Pub Date : 2023-12-30DOI: 10.11113/matematika.v39.n3.1519
S. Ng
Multicollinearity is the problem when there is linear dependency among the independent variables. The Ordinary least squares estimator (OLSE) that is commonly adopted is not suitable for the linear regression model when the independent variables are correlated. This is due to the high variance in OLSE and hence the accuracy of OLSE reduces in the presence of multicollinearity. Hence, the estimator named k-almost unbiased regression estimator (KAURE) was proposed as an alternative to OLSE in this paper. KAURE was developed by using the definition of an almost unbiased estimator to further reduce the bias of Liu-type estimator-special case (LTESC). The properties of KAURE including bias, variance-covariance and mean squared error (MSE) were derived. Theoretical comparison and real-life data comparison were carried out to evaluate the performance of the KAURE based on the MSE criterion. The application of the real-life data supported the theoretical comparison that showed the superiority of KAURE over OLSE and LTESC. The results revealed that KAURE could be considered as an alternative estimator for the linear regression model to combat the problem of multicollinearity.
{"title":"An Almost Unbiased Regression Estimator: Theoretical Comparison and Numerical Comparison in Portland Cement Data","authors":"S. Ng","doi":"10.11113/matematika.v39.n3.1519","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1519","url":null,"abstract":"Multicollinearity is the problem when there is linear dependency among the independent variables. The Ordinary least squares estimator (OLSE) that is commonly adopted is not suitable for the linear regression model when the independent variables are correlated. This is due to the high variance in OLSE and hence the accuracy of OLSE reduces in the presence of multicollinearity. Hence, the estimator named k-almost unbiased regression estimator (KAURE) was proposed as an alternative to OLSE in this paper. KAURE was developed by using the definition of an almost unbiased estimator to further reduce the bias of Liu-type estimator-special case (LTESC). The properties of KAURE including bias, variance-covariance and mean squared error (MSE) were derived. Theoretical comparison and real-life data comparison were carried out to evaluate the performance of the KAURE based on the MSE criterion. The application of the real-life data supported the theoretical comparison that showed the superiority of KAURE over OLSE and LTESC. The results revealed that KAURE could be considered as an alternative estimator for the linear regression model to combat the problem of multicollinearity.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139140198","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 : 2023-12-28DOI: 10.11113/matematika.v39.n3.1502
Siti Nur Idara Rosli, M. I. E. Zulkifly
Surfaces and their descriptions are significant in design, physical science, geology, and other natural phenomena. This study introduces a neutrosophic B´ezier surface approximation with a four-by-four control net for the bicubic situation. The neutrosophic notion defines the neutrosophic control net relation. The control net is mixed with the Bernstein basis function to generate a surface blending function and a neutrosophic bicubic B´ezier surface. Finally, the neutrosophic bicubic B´ezier surface is shown using an approximation approach and data points having neutrosophic properties.
{"title":"Neutrosophic Bicubic Bezier Surface ApproximationModel for Uncertainty Data","authors":"Siti Nur Idara Rosli, M. I. E. Zulkifly","doi":"10.11113/matematika.v39.n3.1502","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1502","url":null,"abstract":"Surfaces and their descriptions are significant in design, physical science, geology, and other natural phenomena. This study introduces a neutrosophic B´ezier surface approximation with a four-by-four control net for the bicubic situation. The neutrosophic notion defines the neutrosophic control net relation. The control net is mixed with the Bernstein basis function to generate a surface blending function and a neutrosophic bicubic B´ezier surface. Finally, the neutrosophic bicubic B´ezier surface is shown using an approximation approach and data points having neutrosophic properties.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139149417","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 : 2023-12-28DOI: 10.11113/matematika.v39.n3.1509
W. N. N. Noranuar, A. Q. Mohamad, L. Y. Jiann, S. Shafie
Carbon nanotubes (CNTs) nanofluids are gaining increased popularity among researchers due to their outstanding thermal properties, leading to numerous promising industrial applications. Analytical solutions discovered in the study of CNTs nanofluids, combined with a Casson-type fluid model, are extremely limited. Therefore, a study on the heat transfer analysis of an unsteady and incompressible Casson carbon nanofluid flow is conducted. Human blood-based single-walled carbon nanotubes (SWCNTs) and human blood-based multi-walled carbon nanotubes (MWCNTs) are considered as nanofluids that move beyond an exponentially accelerated vertical plate. A set of dimensional momentum and energy equations, along with their initial and exponentially accelerated boundary conditions, is employed to represent the problem. The transformation of these equations to the dimensionless expression is achieved by using suitable dimensionless variables. The resulting equations are then tackled using Laplace transformation to acquire the analytical solution for temperature and velocity. Figures and tables are produced for a further analysis of temperature and velocity characteristics. The study shows that an increase in nanoparticle volume fraction enhances nanofluid flow and heat transmission, proving highly beneficial for cancer treatment. However, the flow is retarded due to the increment of Casson parameter values, while an enhancement is observed with a superior accelerating parameter.
{"title":"Heat Transfer Enhancement of Convective Casson Nanofluid Flow by CNTs over Exponentially Accelerated Plate","authors":"W. N. N. Noranuar, A. Q. Mohamad, L. Y. Jiann, S. Shafie","doi":"10.11113/matematika.v39.n3.1509","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1509","url":null,"abstract":"Carbon nanotubes (CNTs) nanofluids are gaining increased popularity among researchers due to their outstanding thermal properties, leading to numerous promising industrial applications. Analytical solutions discovered in the study of CNTs nanofluids, combined with a Casson-type fluid model, are extremely limited. Therefore, a study on the heat transfer analysis of an unsteady and incompressible Casson carbon nanofluid flow is conducted. Human blood-based single-walled carbon nanotubes (SWCNTs) and human blood-based multi-walled carbon nanotubes (MWCNTs) are considered as nanofluids that move beyond an exponentially accelerated vertical plate. A set of dimensional momentum and energy equations, along with their initial and exponentially accelerated boundary conditions, is employed to represent the problem. The transformation of these equations to the dimensionless expression is achieved by using suitable dimensionless variables. The resulting equations are then tackled using Laplace transformation to acquire the analytical solution for temperature and velocity. Figures and tables are produced for a further analysis of temperature and velocity characteristics. The study shows that an increase in nanoparticle volume fraction enhances nanofluid flow and heat transmission, proving highly beneficial for cancer treatment. However, the flow is retarded due to the increment of Casson parameter values, while an enhancement is observed with a superior accelerating parameter.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139151197","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 : 2023-12-28DOI: 10.11113/matematika.v39.n3.1478
Reza Rezaiy, A. Shabri
Forecasting drought plays a vital role in strategic planning and the management of underground water supply. In this study, we utilized autoregressive integrated moving average (ARIMA) and Seasonal ARIMA (SARIMA) models to predict drought events in Afghanistan, based on the standardized precipitation index (SPI). We used monthly average precipitation data from 1991 to 2015 for model training, while data from 2016 to 2020 were employed for model validation. The results of the statistical analysis, which encompassed evaluating Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE), indicated that among the SPI 3, SPI 6, SPI 9, SPI 12, and SPI 24, the SARIMA models applied to the SPI 24 demonstrated the most accurate forecasting performance with RMSE (0.1492), MAE (0.1039), and MAPE (22.3732%) compared to SPI 3, SPI 6, SPI 9, and SPI 12. Subsequently, the ARIMA/SARIMA models were employed to forecast drought events for the upcoming year. It’s noteworthy that this constitutes the first-ever statistical analysis of the drought index in Afghanistan. Therefore, the outcomes of this study can be applied across diverse sectors, including water resource management and environmental precautions.
{"title":"Using the ARIMA/SARIMA Model for Afghanistan's Drought Forecasting Based on Standardized Precipitation Index","authors":"Reza Rezaiy, A. Shabri","doi":"10.11113/matematika.v39.n3.1478","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1478","url":null,"abstract":"Forecasting drought plays a vital role in strategic planning and the management of underground water supply. In this study, we utilized autoregressive integrated moving average (ARIMA) and Seasonal ARIMA (SARIMA) models to predict drought events in Afghanistan, based on the standardized precipitation index (SPI). We used monthly average precipitation data from 1991 to 2015 for model training, while data from 2016 to 2020 were employed for model validation. The results of the statistical analysis, which encompassed evaluating Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE), indicated that among the SPI 3, SPI 6, SPI 9, SPI 12, and SPI 24, the SARIMA models applied to the SPI 24 demonstrated the most accurate forecasting performance with RMSE (0.1492), MAE (0.1039), and MAPE (22.3732%) compared to SPI 3, SPI 6, SPI 9, and SPI 12. Subsequently, the ARIMA/SARIMA models were employed to forecast drought events for the upcoming year. It’s noteworthy that this constitutes the first-ever statistical analysis of the drought index in Afghanistan. Therefore, the outcomes of this study can be applied across diverse sectors, including water resource management and environmental precautions.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139150495","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 : 2023-11-30DOI: 10.11113/matematika.v39.n3.1461
Chibuike Nnamani, Norhaiza Ahmad
Biclustering models allow simultaneous detection of group observations that are related to variables in a data matrix. Such methods have been applied in biological data for classification. Collinearity is a common feature in biological data as there exist interactions between genes and proteins in their respective pathways. Such relationships could seriously reduce the efficiency of biclustering models. In this study, synthetic data are generated to investigate the effect of collinearity on the performance of biclustering models. Specifically, the data are generated and induced with varying degrees of collinearity using Cholesky decomposition, and are implanted with biclusters to produce different sets of synthetic data. The effectiveness of three models namely Biclustering by Cheng and Church (BCCC), Spectral Bicluster (BCSpectral) and Plaid Model in correctly detecting three types of biclusters in the generated data matrix were compared. The results show that all the models investigated are sensitive to changes in the level of collinearity. At low collinearity, all biclustering models were able to detect the implanted biclusters in the data correctly. As the level of collinearity in the data rise, the proportion of detectedbiclusters captured by the models reduces. In particular, BCC outperformed the other two models for moderate to high collinearity with a Jaccard coefficient of 0.499 to 0.875 and 0.746 to 0.936 for one and two implanted biclusters respectively.
双聚类模型可以同时检测与数据矩阵中变量相关的群体观测数据。这种方法已被应用于生物数据的分类。共线性是生物数据的常见特征，因为基因和蛋白质在各自的通路中存在相互作用。这种关系会严重降低双聚类模型的效率。本研究生成合成数据，以研究共线性对双聚类模型性能的影响。具体来说，利用 Cholesky 分解法生成并诱导不同程度的共线性数据，然后植入双聚类，生成不同的合成数据集。比较了三种模型，即 Biclustering by Cheng and Church (BCCCC)、Spectral Bicluster (BCSpectral) 和 Plaid Model 在生成的数据矩阵中正确检测三种双簇的有效性。结果表明，所研究的所有模型对共线性水平的变化都很敏感。在低共线性条件下，所有双簇模型都能正确检测出数据中的植入双簇。随着数据中共线性水平的上升，模型所捕捉到的双簇比例也随之下降。特别是在中度到高度共线性情况下，BCC 的表现优于其他两个模型，对于一个和两个植入双簇的 Jaccard 系数分别为 0.499 到 0.875 和 0.746 到 0.936。
{"title":"Biclustering Models Under Collinearity in Simulated Biological Experiments","authors":"Chibuike Nnamani, Norhaiza Ahmad","doi":"10.11113/matematika.v39.n3.1461","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1461","url":null,"abstract":"Biclustering models allow simultaneous detection of group observations that are related to variables in a data matrix. Such methods have been applied in biological data for classification. Collinearity is a common feature in biological data as there exist interactions between genes and proteins in their respective pathways. Such relationships could seriously reduce the efficiency of biclustering models. In this study, synthetic data are generated to investigate the effect of collinearity on the performance of biclustering models. Specifically, the data are generated and induced with varying degrees of collinearity using Cholesky decomposition, and are implanted with biclusters to produce different sets of synthetic data. The effectiveness of three models namely Biclustering by Cheng and Church (BCCC), Spectral Bicluster (BCSpectral) and Plaid Model in correctly detecting three types of biclusters in the generated data matrix were compared. The results show that all the models investigated are sensitive to changes in the level of collinearity. At low collinearity, all biclustering models were able to detect the implanted biclusters in the data correctly. As the level of collinearity in the data rise, the proportion of detectedbiclusters captured by the models reduces. In particular, BCC outperformed the other two models for moderate to high collinearity with a Jaccard coefficient of 0.499 to 0.875 and 0.746 to 0.936 for one and two implanted biclusters respectively.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139206987","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 : 2023-11-30DOI: 10.11113/matematika.v39.n3.1496
Nurul Syuhada Samsudin, Siti Rohani Mohd Nor
Multi-population mortality model has gained attention from prominent researchers of mortality due to its ability to provide biologically reasonable forecast. Previously, many researchers have proposed several multi-population stochastic mortality models that they considered adequate to produce accurate life expectancy. However, little have been addressed of the variability in full ages and time, which can contribute to an erroneous estimation of life expectancy. Therefore, this study proposed a new multi-population O’Hare with ARIMA, ARIMA-GARCH and ANN in forecasting the mortality rate for male and female in Malaysia, Taiwan, Japan, Hong Kong, Australia, USA, UK, Canada, and Switzerland. Multi-population O’Hare was used as a reference model, whilst ARIMA, ARIMA-GARCH and ANN were incorporated to the reference model to forecast the mortality rates. The adequacy of the proposed model was assessed by using measurement errors which were Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The results showed by multi-population O’Hare with ARIMA-GARCH gave the best forecasting performance for Taiwan, Japan, Australia, USA, UK, Canada, and Switzerland. On the other hand, multi-population O’Hare with ARIMA gave the best forecasting performance for Malaysia, whereas multi-population O’Hare with ANN gave the best forecasting performance for Hong Kong.
多人口死亡率模型因其能够提供生物学上合理的预测而受到死亡率领域著名研究人员的关注。在此之前，许多研究人员提出了几种多人口随机死亡率模型，他们认为这些模型足以得出准确的预期寿命。然而，这些模型很少涉及全年龄和时间的变异性，而这种变异性可能导致对预期寿命的错误估计。因此，本研究提出了一种新的多人口 O'Hare，用 ARIMA、ARIMA-GARCH 和 ANN 预测马来西亚、台湾、日本、香港、澳大利亚、美国、英国、加拿大和瑞士的男性和女性死亡率。多人口 O'Hare 被用作参考模型，而 ARIMA、ARIMA-GARCH 和 ANN 被纳入参考模型以预测死亡率。利用测量误差（平均绝对百分比误差 (MAPE) 和均方根误差 (RMSE)）评估了拟议模型的适当性。结果显示，在台湾、日本、澳大利亚、美国、英国、加拿大和瑞士，多人口 O'Hare 与 ARIMA-GARCH 的预测效果最佳。另一方面，使用 ARIMA 的多人口 O'Hare 对马来西亚的预测效果最好，而使用 ANN 的多人口 O'Hare 对香港的预测效果最好。
{"title":"Multi-Population O’Hare with ARIMA, ARIMA-GARCH and ANN in Forecasting Mortality Rate","authors":"Nurul Syuhada Samsudin, Siti Rohani Mohd Nor","doi":"10.11113/matematika.v39.n3.1496","DOIUrl":"https://doi.org/10.11113/matematika.v39.n3.1496","url":null,"abstract":"Multi-population mortality model has gained attention from prominent researchers of mortality due to its ability to provide biologically reasonable forecast. Previously, many researchers have proposed several multi-population stochastic mortality models that they considered adequate to produce accurate life expectancy. However, little have been addressed of the variability in full ages and time, which can contribute to an erroneous estimation of life expectancy. Therefore, this study proposed a new multi-population O’Hare with ARIMA, ARIMA-GARCH and ANN in forecasting the mortality rate for male and female in Malaysia, Taiwan, Japan, Hong Kong, Australia, USA, UK, Canada, and Switzerland. Multi-population O’Hare was used as a reference model, whilst ARIMA, ARIMA-GARCH and ANN were incorporated to the reference model to forecast the mortality rates. The adequacy of the proposed model was assessed by using measurement errors which were Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). The results showed by multi-population O’Hare with ARIMA-GARCH gave the best forecasting performance for Taiwan, Japan, Australia, USA, UK, Canada, and Switzerland. On the other hand, multi-population O’Hare with ARIMA gave the best forecasting performance for Malaysia, whereas multi-population O’Hare with ANN gave the best forecasting performance for Hong Kong.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139208656","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 : 2023-04-15DOI: 10.11113/matematika.v39.n1.1444
Nur Maisarah Abdul Rashid, M. Ismail, Noor Wahida Md Junus
Predicting cryptocurrency prices are difficult due to dynamic data. At the same time, the hidden market behavior of trend and seasonal components in the history data is also critical as it provides an idea of what the price pattern will be in the future. Hence, this research proposes to identify and model the hidden pattern behavior in terms of component time series instead of removing it via the linear structural time series (STS) model approach. This study focuses on the top five cryptocurrencies relying on the highest market capitalization. From the results obtained, the top five cryptocurrencies have a different trend model, either deterministic or stochastic, which relies on the behavior of data. The five cryptocurrencies also show the crypto winter event, where the trend is downward after six months every year. The linear STS is the best model for predicting three cryptocurrencies’ prices for nonstationary and volatility data behavior. It can also handle the hidden component behavior and is easy to interpret. Since the linear STS model can indirectly retain the information of data, it will assist investors and traders in accurately predicting cryptocurrency prices.
{"title":"Predicting Top Five Cryptocurrency Prices via Linear Structural Time Series (STS) Approach","authors":"Nur Maisarah Abdul Rashid, M. Ismail, Noor Wahida Md Junus","doi":"10.11113/matematika.v39.n1.1444","DOIUrl":"https://doi.org/10.11113/matematika.v39.n1.1444","url":null,"abstract":"Predicting cryptocurrency prices are difficult due to dynamic data. At the same time, the hidden market behavior of trend and seasonal components in the history data is also critical as it provides an idea of what the price pattern will be in the future. Hence, this research proposes to identify and model the hidden pattern behavior in terms of component time series instead of removing it via the linear structural time series (STS) model approach. This study focuses on the top five cryptocurrencies relying on the highest market capitalization. From the results obtained, the top five cryptocurrencies have a different trend model, either deterministic or stochastic, which relies on the behavior of data. The five cryptocurrencies also show the crypto winter event, where the trend is downward after six months every year. The linear STS is the best model for predicting three cryptocurrencies’ prices for nonstationary and volatility data behavior. It can also handle the hidden component behavior and is easy to interpret. Since the linear STS model can indirectly retain the information of data, it will assist investors and traders in accurately predicting cryptocurrency prices.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42714395","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 : 2023-04-15DOI: 10.11113/matematika.v39.n1.1452
Norliza Mohd Zain, Z. Ismail, Muhammad Sabaruddin Ahmad Jamali, Y. J. Lim
Localized plaque causes narrowing of the arterial wall, resulting in an alteration in the flow structure, reducing the flow of fluids reaching the heart and resulting in heart attacks. The formation of stenosis could disturb the normal hemodynamics in blood rheology. A bifurcated artery with different types of stenosis is considered in order to illustrate the four possible formations of plaque between healthy and diseased arteries. Due to the fact that a diseased artery is reported to be less compliant, the artery wall is modelled as a two-dimensional rigid wall. In this model, blood flow is assumed to be steady, laminar, incompressible, and characterized as a generalized power-law model that is non-Newtonian in nature. The numerical simulation is performed using COMSOL Multiphysics, which is based on finite element method. Based on simulation results, different types of stenosis in the bifurcated artery have a significant impact on velocity profiles and wall shear stresses.
{"title":"Wall Shear Stress Distribution of non-Newtonian Blood Flow in Stenosed Bifurcated Artery","authors":"Norliza Mohd Zain, Z. Ismail, Muhammad Sabaruddin Ahmad Jamali, Y. J. Lim","doi":"10.11113/matematika.v39.n1.1452","DOIUrl":"https://doi.org/10.11113/matematika.v39.n1.1452","url":null,"abstract":"Localized plaque causes narrowing of the arterial wall, resulting in an alteration in the flow structure, reducing the flow of fluids reaching the heart and resulting in heart attacks. The formation of stenosis could disturb the normal hemodynamics in blood rheology. A bifurcated artery with different types of stenosis is considered in order to illustrate the four possible formations of plaque between healthy and diseased arteries. Due to the fact that a diseased artery is reported to be less compliant, the artery wall is modelled as a two-dimensional rigid wall. In this model, blood flow is assumed to be steady, laminar, incompressible, and characterized as a generalized power-law model that is non-Newtonian in nature. The numerical simulation is performed using COMSOL Multiphysics, which is based on finite element method. Based on simulation results, different types of stenosis in the bifurcated artery have a significant impact on velocity profiles and wall shear stresses.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42944040","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 : 2023-04-15DOI: 10.11113/matematika.v39.n1.1458
Solomon Isa Rwat, Noor Atinah Ahmad Ahmad
Vaccination has been used as strategy to eradicate the spread of COVID-19. But imperfect vaccine has been reported to induce backward bifurcation and hysteresis in mathematical models of disease transmission. Backward bifurcation is a phenomenon whereby a stable endemic equilibrium exists contemporaneously with a stable disease-free equilibrium when the basic reproduction number is less than 1. This situation can cause difficulty in controlling an epidemic because the basic reproduction is no longer the only means of eradicating the disease. In this paper, we propose a mathematical model for the transmission of disease which includes imperfect vaccination. We show that our model is capable of capturing backward bifurcation under certain conditions. By using parameters that are relevant to COVID-19 transmission in Malaysia, our numerical analysis shows that low vaccine efficacy can trigger backward bifurcation.
{"title":"Backward Bifurcation and Hysteresis in a Mathematical Model of COVID19 with Imperfect Vaccine","authors":"Solomon Isa Rwat, Noor Atinah Ahmad Ahmad","doi":"10.11113/matematika.v39.n1.1458","DOIUrl":"https://doi.org/10.11113/matematika.v39.n1.1458","url":null,"abstract":"Vaccination has been used as strategy to eradicate the spread of COVID-19. But imperfect vaccine has been reported to induce backward bifurcation and hysteresis in mathematical models of disease transmission. Backward bifurcation is a phenomenon whereby a stable endemic equilibrium exists contemporaneously with a stable disease-free equilibrium when the basic reproduction number is less than 1. This situation can cause difficulty in controlling an epidemic because the basic reproduction is no longer the only means of eradicating the disease. In this paper, we propose a mathematical model for the transmission of disease which includes imperfect vaccination. We show that our model is capable of capturing backward bifurcation under certain conditions. By using parameters that are relevant to COVID-19 transmission in Malaysia, our numerical analysis shows that low vaccine efficacy can trigger backward bifurcation.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49195175","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 : 2023-04-15DOI: 10.11113/matematika.v39.n1.1391
Nur Rasyida Mohd Rashid, Bushra Abdul Halim, Iskandar Shah Mohd Zawawi, Husna Nadzirah Abdullah, Nur Iylia Antasha Abu Hassan, Nur Atikah Ismail
Supplier selection is perceived as important decision-making process in any supply chain management. In this study, the best supplier for a company is being determined based on five main criteria chosen which are delivery, capacity, warranty, cost, and quality. The Analytic Hierarchy Process (AHP) and Entropy Measurement (EM) methods are integrated with Data Envelopment Analysis (DEA) was applied to set ranking and choose the best supplier as conventional DEA is not able to provide complete ranking among inefficient units. The mathematical modelling is executed using LINGO software. Supplier 3 has obtained efficient result of score 1 for both hybrid method and in Super Efficiency method as the most efficient supplier. Then, the results are validated using Spearman’s Rank Correlation Coefficient (SRCC) which shows positive correlation between both integrated methods. Finally, findings of this study indicate the feasibility of integrated AHP-DEA and EM-DEA for supplier selection with multiple criteria.
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