Although a lot of crack problems in bi-materials plate were previously treated, few solutions are available under mechanical loadings, arbitrary crack lengths and material combinations. In this paper the dimensionless stress intensity factors (SIFs) of two slanted cracks in the upper plate of bi-materials are considered under mechanical loadings with varying the crack length and material combinations systematically. In order to calculate the dimensionless SIFs accurately, the hypersingular integral equations (HSIEs) was formulated by using the modified complex potentials (MCP) function. The details numerical results of the dimensionless SIFs are given in tabular form and graphical presentations. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. Our results are described with clarifying the effect of the mechanical loadings, bi-elastic constant ratio and element size of cracks on the dimensionless SIFs.
{"title":"Effect of Mechanical Loadings on Two Unequal Slanted Cracks Length in Bi-Materials Plate","authors":"K. Hamzah, N. N. Nik long","doi":"10.47836/mjms.16.2.02","DOIUrl":"https://doi.org/10.47836/mjms.16.2.02","url":null,"abstract":"Although a lot of crack problems in bi-materials plate were previously treated, few solutions are available under mechanical loadings, arbitrary crack lengths and material combinations. In this paper the dimensionless stress intensity factors (SIFs) of two slanted cracks in the upper plate of bi-materials are considered under mechanical loadings with varying the crack length and material combinations systematically. In order to calculate the dimensionless SIFs accurately, the hypersingular integral equations (HSIEs) was formulated by using the modified complex potentials (MCP) function. The details numerical results of the dimensionless SIFs are given in tabular form and graphical presentations. Comparisons with the existing exact solutions show that the numerical results in this paper have high accuracy. Our results are described with clarifying the effect of the mechanical loadings, bi-elastic constant ratio and element size of cracks on the dimensionless SIFs.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44016496","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}
In this paper, we present a continuous time autoregressive moving average (CARMA) model with stochastic speed of mean reversion. This model allows the mean reversion rates to behave stochastically and governed by an Ornstein-Uhlenbeck process. We provide closed-form solution to the CARMA with stochastic speed of mean reversion and formulate the price of temperature insurance using spot-forward relationship framework. We demonstrate the insurance pricing based on the cumulative average temperatures (CAT) index by simulating the temperature variations. We found that our proposed model may explain the temperature evolution well and the price of CAT-based index insurance looks reasonable.
{"title":"Modelling Temperature Using CARMA Processes with Stochastic Speed of Mean Reversion for Temperature Insurance Pricing","authors":"M. Darus, C. M. I. C. Taib","doi":"10.47836/mjms.16.2.07","DOIUrl":"https://doi.org/10.47836/mjms.16.2.07","url":null,"abstract":"In this paper, we present a continuous time autoregressive moving average (CARMA) model with stochastic speed of mean reversion. This model allows the mean reversion rates to behave stochastically and governed by an Ornstein-Uhlenbeck process. We provide closed-form solution to the CARMA with stochastic speed of mean reversion and formulate the price of temperature insurance using spot-forward relationship framework. We demonstrate the insurance pricing based on the cumulative average temperatures (CAT) index by simulating the temperature variations. We found that our proposed model may explain the temperature evolution well and the price of CAT-based index insurance looks reasonable.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48404381","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}
The impact of uncertainty on saving is termed as precautionary saving. Thus, the main objective of this study is to investigate the effect of external global uncertainties on determining the saving-consumption relationship. In particular, we seek to compare the effect of two types of uncertainties, namely the monetary policy versus economic policy uncertainties in determining the behavior of saving-consumption. The results are compared between the top trade openness versus the least trade openness countries. Besides, the study also seeks to check for the existence and hence the effect of cross-section dependency in the relationship. For this purpose, the mean group (MG), pooled mean group (PMG) and common correlated effects mean group (CCEMG) estimators are applied. The data is from the year 1985 to 2017. The results reveal the existence and significance effect of cross-section dependence among countries and uncertainties matter in the saving-consumption relationship. The main factors that contribute to savings are the GDP per capita and the economic policy uncertainty while the main factors that contribute to consumptions are the GDP per capita and the monetary policy uncertainty.
{"title":"Unveiling the Determinants of Saving-Consumption Relationship: A Panel Data Approach","authors":"S. Sek, K. Lai","doi":"10.47836/mjms.16.2.03","DOIUrl":"https://doi.org/10.47836/mjms.16.2.03","url":null,"abstract":"The impact of uncertainty on saving is termed as precautionary saving. Thus, the main objective of this study is to investigate the effect of external global uncertainties on determining the saving-consumption relationship. In particular, we seek to compare the effect of two types of uncertainties, namely the monetary policy versus economic policy uncertainties in determining the behavior of saving-consumption. The results are compared between the top trade openness versus the least trade openness countries. Besides, the study also seeks to check for the existence and hence the effect of cross-section dependency in the relationship. For this purpose, the mean group (MG), pooled mean group (PMG) and common correlated effects mean group (CCEMG) estimators are applied. The data is from the year 1985 to 2017. The results reveal the existence and significance effect of cross-section dependence among countries and uncertainties matter in the saving-consumption relationship. The main factors that contribute to savings are the GDP per capita and the economic policy uncertainty while the main factors that contribute to consumptions are the GDP per capita and the monetary policy uncertainty.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49489175","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}
The aim of this study is to measure the number of components that exhibits from the variables' series. The number of components can be affected by the time series components including trend, seasonal adjustment, and irregular changes. By using a finite mixture model, the number of components can be identifies and thereafter we can formulate a Bayesian regression equation to predict the relationship between exchange rate and international tourism expenditure in Malaysia. Identification of the number of components is an important step to weigh the probability density function for a time series data. The weight of the probability density function is then used for prediction. Besides, a Bayesian method is also used in this study to fit with the finite mixture model due to its consistency characteristic. The Bayesian parameter estimates are close to the predictive distributions because it will integrate the prior distribution with the likelihood function to produce posterior distribution. The results show that there is a two-component normal mixture model exists for the time series data. In addition, a prediction equation is obtained from the analysis.
{"title":"Finite Mixture Model: Prediction of Time Series Data Using Bayesian Method","authors":"S. Phoong, S. Phoong, K. H. Phoong","doi":"10.47836/mjms.16.2.01","DOIUrl":"https://doi.org/10.47836/mjms.16.2.01","url":null,"abstract":"The aim of this study is to measure the number of components that exhibits from the variables' series. The number of components can be affected by the time series components including trend, seasonal adjustment, and irregular changes. By using a finite mixture model, the number of components can be identifies and thereafter we can formulate a Bayesian regression equation to predict the relationship between exchange rate and international tourism expenditure in Malaysia. Identification of the number of components is an important step to weigh the probability density function for a time series data. The weight of the probability density function is then used for prediction. Besides, a Bayesian method is also used in this study to fit with the finite mixture model due to its consistency characteristic. The Bayesian parameter estimates are close to the predictive distributions because it will integrate the prior distribution with the likelihood function to produce posterior distribution. The results show that there is a two-component normal mixture model exists for the time series data. In addition, a prediction equation is obtained from the analysis.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44207183","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}
S. Ismail, K. A. Atan, D. Sejas-Viscarra, Z. Eshkuvatov
In this paper the zeroes of the polynomial F(x,z)=2x4−z3 in Gaussian integers Z[i] are determined, a problem equivalent to finding the solutions of the Diophatine equation x4+y4=z3 in Z[i], with a focus on the case x=y. We start by using an analytical method that examines the real and imaginary parts of the equation F(x,z)=0. This analysis sheds light on the general algebraic behavior of the polynomial F(x,z) itself and its zeroes. This in turn allows us a deeper understanding of the different cases and conditions that give rise to trivial and non-trivial solutions to F(x,z)=0, and those that lead to inconsistencies. This paper concludes with a general formulation of the solutions to F(x,z)=0 in Gaussian integers. Results obtained in this work show the existence of infinitely many non-trivial zeroes for F(x,z)=2x4−z3 under the general form x=(1+i)η3 and c=−2η4 for η∈Z[i].
{"title":"Determination of Gaussian Integer Zeroes of F(x,z)=2x4−z3","authors":"S. Ismail, K. A. Atan, D. Sejas-Viscarra, Z. Eshkuvatov","doi":"10.47836/mjms.16.2.09","DOIUrl":"https://doi.org/10.47836/mjms.16.2.09","url":null,"abstract":"In this paper the zeroes of the polynomial F(x,z)=2x4−z3 in Gaussian integers Z[i] are determined, a problem equivalent to finding the solutions of the Diophatine equation x4+y4=z3 in Z[i], with a focus on the case x=y. We start by using an analytical method that examines the real and imaginary parts of the equation F(x,z)=0. This analysis sheds light on the general algebraic behavior of the polynomial F(x,z) itself and its zeroes. This in turn allows us a deeper understanding of the different cases and conditions that give rise to trivial and non-trivial solutions to F(x,z)=0, and those that lead to inconsistencies. This paper concludes with a general formulation of the solutions to F(x,z)=0 in Gaussian integers. Results obtained in this work show the existence of infinitely many non-trivial zeroes for F(x,z)=2x4−z3 under the general form x=(1+i)η3 and c=−2η4 for η∈Z[i].","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48476975","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}
Security is a matter of significant concern for image media. An effective way to protect images is by digital watermarking. This paper introduces a non-blind digital watermarking scheme using modified non-separable Haar wavelet transform (NSHWT), singular value decomposition (SVD), Arnold's cat map, and Rabin-p cryptosystem to embed a binary watermark image into a color cover image. Aside from robustness, security is also prioritized in the scheme. High robustness is achieved using two transform domain techniques, discrete wavelet transform (DWT) and SVD, while security is heightened with the double encryption by Arnold's cat map scrambling and Rabin-p cryptosystem. A disadvantage of the discrete wavelet transform in digital image watermarking is the calculation complexity and the high cost of changing memory and time. The proposed algorithm uses a modified NSHWT instead of the traditional method of DWT. Therefore, the load of the process on the hardware can significantly be reduced while still maintaining the advantages of DWT. The algorithm is objectively evaluated in terms of imperceptibility, robustness, and embedding capacity for both binary and color watermarks, as well as efficiency. It has been concluded that the proposed scheme performs competently compared with other recent watermarking techniques based on DWT and SVD.
{"title":"Robustness of Modified Non-Separable HaarWavelet Transform and Singular Value Decomposition for Non-blind Digital Image Watermarking","authors":"M. K. A. Razak, K. Abdullah, S. A. Halim","doi":"10.47836/mjms.16.2.08","DOIUrl":"https://doi.org/10.47836/mjms.16.2.08","url":null,"abstract":"Security is a matter of significant concern for image media. An effective way to protect images is by digital watermarking. This paper introduces a non-blind digital watermarking scheme using modified non-separable Haar wavelet transform (NSHWT), singular value decomposition (SVD), Arnold's cat map, and Rabin-p cryptosystem to embed a binary watermark image into a color cover image. Aside from robustness, security is also prioritized in the scheme. High robustness is achieved using two transform domain techniques, discrete wavelet transform (DWT) and SVD, while security is heightened with the double encryption by Arnold's cat map scrambling and Rabin-p cryptosystem. A disadvantage of the discrete wavelet transform in digital image watermarking is the calculation complexity and the high cost of changing memory and time. The proposed algorithm uses a modified NSHWT instead of the traditional method of DWT. Therefore, the load of the process on the hardware can significantly be reduced while still maintaining the advantages of DWT. The algorithm is objectively evaluated in terms of imperceptibility, robustness, and embedding capacity for both binary and color watermarks, as well as efficiency. It has been concluded that the proposed scheme performs competently compared with other recent watermarking techniques based on DWT and SVD.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41796193","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}
A bipartite graph G can be treated as a (1,1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2,2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other. In this article, analogous to complete (1,1) bipartite graphs which have the maximum number of pairs of vertices having distance one between them, a complete (2,2) bipartite graph is defined as follows. A complete (2,2) bipartite graph is a graph which is (2,2) bipartite and has the maximum number of pairs of vertices (u,v) such that d(u,v)=2. Such graphs are characterized and their properties are studied. The expressions are derived for the determinant, the permanent and spectral properties of some classes of complete (2,2) bipartite graphs. A class of graphs among complete (2,2) bipartite graphs having golden ratio in their spectrum is obtained.
{"title":"Complete (2,2) Bipartite Graphs","authors":"S. Hanif, K. A. Bhat, G. Sudhakara","doi":"10.47836/mjms.16.2.13","DOIUrl":"https://doi.org/10.47836/mjms.16.2.13","url":null,"abstract":"A bipartite graph G can be treated as a (1,1) bipartite graph in the sense that, no two vertices in the same part are at distance one from each other. A (2,2) bipartite graph is an extension of the above concept in which no two vertices in the same part are at distance two from each other. In this article, analogous to complete (1,1) bipartite graphs which have the maximum number of pairs of vertices having distance one between them, a complete (2,2) bipartite graph is defined as follows. A complete (2,2) bipartite graph is a graph which is (2,2) bipartite and has the maximum number of pairs of vertices (u,v) such that d(u,v)=2. Such graphs are characterized and their properties are studied. The expressions are derived for the determinant, the permanent and spectral properties of some classes of complete (2,2) bipartite graphs. A class of graphs among complete (2,2) bipartite graphs having golden ratio in their spectrum is obtained.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48314640","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}
In this paper, we study the dynamical properties of set-valued dynamical systems. Specifically, we focus on the sensitivity, transitivity and mixing of set-valued dynamical systems. Under the setting of set-valued case, we define sensitivity and investigate its properties. We also study the transitivity and mixing of set-valued dynamical systems that have been defined. We show that both transitivity and mixing are invariant under topological conjugacy. We also discuss some implication results on the product set-valued function constructed from two different set-valued functions equipped with various transitivity and mixing conditions.
{"title":"Some Properties on Sensitivity, Transitivity and Mixing of Set-Valued Dynamical Systems","authors":"K. S. Wong, Z. Salleh","doi":"10.47836/mjms.16.2.11","DOIUrl":"https://doi.org/10.47836/mjms.16.2.11","url":null,"abstract":"In this paper, we study the dynamical properties of set-valued dynamical systems. Specifically, we focus on the sensitivity, transitivity and mixing of set-valued dynamical systems. Under the setting of set-valued case, we define sensitivity and investigate its properties. We also study the transitivity and mixing of set-valued dynamical systems that have been defined. We show that both transitivity and mixing are invariant under topological conjugacy. We also discuss some implication results on the product set-valued function constructed from two different set-valued functions equipped with various transitivity and mixing conditions.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49394335","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}
The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ,μ∈R) and (μ∈C,λ=0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.
{"title":"Stability Analysis of Diagonally Implicit Two Derivative Runge-Kutta methods for Solving Delay Differential Equations","authors":"N. A. Ahmad, N. Senu, Z. Ibrahim, M. Othman","doi":"10.47836/mjms.16.2.04","DOIUrl":"https://doi.org/10.47836/mjms.16.2.04","url":null,"abstract":"The stability properties of fourth and fifth-order Diagonally Implicit Two Derivative Runge-Kutta method (DITDRK) combined with Lagrange interpolation when applied to the linear Delay Differential Equations (DDEs) are investigated. This type of stability is known as P-stability and Q-stability. Their stability regions for (λ,μ∈R) and (μ∈C,λ=0) are determined. The superiority of the DITDRK methods over other same order existing Diagonally Implicit Runge-Kutta (DIRK) methods when solving DDEs problems are clearly demonstrated by plotting the efficiency curves of the log of both maximum errors versus function evaluations and the CPU time taken to do the integration.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42720907","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}
This article presents a numerical approach for solving the second kind of Volterra integro- differential equation (VIDE). The multistep block-Boole's rule method will estimate the solutions for the linear and nonlinear problems of VIDE. The method computes two solutions for VIDE along the interval. The proposed method is developed by derivation of the Lagrange interpolating polynomial. The convergence and stability analysis of the derived method are discussed. From the perspective of total function calls and time-saving, the computation results explained that the derived method performs better than other existing methods.
{"title":"Boole's Strategy in Multistep Block Method for Volterra Integro-Differential Equation","authors":"Nur Auni Baharum","doi":"10.47836/mjms.16.2.05","DOIUrl":"https://doi.org/10.47836/mjms.16.2.05","url":null,"abstract":"This article presents a numerical approach for solving the second kind of Volterra integro- differential equation (VIDE). The multistep block-Boole's rule method will estimate the solutions for the linear and nonlinear problems of VIDE. The method computes two solutions for VIDE along the interval. The proposed method is developed by derivation of the Lagrange interpolating polynomial. The convergence and stability analysis of the derived method are discussed. From the perspective of total function calls and time-saving, the computation results explained that the derived method performs better than other existing methods.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48870336","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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