function concept and domain, co domain, range.

Keywords: concept map, concept mapping, mathematical concepts, understanding

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Authors: Yasaman Azarmjoo

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Since ancient times, it has been said that mathematics is the mother of all sciences and the foundation of basic concepts in every field and profession. It would be great if, after learning this subject, we could enable students to create games and activities based on the same mathematical concepts. This article explores the design of various mathematical activities in the form of games, utilizing different mathematical topics such as algebra, equations, binary systems, and one-to-one correspondence. The theoretical significance of this article lies in uncovering alternative approaches to teaching and learning mathematics. By employing creative and interactive methods such as game design, it challenges the traditional perception of mathematics as a difficult and laborious subject. The theoretical significance of this article lies in demonstrating that mathematics can be made more accessible and enjoyable, which can result in heightened interest and engagement in the subject. In general, this article reveals another aspect of mathematics.

Keywords: playing with mathematics, algebra and equations, binary systems, one-to-one correspondence

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Authors: Krisstalova Dana, Mazal Jan

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This article deals with geographical conditions in terrain and their effect on the movement of vehicles, their effect on speed and safety of movement of people and vehicles. Finding of the optimal routes outside the communication is studied in the army environment, but it occur in civilian as well, primarily in crisis situation, or by the provision of assistance when natural disasters such as floods, fires, storms etc., have happened. These movements require the optimization of routes when effects of geographical factors should be included. The most important factor is the surface of a terrain. It is based on several geographical factors as are slopes, soil conditions, micro-relief, a type of surface and meteorological conditions. Their mutual impact has been given by coefficient of deceleration. This coefficient can be used for the commander`s decision. New approaches and methods of terrain testing, mathematical computing, mathematical statistics or cartometric investigation are necessary parts of this evaluation.

Keywords: movement in a terrain, geographical factors, surface of a field, mathematical evaluation, optimization and searching paths

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Authors: Yoon Suh Song

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Though music education can broaden one’s capacity for mathematical performance, many countries lag behind in music education. Little empirical evidence is found to identify the connection between math and music. Therefore, this research was set out to explore what music-related variables are associated with mathematical performance. The result of our analysis is as follows: A Pearson's Correlation analysis revealed that PISA math score is strongly correlated with students' Intelligence Quotient (IQ). This lays the foundation for further research as to what factors in students’ IQ lead to a better performance in math.

Keywords: music education, mathematical performance, education, IQ

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Authors: Jaroslav Krutil, Simona Fialová, , František Pochylý

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A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects.

Keywords: nonlinear mathematical model, CFD modeling, hydrodynamic sealing gap, matrices of mass, stiffness, damping

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Authors: Juliana A. Knocikova, Yann Bouret, Médéric Argentina, Laurent Counillon

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Cell volume, together with membrane potential and intracellular hydrogen ion concentration, is an essential biophysical parameter for normal cellular activity. Cell volumes can be altered by osmotically active compounds and extracellular tonicity. In this study, a simple mathematical model of osmotically induced cell swelling and shrinking is presented. Emphasis is given to water diffusion across the membrane. The mathematical description of the cellular behavior consists in a system of coupled ordinary differential equations. We compare experimental data of cell volume alterations driven by differences in osmotic pressure with mathematical simulations under hypotonic and hypertonic conditions. Implications for a future model are also discussed.

Keywords: eukaryotic cell, mathematical modeling, osmosis, volume alterations

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Authors: Vojo George Fasinu, Nadaraj Govender, Predeep Kumar

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An Antenna, which remains the hub of technological development in Africa had been found to be a course that is been taught and designed in an abstract manner in some universities. One of the reasons attached to this is that the appropriate approach of teaching antenna design is not yet understood by many engineering academics in some universities in South Africa. Also, another problem reported is the main difficulty encountered when interpreting and applying some of the mathematical concepts learned into their practical antenna design course. As a result of this, some engineering experts classified antenna as a mysterious technology that could not be described by anybody using mathematical concepts. In view of this, this paper takes it as its point of departure in explaining what an antenna is all about with a strong emphasis on its mathematical modelling. It also argues that the place of modelling mathematical concepts into the teaching of engineering design cannot be overemphasized. Therefore, it explains the mathematical concepts adopted during the teaching of an antenna design course, the Strategies of modelling those mathematics concepts, the behavior of antennas, and their mathematics usage were equally discussed. More so, the paper also sheds more light on mathematical modelling in South Africa context, and also comparative analysis of mathematics concepts taught in mathematics class and mathematics concepts taught in engineering courses. This paper focuses on engineering academics teaching selected topics in electronic engineering (Antenna design), with special attention on the mathematical concepts they teach and how they teach them when teaching the course. A qualitative approach was adopted as a means of collecting data in order to report the naturalistic views of the engineering academics teaching Antenna design. The findings of the study confirmed that some mathematical concepts are being modeled into the teaching of an antenna design with the adoption of some teaching approaches. Furthermore, the paper reports a didactical-realistic mathematical model as a conceptual framework used by the researchers in describing how academics teach mathematical concepts during their teaching of antenna design. Finally, the paper concludes with the importance of mathematical modelling to the engineering academics and recommendations for further researchers.

Keywords: modelling, mathematical concepts, engineering, didactical, realistic model

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Authors: Ujwal Kishor Zore, Shankar Balajirao Kausley, Aniruddha Bhalchandra Pandit

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There are some important design parameters of activated sludge process (ASP) for wastewater treatment and they must be optimally defined to have the optimized plant working. To know them, developing a mathematical model is a way out as it is nearly commensurate the real world works. In this study, a mathematical model was developed for ASP, solved under activated sludge model no 1 (ASM 1) conditions and MATLAB tool was used to solve the mathematical equations. For its real-life validation, the developed model was tested for the inputs from the municipal wastewater treatment plant and the results were quite promising. Additionally, the most cardinal assumptions required to design the treatment plant are discussed in this paper. With the need for computerization and digitalization surging in every aspect of engineering, this mathematical model developed might prove to be a boon to many biological wastewater treatment plants as now they can in no time know the design parameters which are required for a particular type of wastewater treatment.

Keywords: waste water treatment, activated sludge process, mathematical modeling, optimization

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Authors: Tareq Oshan

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Facility location and size decisions are important to any company because they affect profitability and success. However, warehouses are exposed to various risks of failure that affect their activity. This paper presents a mixed-integer non-linear mathematical model that can be used to determine optimal warehouse locations and sizes, which warehouses to fortify, and which branches should be assigned to specific warehouses when there is a risk of warehouse failure. Every branch is assigned to a fortified primary warehouse or a nonfortified primary warehouse and a fortified backup warehouse. The standard method and an introduced method, based on the average probabilities, for linearizing this mathematical model were used. A Canadian case study was used to demonstrate the developed mathematical model, followed by some sensitivity analysis.

Keywords: supply chain network design, fortified warehouse, mixed-integer mathematical model, warehouse failure risk

Procedia PDF Downloads 207