{"title":"Direct 4-point 1-step block method for solving Dirichlet boundary value problem","authors":"M. Hasni, Z. Majid, N. Senu","doi":"10.1109/ICREM.2015.7357030","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357030","url":null,"abstract":"This paper presents 4-point 1-step block method (4LBVP) to solve the linear 2nd order boundary value problem (BVP) with Dirichlet boundary condition. 4LBVP will solve the linear 2nd order BVP with Dirichlet boundary condition directly without the need to reduce it first into the system of 1st order equations. 4LBVP will produce several numerical solutions simultaneously in one step. The formulation of the 4LBVP will be based on the Lagrange interpolating polynomial. 4LBVP will be used together with the linear shooting technique to produce the numerical solutions. Comparison with other methods will be given to show the advantages of this method.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116501691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal singular controls for VSEIR model of Tuberculosis","authors":"M. S. Sinaga, Y. Rangkuti","doi":"10.1109/ICREM.2015.7357027","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357027","url":null,"abstract":"The optimality singular controls of a VSEIR model of Tuberculosis are analyzed in this paper. There are controls that correspond to time- vary the vaccination and treatment schedules. A Hamiltonian (H) of the model is defined. The model is splited into separate one-dimensional problems, the so-called switching functions. The extreme occurs when a switching function disappears suddenly over an open interval. In which the derivatives of switching function must disappears suddenly and this typically allows computing such a control. The second-order of the function is not vanishing, which satisfied Legendre-Clebsh condition, and thus the controls of these kinds are called singular. In this work, our main emphasis is on a complete analysis of the optimum properties corresponding to trajectories. The result shows that vaccination control is singular, but treatment is not. This means that the model reached the optimality control for vaccination schedule, but not treatment schedule.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117034558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Application of the quadrature-difference method for solving Fredholm integro-differential equations","authors":"C. Jalius, Z. Majid","doi":"10.1109/ICREM.2015.7357028","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357028","url":null,"abstract":"Application of the quadrature-difference method for solving Fredholm integro-differential equations (FIDEs) is presented in this paper. The FIDEs will be discretized by using the combinations of Simpsons quadrature rule with finite difference. The method converts the FIDEs to a matrix equation which corresponds to a system of linear algebraic equations. The formulation and the implementation of the proposed method are also presented. Several numerical examples are presented to illustrate the performance of the proposed method.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"445 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129838819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An implicit multistep block method for fuzzy differential equations","authors":"Azizah Ramli, Z. Majid","doi":"10.1109/ICREM.2015.7357031","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357031","url":null,"abstract":"A 2-point diagonally implicit multistep block method of order five is proposed. It is implemented to find the approximation for first-order fuzzy differential equations (FDEs) under on Seikkala derivative. This block method operates by approximating two points at yn+1 and yn+2 concurrently in a step. Both formulas are derived by using Lagrange interpolating polynomial. The method is generated by combining the predictor and corrector formulas in the PE(CE)m mode, where m is the number of iteration. The performances of the method are illustrated by solving problem and the numerical findings are compared with the existing method.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131163324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Behavior of TEM model with control parameter regulation","authors":"Notiragayu","doi":"10.1109/ICREM.2015.7357057","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357057","url":null,"abstract":"This paper is concerned with a mathematical derivation of the nonlinear time-discrete Technology Emission Means (TEM) model that discuss its behavior from the perspective of discrete dynamical systems. Nonlinear time-discrete dynamics tends to chaotic behavior. The addition of a control parameter into the dynamics of this model has led to new results in the field of time-discrete control systems. In this paper, we added another control parameter into the TEM model in the form of regulation. More ever we discuss stability theory of the TEM model, numerical solutions and compare their behavior before and after the addition of the regulatory control parameter. Finally, we obtained that by adding regulatory control parameter more stable than before.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133061908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Portfolio selection in Indonesia stock market with fuzzy bi-objective linear programming","authors":"R. Subekti, R. Kusumawati","doi":"10.1109/ICREM.2015.7357034","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357034","url":null,"abstract":"Selecting a portfolio which has the lowest investment risk and also the highest investment return known as a portfolio selection problem. An alternative way finding optimum solution of this bi-objective programming problem is transforming the problem into a single objective programming problem using fuzzy decision-making theory. The investment risk is expressed by mean absolute deviation of the return assets, while the investment return is expressed by the average of return assets. This fuzzy bi-objective linear programming (FBLP) is applied to construct an optimum portfolio in Indonesian stock market. The numerical result of FBLP is the same compared with weighted sum approach, but FBLP integrates better the knowledge and subjective opinion of investor where the range rate of risk which can be accepted by investor is incorporated in the model.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133009779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The enhancement of student's Mathematical connection ability and self-regulation learning with metacognitive learning approach in Junior High School","authors":"M. Fauzi","doi":"10.1109/ICREM.2015.7357048","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357048","url":null,"abstract":"The Objective of this research is to examine the effects of Mathematics learning utilizing the group meta cognitive approach (GMCA), learning with classical meta cognitive approach (CMCA) as experimental groups, and the conventional learning (CL) as control group among students of public Junior High School 12 and 15 in Bandung. The research method which used is an experimental method with prior knowledge test, mathematical connection ability test, student's mathematical self regulation scale, learning observation sheet, student's feeling sheet after learning, interview manual, student profile, teaching material and field daily note and document as instruments. Data analysis analyses which are test- t, one-way ANOVA, and two-way ANOVA. The results show: 1) as a whole, MCA and self-regulation learning (SRL) of students getting GMCA and CMCA learning is significantly higher (29,045) and (26,857) than students of conventional learning (24,782). Nevertheless, MCA N-Gain of students getting GMCA learning is in medium category, whereas MCA N-Gain students getting CMCA learning and CL are included in low category, 2) There is no interaction between learning approach (GMCA, CMCA and CL) and school level toward MPA, and 3) There is interaction between learning approach and school level toward student's self regulation learning 4) There is no interaction between learning approach and mathematical prior ability (MPA) toward SRL.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121154810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Interaction of solitons with delta potential in the Cubic-Quintic Nonlinear Schrodinger Equation","authors":"N. Aklan, B. Umarov","doi":"10.1109/ICREM.2015.7357033","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357033","url":null,"abstract":"The study of soliton scattering of the Nonlinear Schrodinger Equation (NLSE) has brought a wide focus by researchers especially in physics field such as Bose-Einstein condensates, nonlinear optics, plasma physics, condensed matter physics, etc. This paper concentrates on the effect of potentials to the soliton scattering in the generalized NLSE, Cubic-Quintic Nonlinear Schrodinger Equation (CQNLSE). To derive the equations for soliton parameters evolution during the scattering process, we have applied the approximate analytical method, namely the variational approximation method. The accuracy of approximations was checked by direct numerical simulations of CQNLSE with soliton initially located far from potential. In case of the potential in the form of delta function, depending on initial velocity of the soliton, it was shown the soliton may be reflected by potential or transmitted through it. The critical values of the velocity separating these two scenarios have been identified.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116706331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Single-valued core selection and aggregate-monotonic solutions to equitable cost allocation","authors":"N. L. Bach","doi":"10.1109/ICREM.2015.7357039","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357039","url":null,"abstract":"Single-valued core selection, equity and aggregate monotonicity are desirable properties for cost allocation but offer challenges to develop suitable allocation methods to satisfy. This paper attempts to develop a new solution approach to meeting these properties. The idea is first to identify the critical value of the grand total cost for non-empty core, using an LP to maximize the grand cost subject to individual and group rationality conditions. The critical grand cost is then allocated by any single-valued core allocation methods available such as the nucleolus and its variants. The non-critical grand cost values are allocated simply by scaling up or down from the critical case so as to ensure aggregate-monotonicity. In addition, a new core allocation method is proposed for the critical case, based on prorating the best and worse costs that are feasible bounds for each player in the grand cooperation. Existence of such proration fractions is proved along with lower and upper bounds identified explicitly, which indicates some sense of equity. The new method is found to be desirable for the cases with two or three players, and more research is being conducted for general cases of more than three players.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133461888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A synthetic revised m-of-k runs rules control chart","authors":"Z. L. Chong, M. Khoo, S. Teh, W. L. Teoh","doi":"10.1109/ICREM.2015.7357064","DOIUrl":"https://doi.org/10.1109/ICREM.2015.7357064","url":null,"abstract":"Control charts are commonly used for quality improvement in a manufacturing process. In this paper, we proposed a newer control chart, namely the synthetic revised m-of-k (R - m/k) runs rules chart to monitor the shift in the mean of a process. The newly proposed chart is obtained by integrating the R - m/k runs rules sub-chart and the conforming run length (CRL) sub-chart. The efficiency of a chart can be studied via the average run length (ARL) criterion. The out-of-control ARL result of the proposed chart is compared with its original counterparts, namely the synthetic and R - m/k runs rules charts, as well as the EWMA chart. The performance comparison indicates that the proposed synthetic R - m/k runs rules chart surpasses all the charts under comparison for detecting most sizes of the mean shifts. Therefore, the proposed synthetic R - m/k runs rules chart is a viable substitute for the standard synthetic and R - m/k runs rules charts.","PeriodicalId":448746,"journal":{"name":"2015 International Conference on Research and Education in Mathematics (ICREM7)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134406136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}