Search results for: mathematical programming problem

Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Said Fares, Mary Fares

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It is well documented that introductory computer programming courses are difficult and that failure rates are high. The aim of this project was to reduce the high failure and withdrawal rates in learning to program. This paper presents a number of changes in module organization and instructional delivery system in teaching CS1. Daily out of class help sessions and tutoring services were applied, interactive lectures and laboratories, online resources, and timely feedback were introduced. Five years of data of 563 students in 21 sections was collected and analyzed. The primary results show that the failure and withdrawal rates were cut by more than half. Student surveys indicate a positive evaluation of the modified instructional approach, overall satisfaction with the course and consequently, higher success and retention rates.

Keywords: failure rate, interactive learning, student engagement, CS1

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Authors: Manish Jain, Dinesh Gopalani

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Growing dependency of mankind on software technology increases the need for thorough testing of the software applications and automated testing techniques that support testing activities. We have outlined our testing strategy for performing various types of automated testing of Java applications using AspectJ which has become the de-facto standard for Aspect Oriented Programming (AOP). Likewise JUnit, a unit testing framework is the most popular Java testing tool. In this paper, we have evaluated our proposed AOP approach for automated testing and JUnit on various parameters. First we have provided the similarity between the two approaches and then we have done a detailed comparison of the two testing techniques on factors like lines of testing code, learning curve, testing of private members etc. We established that our AOP testing approach using AspectJ has got several advantages and is thus particularly more effective than JUnit.

Keywords: aspect oriented programming, AspectJ, aspects, JU-nit, software testing

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Authors: Liu Yi, Bao Liyong

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Aiming at the problem of low efficiency of pipelined scheduling in periodic query-qualified service, this paper proposes a system service resource scheduling strategy with parallel optimized qualified service polling control. The paper constructs the polling queuing system and its mathematical model; firstly, the first-order and second-order characteristic parameter equations are obtained by partial derivation of the probability mother function of the system state variables, and the complete mathematical, analytical expressions of each system parameter are deduced after the joint solution. The simulation experimental results are consistent with the theoretical calculated values. The system performance analysis shows that the average captain and average period of the system have been greatly improved, which can better adapt to the service demand of delay-sensitive data in the dense data environment.

Keywords: polling, parallel scheduling, mean queue length, average cycle time

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Authors: J. Thiele

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Teachers working at vocational Colleges are often confronted with the problem, that many students graduated from different schools and therefore each had a different education. Especially in mathematics many students lack fundamentals or had different priorities at their previous schools. Furthermore, these vocational Colleges have to provide Graduations for many different working-fields, with different core themes. The Colleges are interested in measuring the different Education levels of their students and providing assistance for those who need to catch up. The Project mathe-meistern was initiated to remedy this problem at vocational Colleges. For this purpose, online-tests were developed. The aim of these tests is to evaluate basic mathematical abilities of the students. The tests are online Multiple-Choice-Tests with a total of 65 Items. They are accessed online with a unique Transaction-Number (TAN) for each participant. The content is divided in several Categories (Arithmetic, Algebra, Fractions, Geometry, etc.). After each test, the student gets a personalized summary depicting their strengths and weaknesses in mathematical Basics. Teachers can visit a special website to examine the results of their classes or single students. In total 5830 students did participate so far. For standardization and optimization purposes the tests are being evaluated, using the classic and probabilistic Test-Theory regarding Objectivity, Reliability and Validity, annually since 2015. This Paper is about the Optimization process considering the Rasch-scaling and Standardization of the tests. Additionally, current results using standardized tests will be discussed. To achieve this Competence levels and Types of errors of students attending vocational Colleges in Nordrheinwestfalen, Germany, were determined, using descriptive Data and Distractorevaluations.

Keywords: diagnostical tests in mathematics, distractor devaluation, test-optimization, test-theory

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Authors: Guilherme Baldo Carlos

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The flexible job-shop scheduling problem (FJSP) is an NP-hard combinatorial optimization problem, which can be applied to model several applications in a wide array of industries. This problem will have its importance increase due to the shift in the production mode that modern society is going through. The demands are increasing and for products personalized and customized. This work aims to apply a meta-heuristic called a genetic algorithm (GA) to solve this problem. A GA is a meta-heuristic inspired by the natural selection of Charles Darwin; it produces a population of individuals (solutions) and selects, mutates, and mates the individuals through generations in order to find a good solution for the problem. The results found indicate that the GA is suitable for FJSP solving.

Keywords: genetic algorithm, evolutionary algorithm, scheduling, flexible job-shop scheduling

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Authors: Bita Payami-Shabestari, Dariush Eslami

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The purpose of this paper is to develop a multi-product economic production quantity model under vendor management inventory policy and restrictions including limited warehouse space, budget, and number of orders, average shortage time and maximum permissible shortage. Since the “costs” cannot be predicted with certainty, it is assumed that data behave under uncertain environment. The problem is first formulated into the framework of a bi-objective of multi-product economic production quantity model. Then, the problem is solved with three multi-objective decision-making (MODM) methods. Then following this, three methods had been compared on information on the optimal value of the two objective functions and the central processing unit (CPU) time with the statistical analysis method and the multi-attribute decision-making (MADM). The results are compared with statistical analysis method and the MADM. The results of the study demonstrate that augmented-constraint in terms of optimal value of the two objective functions and the CPU time perform better than global criteria, and goal programming. Sensitivity analysis is done to illustrate the effect of parameter variations on the optimal solution. The contribution of this research is the use of random costs data in developing a multi-product economic production quantity model under vendor management inventory policy with several constraints.

Keywords: economic production quantity, random cost, supply chain management, vendor-managed inventory

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Authors: Erika Ruíz, Luis Amaya, Diego Carreño

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The main objective of this study is to design a mathematical model for the logistics of mining collection centers in the northern region of the department of Boyacá (Colombia), determining the structure that facilitates the flow of products along the supply chain. In order to achieve this, it is necessary to define a suitable design of the distribution network, taking into account the products, customer’s characteristics and the availability of information. Likewise, some other aspects must be defined, such as number and capacity of collection centers to establish, routes that must be taken to deliver products to the customers, among others. This research will use one of the operation research problems, which is used in the design of distribution networks known as Location Routing Problem (LRP).

Keywords: location routing problem, logistic, mining collection, model

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Authors: Laissa Mae Francisco, John Rolex Ingreso, Anna Krizel Menguito, Criselda Robrigado, Rej Maegan Tuazon

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This study aims to determine and describe the existing relationship between number sense proficiency and problem-solving performance of grade seven students from Victorino Mapa High School, Manila. A paper pencil exam containing of 50-item number sense test and 5-item problem-solving test which measures their number sense proficiency and problem-solving performance adapted from McIntosh, Reys, and Bana were used as the research instruments. The data obtained from this study were interpreted and analyzed using the Pearson – Product Moment Coefficient of Correlation to determine the relationship between the two variables. It was found out that students who were low in number sense proficiency tend to be the students with poor problem-solving performance and students with medium number sense proficiency are most likely to have an average problem-solving performance. Likewise, students with high number sense proficiency are those who do excellently in problem-solving performance.

Keywords: number sense, performance, problem solving, proficiency

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Authors: Shih-Pin Chen, Shih-Syuan You

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Fuzzy regression models are useful for investigating the relationship between explanatory variables and responses in fuzzy environments. To overcome the deficiencies of previous models and increase the explanatory power of fuzzy data, the graded mean integration (GMI) representation is applied to determine representative crisp regression coefficients. A fuzzy regression model is constructed based on the modified dissemblance index (MDI), which can precisely measure the actual total error. Compared with previous studies based on the proposed MDI and distance criterion, the results from commonly used test examples show that the proposed fuzzy linear regression model has higher explanatory power and forecasting accuracy.

Keywords: dissemblance index, fuzzy linear regression, graded mean integration, mathematical programming

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Authors: Pei Chin Lim

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School of Mathematics and Science of Singapore Polytechnic offers a Basic Mathematics module to students who did not pass GCE O-Level Additional Mathematics. These students are weaker in Mathematics. In particular, they struggle with word problems and tend to leave them blank in tests and examinations. In order to improve students’ problem-solving skills, the school redesigned the Basic Mathematics module to incorporate Polya’s problem-solving methodology. During tutorial lessons, students have to work through learning activities designed to raise their metacognitive awareness by following Polya’s problem-solving process. To assess the effectiveness of the redesign, students’ working for a challenging word problem in the mid-semester test were analyzed. Sixty-five percent of students attempted to understand the problem by making sketches. Twenty-eight percent of students went on to devise a plan and implement it. Only five percent of the students still left the question blank. These preliminary results suggest that with regular exposure to an explicit and systematic problem-solving approach, weak students’ problem-solving skills can potentially be improved.

Keywords: mathematics education, metacognition, problem solving, weak students

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Authors: Jian Zheng, Yoshiyasu Takahashi, Yuichi Kobayashi, Tatsuhiro Sato

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In the study, we present a conceptual framework for developing a scheduling system that can generate self-explanatory and easy-understanding schedules. To this end, a user interface is conceived to help planners record factors that are considered crucial in scheduling, as well as internal and external sources relating to such factors. A hybrid approach combining machine learning and constraint programming is developed to generate schedules and the corresponding factors, and accordingly display them on the user interface. Effects of the proposed system on scheduling are discussed, and it is expected that scheduling efficiency and system understandability will be improved, compared with previous scheduling systems.

Keywords: constraint programming, factors considered in scheduling, machine learning, scheduling system

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Authors: D. Calogine, O. Chau, S. Dotti, O. Ramiarinjanahary, P. Rasoavonjy, F. Tovondahiniriko

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Mafate is a natural circus in the north-western part of Reunion Island, without an electrical grid and road network. A micro-grid concept is being experimented in this area, composed of a photovoltaic production combined with electrochemical batteries, in order to meet the local population for self-consumption of electricity demands. This work develops a discrete model as well as a stochastic model in order to reach an optimal equilibrium between production and consumptions for a cluster of houses. The management of the energy power leads to a large linearized programming system, where the time interval of interest is 24 hours The experimental data are solar production, storage energy, and the parameters of the different electrical devices and batteries. The unknown variables to evaluate are the consumptions of the various electrical services, the energy drawn from and stored in the batteries, and the inhabitants’ planning wishes. The objective is to fit the solar production to the electrical consumption of the inhabitants, with an optimal use of the energies in the batteries by satisfying as widely as possible the users' planning requirements. In the discrete model, the different parameters and solutions of the linear programming system are deterministic scalars. Whereas in the stochastic approach, the data parameters and the linear programming solutions become random variables, then the distributions of which could be imposed or established by estimation from samples of real observations or from samples of optimal discrete equilibrium solutions.

Keywords: photovoltaic production, power consumption, battery storage resources, random variables, stochastic modeling, estimations of probability distributions, mixed integer linear programming, smart micro-grid, self-consumption of electricity.

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Authors: Hamed K. Esfahani, Bithin Datta

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Transport of reactive chemical contaminant species in groundwater aquifers is a complex and highly non-linear physical and geochemical process especially for real life scenarios. Simulating this transport process involves solving complex nonlinear equations and generally requires huge computational time for a given aquifer study area. Development of optimal remediation strategies in aquifers may require repeated solution of such complex numerical simulation models. To overcome this computational limitation and improve the computational feasibility of large number of repeated simulations, Genetic Programming based trained surrogate models are developed to approximately simulate such complex transport processes. Transport process of acid mine drainage, a hazardous pollutant is first simulated using a numerical simulated model: HYDROGEOCHEM 5.0 for a contaminated aquifer in a historic mine site. Simulation model solution results for an illustrative contaminated aquifer site is then approximated by training and testing a Genetic Programming (GP) based surrogate model. Performance evaluation of the ensemble GP models as surrogate models for the reactive species transport in groundwater demonstrates the feasibility of its use and the associated computational advantages. The results show the efficiency and feasibility of using ensemble GP surrogate models as approximate simulators of complex hydrogeologic and geochemical processes in a contaminated groundwater aquifer incorporating uncertainties in historic mine site.

Keywords: geochemical transport simulation, acid mine drainage, surrogate models, ensemble genetic programming, contaminated aquifers, mine sites

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Authors: Leon Pan

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The first programming course within post-secondary education has long been recognized as a challenging endeavor for both educators and students alike. Historically, these courses have exhibited high failure rates and a notable number of dropouts. Instructors often lament students' lack of effort in their coursework, and students often express frustration that the teaching methods employed are not effective. Drawing inspiration from the successful principles of Extreme Programming, this study introduces an approach—the Extremes-based teaching model — aimed at enhancing the teaching of introductory programming courses. To empirically determine the effectiveness of the model, a comparison was made between a section taught using the extreme-based model and another utilizing traditional teaching methods. Notably, the extreme-based teaching class required students to work collaboratively on projects while also demanding continuous assessment and performance enhancement within groups. This paper details the application of the extreme-based model within the post-secondary online classroom context and presents the compelling results that emphasize its effectiveness in advancing the teaching and learning experiences. The extreme-based model led to a significant increase of 13.46 points in the weighted total average and a commendable 10% reduction in the failure rate.

Keywords: extreme-based teaching model, innovative pedagogical methods, project-based learning, team-based learning

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Authors: N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev

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Nonlinear analysis of the phase locked loop (PLL)-based circuits is a challenging task. Thus, the simulation is widely used for their study. In this work, we consider a mathematical model of the optical Costas loop and demonstrate the limitations of simulation approach related to the existence of so-called hidden oscillations in the phase space of the model.

Keywords: optical Costas loop, mathematical model, simulation, hidden oscillation

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Authors: Yulii D. Shikhmurzaev

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The modelling of the non-isothermal free-surface flows coupled with the solidification process has become the topic of intensive research with the advent of additive manufacturing, where complex 3-dimensional structures are produced by successive deposition and solidification of microscopic droplets of different materials. The issue is that both the spreading of liquids over solids and the propagation of the solidification front into the fluid and along the solid substrate pose fundamental difficulties for their mathematical modelling. The first of these processes, known as ‘dynamic wetting’, leads to the well-known ‘moving contact-line problem’ where, as shown recently both experimentally and theoretically, the contact angle formed by the free surfac with the solid substrate is not a function of the contact-line speed but is rather a functional of the flow field. The modelling of the propagating solidification front requires generalization of the classical Stefan problem, which would be able to describe the onset of the process and the non-equilibrium regime of solidification. Furthermore, given that both dynamic wetting and solification occur concurrently and interactively, they should be described within the same conceptual framework. The present work addresses this formidable problem and presents a mathematical model capable of describing the key element of additive manufacturing in a self-consistent and singularity-free way. The model is illustrated simple examples highlighting its main features. The main idea of the work is that both dynamic wetting and solidification, as well as some other fluid flows, are particular cases in a general class of flows where interfaces form and/or disappear. This conceptual framework allows one to derive a mathematical model from first principles using the methods of irreversible thermodynamics. Crucially, the interfaces are not considered as zero-mass entities introduced using Gibbsian ‘dividing surface’ but the 2-dimensional surface phases produced by the continuum limit in which the thickness of what physically is an interfacial layer vanishes, and its properties are characterized by ‘surface’ parameters (surface tension, surface density, etc). This approach allows for the mass exchange between the surface and bulk phases, which is the essence of the interface formation. As shown numerically, the onset of solidification is preceded by the pure interface formation stage, whilst the Stefan regime is the final stage where the temperature at the solidification front asymptotically approaches the solidification temperature. The developed model can also be applied to the flow with the substrate melting as well as a complex flow where both types of phase transition take place.

Keywords: dynamic wetting, interface formation, phase transition, solidification

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Authors: Ramazan I. Kadiev, Arcady Ponosov

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Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Zeynep Sener, Mehtap Dursun

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Supplier evaluation and selection is one of the most important components of an effective supply chain management system. Due to the expanding competition in healthcare, selecting the right medical device suppliers offers great potential for increasing quality while decreasing costs. This paper proposes a fuzzy decision making approach for medical supplier selection. A real-world medical device supplier selection problem is presented to illustrate the application of the proposed decision methodology.

Keywords: fuzzy decision making, fuzzy multiple objective programming, medical supply chain, supplier selection

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Authors: Hashini E. Mohottala

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We report the combine use of Wikispaces (WikiS) and Group Problem Solving (GPS) sessions conducted in the introductory level physics classes. As a part of this new teaching tool, some essay type problems were posted on the WikiS in weekly basis and students were encouraged to participate in problem solving without providing numerical final answers but the steps. Wikispace is used as a platform for students to meet online and create discussions. Each week students were further evaluated on problem solving skills opening up more opportunity for peer interaction through GPS. Each group was given a different problem to solve and the answers were graded. Students developed a set of skills in decision-making, problem solving, communication, negotiation, critical and independent thinking and teamwork through the combination of WikiS and GPS.

Keywords: group problem solving (GPS), wikispace (WikiS), physics education, learning

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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: Sourabh Joshi, Tarun Sharma, Anurag Sharma

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Ant Colony Optimization is heuristic Algorithm which has been proven a successful technique applied on number of combinatorial optimization problems. Two variants of Ant Colony Optimization algorithm named Ant System and Max-Min Ant System are implemented in MATLAB to solve travelling Salesman Problem and the results are compared. In, this paper both systems are analyzed by solving the some Travelling Salesman Problem and depict which system solve the problem better in term of cost and time.

Keywords: Ant Colony Optimization, Travelling Salesman Problem, Ant System, Max-Min Ant System

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Authors: Saeyoung Lee

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As the enthusiasm for education in Korea is too much high, it is well known by others that children in Korea get good scores in Mathematics. However, behind of this good reputation, children in Korea are easy to get lose self-confidence, tend to complaint and rarely participate in the class because of too much competition which leads to lack of competences. In this regard, the main goals of this paper are, by applying the programme based on peer-communication on Mathematics education field, it would like to improve self-managemental competence to make children gain self-confidence, communicative competence to make them deal with complaint and communitive competence to make them participated in the class for the age of 10 children to solve this problem. 14 children the age of 10 in one primary school in Gangnam, Seoul, Korea had participated in the research from March 2018 to October 2018. They were under the programme based on peer-communication during the period. Every Mathematics class maintained the same way. Firstly a problem was given to children. Secondly, children were asked to find many ways to solve the problem as much as they could by themselves. Thirdly all ways to solve the problem by children were posted on the board and three of the children made a group to distinguish the ways from valid to invalid. Lastly, all children made a discuss to find one way which is the most efficient among valid ways. Pre-test was carried out by the questionnaire based on Likert scale before applying the programme. The result of the pre-test was 3.89 for self-managemental competence, 3.91 for communicative competence and 4.19 for communitive competence. Post-test was carried out by the same questionnaire after applying the programme. The result of the post-test was 3.93 for self-managemental competence, 4.23 for communicative competence and 4.20 for communitive competence. That means by applying the programme based on peer-communication on Mathematics education field, the age of 10 children in Korea could improve self-managemental, communicative and communitive competence. Especially it works very well on communicative competence by increasing 0.32 points as it marked. Considering this research, Korean Mathematics education based on competition which leads to lack of competences should be changed to cooperative structure to make students more competent rather than just getting good scores. In conclusion, innovative teaching methods which are focused on improving competences such as the programme based on peer-communication which was applied in this research are strongly required to be studied and widely used.

Keywords: competences, mathematics education, peer-communication, primary education

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Authors: Oibar Martinez, Clara Oliver, Jose Miguel Miranda

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The study of dispersion phenomena in electromagnetic waves reflected by conductors at infrared and lower frequencies is a topic which finds a number of applications. We aim to explain in this work what are the most relevant ones and how this phenomenon is modeled from both optics and electromagnetics points of view. We also explain here how the amplitude of an electromagnetic wave reflected by a lossy conductor could depend on both the frequency of the incident wave, as well as on the electrical properties of the conductor, and we illustrate this phenomenon with a practical example. The mathematical analysis made by a specialist in electromagnetics or a microwave engineer is apparently very different from the one made by a specialist in optics. We show here how both approaches lead to the same physical result and what are the key concepts which enable one to understand that despite the differences in the equations the solution to the problem happens to be the same. Our study starts with an analysis made by using the complex refractive index and the reflectance parameter. We show how this reflectance has a dependence with the square root of the frequency when the reflecting material is a good conductor, and the frequency of the wave is low enough. Then we analyze the same problem with a less known approach, which is based on the reflection coefficient of the electric field, a parameter that is most commonly used in electromagnetics and microwave engineering. In summary, this paper presents a mathematical study illustrated with a worked example which unifies the modeling of dispersion effects made by specialists in optics and the one made by specialists in electromagnetics. The main finding of this work is that it is possible to reproduce the dependence of the Fresnel reflectance with frequency from the intrinsic impedance of the reflecting media.

Keywords: dispersion, electromagnetic waves, microwaves, optics

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Authors: Boris Melnikov, Dmitrii Chaikovskii, Elena Melnikova

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The traveling salesman problem (TSP) is a well-known optimization problem that seeks to find the shortest possible route that visits a set of points and returns to the starting point. In this paper, we apply some heuristics of the TSP for the task of restoring the DNA matrix. This restoration problem is often considered in biocybernetics. For it, we must recover the matrix of distances between DNA sequences if not all the elements of the matrix under consideration are known at the input. We consider the possibility of using this method in the testing of distance calculation algorithms between a pair of DNAs to restore the partially filled matrix.

Keywords: optimization problems, DNA matrix, partially filled matrix, traveling salesman problem, heuristic algorithms

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Authors: A. Schuchter, M. Promegger

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The outbreak of the COVID-19 pandemic has shown us that online education is so much more than just a cool feature for teachers – it is an essential part of modern teaching. In online math teaching, it is common to use tools to share screens, compute and calculate mathematical examples, while the students can watch the process. On the other hand, flipped classroom models are on the rise, with their focus on how students can gather knowledge by watching videos and on the teacher’s use of technological tools for information transfer. This paper proposes a co-educational teaching approach for coding and engineering subjects with the help of drone-building to spark interest in technology and create a platform for knowledge transfer. The project combines aspects from mathematics (matrices, vectors, shaders, trigonometry), physics (force, pressure and rotation) and coding (computational thinking, block-based programming, JavaScript and Python) and makes use of collaborative-shared 3D Modeling with clara.io, where students create mathematics knowhow. The instructor follows a problem-based learning approach and encourages their students to find solutions in their own time and in their own way, which will help them develop new skills intuitively and boost logically structured thinking. The collaborative aspect of working in groups will help the students develop communication skills as well as structural and computational thinking. Students are not just listeners as in traditional classroom settings, but play an active part in creating content together by compiling a Handbook of Knowledge (called “open book”) with examples and solutions. Before students start calculating, they have to write down all their ideas and working steps in full sentences so other students can easily follow their train of thought. Therefore, students will learn to formulate goals, solve problems, and create a ready-to use product with the help of “reverse engineering”, cross-referencing and creative thinking. The work on drones gives the students the opportunity to create a real-life application with a practical purpose, while going through all stages of product development.

Keywords: flipped classroom, co-creational education, coding, making, drones, co-education, ARCS-model, problem-based learning

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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: Yenny Paola Morales Cortés, Fabián Rico Rodríguez, Juan Carlos Serrato Bermúdez, Carlos Arturo Martínez Riascos

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Numerous benefits of galactooligosaccharides (GOS) as prebiotics have motivated the study of enzymatic processes for their production. These processes have special complexities due to several factors that make difficult high productivity, such as enzyme type, reaction medium pH, substrate concentrations and presence of inhibitors, among others. In the present work the production of galactooligosaccharides (with different degrees of polymerization: two, three and four) from lactose was studied. The study considers the formulation of a mathematical model that predicts the production of GOS from lactose using the enzyme β-galactosidase. The effect of pH in the reaction was studied. For that, phosphate buffer was used and with this was evaluated three pH values (6.0.6.5 and 7.0). Thus it was observed that at pH 6.0 the enzymatic activity insignificant. On the other hand, at pH 7.0 the enzymatic activity was approximately 27 times greater than at 6.5. The last result differs from previously reported results. Therefore, pH 7.0 was chosen as working pH. Additionally, the enzyme concentration was analyzed, which allowed observing that the effect of the concentration depends on the pH and the concentration was set for the following studies in 0.272 mM. Afterwards, experiments were performed varying the lactose concentration to evaluate its effects on the process and to generate the data for the adjustment of the mathematical model parameters. The mathematical model considers the reactions of lactose hydrolysis and transgalactosylation for the production of disaccharides and trisaccharides, with their inverse reactions. The production of tetrasaccharides was negligible and, because of that, it was not included in the model. The reaction was monitored by HPLC and for the quantitative analysis of the experimental data the Matlab programming language was used, including solvers for differential equations systems integration (ode15s) and nonlinear problems optimization (fminunc). The results confirm that the transgalactosylation and hydrolysis reactions are reversible, additionally inhibition by glucose and galactose is observed on the production of GOS. In relation to the production process of galactooligosaccharides, the results show that it is necessary to have high initial concentrations of lactose considering that favors the transgalactosylation reaction, while low concentrations favor hydrolysis reactions.

Keywords: β-galactosidase, galactooligosaccharides, inhibition, lactose, Matlab, modeling

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Authors: Terence Soule, Tami Al Ghamdi

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To study how to transfer knowledge from multiple source problems to the target problem, we modeled the Transfer Learning (TL) process using Genetic Algorithms as the model solver. TL is the process that aims to transfer learned data from one problem to another problem. The TL process aims to help Machine Learning (ML) algorithms find a solution to the problems. The Genetic Algorithms (GA) give researchers access to information that we have about how the old problem is solved. In this paper, we have five different source problems, and we transfer the knowledge to the target problem. We studied different scenarios of the target problem. The results showed combined knowledge from multiple source problems improves the GA performance. Also, the process of combining knowledge from several problems results in promoting diversity of the transferred population.

Keywords: transfer learning, genetic algorithm, evolutionary computation, source and target

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