Search results for: trajectories mathematical proves

Authors: Jitendra Singh, Vivek Kumar

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In this paper, a susceptible infective susceptible mathematical model is proposed and analyzed where the migration of human population is given by migration function. It is assumed that the disease is transmitted by direct contact of susceptible and infective populations with constant contact rate. The equilibria and their stability are studied by using the stability theory of ordinary differential equations and computer simulation. The model analysis shows that the spread of infectious disease increases when human population immigration increases in the habitat but it decreases if emigration increases.

Keywords: SIS (Susceptible Infective Susceptible) model, migration function, susceptible, stability

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Authors: Amanbek Jainakov, Abdikerim Kurbanaliev

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The work presents the results of mathematical modeling of large-scale flows in areas with a complex topographic relief. The Reynolds-averaged Navier—Stokes equations constitute the basis of the three-dimensional unsteady modeling. The well-known Volume of Fluid method implemented in the solver interFoam of the open package OpenFOAM 2.3 is used to track the free-boundary location. The mathematical model adequacy is checked by comparing with experimental data. The efficiency of the applied technology is illustrated by the example of modeling the breakthrough of the dams of the Andijan (Uzbekistan) and Papan (near the Osh town, Kyrgyzstan) reservoir.

Keywords: three-dimensional modeling, free boundary, the volume-of-fluid method, dam break, flood, OpenFOAM

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Tala Toonsi, Marah Alagha, Lina Alnowaiser, Hala Rajab

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This report is about the Photomath app, which is an AI application that uses image recognition technology, specifically optical character recognition (OCR) algorithms. The (OCR) algorithm translates the images into a mathematical equation, and the app automatically provides a step-by-step solution. The application supports decimals, basic arithmetic, fractions, linear equations, and multiple functions such as logarithms. Testing was conducted to examine the usage of this app, and results were collected by surveying ten participants. Later, the results were analyzed. This paper seeks to answer the question: To what level the artificial intelligence features are accurate and the speed of process in this app. It is hoped this study will inform about the efficiency of AI in Photomath to the users.

Keywords: photomath, image recognition, app, OCR, artificial intelligence, mathematical equations.

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Authors: Ram Kishor

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The Lyapunov characteristic exponent (LCE) is an important tool to describe behavior of a dynamical system, which measures the average rate of divergence (or convergence) of a trajectory emanating in the vicinity of initial point. To analyze the behavior of nearby trajectory emanating in the neighborhood of an equilibrium point in the restricted three-body problem under the influence of perturbations in the form of radiation pressure and oblateness, we compute LCEs of first order with the help of slandered method which is based on variational equation of the system. It is observed that trajectories are chaotic in nature due positive LCEs. Also, we analyze the effect of radiation pressure and oblateness on the LCEs. Results are applicable to study the behavior of more generalized RTBP in the presence of perturbations such as PR drag, solar wind drag etc.

Keywords: Lyapunov characteristic exponent, RTBP, radiation pressure, oblateness

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Authors: Javad Khaligh, Aghileh Heydari, Ali Akbar Heydari

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Mathematical epidemiological models for the spread of disease through a population are used to predict the prevalence of a disease or to study the impacts of treatment or prevention measures. Initial conditions for these models are measured from statistical data collected from a population since these initial conditions can never be exact, the presence of chaos in mathematical models has serious implications for the accuracy of the models as well as how epidemiologists interpret their findings. This paper confirms the chaotic behavior of a model for dengue fever and SI by investigating sensitive dependence, bifurcation, and 0-1 test under a variety of initial conditions.

Keywords: epidemiological models, SEIR disease model, bifurcation, chaotic behavior, 0-1 test

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Authors: Maya Arlini Puspasari, Shafira Karamina Alifah, Hardianto Iridiastadi

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High mental workload can lead to fatigue and further result in decreased concentration and work performance. This study is conducted to see the effects of mental workload towards mental fatigue. Mental fatigue measurement was conducted at the first and the last 10 minutes of the working time using electroencephalogram, while mental workload measurement was conducted after the work is completed using the NASA-TLX questionnaire. The result shows that there is an increase in alpha band which indicates an increase in mental fatigue. This study also shows absolute alpha is more sensitive compared to the relative alpha. This study proves that there is a relationship between mental workload and mental fatigue although not relatively strong.

Keywords: mental workload, electroencephalogram, customer care agents, NASA-TLX

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

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The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: children growth percentile, children physical development, fractional calculus, linear and polynomial model

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Authors: Ana Maria Reis D'Azevedo Breda, Catarina Maria Neto da Cruz

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The Japanese art of origami provides a rich context for designing exploratory mathematical activities for children and young people. By folding a simple sheet of paper, fascinating and surprising planar and spatial configurations emerge. Equally surprising is the unfolding process, which also produces striking patterns. The procedure of folding, unfolding, and folding again allows the exploration of interesting geometric patterns. When adequately and systematically done, we may deduce some of the mathematical rules ruling origami. As the child/youth folds the sheet of paper repeatedly, he can physically observe how the forms he obtains are transformed and how they relate to the pattern of the corresponding unfolding, creating space for the understanding/discovery of mathematical principles regulating the folding-unfolding process. As part of a 2023 Summer Academy organized by a Portuguese university, a session entitled “Folding, Thinking and Generalizing” took place. Twenty-three students attended the session, all enrolled in the 2nd cycle of Portuguese Basic Education and aged between 10 and 12 years old. The main focus of this session was to foster the development of critical cognitive and socio-emotional skills among these young learners using origami. These skills included creativity, critical analysis, mathematical reasoning, collaboration, and communication. Employing a qualitative, descriptive, and interpretative analysis of data collected during the session through field notes and students’ written productions, our findings reveal that structured origami-based activities not only promote student engagement with mathematical concepts in a playful and interactive but also facilitate the development of socio-emotional skills, which include collaboration and effective communication between participants. This research highlights the value of integrating origami into educational practices, highlighting its role in supporting comprehensive cognitive and emotional learning experiences.

Keywords: skills, origami rules, active learning, hands-on activities

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Authors: N. K. Mohd Affendi, T. A. R. Tuan Abdullah, S. A. Syed Mustaffa

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In power industry transformer is an important component and most of us familiar by the functioning principle of a transformer electrically. There are many losses occur during the operation of a transformer that causes heat generation. This heat, if not dissipated properly will reduce the lifetime and effectiveness of the transformer. Transformer cooling helps in maintaining the temperature rise of various paths. This paper proposed to minimize the ambient temperature of the transformer room in order to lower down the temperature of the transformer. A simulation has been made using finite element methods programs called FEMM (Finite Elements Method Magnetics) to create a virtual model based on actual measurement of a transformer. The generalization of the two-dimensional (2D) FEMM results proves that by minimizing the ambient temperature, the heat of the transformer is decreased. The modeling process and of the transformer heat flow has been presented.

Keywords: heat generation, temperature rise, ambient temperature, FEMM

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Authors: Fernanda A. P. Peres, Thiago N. Peres, Flavio S. Fogliatto, Michel J. Anzanello

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Batch processes are widely used in food industry and have an important role in the production of high added value products, such as chocolate. Process performance is usually described by variables that are monitored as the batch progresses. Data arising from these processes are likely to display a strong correlation-autocorrelation structure, and are usually monitored using control charts based on multiway principal components analysis (MPCA). Process control of a new batch is carried out comparing the trajectories of its relevant process variables with those in a reference set of batches that yielded products within specifications; it is clear that proper determination of the reference set is key for the success of a correct signalization of non-conforming batches in such quality control schemes. In chocolate manufacturing, misclassifications of non-conforming batches in the conching phase may lead to significant financial losses. In such context, the accuracy of process control grows in relevance. In addition to that, the main assumption in MPCA-based monitoring strategies is that all batches are synchronized in duration, both the new batch being monitored and those in the reference set. Such assumption is often not satisfied in chocolate manufacturing process. As a consequence, traditional techniques as MPCA-based charts are not suitable for process control and monitoring. To address that issue, the objective of this work is to compare the performance of three dynamic time warping (DTW) methods in the alignment and synchronization of chocolate conching process variables’ trajectories, aimed at properly determining the reference distribution for multivariate statistical process control. The power of classification of batches in two categories (conforming and non-conforming) was evaluated using the k-nearest neighbor (KNN) algorithm. Real data from a milk chocolate conching process was collected and the following variables were monitored over time: frequency of soybean lecithin dosage, rotation speed of the shovels, current of the main motor of the conche, and chocolate temperature. A set of 62 batches with durations between 495 and 1,170 minutes was considered; 53% of the batches were known to be conforming based on lab test results and experts’ evaluations. Results showed that all three DTW methods tested were able to align and synchronize the conching dataset. However, synchronized datasets obtained from these methods performed differently when inputted in the KNN classification algorithm. Kassidas, MacGregor and Taylor’s (named KMT) method was deemed the best DTW method for aligning and synchronizing a milk chocolate conching dataset, presenting 93.7% accuracy, 97.2% sensitivity and 90.3% specificity in batch classification, being considered the best option to determine the reference set for the milk chocolate dataset. Such method was recommended due to the lowest number of iterations required to achieve convergence and highest average accuracy in the testing portion using the KNN classification technique.

Keywords: batch process monitoring, chocolate conching, dynamic time warping, reference set distribution, variable duration

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Authors: Abdullahi Mohammed Auwal

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Formation and change or decamping from one political party to another have now become a common trend in Nigeria. Many of the parties’ members who could not secure positions and or win elections in their parties or are not very much satisfied with the trends occurring in the party’s internal democratic principles and mechanisms, change their respective parties. This paper developed/presented and analyzed the used of non linear mathematical model for defections between two political parties using epidemiological approach. The whole population was assumed to be a constant and homogeneously mixed. Equilibria have been analytically obtained and their local and global stability discussed. Conditions for the co-existence of both the political parties have been determined, in the study of defections between People Democratic Party (PDP) and All Progressive Congress (APC) in Nigeria using numerical simulations to support the analytical results.

Keywords: model, political parties, deffection, stability, equilibrium, epidemiology

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

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This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: adsorption, mathematical modeling, nanocarbons, numerical analysis

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Authors: Fatma Susilawati Mohamad, Azizah Abdul Manaf, Fadhillah Ahmad, Zarina Mohamad, Wan Suryani Wan Awang

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A simple and robust multi-class linear classifier is proposed and implemented. For a pair of classes of the linear boundary, a collection of segments of hyper planes created as perpendicular bisectors of line segments linking centroids of the classes or part of classes. Nearest Neighbor and Linear Discriminant Analysis are compared in the experiments to see the performances of each classifier in discriminating ripeness of oil palm. This paper proposes a multi-class linear classifier using Linear Discriminant Analysis (LDA) for image identification. Result proves that LDA is well capable in separating multi-class features for ripeness identification.

Keywords: multi-class, linear classifier, nearest neighbor, linear discriminant analysis

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Authors: Vishal D. Pandya

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A great deal of perceptible change has been taking place in the way our institutions of higher learning are being managed in India today. It is believed that managers, whose intuition proves to be accurate, often tend to be the most successful, and this is what makes them almost like entrepreneurs. A certain entrepreneurial spirit is what is expected and requires a degree of insight of the manager to be successful depending upon the situational and more importantly, the heterogeneity as well as the socio-cultural aspect. Teachers in Higher Education have to play multiple roles to make sure that the Learning-Teaching process becomes effective in the real sense of the term. This paper makes an effort to take a close look at that, especially in the context of the management of English language teaching in Higher Education and, therefore, focuses on the management of English language teaching in higher education by understanding target situation analyses at the socio-cultural level.

Keywords: management, language teaching, English language teaching, higher education

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

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Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: gravity gradient, gravity gradient sensor, accelerometer, single-axis rotation modulation

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Authors: Nicolás Clavijo Buriticá, Laura Viviana Triana Sanchez

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This research develops a productive context associated with the aquaculture industry in northern Tolima-Colombia, specifically in the town of Lerida. Strategic aspects of chain of fish Production-Distribution, especially those related to supply network design of an association devoted to cultivating, farming, processing and marketing of fish are addressed. This research is addressed from a special approach of Supply Chain Management (SCM) which guides management objectives to the system sustainability; this approach is called Sustainable Supply Chain Management (SSCM). The network design of fish production-distribution system is obtained for the case study by two mathematical programming models that aims to maximize the economic benefits of the chain and minimize total supply chain costs, taking into account restrictions to protect the environment and its implications on system productivity. The results of the mathematical models validated in the productive situation of the partnership under study, called Asopiscinorte shows the variation in the number of open or closed locations in the supply network that determines the final network configuration. This proposed result generates for the case study an increase of 31.5% in the partial productivity of storage and processing, in addition to possible favorable long-term implications, such as attending an agile or not a consumer area, increase or not the level of sales in several areas, to meet in quantity, time and cost of work in progress and finished goods to various actors in the chain.

Keywords: Sustainable Supply Chain, mathematical programming, aquaculture industry, Supply Chain Design, Supply Chain Configuration

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Authors: Saeed Mahjoub Moghadas, Farhad Asadi, Shahed Torkamandi, Hassan Moradi, Mahmood Purgamshidian

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In this paper, we present real-time obstacle avoidance approach for both autonomous and non-autonomous DS-based controllers and also based on dynamical systems (DS) method. In this approach, we can modulate the original dynamics of the controller and it allows us to determine safety margin and different types of DS to increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle and especially when robot moves very fast in changeable complex environments. The method is validated in simulation and influence of different autonomous and non-autonomous DS such as limit cycles, and unstable DS on this algorithm and also the position of different obstacles in complex environment is explained. Finally, we describe how the avoidance trajectories can be verified through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, DS-based controllers

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Authors: Fouad Inel, Lakhdar Khochemane

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This article presents a comparative response specification performance between two controllers of three and four cable based robots for various applications. The main objective of this work is: the first is to use the direct and inverse geometric model to study and simulate the end effector position of the robot with three and four cables. A graphical user interface has been implemented in order to visualizing the position of the robot. Secondly, we present the determination of static and dynamic tensions and lengths of cables required to flow different trajectories. At the end, we study the response of our systems in closed loop with a Proportional-IntegratedDerivative (PID) and Proportional-Integrated (PD) controllers then this last are compared the results of the same examples using MATLAB/Simulink; we found that the PID method gives the better performance, such as rapidly speed response, settling time, compared to PD controller.

Keywords: dynamic modeling, geometric modeling, graphical user interface, open loop, parallel cable-based robots, PID/PD controllers

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Authors: Nugzar Todua

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The paper studies the role of food labeling in order to promote healthy eating issue in Georgia. The main focus of the research is directed to consumer attitudes regarding food labeling. The methodology of the paper is based on the focus group work, as well as online and face to face surveys. The data analysis has been provided through ANOVA. The study proves that the impact of variables such as the interest, awareness, reliability, assurance and satisfaction of consumers' on buying decision, is statistically important. The study reveals that consumers’ perception regarding to food labeling is positive, but their level of knowledge and ability is rather low. It is urgent to strengthen marketing promotions strategies in the process of implementations of food security policy in Georgia.

Keywords: food labeling, buying decision, Georgian consumers, marketing research

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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: Julie Delany

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To thrive in today’s digital climate, it is vital that organisations adopt new technology and prepare for rising digital trends. This proves more difficult in government where, traditionally, people lack change readiness. While individuals may have a desire to work smarter, this does not necessarily mean embracing technology. This paper discusses the rollout of an application into a small department of highly experienced nurses. The goal was to both streamline the department's workflow and provide a platform for gathering essential business metrics. The biggest challenges were adoption and motivating the nurses to change their routines and learn new computer skills. Two-thirds struggled with the change, and as a result, some jeopardised the validity of the business metrics. In conclusion, there are lessons learned and recommendations for similar projects.

Keywords: change ready, information technology, end-user, iterative method, rollout plan, data analytics

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Authors: Yuan-Jye Tseng, Yi-Shiuan Chen

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The paper presented a sustainable design model for integrated evaluation of the design and supply chain of a product for the sustainable objectives. To design a product, there can be alternative ways to assign the detailed specifications to fulfill the same design objectives. In the design alternative cases, different material and manufacturing processes with various supply chain activities may be required for the production. Therefore, it is required to evaluate the different design cases based on the sustainable objectives. In this research, a closed-loop design model is developed by integrating the forward design model and reverse design model. From the supply chain point of view, the decisions in the forward design model are connected with the forward supply chain. The decisions in the reverse design model are connected with the reverse supply chain considering the sustainable objectives. The purpose of this research is to develop a mathematical model for analyzing the design cases by integrated evaluating the criteria in the closed-loop design and the closed-loop supply chain. The decision variables are built to represent the design cases of the forward design and reverse design. The cost parameters in a forward design include the costs of material and manufacturing processes. The cost parameters in a reverse design include the costs of recycling, disassembly, reusing, remanufacturing, and disposing. The mathematical model is formulated to minimize the total cost under the design constraints. In practical applications, the decisions of the mathematical model can be used for selecting a design case for the purpose of sustainable design of a product. An example product is demonstrated in the paper. The test result shows that the sustainable design model is useful for integrated evaluation of the design and the supply chain to achieve the sustainable objectives.

Keywords: closed-loop design, closed-loop supply chain, design evaluation, supply chain management, sustainable design model

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Authors: Florin Leon

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This paper describes a simulator of traffic scenarios tailored to facilitate autonomous driving model training for urban environments. With the rising prominence of self-driving vehicles, the need for diverse datasets is very important. The proposed simulator provides a flexible framework that allows the generation of custom scenarios needed for the validation and enhancement of trajectory prediction algorithms. Its controlled yet dynamic environment addresses the challenges associated with real-world data acquisition and ensures adaptability to diverse driving scenarios. By providing an adaptable solution for scenario creation and algorithm testing, this tool proves to be a valuable resource for advancing autonomous driving technology that aims to ensure safe and efficient self-driving vehicles.

Keywords: autonomous driving, car simulator, machine learning, model training, urban simulation environment

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Authors: Cristian Patrascioiu, Loredana Negoita

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This paper is focused on modeling and simulation of the tubular heaters. The paper is structured in four parts: the structure of the tubular convection section, the heat transfer model, the adaptation of the mathematical model and the solving model. The main hypothesis of the heat transfer modeling is that the heat exchanger of the convective tubular heater is a lumped system. In the same time, the model uses the heat balance relations, Newton’s law and criteria relations. The numerical program achieved allows for the estimation of the burn gases outlet temperature and the heated flow outlet temperature.

Keywords: heat exchanger, mathematical modelling, nonlinear equation system, Newton-Raphson algorithm

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid Hopfield neural network is proposed for the dynamic, flexible job shop scheduling problem. A new heuristic based and easy to implement energy function is designed for the Hopfield neural network, which penalizes the constraints violation and decreases makespan. Moreover, for enhancing the performance, several heuristics are integrated to it that achieve active, and non-delay schedules also, prevent early convergence of the neural network. The suggested algorithm that is designed as a generalization of the previous studies for the flexible and dynamic scheduling problems can be used for solving real scheduling problems. Comparison of the presented hybrid method results with the previous studies results proves its efficiency.

Keywords: dynamic flexible job shop scheduling, neural network, heuristics, constrained optimization

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Authors: S. Gherbi, F. Bouchareb

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This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: delayed systems, fuzzy immune PID, optimization, Smith predictor

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Authors: Gurmeet Singh Cheema, Gurjinder Singh, Amardeep Singh Kang

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Aluminium alloy 6061 is a medium to high strength heat-treatable alloy which has very good corrosion resistance and very good weldability. Friction Stir Welding was developed and this technique has attracted considerable interest from the aerospace and automotive industries since it is able to produce defect free joints particularly for light metals i.e aluminum alloy and magnesium alloy. In the friction stir welding process, welding parameters such as tool rotational speed, welding speed and tool shoulder diameter play a major role in deciding the weld quality. In this research work, an attempt has been made to understand the effect of tool rotational speed, welding speed and tool shoulder diameter on friction stir welded AA6061 aluminium alloy joints. Statistical tool such as central composite design is used to develop the mathematical relationships. The mathematical model was developed to predict mechanical properties of friction stir welded aluminium alloy joints at the 95% confidence level.

Keywords: aluminium alloy, friction stir welding, central composite design, mathematical relationship

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Authors: Jeongim Kang, Moon Hee Kim, Seong Baeg Kim

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This paper proposes a novel e-learning model that is based on a dynamic formative evaluation. On evaluating the existing format of e-learning, conditions regarding repetitive learning to achieve mastery, causes issues for learners to lose tension and become neglectful of learning. The dynamic formative evaluation proposed is able to supplement limitation of the existing approaches. Since a repetitive learning method does not provide a perfect feedback, this paper puts an emphasis on the dynamic formative evaluation that is able to maximize learning achievement. Through the dynamic formative evaluation, the instructor is able to refer to the evaluation result when making estimation about the learner. To show the flow chart of learning, based on the dynamic formative evaluation, the model proves its effectiveness and validity.

Keywords: online learning, dynamic formative evaluation, mastery learning, repetitive learning method, learning achievement

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Authors: Jacob A. Braun

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This paper uses mathematical modeling to show the spread of Herpes Simplex type-2 with and without the usage of condoms in a college population. The model uses four differential equations to calculate the data for the simulation. The dt increment used is one week. It also runs based on a fixated period. The period chosen was five years to represent time spent in college. The average age of the individual is 21, once again to represent the age of someone in college. In the total population, there are almost two times as many women who have Herpes Simplex Type-2 as men. Additionally, Herpes Simplex Type-2 does not have a known cure. The goal of the model is to show how condom usage affects women’s chances of receiving the virus in the hope of being able to reduce the number of women infected. In the end, the model demonstrates that condoms offer significant protection to women from the virus. Since fewer women are infected with the virus when condoms are used, in turn, fewer males are infected. Since Herpes Simplex Type-2 affects the carrier for their whole life, a small decrease of infections could lead to large ramifications over time. Specifically, a small decrease of infections at a young age, such as college, could have a very big effect on the long-term number of people infected with the virus.

Keywords: college, condom, Herpes, mathematical modelling

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