M. Letchumanan, S. K. S. Husain, A. F. Ayub, R. Kamaruddin, Nurul Nadwa Zulkifli
The purpose of this study was to investigate the factors that influence promotion of higher order thinking skills (HOTS) among mathematics higher learning institution students in technology enhanced learning environment (TEL) in Malaysia. The study used descriptive research design. Data of the study was collected by using quantitative research approach. A total of 250 students from three public universities participated in the study. The study explores the relationship between students' attitude towards technology use and organisation support towards promotion of HOTS in mathematics TEL environment. Results from structural equation modelling reported that students' attitude towards technology use had a positive direct relationship with HOTS. Meanwhile, organisation support had a positive direct relationship with students' attitude towards technology use which in turn indirectly influence promotion of HOTS. The hypothesized structural equation model accounted for 20.2% of the variance in HOTS. The results indicated a need for further studies in order to examine factors that predict promotion of HOTS in mathematics TEL at higher learning institutions in Malaysia.
{"title":"Determining the Factors that Promote Higher Order Thinking Skills in Mathematics Technology Enhanced Learning Environment: Perspective from University Students","authors":"M. Letchumanan, S. K. S. Husain, A. F. Ayub, R. Kamaruddin, Nurul Nadwa Zulkifli","doi":"10.47836/mjms.17.1.02","DOIUrl":"https://doi.org/10.47836/mjms.17.1.02","url":null,"abstract":"The purpose of this study was to investigate the factors that influence promotion of higher order thinking skills (HOTS) among mathematics higher learning institution students in technology enhanced learning environment (TEL) in Malaysia. The study used descriptive research design. Data of the study was collected by using quantitative research approach. A total of 250 students from three public universities participated in the study. The study explores the relationship between students' attitude towards technology use and organisation support towards promotion of HOTS in mathematics TEL environment. Results from structural equation modelling reported that students' attitude towards technology use had a positive direct relationship with HOTS. Meanwhile, organisation support had a positive direct relationship with students' attitude towards technology use which in turn indirectly influence promotion of HOTS. The hypothesized structural equation model accounted for 20.2% of the variance in HOTS. The results indicated a need for further studies in order to examine factors that predict promotion of HOTS in mathematics TEL at higher learning institutions in Malaysia.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48626241","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. F. Embong, M. I. E. Zulkifly, D. N. A. Awg Arifin
In the present paper we consider a genetic algebra induced by b−bistochastic Quadratic Stochastic Operators (QSOs) which is called b−bistochastic genetic algebra. First, we characterize their nontrivial character function on Rn. It turns out that, the given character function is not unique, hence full descriptions of such functions on R1 and R2 are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of b−bistochastic genetic algebras defined on R1 and R2 are described. In this work, the existence of non-trivial derivations on such algebras are given.
{"title":"Genetic Algebras generated by b−bistochastic Quadratic Stochastic Operators: The Character and Associativity","authors":"A. F. Embong, M. I. E. Zulkifly, D. N. A. Awg Arifin","doi":"10.47836/mjms.17.1.03","DOIUrl":"https://doi.org/10.47836/mjms.17.1.03","url":null,"abstract":"In the present paper we consider a genetic algebra induced by b−bistochastic Quadratic Stochastic Operators (QSOs) which is called b−bistochastic genetic algebra. First, we characterize their nontrivial character function on Rn. It turns out that, the given character function is not unique, hence full descriptions of such functions on R1 and R2 are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of b−bistochastic genetic algebras defined on R1 and R2 are described. In this work, the existence of non-trivial derivations on such algebras are given.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48366712","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 work, we are interested in studying variations in plasma glucose and insulin levels over time using a fractional-order version of a mathematical model. Applying the fractional-order Caputo derivative, we can investigate different concentration rates among insulin, glucose, and healthy β-cells. The main aim is to obtain the numerical solution of the proposed model in order to show variations in plasma glucose and insulin levels over time, by applying the generalized Euler method. The local stability analysis of the proposed (discretization) Caputo fractional-order model was discussed. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of Mathematica. Numerical simulations were in good agreement with the theoretical findings. Three specific numerical examples are given as applications of the main results.
{"title":"On the Solution of a Nonlinear Fractional-Order Glucose-Insulin System Incorporating β\u0000-cells Compartment","authors":"A. Ahmad","doi":"10.47836/mjms.17.1.01","DOIUrl":"https://doi.org/10.47836/mjms.17.1.01","url":null,"abstract":"In this work, we are interested in studying variations in plasma glucose and insulin levels over time using a fractional-order version of a mathematical model. Applying the fractional-order Caputo derivative, we can investigate different concentration rates among insulin, glucose, and healthy β-cells. The main aim is to obtain the numerical solution of the proposed model in order to show variations in plasma glucose and insulin levels over time, by applying the generalized Euler method. The local stability analysis of the proposed (discretization) Caputo fractional-order model was discussed. To check the feasibility of our analysis, we have investigated some numerical simulations for various fractional orders by varying values of the parameters with help of Mathematica. Numerical simulations were in good agreement with the theoretical findings. Three specific numerical examples are given as applications of the main results.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49007823","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 neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer.
{"title":"Neighbors Degree Sum Energy of Commuting and Non-Commuting Graphs for Dihedral Groups","authors":"M. U. Romdhini, A. Nawawi, C.Y. Chen","doi":"10.47836/mjms.17.1.05","DOIUrl":"https://doi.org/10.47836/mjms.17.1.05","url":null,"abstract":"The neighbors degree sum (NDS) energy of a graph is determined by the sum of its absolute eigenvalues from its corresponding neighbors degree sum matrix. The non-diagonal entries of NDS−matrix are the summation of the degree of two adjacent vertices, or it is zero for non-adjacent vertices, whereas for the diagonal entries are the negative of the square of vertex degree. This study presents the formulas of neighbors degree sum energies of commuting and non-commuting graphs for dihedral groups of order 2n, D2n, for two cases−odd and even n. The results in this paper comply with the well known fact that energy of a graph is neither an odd integer nor a square root of an odd integer.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45566849","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 work, through the Riemann-Liouville fractional integrals, we give Hermite-Hadamard type inequalities for exponentially sub-additive functions. For the product of exponentially sub-additive functions, we present fractional integral inequalities. It is also shown that the results proved here are the refinements and extensions of several existing results in the field of Hermite-Hadamard like inequalities.
{"title":"Hermite-Hadamard Like Inequalities for Exponentially Subadditive Functions via Fractional Integrals","authors":"S. Abbas, M. A. Ali, A. Hanif, H. Budak","doi":"10.47836/mjms.17.1.04","DOIUrl":"https://doi.org/10.47836/mjms.17.1.04","url":null,"abstract":"In this work, through the Riemann-Liouville fractional integrals, we give Hermite-Hadamard type inequalities for exponentially sub-additive functions. For the product of exponentially sub-additive functions, we present fractional integral inequalities. It is also shown that the results proved here are the refinements and extensions of several existing results in the field of Hermite-Hadamard like inequalities.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46741503","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, a generalization of a classical result by Gander concerning the characterization of third-order methods is addressed. New and classical methods are included in the family. In particular, a new construction of the well-known Chebyshev method is presented. Other methods, based on exponential and logarithmic fittings respectively, are rediscovered too. The proposed methods have a local cubic order of convergence and can be competitive with other third-order methods in the literature, as can be seen from the numerical examples presented.
{"title":"Third Order Root-Finding Methods based on a Generalization of Gander's Result","authors":"Busquier Sonia, Gutiérrez José M., Ramos Higinio","doi":"10.47836/mjms.16.4.01","DOIUrl":"https://doi.org/10.47836/mjms.16.4.01","url":null,"abstract":"In this paper, a generalization of a classical result by Gander concerning the characterization of third-order methods is addressed. New and classical methods are included in the family. In particular, a new construction of the well-known Chebyshev method is presented. Other methods, based on exponential and logarithmic fittings respectively, are rediscovered too. The proposed methods have a local cubic order of convergence and can be competitive with other third-order methods in the literature, as can be seen from the numerical examples presented.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43368501","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 quadratic stochastic operator (QSO) is frequently acknowledged as the analysis source to investigate dynamical properties and modeling in numerous areas. Countless classes of QSO have been investigated since the operator was introduced in 1920s. The study of QSOs is still an open problem in the nonlinear operator theory field, especially QSOs on infinite state space. We are interested in the dynamics of Geometric QSO generated by a 2-partition defined on countable state space. We first show the system of equations formed from defined Geometric QSO with infinite-dimensional space can be simplified into a one-dimensional setting, corresponding to the number of defined partitions. The trajectory behavior of such a system is investigated by using functional analysis approach, where the operator either converges to a unique fixed point or has a second-order cycle. It is shown that such an operator can be either regular or nonregular for arbitrary initial points depending on the value of parameters. In this research, we present two cases, i.e., two different parameters and three different parameters. We display the form of the fixed point and periodic points of period-2. Moreover, an example for the nonregular transformation will be provided, where such QSO has 2-periodic points.
{"title":"On the Dynamics of Geometric Quadratic Stochastic Operator Generated by 2-Partition on Countable State Space","authors":"S. N. Karim, N. Z. A. Hamzah, N. Ganikhodjaev","doi":"10.47836/mjms.16.4.06","DOIUrl":"https://doi.org/10.47836/mjms.16.4.06","url":null,"abstract":"A quadratic stochastic operator (QSO) is frequently acknowledged as the analysis source to investigate dynamical properties and modeling in numerous areas. Countless classes of QSO have been investigated since the operator was introduced in 1920s. The study of QSOs is still an open problem in the nonlinear operator theory field, especially QSOs on infinite state space. We are interested in the dynamics of Geometric QSO generated by a 2-partition defined on countable state space. We first show the system of equations formed from defined Geometric QSO with infinite-dimensional space can be simplified into a one-dimensional setting, corresponding to the number of defined partitions. The trajectory behavior of such a system is investigated by using functional analysis approach, where the operator either converges to a unique fixed point or has a second-order cycle. It is shown that such an operator can be either regular or nonregular for arbitrary initial points depending on the value of parameters. In this research, we present two cases, i.e., two different parameters and three different parameters. We display the form of the fixed point and periodic points of period-2. Moreover, an example for the nonregular transformation will be provided, where such QSO has 2-periodic points.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43549724","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}
T. J. Podile, A. R. Adem, S. O. Mbusi, B. Muatjetjeja
Multiple exp-function technique and group analysis is accomplished for a comprehensive (2+1)-dimensional Hirota-Satsuma-Ito equation that appears in many sectors of nonlinear science such as for example in fluid dynamics. Travelling wave solutions are computed and it is displayed that this underlying equation gives kink solutions. The invariant reductions and further closed-form solutions are processed. Conserved currents are developed and their physical ramifications are illustrated.
{"title":"Multiple Exp-Function Solutions, Group Invariant Solutions and Conservation Laws of a Generalized (2+1)-dimensional Hirota-Satsuma-Ito Equation","authors":"T. J. Podile, A. R. Adem, S. O. Mbusi, B. Muatjetjeja","doi":"10.47836/mjms.16.4.11","DOIUrl":"https://doi.org/10.47836/mjms.16.4.11","url":null,"abstract":"Multiple exp-function technique and group analysis is accomplished for a comprehensive (2+1)-dimensional Hirota-Satsuma-Ito equation that appears in many sectors of nonlinear science such as for example in fluid dynamics. Travelling wave solutions are computed and it is displayed that this underlying equation gives kink solutions. The invariant reductions and further closed-form solutions are processed. Conserved currents are developed and their physical ramifications are illustrated.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43360810","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 use of S-boxes (substitution boxes) to provide nonlinear properties is known to be a common way to design a block cipher. These nonlinear properties are necessary to ensure the security of a block cipher. This manuscript proposes a design construction of a new S-box using affine transformation via cellular automata as a permutation matrix. We incorporate this cellular-automaton permutation matrix into the AES S box structure and test various irreducible polynomials. Nonlinearity, bijection, bit independence criterion, strict avalanche effect, linear approximation probability, and differential uniformity are the standard performance requirements used to evaluate the S-boxes that arise. Using this method, we are able to determine an irreducible polynomial that enables the construction of a new S-box design that can achieve an ideal strict avalanche criterion (SAC), which will subsequently provide efficiency in the design of block ciphers.
{"title":"A New Design of Substitution Box with Ideal Strict Avalanche Criterion","authors":"N. F. Mohd Esa, S. F. Abdul-Latip, N. A. Abu","doi":"10.47836/mjms.16.4.04","DOIUrl":"https://doi.org/10.47836/mjms.16.4.04","url":null,"abstract":"The use of S-boxes (substitution boxes) to provide nonlinear properties is known to be a common way to design a block cipher. These nonlinear properties are necessary to ensure the security of a block cipher. This manuscript proposes a design construction of a new S-box using affine transformation via cellular automata as a permutation matrix. We incorporate this cellular-automaton permutation matrix into the AES S box structure and test various irreducible polynomials. Nonlinearity, bijection, bit independence criterion, strict avalanche effect, linear approximation probability, and differential uniformity are the standard performance requirements used to evaluate the S-boxes that arise. Using this method, we are able to determine an irreducible polynomial that enables the construction of a new S-box design that can achieve an ideal strict avalanche criterion (SAC), which will subsequently provide efficiency in the design of block ciphers.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42429661","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 paper discusses the generalized Johansen-Ledoit-Sornette (GJLS) model in determining and predicting the size of rational speculative bubbles in stock market. In this study, the GJLS model is used as an approach to detect the presence and prediction of rational speculative bubble sizes of the stock market. The stock markets chosen in this study are Hang Seng, Nikkei 225 and S&P 500. This is because China, Japan and United States are countries that pioneers the world economy. This paper presents step by step on finding the linear and non-linear parameters in the generalized Johansen-Ledoit-Sornette model using the Ordinary Least Squares method for the linear parameters and formulas for the non-linear parameters. There are 7 parameters that need to be identified which are A,B and C for linear parameter and ω, φ, β and t for the non-linear parameter. Then, the size of speculative rational bubbles is determined and predict using the GJLS model. The size of speculative rational bubbles for future cycle is forecasted. Then, the effect of the presence of rational speculative bubbles towards the economy is discussed.
{"title":"Estimation on Rational Speculative Bubbles in Stock Market by Using Generalised Johansen-Ledoit-Sornette Model","authors":"N. Borhan, N. Halim","doi":"10.47836/mjms.16.4.05","DOIUrl":"https://doi.org/10.47836/mjms.16.4.05","url":null,"abstract":"This paper discusses the generalized Johansen-Ledoit-Sornette (GJLS) model in determining and predicting the size of rational speculative bubbles in stock market. In this study, the GJLS model is used as an approach to detect the presence and prediction of rational speculative bubble sizes of the stock market. The stock markets chosen in this study are Hang Seng, Nikkei 225 and S&P 500. This is because China, Japan and United States are countries that pioneers the world economy. This paper presents step by step on finding the linear and non-linear parameters in the generalized Johansen-Ledoit-Sornette model using the Ordinary Least Squares method for the linear parameters and formulas for the non-linear parameters. There are 7 parameters that need to be identified which are A,B and C for linear parameter and ω, φ, β and t for the non-linear parameter. Then, the size of speculative rational bubbles is determined and predict using the GJLS model. The size of speculative rational bubbles for future cycle is forecasted. Then, the effect of the presence of rational speculative bubbles towards the economy is discussed.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43380782","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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