Search results for: dropping method

Authors: Autcha Araveeporn

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This paper presents a study about a nonparametric regression model consisting of a smoothing spline method and a penalized spline regression method. We also compare the techniques used for estimation and prediction of nonparametric regression model. We tried both methods with crude oil prices in dollars per barrel and the Stock Exchange of Thailand (SET) index. According to the results, it is concluded that smoothing spline method performs better than that of penalized spline regression method.

Keywords: nonparametric regression model, penalized spline regression method, smoothing spline method, Stock Exchange of Thailand (SET)

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Authors: Amal Alshahrani, Allan Ramsay

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Paraphrasing is one of the important tasks in natural language processing; i.e. alternative ways to express the same concept by using different words or phrases. Paraphrases can be used in many natural language applications, such as Information Retrieval, Machine Translation, Question Answering, Text Summarization, or Information Extraction. To obtain pairs of sentences that are paraphrases we create a system that automatically extracts paraphrases from a corpus, which is built from different sources of news article since these are likely to contain paraphrases when they report the same event on the same day. There are existing simple standard approaches (e.g. TF-IDF vector space, cosine similarity) and alignment technique (e.g. Dynamic Time Warping (DTW)) for extracting paraphrase which have been applied to the English. However, the performance of these approaches could be affected when they are applied to another language, for instance Arabic language, due to the presence of phenomena which are not present in English, such as Free Word Order, Zero copula, and Pro-dropping. These phenomena will affect the performance of these algorithms. Thus, if we can analysis how the existing algorithms for English fail for Arabic then we can find a solution for Arabic. The results are promising.

Keywords: natural language processing, TF-IDF, cosine similarity, dynamic time warping (DTW)

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Authors: Bale Baidi Blaise, Gilles Marckmann, Liman Kaoye, Talaka Dya, Moustapha Bachirou, Gambo Betchewe, Tibi Beda

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This work highlights the capabilities of particles swarm optimization (PSO) method to identify parameters of hyperelastic models. The study compares this method with Genetic Algorithm (GA) method, Least Squares (LS) method, Pattern Search Algorithm (PSA) method, Beda-Chevalier (BC) method and the Levenberg-Marquardt (LM) method. Four classic hyperelastic models are used to test the different methods through parameters identification. Then, the study compares the ability of these models to reproduce experimental Treloar data in simple tension, biaxial tension and pure shear.

Keywords: particle swarm optimization, identification, hyperelastic, model

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Authors: M. K. Balyan

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

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

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Bib Paruhum Silalahi, Djihad Wungguli, Sugi Guritman

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Steepest descent method is a simple gradient method for optimization. This method has a slow convergence in heading to the optimal solution, which occurs because of the zigzag form of the steps. Barzilai and Borwein modified this algorithm so that it performs well for problems with large dimensions. Barzilai and Borwein method results have sparked a lot of research on the method of steepest descent, including alternate minimization gradient method and Yuan method. Inspired by previous works, we modified the step size of the steepest descent method. We then compare the modification results against the Barzilai and Borwein method, alternate minimization gradient method and Yuan method for quadratic function cases in terms of the iterations number and the running time. The average results indicate that the steepest descent method with the new step sizes provide good results for small dimensions and able to compete with the results of Barzilai and Borwein method and the alternate minimization gradient method for large dimensions. The new step sizes have faster convergence compared to the other methods, especially for cases with large dimensions.

Keywords: steepest descent, line search, iteration, running time, unconstrained optimization, convergence

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Authors: S. Shahrooi, A. Talavari

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Numeral study on the crack and discontinuity using element-free methods has been widely spread in recent years. In this study, for stress intensity factor calculation of the cracked axis under torsional loading has been used from a new element-free method as MLPG method. Region range is discretized by some dispersed nodal points. From method of moving least square (MLS) utilized to create the functions using these nodal points. Then, results of meshless method and finite element method (FEM) were compared. The results is shown which the element-free method was of good accuracy.

Keywords: stress intensity factor, crack, torsional loading, meshless method

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Authors: David Yartel, Johnmark Ampomah Mensah Fobi, Ernest Yeboah Acheampong, Sintim Musah

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Football has gone through a series of technological reforms targeted at improving the game for its audience. Yet, promote sanity of the game led to the introduction of the video assistant referee (VAR) to ‘check’ or ‘review’ an incident to clarify incidents and communicate the outcome to the referee and the fans. This is to reduce controversies regarding incidents on the pitch of play. In this study, we seek to survey the views of football fans to understand their perception of the video assistant referee, whether it has brought sanity or reduce the uncertainty regarding the decisions after reviews. The exploratory study focuses on 420 fans arbitrarily sampled on the university campuses to answer questionnaires based on the introduction of the video assistant referee. Results show that the VAR has interrupted the flow of the game, dropping passion, increased controversies including decisions from the referees’ call room leading to ensuing fans conflict, especially when it is against their team and vice versa. The study concludes by addressing some of their concerns as the VAR has come to minimise perceptions of incidents and engender fairness for teams.

Keywords: football fans, football incidents, football match, video assistant referee, technology

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Authors: Abu Hashan Md Mashud, M. Sharif Uddin, Aminur Rahman Khan

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In this paper, we formulate a new problem as a linear programming and Integer Programming problem and maximize profit within the limited budget and limited resources based on the construction of a tea garden problem. It describes a new idea about how to optimize profit and focuses on the practical aspects of modeling and the challenges of providing a solution to a complex real life problem. Finally, a comparative study is carried out among Graphical method, Simplex method and Branch and bound method.

Keywords: integer programming, tea garden, graphical method, simplex method, branch and bound method

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Authors: Christian Gabriel Mariveles, Darelle Jay Gallardo, Leslie Dayaoen, Laurenz Paul Diaz

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True experimental research with descriptive analysis was conducted. Utilizing Quicklime (Calcium Oxide) for self-healing properties of coconut husk fibre concrete brick. There are 2 setups established: the first one has the 1:1:2 ratio of calcium oxide, cement and sand, and the second one has a 2:1:2 ratio of the same variables. The bricks are made from the residences along Barangay Greater Lagro. The mixture of sand and cement is mixed with coconut husk fibers and then molded with different ratios in the molder. After the drying of cement, the researchers tested the bricks in the laboratory for compressive strength. The brick with the highest PSI is picked by the researchers to drop into freefall testing, and it makes remarkable remarks as it is deformed after dropping to different heights with a maximum of 20 feet. Unfortunately, the self-healing capabilities were not observed during the 12 weeks of monitoring. However, the brick was weighed after 12 weeks of monitoring, and it increased in weight by 0.030 kg. from 1.833 kg. to 1.863 kg. meaning that this ratio 2 has the potential to self-heal, but 12 weeks of monitoring by the researchers is not enough to conclude that it has a significant difference.

Keywords: self healing, coconut husk bricks, research, calcium oxide, utilizing quicklime

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Authors: Hasn Perera, Is Almeida, Hnk Perera, Mzf Mohammed, Ade Silva, H. Wijesinghe, Ajal Fernando

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Introduction: Dengue is a major Public Health burden of two clinical entities, Dengue Fever & Dengue Haemorrhagic Fever (DHF). The vast majority of dengue deaths occur in DHF patients, where the diagnosis hinges on the presence of fluid leakage. Limited Ultrasound Scans (USS) of chest and abdomen are used widely at Centre for Clinical Management of Dengue & Dengue Haemorrhagic Fever (CCMDDHF), as the primary method for detecting fluid leaking in DHF. This study analyses the relationship between haematological and USS findings at the onset of leaking and to further determine the usefulness of ultrasound in diagnosing DHF. Methods: A prospective analysis of 80 serologically confirmed dengue patients initially admitted to a General Medical and Paediatric wards who were subsequently transferred to the CCMDDHF from March to September 2017 were analysed. In addition to repeated blood counts and capillary haematocrits’, serial USS were done to detect the onset fluid leaking by three competent and experienced doctors at CCMDDHF. Results: 80 patients (male: female: 38:42) with a mean age of 20 years (SD ±16.8, range 3-74) were evaluated. Dropping of platelet counts below 100,000 and haematocrit rise towards 20% started 4±1.3 day of fever with a mean platelet value of 69x103(range17-98x103). Gallbladder wall thickening was the commonest (98.7%) USS finding followed by fluid in hepato-renal pouch (95%), pelvic fluid (58.7%), right-sided pleural effusion (35%), bilateral effusions (7.5%). USS evidence of plasma leakage was detected in 11.25 %( n=9) of DHF cases from 1 day before significant haematocrit rise was noted. 35 (43.7%) patients with lowering platelets and haematocrit rise showed no objective evidence of plasma leaking on ultrasound scan. Conclusion: This outbreak underscores the importance of USS as a useful, sensitive and cost-effective tool for early diagnosis of suspected DHF cases, facilitating the tracking of progress of leaking and management of epidemics.

Keywords: dengue, ultrasound, plasma leaking, South Asia

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Authors: Osamu Igawa, Hiroshi Kouchiwa, Yuji Ito

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In recent years, a reconstruction project for sewer pipelines has been progressing in Japan with the aim of renewing old sewer culverts. However, it is difficult to secure a sufficient base area for shafts in an urban area because many streets are narrow with a complex layout. As a result, construction in such urban areas is generally very demanding. In urban areas, there is a strong requirement for a safe, reliable and economical construction method that does not disturb the public’s daily life and urban activities. With this in mind, we developed a new construction method called the 'shield switching type micro-tunneling method' which integrates the micro-tunneling method and shield method. In this method, pipeline is constructed first for sections that are gently curved or straight using the economical micro-tunneling method, and then the method is switched to the shield method for sections with a sharp curve or a series of curves without establishing an intermediate shaft. This paper provides the information, features and construction examples of this newly developed method.

Keywords: micro-tunneling method, secondary lining applied RC segment, sharp curve, shield method, switching type

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Authors: E. Popov, N. Yorino, Y. Zoka, Y. Sasaki, H. Sugihara

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This paper discusses the performance of critical trajectory method (CTrj) for power system transient stability analysis under various loading settings and heavy fault condition. The method obtains Controlling Unstable Equilibrium Point (CUEP) which is essential for estimation of power system stability margins. The CUEP is computed by applying the CTrjto the boundary controlling unstable equilibrium point (BCU) method. The Proposed method computes a trajectory on the stability boundary that starts from the exit point and reaches CUEP under certain assumptions. The robustness and effectiveness of the method are demonstrated via six power system models and five loading conditions. As benchmark is used conventional simulation method whereas the performance is compared with and BCU Shadowing method.

Keywords: power system, transient stability, critical trajectory method, energy function method

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Authors: Sakchai Satienperakul, Manoch Thanomwat, Jutiporn Seedasama

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A paper based analytical devices (PADs) for the analysis of Fe (III) ion in natural water samples is developed, using reagent from guava leaf extract. The extraction is simply performed in deionized water pH 7, where tannin extract is obtained and used as an alternative natural reagent. The PADs are fabricated by ink-jet printing using alkenyl ketene dimer (AKD) wax. The quantitation of Fe (III) is carried out using reagent from guava leaf extract prepared in acetate buffer at the ratio of 1:1. A color change to gray-purple is observed by naked eye when dropping sample contained Fe (III) ion on PADs channel. The reflective absorption measurement is performed for creating a standard curve. The linear calibration range is observed over the concentration range of 2-10 mg L-1. Detection limited of Fe (III) is observed at 2 mg L-1. In its optimum form, the PADs is stable for up to 30 days under oxygen free conditions. The small dimensions, low volume requirement and alternative natural reagent make the proposed PADs attractive for on-site environmental monitoring and analysis.

Keywords: green chemical analysis, guava leaf extract, lab on a chip, paper based analytical device

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Sung-Sik Park, Han Chang, Kyung-Hun Chae, Sae-Byeok Lee

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In this study, a three-dimensional (3D) Particle method without using grid was developed for analyzing large deformation of soils instead of using ordinary finite element method (FEM) or finite difference method (FDM). In the 3D Particle method, the governing equations were discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. The Mohr-Coulomb failure criterion was incorporated into the 3D Particle method to determine soil failure. The yielding and hardening behavior of soil before failure was also considered by varying viscosity of soil. First of all, an unconfined compression test was carried out and the large deformation following soil yielding or failure was simulated by the developed 3D Particle method. The results were also compared with those of a commercial FEM software PLAXIS 3D. The developed 3D Particle method was able to simulate the 3D large deformation of soils due to soil yielding and calculate the variation of normal and shear stresses following clay deformation.

Keywords: particle method, large deformation, soil column, confined compressive stress

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Authors: Nur Rokhman

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A mathematical function gives relationship between the variables composing the function. Interpolation can be viewed as a process of finding mathematical function which goes through some specified points. There are many interpolation methods, namely: Lagrange method, Newton method, Spline method etc. For some specific condition, such as, big amount of interpolation points, the interpolation function can not be written explicitly. This such function consist of computational steps. The solution of equations involving the interpolation function is a problem of solution of non linear equation. Newton method will not work on the interpolation function, for the derivative of the interpolation function cannot be written explicitly. This paper shows the use of Secton method to determine the numerical solution of the function involving the interpolation function. The experiment shows the fact that Secton method works better than Newton method in finding the root of Lagrange interpolation function.

Keywords: Secton method, interpolation, non linear function, numerical solution

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Authors: B. Chikh, L. Moussa, H. Bechtoula, Y. Mehani, A. Zerzour

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This study presents a new method, applicable to evaluation and design of structures has been developed and illustrated by comparison with the capacity spectrum method (CSM, ATC-40). This method uses inelastic spectra and gives peak responses consistent with those obtained when using the nonlinear time history analysis. Hereafter, the seismic demands assessment method is called in this paper DSM, Ductility Spectrum Method. It is used to estimate the seismic deformation of Single-Degree-Of-Freedom (SDOF) systems based on DDRS, Ductility Demand Response Spectrum, developed by the author.

Keywords: seismic demand, capacity, inelastic spectra, design and structure

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Authors: Saheed A. Gbadegeshin

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Commercialization method is a means to make inventions available at the market for final consumption. It is described as an important tool for keeping business enterprises sustainable and improving national economic growth. Thus, there are several scholarly publications on it, either presenting or testing different methods for commercialization. However, young entrepreneurs, technologists and scientists would like to know the best method to commercialize their innovations. Then, this question arises: What is the best commercialization method? To answer the question, a systematic literature review was conducted, and practitioners were interviewed. The literary results revealed that there are many methods but new methods are needed to improve commercialization especially during these times of economic crisis and political uncertainty. Similarly, the empirical results showed there are several methods, but the best method is the one that reduces costs, reduces the risks associated with uncertainty, and improves customer participation and acceptability. Therefore, it was concluded that new commercialization method is essential for today's high technologies and a method was presented.

Keywords: commercialization method, technology, knowledge, intellectual property, innovation, invention

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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: Nadeem H. Meikha , Nazad H. Qader, Basheer M. Hasafa

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The trial was conducted to examine the effect of He-Ne laser therapy on the testis and serum testosterone level in adult rats. Thirty five albino Western adult male rats aged 3-4 months and weighing approximately 250-300 g were used and divided into three treatments. Testicular tissue of rats in the first and second treatments were exposed once daily for three successively days to a dose of irradiation 1.02 j/cm2 (40 second), and to 2.03 j/cm2 (80 second) respectively, while the third group left without any treatments (control). The results showed that the process of irradiation adversely affected on the level of serum testosterone concentration of the irradiated rats in the first and second treatment comparing to the normal level in the control group. While the histological examination showed that decrease in number of germ cells with 40 second of irradiation at day three, with 80 second of irradiation the decreased started at day two and three. The spermatids number decreased in rate low, medium, high respectively for three days of 40 second of irradiation, while the spermatids number were adversely affected by dropping in a rate of medium, large and very large for three days of 80 second of irradiation, respectively. In conclusion our study revealed that any reduction in sertoli cells causes adverse affect on both spermatids and germinal cells which increase with the increasing of duration and repetition of irradiation.

Keywords: He-Ne laser, rats, testosterone, spermatids

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Authors: Marinel Dayawon

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Student participation in classroom activities is vital in the teaching- learning the process as it develops self-confidence, social relationships and good academic performance of students. It is the teacher’s empathetic manner and creativity to create solutions that encourage teamwork and mutual support while dropping the academic competition within the class that hinder every shy student to walk with courage and talk with conviction because they consider their ideas, weak, as compared to the bright students. This study aimed to explore the different design thinking strategies that will change the mindset of shy students in classroom activities, maximizing their participation in all given tasks while sharing their views through ideation and providing them a wider world through compromise agreement within the members of the group, sensitivity to one’s idea, thus, arriving at a collective decision in the development of a prototype that indicates improvement in their classroom involvement. The study used the qualitative type of research. Triangulation is done through participant observation, focus group discussion and interview, documented through photos and videos. The respondents were the second- year Bachelor of Secondary Education students of the Institute of Teacher Education at Isabela State University- Cauayan City Campus. The result of the study revealed that reticent students when involved in game activities through a slap and tap method, writing their clustered ideas, using sticky notes is excited in sharing ideas as it doesn’t use oral communication. It is also observed after three weeks of using the design thinking strategies; shy students volunteer as secretary, rapporteur or group leader in the team- building activities as it represents the ideas of the heterogeneous group, removing the individual identity of the ideas. Superior students learned to listen to the ideas of the reticent students and involved them in the prototyping process of designing a remediation program for high school students showing reticence in the classroom, making their experience as a benchmark. The strategies made a 360- degrees transformation of the shy students, producing their journal log, in their journey to being open. Thus, faculty members are now adopting the design thinking approach.

Keywords: design thinking activities, qualitative, reticent students, Isabela, Philippines

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Authors: Aicha Zohbie

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The purpose of this paper is to critically compare two teaching methods: the communicative method and the grammar-translation method. The paper presents the importance of language awareness as an approach to teaching and learning language and some challenges that language teachers face. In addition, the paper strives to determine whether the adoption of communicative teaching methods or the grammar teaching method would be more effective to teach a language. A variety of features are considered for comparing the two methods: the purpose of each method, techniques used, teachers’ and students’ roles, the use of L1, the skills that are emphasized, the correction of students’ errors, and the students’ assessments. Finally, the paper includes suggestions and recommendations for implementing an approach that best meets the students’ needs in a classroom.

Keywords: language teaching methods, language awareness, communicative method grammar translation method, advantages and disadvantages

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: M. S. Baazzim, M. S. Al-Saud, M. A. El-Kady

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In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.

Keywords: cable ampacity, finite element method, underground cable, thermal rating

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Authors: Elmira Ghanbari, Jan Van Esch, Stephen J. Picken, Sahil Aggarwal

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Organogels are formed by the assembly of low molecular weight gelators (LMWG) into fibrous structures. The assembly of these molecules into crystalline fibrous structures occurs as a result of reversible interactions such as π-stacking, hydrogen-bonding, and van der Waals interactions. Bisamide organogelators with two amide groups have been used as one of LMWGs which show efficient assembly behavior via hydrogen bonding for network formation, the formation of a crystalline network for solvent entrapment. In this study, different bisamide gelators with different lengths of alkyl chains have been added to the bisamide parent gels. The effect of the addition of bisamide additives on the gelation of bisamide gels is described. Investigation of the thermal properties of the gels by differential scanning calorimetry and dropping ball techniques indicated that the bisamide gels can be formed by the addition of a high concentration of the second bisamide components. The microstructure of the gels with different gelator components has been visualized with scanning electron microscopy (SEM) which has shown systematic woven, platelet-like, and a combination of those morphologies for different gels. Examining the addition of a range of bisamide additives with different structural characteristics than the parent bisamide gels has confirmed the effect of the molecular structure on the morphology of the bisamide gels and their final properties.

Keywords: bisamide organogelator additives, gel morphology, gel properties, self-assembly

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: L. Fridrichova, R. Knížek, V. Bajzík

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Drape is one of the important visual characteristics of the fabric. This paper is introducing an innovative method of measurement and evaluation of the drape shape of the fabric. The measuring principle is based on the possibility of multiple vertical strain of the fabric. This method more accurately simulates the real behavior of the fabric in the process of draping. The method is fully automated, so the sample can be measured by using any number of cycles in any time horizon. Using the present method of measurement, we are able to describe the viscoelastic behavior of the fabric.

Keywords: drape, drape shape, automated drapemeter, fabric

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Chui Ka Shing

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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

Procedia PDF Downloads 186