Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1014
S. R. M. Nor, F. Yusof, A. Bahar
The incorporation of non-linear pattern of early ages has opened new research directions on improving the existing stochastic mortality model structure. Several authors have outlined the importance of encompassing the full age range in dealing with longevity risk exposure by not to ignore the dependence between young and old age. In this study, we consider the two extensions of Cairns, Blake and Dowd model that incorporate the irregularity profile seen at the mortality of lower ages which are Plat and O’Hare and Li. The models’ performances in terms of in-sample fitting and out-sample forecasts were examined and compared. The results indicated that O’Hare and Li model performs better as compared to Plat model
{"title":"Comparison of Stochastic Mortality Model for Wider Age Range","authors":"S. R. M. Nor, F. Yusof, A. Bahar","doi":"10.11113/MATEMATIKA.V34.N2.1014","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1014","url":null,"abstract":"The incorporation of non-linear pattern of early ages has opened new research directions on improving the existing stochastic mortality model structure. Several authors have outlined the importance of encompassing the full age range in dealing with longevity risk exposure by not to ignore the dependence between young and old age. In this study, we consider the two extensions of Cairns, Blake and Dowd model that incorporate the irregularity profile seen at the mortality of lower ages which are Plat and O’Hare and Li. The models’ performances in terms of in-sample fitting and out-sample forecasts were examined and compared. The results indicated that O’Hare and Li model performs better as compared to Plat model","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43147096","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.977
Lee Chang Kerk, Rohanin Ahmad
Optimization is central to any problem involving decision making. Thearea of optimization has received enormous attention for over 30 years and it is still popular in research field to this day. In this paper, a global optimization method called Kerk and Rohanin’s Trusted Interval will be introduced. The method introduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only considers the convex part where minimizers existed on a function is applied. This mechanism allows the method to filter out concave parts and some unrelated parts automatically. The identified convex parts are called trusted intervals. The descent property and the globally convergent of the method was shown in this paper. 15 test problems have been used to show the ability of the algorithm proposed in locating global minimizer.
{"title":"Algorithm for Solution of Non-convex Optimization Problem Through Piece-wise Convex Transformation","authors":"Lee Chang Kerk, Rohanin Ahmad","doi":"10.11113/MATEMATIKA.V34.N2.977","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.977","url":null,"abstract":"Optimization is central to any problem involving decision making. Thearea of optimization has received enormous attention for over 30 years and it is still popular in research field to this day. In this paper, a global optimization method called Kerk and Rohanin’s Trusted Interval will be introduced. The method introduced is able to identify all local solutions by converting non-convex optimization problems into piece-wise convex optimization problems. A mechanism which only considers the convex part where minimizers existed on a function is applied. This mechanism allows the method to filter out concave parts and some unrelated parts automatically. The identified convex parts are called trusted intervals. The descent property and the globally convergent of the method was shown in this paper. 15 test problems have been used to show the ability of the algorithm proposed in locating global minimizer.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48654181","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}
Pub Date : 2018-12-02DOI: 10.11113/matematika.v34.n2.898
G. Afrouzi, S. Kolagar, A. Hadjian, Jiafa Xu
An existence result of multiple solutions for a class of two-point fractional boundary value equations depending upon a positive parameter is established. Our main tool is a three critical points theorem due to Bonanno and Marano [G. Bonanno and S.A. Marano,On the structure of the critical set of non-differentiable functions with a weakcompactness condition, Appl. Anal. 89 (2010), 1-10].
{"title":"Variational Approach for a Class of Two-point Fractional Boundary Value Systems","authors":"G. Afrouzi, S. Kolagar, A. Hadjian, Jiafa Xu","doi":"10.11113/matematika.v34.n2.898","DOIUrl":"https://doi.org/10.11113/matematika.v34.n2.898","url":null,"abstract":"An existence result of multiple solutions for a class of two-point fractional boundary value equations depending upon a positive parameter is established. Our main tool is a three critical points theorem due to Bonanno and Marano [G. Bonanno and S.A. Marano,On the structure of the critical set of non-differentiable functions with a weakcompactness condition, Appl. Anal. 89 (2010), 1-10].","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47509957","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1016
Y. Daniel, A. A. Zainal, Z. Ismail, F. Salah
In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.
{"title":"Electrical Unsteady MHD Natural Convection Flow of Nanofluid with Thermal Stratification and Heat Generation/Absorption","authors":"Y. Daniel, A. A. Zainal, Z. Ismail, F. Salah","doi":"10.11113/MATEMATIKA.V34.N2.1016","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1016","url":null,"abstract":"In this paper, we analyzed the effects of thermal radiation, chemical reaction, heat generation/absorption, magnetic and electric fields on unsteady natural convection flow and heat transfer due to nanofluid over a permeable stretching sheet. The transport equations used passively controlled boundary condition rather than actively. A similarity solution is employed to transformed the governing equations from nonlinear partial differential equations to a set of ordinary differential equations, and then solve using Keller box method. It was found that the temperature is a decreasing function with the thermal stratification due to the fact the density of the fluid in the lower vicinity is much higher compared to the upper region, whereas the thermal radiation, viscous dissipation and heat generation enhanced the nanofluid temperature and thermal layer thickness.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44705434","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.941
S. Bako, M. Adam, A. Fitrianto
Recent studies have shown that independent identical distributed Gaussian random variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a stationary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto (GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads to overestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate. Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the Gumbel-GPD shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an underestimation of the parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel-GPD.
{"title":"Impact of Dependence on Parameter Estimates of Autoregressive Process with Gumbel Distributed Innovation","authors":"S. Bako, M. Adam, A. Fitrianto","doi":"10.11113/MATEMATIKA.V34.N2.941","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.941","url":null,"abstract":"Recent studies have shown that independent identical distributed Gaussian random variables is not suitable for modelling extreme values observed during extremal events. However, many real life data on extreme values are dependent and stationary rather than the conventional independent identically distributed data. We propose a stationary autoregressive (AR) process with Gumbel distributed innovation and characterise the short-term dependence among maxima of an (AR) process over a range of sample sizes with varying degrees of dependence. We estimate the maximum likelihood of the parameters of the Gumbel AR process and its residuals, and evaluate the performance of the parameter estimates. The AR process is fitted to the Gumbel-generalised Pareto (GPD) distribution and we evaluate the performance of the parameter estimates fitted to the cluster maxima and the original series. Ignoring the effect of dependence leads to overestimation of the location parameter of the Gumbel-AR (1) process. The estimate of the location parameter of the AR process using the residuals gives a better estimate. Estimate of the scale parameter perform marginally better for the original series than the residual estimate. The degree of clustering increases as dependence is enhance for the AR process. The Gumbel-AR(1) fitted to the Gumbel-GPD shows that the estimates of the scale and shape parameters fitted to the cluster maxima perform better as sample size increases, however, ignoring the effect of dependence lead to an underestimation of the parameter estimates of the scale parameter. The shape parameter of the original series gives a superior estimate compare to the threshold excesses fitted to the Gumbel-GPD.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47656712","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1044
M. Shaymaa, Z. A. Aziz, A. Bahar, M. K. N. Shamsuddin
Riverbank filtration (RBF) system is a surface water technology that is based on the natural treatment of filtration instead of the use of chemicals, to pretreat surface water and provides public water supplies. Hydraulic conductivity value is one of the significant factors affecting the water quality in RBF systems.In this article, an analytical modelling is developed to investigate the effect of this parameter on one dimensional contaminant transport in RBF system. The model is solved by using Green’s function approach. The model is applied for the first RBF system conducted in Malaysia. Generally, the results show that increasing the hydraulic conductivity value lead to an increase in contaminant concentration inpumping well area.
{"title":"Modelling The Effect of Hydraulic Conductivity on One Dimensional Contaminant Transport in RBF System","authors":"M. Shaymaa, Z. A. Aziz, A. Bahar, M. K. N. Shamsuddin","doi":"10.11113/MATEMATIKA.V34.N2.1044","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1044","url":null,"abstract":"Riverbank filtration (RBF) system is a surface water technology that is based on the natural treatment of filtration instead of the use of chemicals, to pretreat surface water and provides public water supplies. Hydraulic conductivity value is one of the significant factors affecting the water quality in RBF systems.In this article, an analytical modelling is developed to investigate the effect of this parameter on one dimensional contaminant transport in RBF system. The model is solved by using Green’s function approach. The model is applied for the first RBF system conducted in Malaysia. Generally, the results show that increasing the hydraulic conductivity value lead to an increase in contaminant concentration inpumping well area.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45642001","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1000
M. H. Hooi, W. Tiong, K. Tay, K. Chiew, S. Sze
In this paper, we look at the propagation of internal solitary waves overthree different types of slowly varying region, i.e. a slowly increasing slope, a smoothbump and a parabolic mound in a two-layer fluid flow. The appropriate mathematicalmodel for this problem is the variable-coefficient extended Korteweg-de Vries equation.The governing equation is then solved numerically using the method of lines. Ournumerical simulations show that the internal solitary waves deforms adiabatically onthe slowly increasing slope. At the same time, a trailing shelf is generated as theinternal solitary wave propagates over the slope, which would then decompose intosecondary solitary waves or a wavetrain. On the other hand, when internal solitarywaves propagate over a smooth bump or a parabolic mound, a trailing shelf of negativepolarity would be generated as the results of the interaction of the internal solitarywave with the decreasing slope of the bump or the parabolic mound. The secondarysolitary waves is observed to be climbing the negative trailing shelf.
{"title":"Numerical Simulation of Shoaling Internal Solitary Waves in Two-layer Fluid Flow","authors":"M. H. Hooi, W. Tiong, K. Tay, K. Chiew, S. Sze","doi":"10.11113/MATEMATIKA.V34.N2.1000","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1000","url":null,"abstract":"In this paper, we look at the propagation of internal solitary waves overthree different types of slowly varying region, i.e. a slowly increasing slope, a smoothbump and a parabolic mound in a two-layer fluid flow. The appropriate mathematicalmodel for this problem is the variable-coefficient extended Korteweg-de Vries equation.The governing equation is then solved numerically using the method of lines. Ournumerical simulations show that the internal solitary waves deforms adiabatically onthe slowly increasing slope. At the same time, a trailing shelf is generated as theinternal solitary wave propagates over the slope, which would then decompose intosecondary solitary waves or a wavetrain. On the other hand, when internal solitarywaves propagate over a smooth bump or a parabolic mound, a trailing shelf of negativepolarity would be generated as the results of the interaction of the internal solitarywave with the decreasing slope of the bump or the parabolic mound. The secondarysolitary waves is observed to be climbing the negative trailing shelf.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42360873","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.935
M. Adam, Babaginda Ibrahim Babura, Kathiresan Gopal
The box plot has been used for a very long time since 70s in checking the existence of outliers and the asymmetrical shape of data. The existing box plot is constructed using ve values of statistics calculated from either the discrete or continous data. Many improvement of box plots have deviated from the elegant and simplier approach of exploratory data analysis by incorporating many other statistic values resulting the turning back of the noble philosophy behind the creation of box plot.The modication using range value with the minimum and maximum values are being incorporated to suit the need of selected discrete distribution when outliers is not an important criteria anymore. The new modication of box plot is not based on the asymmetrical shape of distribution but more on the spread of the data and partitioning data into range measure. The new propose name for the box plot with only three values of statistics is called range-box plot.
{"title":"Range-Box Plotting Relating to Discrete Distribution","authors":"M. Adam, Babaginda Ibrahim Babura, Kathiresan Gopal","doi":"10.11113/MATEMATIKA.V34.N2.935","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.935","url":null,"abstract":"The box plot has been used for a very long time since 70s in checking the existence of outliers and the asymmetrical shape of data. The existing box plot is constructed using ve values of statistics calculated from either the discrete or continous data. Many improvement of box plots have deviated from the elegant and simplier approach of exploratory data analysis by incorporating many other statistic values resulting the turning back of the noble philosophy behind the creation of box plot.The modication using range value with the minimum and maximum values are being incorporated to suit the need of selected discrete distribution when outliers is not an important criteria anymore. The new modication of box plot is not based on the asymmetrical shape of distribution but more on the spread of the data and partitioning data into range measure. The new propose name for the box plot with only three values of statistics is called range-box plot.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44608522","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.988
Ahmet Daşdemir
A mathematical model to investigate the dynamic response of a piezoelectric plate-strip with initial stress under the action of a time-harmonic force resting on a rigid foundation is presented within the scope of the three-dimensional linearized theory of electro-elasticity waves in initially stressed bodies (TLTEEWISB). The governing system of equations of motion is solved by employing the Finite Element Method (FEM). The numerical results illustrating the dependencies of different problem parameters are investigated. In particular, the influence of a change in the value of the initial stress parameter on the dynamic response of the plate-strip is discussed.
{"title":"A Mathematical Model for Forced Vibration of Pre-Stressed Piezoelectric Plate-Strip Resting On Rigid Foundation","authors":"Ahmet Daşdemir","doi":"10.11113/MATEMATIKA.V34.N2.988","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.988","url":null,"abstract":"A mathematical model to investigate the dynamic response of a piezoelectric plate-strip with initial stress under the action of a time-harmonic force resting on a rigid foundation is presented within the scope of the three-dimensional linearized theory of electro-elasticity waves in initially stressed bodies (TLTEEWISB). The governing system of equations of motion is solved by employing the Finite Element Method (FEM). The numerical results illustrating the dependencies of different problem parameters are investigated. In particular, the influence of a change in the value of the initial stress parameter on the dynamic response of the plate-strip is discussed.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48421702","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}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1028
A. Ashaari, T. Ahmad, Wan Munirah Wan Mohamad
Pressurized water reactor (PWR) type AP1000 is a third generation of a nuclear power plant. The primary system of PWR using uranium dioxide to generate heat energy via fission process. The process influences temperature, pressure and pH value of water chemistry of the PWR. The aim of this paper is to transform the primary system of PWR using fuzzy autocatalytic set (FACS). In this work, the background of primary system of PWR and the properties of the model are provided. The simulation result, namely dynamic concentration of PWR is verified against published data.
{"title":"Transformation of Pressurized Water Reactor (AP1000) to Fuzzy Graph","authors":"A. Ashaari, T. Ahmad, Wan Munirah Wan Mohamad","doi":"10.11113/MATEMATIKA.V34.N2.1028","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1028","url":null,"abstract":"Pressurized water reactor (PWR) type AP1000 is a third generation of a nuclear power plant. The primary system of PWR using uranium dioxide to generate heat energy via fission process. The process influences temperature, pressure and pH value of water chemistry of the PWR. The aim of this paper is to transform the primary system of PWR using fuzzy autocatalytic set (FACS). In this work, the background of primary system of PWR and the properties of the model are provided. The simulation result, namely dynamic concentration of PWR is verified against published data.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45794750","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}
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