Search results for: electoral mathematics

Authors: Jiming Yang

Abstract:

A kind of singularly perturbed boundary value problems is under consideration. In order to obtain its approximation, simple upwind difference discretization is applied. We use a moving mesh iterative algorithm based on equi-distributing of the arc-length function of the current computed piecewise linear solution. First, a maximum norm a posteriori error estimate on an arbitrary mesh is derived using a different method from the one carried out by Chen [Advances in Computational Mathematics, 24(1-4) (2006), 197-212.]. Then, basing on the properties of discrete Green-s function and the presented posteriori error estimate, we theoretically prove that the discrete solutions computed by the algorithm are first-order uniformly convergent with respect to the perturbation parameter ε.

Keywords: Convergence analysis, green's function, singularly perturbed, equi-distribution, moving mesh.

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Authors: Nicoletta Adamo-Villani

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The object of this research is the design and evaluation of an immersive Virtual Learning Environment (VLE) for deaf children. Recently we have developed a prototype immersive VR game to teach sign language mathematics to deaf students age K- 4 [1] [2]. In this paper we describe a significant extension of the prototype application. The extension includes: (1) user-centered design and implementation of two additional interactive environments (a clock store and a bakery), and (2) user-centered evaluation including development of user tasks, expert panel-based evaluation, and formative evaluation. This paper is one of the few to focus on the importance of user-centered, iterative design in VR application development, and to describe a structured evaluation method.

Keywords: 3D Animation, Virtual Reality, Virtual Learning Environments, User-Centered Design, User-centered Evaluation.

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Authors: Saipunidzam Mahamad, Mohammad Noor Ibrahim, Mohamad Izzriq Ab Malek Foad, ShakirahMohd Taib

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With the proliferation of the mobile device technologies, mobile learning can be used to complement and improve traditional learning problems. Both students and teachers need a proper and handy system to monitor and keep track the performance of the students. This paper presents an implementation of M-learning for primary school in Malaysia by using an open source technology. It focuses on learning mathematics using handheld devices for primary schools- students aged 11 and 12 years old. Main users for this system include students, teachers and the administrator. This application suggests a new mobile learning environment with mobile graph for tracking the students- progress and performance. The purpose of this system is not to replace traditional classroom but to complement the learning process. In a testing conducted, students who used this system performed better in their examination.

Keywords: M-Learning, Automated Mobile Graph.

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Authors: Tai-Hwa Emily Lu

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This study was a part of the three-year longitudinal research on setting up an math learning model for the disadvantaged students in Taiwan. A target 2nd grade class with 10 regular students and 6 disadvantaged students at a disadvantaged area in Taipei participated in this study. Two units of a market basal math textbook concerning fractions, three-dimensional figures, weight and capacity were adapted to enhance their math learning motivations, confidences and effects. The findings were (1) curriculum adaptation was effective on enhancing students- learning motivations, confidences and effects; (2) story-type problems and illustrations decreased difficulties on understanding math language for students from new immigrant families and students with special needs; (3) “concrete – semiconcrete – abstract" teaching strategies and hands-on activities were essential to raise students learning interests and effects; and (4) curriculum adaptation knowledge and skills needed to be included in the pre- and in-service teacher training programs.

Keywords: curriculum adaptations, mathematics, disadvantaged students, inclusive classroom

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Authors: Rudy Agustriyanto, Akbarningrum Fatmawati

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The utilization of cheese whey as a fermentation substrate to produce bio-ethanol is an effort to supply bio-ethanol demand as a renewable energy. Like other process systems, modeling is also required for fermentation process design, optimization and plant operation. This research aims to study the fermentation process of cheese whey by applying mathematics and fundamental concept in chemical engineering, and to investigate the characteristic of the cheese whey fermentation process. Steady state simulation results for inlet substrate concentration of 50, 100 and 150 g/l, and various values of hydraulic retention time, showed that the ethanol productivity maximum values were 0.1091, 0.3163 and 0.5639 g/l.h respectively. Those values were achieved at hydraulic retention time of 20 hours, which was the minimum value used in this modeling. This showed that operating reactor at low hydraulic retention time was favorable. Model of bio-ethanol production from cheese whey will enhance the understanding of what really happen in the fermentation process.

Keywords: Cheese whey, ethanol, fermentation, modeling.

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Authors: Harpreet Singh Dhillon, Abhijit Mitra

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A reduced-bit multiplication algorithm based on the ancient Vedic multiplication formulae is proposed in this paper. Both the Vedic multiplication formulae, Urdhva tiryakbhyam and Nikhilam, are first discussed in detail. Urdhva tiryakbhyam, being a general multiplication formula, is equally applicable to all cases of multiplication. It is applied to the digital arithmetic and is shown to yield a multiplier architecture which is very similar to the popular array multiplier. Due to its structure, it leads to a high carry propagation delay in case of multiplication of large numbers. Nikhilam Sutra, on the other hand, is more efficient in the multiplication of large numbers as it reduces the multiplication of two large numbers to that of two smaller numbers. The framework of the proposed algorithm is taken from this Sutra and is further optimized by use of some general arithmetic operations such as expansion and bit-shifting to take advantage of bit-reduction in multiplication. We illustrate the proposed algorithm by reducing a general 4x4-bit multiplication to a single 2 x 2-bit multiplication operation.

Keywords: Multiplication, algorithm, Vedic mathematics, digital arithmetic, reduced-bit.

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Authors: Mohamed Chabi, Mohammad Shahid Jamil, Mahmoud I Syam

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The purpose of this study is to determine whether paper assessment especially in the subject mathematics will ever be completely replaced by online assessment using Learning Management System and Content Management System such as blackboard. Testing students has moved from the traditional scribbling and sketching on paper towards working online on a screen and keyboard. It is found that online assessment by using selective types of questions like multiple choices, true or false and final answer questions don’t reflect the actual understanding of students in solving the problems and teachers can’t determine the weakness points of students. In addition, it is showed that OBMCQs are a very good tool for self-assessment and when teachers are testing for knowledge and facts. But when it comes to the skills, OBMCQs are poor tools for measuring the ability to apply knowledge to complex math problem. 

Keywords: Paper assessment, online assessment, learning management system, content management system.

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Authors: Mihai Rebenciuc, Simona Mihaela Bibic

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Branch of modern mathematics, graphs represent instruments for optimization and solving practical applications in various fields such as economic networks, engineering, network optimization, the geometry of social action, generally, complex systems including contemporary urban problems (path or transport efficiencies, biourbanism, & c.). In this paper is studied the interconnection of some urban network, which can lead to a simulation problem of a digraph through another digraph. The simulation is made univoc or more general multivoc. The concepts of fragment and atom are very useful in the study of connectivity in the digraph that is simulation - including an alternative evaluation of k- connectivity. Rough set approach in (bi)digraph which is proposed in premier in this paper contribute to improved significantly the evaluation of k-connectivity. This rough set approach is based on generalized rough sets - basic facts are presented in this paper.

Keywords: (Bi)digraphs, rough set theory, systems of interacting agents, complex systems.

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Authors: Zuwairie Ibrahim, Yusei Tsuboi, Osamu Ono, Marzuki Khalid

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Deoxyribonucleic Acid or DNA computing has emerged as an interdisciplinary field that draws together chemistry, molecular biology, computer science and mathematics. Thus, in this paper, the possibility of DNA-based computing to solve an absolute 1-center problem by molecular manipulations is presented. This is truly the first attempt to solve such a problem by DNA-based computing approach. Since, part of the procedures involve with shortest path computation, research works on DNA computing for shortest path Traveling Salesman Problem, in short, TSP are reviewed. These approaches are studied and only the appropriate one is adapted in designing the computation procedures. This DNA-based computation is designed in such a way that every path is encoded by oligonucleotides and the path-s length is directly proportional to the length of oligonucleotides. Using these properties, gel electrophoresis is performed in order to separate the respective DNA molecules according to their length. One expectation arise from this paper is that it is possible to verify the instance absolute 1-center problem using DNA computing by laboratory experiments.

Keywords: DNA computing, operation research, 1-center problem.

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Authors: Mikhail Bouniaev

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The paper reviews design and implementation of a Calculus Course required for the Biomedical Competency Based Program developed as a joint project between The University of Texas Rio Grande Valley, and the University of Texas’ Institute for Transformational Learning, from the theoretical perspective as presented in scholarly work on active learning, formative assessment, and on-line teaching. Following a four stage curriculum development process (objective, content, delivery, and assessment), and theoretical recommendations that guarantee effectiveness and efficiency of assessment in active learning, we discuss the practical recommendations on how to incorporate a strong formative assessment component to address disciplines’ needs, and students’ major needs. In design and implementation of this project, we used Constructivism and Stage-by-Stage Development of Mental Actions Theory recommendations.

Keywords: Active learning, assessment, Calculus, cognitive demand, constructivism, mathematics, Stage-by-Stage Development of Mental Action Theory.

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Authors: Areej M. Abduldaim, Nadia M. G. Al-Saidi

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Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved.

Keywords: Cryptosystem, identification, skew π-Armendariz rings, skew polynomial rings, zero knowledge protocol.

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Authors: Veronica Diaz Quezada

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In this article, the performance and errors are featured and analysed in the limit problems solving of a real-valued function, in correspondence to competency-based education in engineering careers, in the south of Chile. The methodological component is contextualised in a qualitative research, with a descriptive and explorative design, with elaboration, content validation and application of quantitative instruments, consisting of two parallel forms of open answer tests, based on limit application problems. The mathematical competences and errors made by students from five engineering careers from a public University are identified and characterized. Results show better performance only to solve routine-context problem-solving competence, thus they are oriented towards a rational solution or they use a suitable problem-solving method, achieving the correct solution. Regarding errors, most of them are related to techniques and the incorrect use of theorems and definitions of real-valued function limits of real variable.

Keywords: Engineering education, errors, limits, mathematics competences, problem solving.

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Authors: Shobha Sharma, Amita Dev, Akanksha Kant

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Digital signal processor, image signal processor and FIR filters have multipliers as an important part of their design. On the basis of Vedic mathematics, Vedic multipliers have come out to be very fast multipliers. One of the image processing applications is edge detection. This research presents a small area and high speed 8 bit Vedic multiplier system comprising of compressor based adders. This results in faster edge detection. This architecture is tested on Xilinx vertex 4 FPGA board and simulations were carried out using the Xilinx synthesis tool. Comparisons are made and this system is found to be smaller in area with high speed (the lesser propagation delay). This compressor based Vedic multiplier is 1.1 times speedier than a typical Vedic multiplier. Also, this Vedic Multiplier is 2 times speedier than a ‘simple’ multiplier.

Keywords: Detection of edges, Vedic multiplier, image processing, Urdhva Tiryakbhyam sutra.

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Authors: Truong Quang Dang Khoa, Masahiro Nakagawa

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Brain Computer Interface (BCI) has been recently increased in research. Functional Near Infrared Spectroscope (fNIRs) is one the latest technologies which utilize light in the near-infrared range to determine brain activities. Because near infrared technology allows design of safe, portable, wearable, non-invasive and wireless qualities monitoring systems, fNIRs monitoring of brain hemodynamics can be value in helping to understand brain tasks. In this paper, we present results of fNIRs signal analysis indicating that there exist distinct patterns of hemodynamic responses which recognize brain tasks toward developing a BCI. We applied two different mathematics tools separately, Wavelets analysis for preprocessing as signal filters and feature extractions and Neural networks for cognition brain tasks as a classification module. We also discuss and compare with other methods while our proposals perform better with an average accuracy of 99.9% for classification.

Keywords: functional near infrared spectroscope (fNIRs), braincomputer interface (BCI), wavelets, neural networks, brain activity, neuroimaging.

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Authors: Haohao Wang

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Technology, multimedia in Open Educational Resources, can contribute positively to student performance in an online instructional environment. Student performance data of past four years were obtained from an online course entitled Applied Calculus (MA139). This paper examined the data to determine whether multimedia (independent variable) had any impact on student performance (dependent variable) in online math learning, and how students felt about the value of the technology. Two groups of student data were analyzed, group 1 (control) from the online applied calculus course that did not use multimedia instructional materials, and group 2 (treatment) of the same online applied calculus course that used multimedia instructional materials. For the MA139 class, results indicate a statistically significant difference (p = .001) between the two groups, where group 1 had a final score mean of 56.36 (out of 100), group 2 of 70.68. Additionally, student testimonials were discussed in which students shared their experience in learning applied calculus online with multimedia instructional materials.

Keywords: Online learning, Open Educational Resources, Multimedia, Technology.

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Authors: M. Y. Misro, A. Ramli, J. M. Ali

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Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use different approach to find the best approximation for the curve so that it will resembles highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first, the Bezier curve estimates the real shape of the curve which can be verified visually. Even though, fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed are acceptable. We verified our result with the manual calculation of the curvature from the map.

Keywords: Speed estimation, path constraints, reference trajectory, Bezier curve.

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Authors: Fethi Soltani, Adel Almarashi, Idir Mechai

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Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators.

Keywords: Fourier multiplier operators, Gauss-Kronrod method of integration, Paley-Wiener space, Tikhonov regularization.

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Authors: Vaibhav Kant Singh, Vijay Shah, Yogendra Kumar Jain, Anupam Shukla, A.S. Thoke, Vinay KumarSingh, Chhaya Dule, Vivek Parganiha

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Data mining, which is the exploration of knowledge from the large set of data, generated as a result of the various data processing activities. Frequent Pattern Mining is a very important task in data mining. The previous approaches applied to generate frequent set generally adopt candidate generation and pruning techniques for the satisfaction of the desired objective. This paper shows how the different approaches achieve the objective of frequent mining along with the complexities required to perform the job. This paper will also look for hardware approach of cache coherence to improve efficiency of the above process. The process of data mining is helpful in generation of support systems that can help in Management, Bioinformatics, Biotechnology, Medical Science, Statistics, Mathematics, Banking, Networking and other Computer related applications. This paper proposes the use of both upward and downward closure property for the extraction of frequent item sets which reduces the total number of scans required for the generation of Candidate Sets.

Keywords: Data Mining, Candidate Sets, Frequent Item set, Pruning.

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Authors: Amal A. Abdel-Sattar

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The curriculum of architecture department in Prince Sultan University includes ‘Building Surveying’ course which is usually a part of civil engineering courses. As a fundamental requirement of the course, it requires a strong background in mathematics and physics, which are not usually preferred subjects to the architecture students and many of them are not giving the required and necessary attention to these courses during their preparation year before commencing their architectural study. This paper introduces the concept and the methodology of the student-centered learning approach in the course of building surveying for architects. One of the major outcomes is the improvement in the students’ involvement in the course and how this will cover and strength their analytical weak points and improve their mathematical skills. The study is conducted through three semesters with a total number of 99 students. The effectiveness of the student-centered learning approach is studied using the student survey at the end of each semester and teacher observations. This survey showed great acceptance of the students for these methods. Also, the teachers observed a great improvement in the students’ mathematical abilities and how keener they became in attending the classes which were clearly reflected on the low absence record.

Keywords: Architecture, building surveying, student-centered learning, teaching, and learning.

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Authors: V. S. Klimash, Ye Min Thu

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

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

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Authors: Po-Chun Lin, Jyh-Cherng Gu

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This study adopted previous fault patterns, results of detection analysis, historical records and data, and experts- experiences to establish fuzzy principles and estimate the failure probability index of components of a power transformer. Considering that actual parameters and limiting conditions of parameters may differ, this study used the standard data of IEC, IEEE, and CIGRE as condition parameters. According to the characteristics of each condition parameter, relative degradation was introduced to reflect the degree of influence of the factors on the transformer condition. The method of fuzzy mathematics was adopted to determine the subordinate function of the transformer condition. The calculation used the Matlab Fuzzy Tool Box to select the condition parameters of coil winding, iron core, bushing, OLTC, insulating oil and other auxiliary components and factors (e.g., load records, performance history, and maintenance records) of the transformer to establish the fuzzy principles. Examples were presented to support the rationality and effectiveness of the evaluation method of power transformer performance conditions, as based on fuzzy comprehensive evaluation.

Keywords: Fuzzy, relative degradation degree, condition-basedmaintenance, power transformer

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Authors: Mohd Agos Salim Nasir, Ros Fadilah Deraman, Siti Salmah Yasiran

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The Goursat partial differential equation arises in linear and non linear partial differential equations with mixed derivatives. This equation is a second order hyperbolic partial differential equation which occurs in various fields of study such as in engineering, physics, and applied mathematics. There are many approaches that have been suggested to approximate the solution of the Goursat partial differential equation. However, all of the suggested methods traditionally focused on numerical differentiation approaches including forward and central differences in deriving the scheme. An innovation has been done in deriving the Goursat partial differential equation scheme which involves numerical integration techniques. In this paper we have developed a new scheme to solve the Goursat partial differential equation based on the Adomian decomposition (ADM) and associated with Boole-s integration rule to approximate the integration terms. The new scheme can easily be applied to many linear and non linear Goursat partial differential equations and is capable to reduce the size of computational work. The accuracy of the results reveals the advantage of this new scheme over existing numerical method.

Keywords: Goursat problem, partial differential equation, Adomian decomposition method, Boole's integration rule.

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Authors: Sophie Huck, Knut Linke

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This study will examine how IT practitioners can be motivated for IT studies and which kind of support they need during their occupational studies. Within this research project, the challenge of supporting students being engaged in business for several years arose. Here, it is especially important to successfully guide them through their studies. The problem of this group is that they finished their school education years ago. In order to gather first experiences, preliminary e-learning courses were introduced and tested with a group of users studying General Management. They had to work with these courses and have been questioned later on about their approach to the different methods. Moreover, a second group of potential students was interviewed with the help of online questionnaires to give information about their expectations regarding extra occupational studies. We also want to present best practices and cases in e-education in the subarea of mathematics and distance learning. Within these cases and practices, we use state of the art systems and technologies in e-education to find a way to increase teaching quality and the success of students. Our research indicated that the first group of enrolled students appreciated the new preliminary e-learning courses. The second group of potential students was convinced of this way of learning as a significant component of extra occupational studies. It can be concluded that this part of the project clarified the acceptance of the e-learning strategy by both groups and led to satisfactory results with the enrolled students.

Keywords: E-learning evaluation, self-learning, virtual classroom, virtual learning environments.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, F. A. Ahmed

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In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.

Keywords: Equivalent Martingale Measure, European Put Option, Girsanov Theorem, Martingales, Monte Carlo method, option price valuation, option price valuation formula.

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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: Raluca Ionela Maxim

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Designing a gender responsive Science, Technology, Engineering and Mathematics (STEM) mobile game based learning solution (mGBL) is a challenge in terms of content, gamification level and equal engagement of girls and boys. The goal of this case study was to research and create a high-fidelity prototype design of a mobile game that contains role-models as avatars that guide and expose girls and boys to STEM learning content. For this research purpose it was applied the methodology of design sprint with five-phase process that combines design thinking principles. The technique of this methodology comprises smart interviews with STEM experts, mind-map creation, sketching, prototyping and usability testing of the interactive prototype of the gender responsive STEM mGBL. The results have shown that the effect of the avatar/role model had a positive impact. Therefore, by exposing students (boys and girls) to STEM role models in an mGBL tool is helpful for the decreasing of the gender inequalities in STEM fields.

Keywords: Design thinking, design sprint, gender-responsive STEM education, mobile game based learning, role-models.

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Authors: Omar M. Elmabrouk., Roaa Y. Taha., Najat M. Ebrahim, Sabbreen A. Mohammed

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Power transformers are the most crucial part of power electrical system, distribution and transmission grid. This part is maintained using predictive or condition-based maintenance approach. The diagnosis of power transformer condition is performed based on Dissolved Gas Analysis (DGA). There are five main methods utilized for analyzing these gases. These methods are International Electrotechnical Commission (IEC) gas ratio, Key Gas, Roger gas ratio, Doernenburg, and Duval Triangle. Moreover, due to the importance of the transformers, there is a need for an accurate technique to diagnose and hence predict the transformer condition. The main objective of this technique is to avoid the transformer faults and hence to maintain the power electrical system, distribution and transmission grid. In this paper, the DGA was utilized based on the data collected from the transformer records available in the General Electricity Company of Libya (GECOL) which is located in Benghazi-Libya. The Fuzzy Logic (FL) technique was implemented as a diagnostic approach based on IEC gas ratio method. The FL technique gave better results and approved to be used as an accurate prediction technique for power transformer faults. Also, this technique is approved to be a quite interesting for the readers and the concern researchers in the area of FL mathematics and power transformer.

Keywords: Fuzzy logic, dissolved gas-in-oil analysis, DGA, prediction, power transformer.

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Authors: Amir Farkhonde

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The major objective of this study was to devise a method for solving mathematical problems. Three concepts including faculty of understanding, faculty of guess, and free mind or beginner's mind provided the foundation for this method. An explanatory approach along with a hermeneutic process was taken in this study to support the assumption that mathematical knowledge is constantly developing and it seems essential for students to solve math problems on their own using their faculty of understanding (interpretive dialogue) and faculty of guess. For doing so, a kind of movement from the mathematical problem to mathematical knowledge should be adopted for teaching students a new math topic. The research method of this paper is review, descriptive and conception development. This paper first reviews the research findings on the NRICH’S project (NRICH is part of the family of activities in the Millennium Mathematics Project) with the aim that these findings form the theoretical basis of the problem-solving method. Then, the curriculum, the conceptual structure of the new method, how to design the problem and an example of it are discussed. In this way, students are immersed in the story of discovering and understanding the problem formula, and interpretive dialogue with the text continues by following the questions posed by the problem and constantly reconstructing the answer to find a formula or solution to solve the problem.

Keywords: Interpretive dialogue, NRICH, inventing, a method of problem solving.

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Authors: Petr Cernohorsky, Jan Voracek

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Well-developed strategic marketing planning is the essential prerequisite for establishment of the right and unique competitive advantage. Typical market, however, is a heterogeneous and decentralized structure with natural involvement of individual or group subjectivity and irrationality. These features cannot be fully expressed with one-shot rigorous formal models based on, e.g. mathematics, statistics or empirical formulas. We present an innovative solution, extending the domain of agent based computational economics towards the concept of hybrid modeling in service provider and consumer market such as telecommunications. The behavior of the market is described by two classes of agents - consumer and service provider agents - whose internal dynamics are fundamentally different. Customers are rather free multi-state structures, adjusting behavior and preferences quickly in accordance with time and changing environment. Producers, on the contrary, are traditionally structured companies with comparable internal processes and specific managerial policies. Their business momentum is higher and immediate reaction possibilities limited. This limitation underlines importance of proper strategic planning as the main process advising managers in time whether to continue with more or less the same business or whether to consider the need for future structural changes that would ensure retention of existing customers or acquisition of new ones.

Keywords: Agent-based computational economics, hybrid modeling, strategic marketing, system dynamics.

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Authors: Penn P. Wu, Jeannie Jo

Abstract:

Blockchain technology has rapidly gained popularity in industry. This paper attempts to assist academia to answer four questions. First, should community colleges begin offering education to nurture blockchain-literate students for the job market? Second, what are the appropriate topical areas to cover? Third, should it be an individual course? And forth, should it be a technical or management course? This paper starts with identifying the knowledge domains of blockchain technology and the topical areas each domain has, and continues with placing them in appropriate academic territories (Computer Sciences vs. Business) and subjects (programming, management, marketing, and laws), and then develops an evaluation model to determine the appropriate topical area for community colleges to teach. The evaluation is based on seven factors: maturity of technology, impacts on management, real-world applications, subject classification, knowledge prerequisites, textbook readiness, and recommended pedagogies. The evaluation results point to an interesting direction that offering an introductory course is an ideal option to guide students through the learning journey of what blockchain is and how it applies to business. Such an introductory course does not need to engage students in the discussions of mathematics and sciences that make blockchain technologies possible. While it is inevitable to brief technical topics to help students build a solid knowledge foundation of blockchain technologies, community colleges should avoid offering students a course centered on the discussion of developing blockchain applications.

Keywords: Blockchain, pedagogies, blockchain technologies, blockchain course, blockchain pedagogies.

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