In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy of the solution. Stability of the proposed method is examined and the corresponding region of stability is depicted. The new fifth algebraic order trigonometrically-fitted predictor-corrector method is applied to solve the initial value problems whose solutions involved trigonometric functions. Numerical results presented proved that the prospective method is more efficient than the widely used methods for the numerical solution of linear ordinary differential equations with oscillating solutions.
{"title":"Trigonometrically-Fitted Fifth Order Four-Step Predictor-Corrector Method for Solving Linear Ordinary Differential Equations with Oscillatory Solutions","authors":"M. Salih, F. Ismail","doi":"10.47836/mjms.16.4.07","DOIUrl":"https://doi.org/10.47836/mjms.16.4.07","url":null,"abstract":"In this paper, we proposed a trigonometrically-fitted fifth order four-step predictor-corrector method based on the four-step Adams-Bashforth method as predictor and five-step Adams-Moulton method as corrector to solve linear ordinary differential equations with oscillatory solutions. This method is constructed which exactly integrate initial value problems whose solutions can be expressed as linear combinations of the set functions {sin(υx),cos(υx)} with υ ∈ R, where v represents an approximation of the frequency of the problem. The frequency will be used in the method to raise the accuracy of the solution. Stability of the proposed method is examined and the corresponding region of stability is depicted. The new fifth algebraic order trigonometrically-fitted predictor-corrector method is applied to solve the initial value problems whose solutions involved trigonometric functions. Numerical results presented proved that the prospective method is more efficient than the widely used methods for the numerical solution of linear ordinary differential equations with oscillating solutions.","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":"44768285","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}
Statistical approach often provides techniques in exploring more on the algebraic properties of finite groups. In this paper, two new group probabilities are defined in which the group elements having certain common characteristics are considered. Let G be a finite group, the order product prime probability is defined as the probability that two randomly selected elements x and y in G satisfy |x||y|=ps and the order product prime commutativity degree is the probability that elements satisfying the above property commutes. Some formulas for computing these probabilities for dihedral groups are obtained.
{"title":"The Order Product Prime Probability and Commutativity Degree for Some Finite Groups","authors":"N. M. Mohd Ali, S. I. Isah, M. Bello","doi":"10.47836/mjms.16.4.02","DOIUrl":"https://doi.org/10.47836/mjms.16.4.02","url":null,"abstract":"Statistical approach often provides techniques in exploring more on the algebraic properties of finite groups. In this paper, two new group probabilities are defined in which the group elements having certain common characteristics are considered. Let G be a finite group, the order product prime probability is defined as the probability that two randomly selected elements x and y in G satisfy |x||y|=ps and the order product prime commutativity degree is the probability that elements satisfying the above property commutes. Some formulas for computing these probabilities for dihedral groups are obtained.","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":"42944647","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 induced subgraph of a unit graph with vertex set as the non unit elements of a ring R is a graph obtained by deleting all unit elements of R. In a graph , a subset of the vertex set is called a perfect code if the balls with radius 1 centred on the subset are pairwise disjoint and their unions yield the whole vertex set. In this paper, we determine the perfect codes of induced subgraphs of the unit graphs associated with some finite commutative rings R with unity that has a vertex set as non unit elements of R. Moreover, we classify the commutative rings in which their associated induced subgraphs of unit graphs admit the trivial and non-trivial perfect codes. We also characterize the commutative rings based on the induced subgraph of unit graphs that do not admit the perfect codes. Furthermore, we prove that the complement induced subgraph of unit graph admit only the trivial subring perfect code.
{"title":"Subset Perfect Codes of Finite Commutative Rings Over Induced Subgraphs of Unit Graphs","authors":"M. H. Mudaber, N. Sarmin, I. Gambo","doi":"10.47836/mjms.16.4.10","DOIUrl":"https://doi.org/10.47836/mjms.16.4.10","url":null,"abstract":"The induced subgraph of a unit graph with vertex set as the non unit elements of a ring R is a graph obtained by deleting all unit elements of R. In a graph , a subset of the vertex set is called a perfect code if the balls with radius 1 centred on the subset are pairwise disjoint and their unions yield the whole vertex set. In this paper, we determine the perfect codes of induced subgraphs of the unit graphs associated with some finite commutative rings R with unity that has a vertex set as non unit elements of R. Moreover, we classify the commutative rings in which their associated induced subgraphs of unit graphs admit the trivial and non-trivial perfect codes. We also characterize the commutative rings based on the induced subgraph of unit graphs that do not admit the perfect codes. Furthermore, we prove that the complement induced subgraph of unit graph admit only the trivial subring perfect code.","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":"47700905","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 the paper, we propose a series of convolution identities for the sequence of Catalan numbers. The proofs of two of them are provided and the other identities are proposed as conjectures. We include a simple Maple code to generate and confirm the identities.
{"title":"Some Convolution Identities for Catalan Numbers","authors":"I. Rakhimov, K. A. Mohd Atan, N. A. Hadi","doi":"10.47836/mjms.16.4.09","DOIUrl":"https://doi.org/10.47836/mjms.16.4.09","url":null,"abstract":"In the paper, we propose a series of convolution identities for the sequence of Catalan numbers. The proofs of two of them are provided and the other identities are proposed as conjectures. We include a simple Maple code to generate and confirm the identities.","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":"46535835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Convergence of Operator With Rapidly Decreasing Wavelet Functions","authors":"R. S. Shamsah, A. Ahmedov, A. Kılıçman, H. Zainuddin","doi":"10.47836/mjms.16.4.03","DOIUrl":"https://doi.org/10.47836/mjms.16.4.03","url":null,"abstract":"The expansion of (2D) wavelet functions with respect to Lp(R2) space converging almost everywhere for 1<p<∞ throughout the length of the Lebesgue set points of space functions is investigated in this research. The convergence is established by assuming some wavelet function minimal regularity ψj1,j2,k1,k2 under the current description of the wavelet projection operator known as 2D Hard Sampling Operator. Note that the feature of fast decline in 2D is derived here. Another condition is used, for instance, the wavelet expansion's boundedness under the Hard Sampling Operator. The bound (limit) is governed in magnitude with respect to the maximal equality of the Hardy-Littlewood maximal operator. Some ideas presented in this work are to find a new method to prove the convergence theory for a new type of conditional wavelet operator. Propose some conditions for wavelets functions and their expansion can support the operator to be convergence. It also performs a comparison with the identity convergent operator is our method for achieving this convergence.","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":"44066677","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}
M. Letchumanan, S. Husain, A. F. Ayub, R. Kamaruddin, Nurul Nadwa Zulkifli
This study investigates factors that influence the use of information and communication technology (ICT) tools by academicians to promote higher order thinking skills (HOTS) among university mathematics students. The study adapted constructs such as performance expectancy, effort expectancy and facilitating conditions from the Unified Theory of Acceptance and Use of Technology. The study applied descriptive research design and used quantitative and qualitative approach in the form of questionnaire and interview to gather data from 86 academicians from three local public universities in Malaysia. The data were analysed in terms of descriptive analysis and content analysis. The result showed that the technology, instructor, student, learning material, task and organisational factors play important roles in promoting HOTS among students. The study contributed to expanding readers' understanding of the factors that influence the use of ICT tools by academicians to promote HOTS among university students.
{"title":"Migrating to Technology Integrated Classes to Promote Higher Order Thinking Skills among University Students: Perspectives from Mathematics Academicians","authors":"M. Letchumanan, S. Husain, A. F. Ayub, R. Kamaruddin, Nurul Nadwa Zulkifli","doi":"10.47836/mjms.16.4.08","DOIUrl":"https://doi.org/10.47836/mjms.16.4.08","url":null,"abstract":"This study investigates factors that influence the use of information and communication technology (ICT) tools by academicians to promote higher order thinking skills (HOTS) among university mathematics students. The study adapted constructs such as performance expectancy, effort expectancy and facilitating conditions from the Unified Theory of Acceptance and Use of Technology. The study applied descriptive research design and used quantitative and qualitative approach in the form of questionnaire and interview to gather data from 86 academicians from three local public universities in Malaysia. The data were analysed in terms of descriptive analysis and content analysis. The result showed that the technology, instructor, student, learning material, task and organisational factors play important roles in promoting HOTS among students. The study contributed to expanding readers' understanding of the factors that influence the use of ICT tools by academicians to promote HOTS among university students.","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":"41781981","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}
Scheduling is very important concept in each and every field of life especially in case of manufacturing process. Actually, a production schedule is the time table that tells the time at which an assignment will be processed on various machines. The Schedule also gives the information about starting and finishing of a work on one machine. This paper also deals with the theory of Scheduling. The main attraction of this study is the optimization done on like Parallel machines with the help of Fuzzy Processing Times. Here the problem of optimization on Two Stage Flow Shop Model has been taken into consideration. This paper reveals an algorithm using Branch and bound method for scheduling on three like parallel machines available at initial stage and solo machine at next stage having processing period of all works as fuzzy triangular numbers involving transportation time from first stage to second stage. Algorithm provides an optimal sequence of jobs for minimizing make span as well as the unit operational cost of each job on all three parallel machines. Numerical example has also been discussed for elaborating this situation. The proposed model is the extension of model presented by Deepak Gupta and Sonia Goel [18].
{"title":"Bi-Objective Flow Shop Scheduling with Equipotential Parallel Machines","authors":"K. Malhotra, D. Gupta, S. Goel, A. K. Tripathi","doi":"10.47836/mjms.16.3.04","DOIUrl":"https://doi.org/10.47836/mjms.16.3.04","url":null,"abstract":"Scheduling is very important concept in each and every field of life especially in case of manufacturing process. Actually, a production schedule is the time table that tells the time at which an assignment will be processed on various machines. The Schedule also gives the information about starting and finishing of a work on one machine. This paper also deals with the theory of Scheduling. The main attraction of this study is the optimization done on like Parallel machines with the help of Fuzzy Processing Times. Here the problem of optimization on Two Stage Flow Shop Model has been taken into consideration. This paper reveals an algorithm using Branch and bound method for scheduling on three like parallel machines available at initial stage and solo machine at next stage having processing period of all works as fuzzy triangular numbers involving transportation time from first stage to second stage. Algorithm provides an optimal sequence of jobs for minimizing make span as well as the unit operational cost of each job on all three parallel machines. Numerical example has also been discussed for elaborating this situation. The proposed model is the extension of model presented by Deepak Gupta and Sonia Goel [18].","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46382038","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 new subclass of complex-valued harmonic univalent functions f(z)=h(z)+g(z)¯¯¯¯¯¯¯¯¯ in the open disk U={z:z∈C and |z|<1} defined by using a linear operator. We investigate coefficient condition, extreme points, distortion and convex combination for this subclass.
{"title":"A New Subclass of Harmonic Univalent Functions Defined by a Linear Operator","authors":"A. N. Metkari, N. Sangle, M. Darus","doi":"10.47836/mjms.16.3.05","DOIUrl":"https://doi.org/10.47836/mjms.16.3.05","url":null,"abstract":"In this paper, a new subclass of complex-valued harmonic univalent functions f(z)=h(z)+g(z)¯¯¯¯¯¯¯¯¯ in the open disk U={z:z∈C and |z|<1} defined by using a linear operator. We investigate coefficient condition, extreme points, distortion and convex combination for this subclass.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49614594","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 deals with the classical and Bayesian estimation in exponential power distribution based on Type-I progressive hybrid censoring with binomial removals at each stage. Based on the considered censoring scheme, the maximum likelihood estimates and their coverage probabilities are computed by the Monte Carlo simulation technique. MCMC technique is used to obtain the Bayes estimates under the informative priors. The performance of both the approaches is evaluated in terms of their absolute bias and mean square error (MSE) as well as the width of the confidence interval. Applicability of the suggested approach is illustrated by analysis of a real-life dataset.
{"title":"Classical and Bayesian Estimation in Exponential Power Distribution under Type-I Progressive Hybrid Censoring with Binomial Removals","authors":"R. Kishan, P. Sangal","doi":"10.47836/mjms.16.3.9","DOIUrl":"https://doi.org/10.47836/mjms.16.3.9","url":null,"abstract":"This article deals with the classical and Bayesian estimation in exponential power distribution based on Type-I progressive hybrid censoring with binomial removals at each stage. Based on the considered censoring scheme, the maximum likelihood estimates and their coverage probabilities are computed by the Monte Carlo simulation technique. MCMC technique is used to obtain the Bayes estimates under the informative priors. The performance of both the approaches is evaluated in terms of their absolute bias and mean square error (MSE) as well as the width of the confidence interval. Applicability of the suggested approach is illustrated by analysis of a real-life dataset.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45087434","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. Al-Zahrani, F. E. I. Elsmih, K. Al-Zahrani, S. Saber
In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.
{"title":"A Fractional Order SITR Model for Forecasting of Transmission of COVID-19: Sensitivity Statistical Analysis","authors":"S. Al-Zahrani, F. E. I. Elsmih, K. Al-Zahrani, S. Saber","doi":"10.47836/mjms.16.3.08","DOIUrl":"https://doi.org/10.47836/mjms.16.3.08","url":null,"abstract":"In this work, we investigate the effects of the contact rate between people on the covid-19 virus transmission through a susceptible-infected-treatment-recovered (SITR) fractional mathematical model. Several strategies are introduced, and the development methodology is constructed up in various cases based on the rate of individual contact, due to confinement and social distancing rules, which can be useful in reducing infection. The existence and uniqueness of the proposed model solution are established, as well as the basic reproduction number. The basic reproduction number has been used to control the dynamics of the fractional SITR model completely, which determines whether or not the infection is extinguished. The global stability of the infection-free balance and endemic equilibrium point of the proposed model has been fully established using the Lyapunov-LaSalle type theorem. Furthermore, a sensitivity analysis is carried out to find out which parameter is the most dominant to affect the disease's endemicity and to see how changes in parameters affect Covid-19's beginning disease transmission. The fractional Adams-Bashforth method is used to compute an iterative solution to the model. Finally, using the model parameter values to explain the importance of the arbitrary fractional-order derivative, the numerical results using MATLAB are presented.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47498953","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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