We define notions such as pseudo-orbit, topological shadowing, and topological chain transitivity of iterated function systems on compact uniform spaces. We prove that these notions are invariant under topological conjugacy on a compact uniform space. For an IFS on a compact uniform space with topological shadowing property, we show that the topological chain transitivity implies topological transitivity. We also show that in a connected compact uniform space, notions such as topological chain mixing, totally topological chain transitive, topological chain transitive, and topological chain recurrent are equivalent.
{"title":"On Topological Shadowing and Chain Properties of IFS on Uniform Spaces","authors":"T. T. Devi, K. B. Mangang","doi":"10.47836/mjms.16.3.07","DOIUrl":"https://doi.org/10.47836/mjms.16.3.07","url":null,"abstract":"We define notions such as pseudo-orbit, topological shadowing, and topological chain transitivity of iterated function systems on compact uniform spaces. We prove that these notions are invariant under topological conjugacy on a compact uniform space. For an IFS on a compact uniform space with topological shadowing property, we show that the topological chain transitivity implies topological transitivity. We also show that in a connected compact uniform space, notions such as topological chain mixing, totally topological chain transitive, topological chain transitive, and topological chain recurrent are equivalent.","PeriodicalId":43645,"journal":{"name":"Malaysian Journal of Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2022-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70928589","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 proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analytical works. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.
{"title":"Numerical Simulations of the Fractional-Order SIQ Mathematical Model of Corona Virus Disease Using the Nonstandard Finite Difference Scheme","authors":"N. Raza, A. Bakar, A. Khan, C. Tunç","doi":"10.47836/mjms.16.3.01","DOIUrl":"https://doi.org/10.47836/mjms.16.3.01","url":null,"abstract":"This paper proposes a novel nonlinear fractional-order pandemic model with Caputo derivative for corona virus disease. A nonstandard finite difference (NSFD) approach is presented to solve this model numerically. This strategy preserves some of the most significant physical properties of the solution such as non-negativity, boundedness and stability or convergence to a stable steady state. The equilibrium points of the model are analyzed and it is determined that the proposed fractional model is locally asymptotically stable at these points. Non-negativity and boundedness of the solution are proved for the considered model. Fixed point theory is employed for the existence and uniqueness of the solution. The basic reproduction number is computed to investigate the dynamics of corona virus disease. It is worth mentioning that the non-integer derivative gives significantly more insight into the dynamic complexity of the corona model. The suggested technique produces dynamically consistent outcomes and excellently matches the analytical works. To illustrate our results, we conduct a comprehensive quantitative study of the proposed model at various quarantine levels. Numerical simulations show that can eradicate a pandemic quickly if a human population implements obligatory quarantine measures at varying coverage levels while maintaining sufficient knowledge.","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":"41954416","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}
It is well-known that cryptography is a branch of secrecy in science and mathematics, which usually preserves the confidentiality and authenticity of the information, where its growth is parallel with the rapid evolution of the internet and communication. As one of the prominent public key cryptosystems, the Elliptic Curve Cryptosystem (ECC) offers efficiency and complex mathematical operations with a smaller bit compared to other types of public key schemes. Throughout the evolution of cryptography, ElGamal Elliptic Curve Cryptosystem (ElGamal ECC) revolved from ElGamal public key scheme for user efficiency and privacy. In this study, an improved method will be introduced using ElGamal ECC as the foundation with the incorporation of the Bézier curve coefficient matrix, where the ElGamal ECC value is considered as the control point of the Bézier curve during the encryption and decryption processes. The proposed method is designed to develop a robust ciphertext system algorithm for better efficiency and to increase the level of protection in ElGamal ECC. In this paper, the performance of the proposed method is compared with the normal ElGamal ECC. The results of this study show that the proposed method offers no significant difference in terms of the implementation time during the encryption and decryption process. However, it does offer extra layers of protection when operated with complex mathematical operations.
{"title":"Bézier Coefficients Matrix for ElGamal Elliptic Curve Cryptosystem","authors":"N. Ismail, M. Misro","doi":"10.47836/mjms.16.3.06","DOIUrl":"https://doi.org/10.47836/mjms.16.3.06","url":null,"abstract":"It is well-known that cryptography is a branch of secrecy in science and mathematics, which usually preserves the confidentiality and authenticity of the information, where its growth is parallel with the rapid evolution of the internet and communication. As one of the prominent public key cryptosystems, the Elliptic Curve Cryptosystem (ECC) offers efficiency and complex mathematical operations with a smaller bit compared to other types of public key schemes. Throughout the evolution of cryptography, ElGamal Elliptic Curve Cryptosystem (ElGamal ECC) revolved from ElGamal public key scheme for user efficiency and privacy. In this study, an improved method will be introduced using ElGamal ECC as the foundation with the incorporation of the Bézier curve coefficient matrix, where the ElGamal ECC value is considered as the control point of the Bézier curve during the encryption and decryption processes. The proposed method is designed to develop a robust ciphertext system algorithm for better efficiency and to increase the level of protection in ElGamal ECC. In this paper, the performance of the proposed method is compared with the normal ElGamal ECC. The results of this study show that the proposed method offers no significant difference in terms of the implementation time during the encryption and decryption process. However, it does offer extra layers of protection when operated with complex mathematical operations.","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":"42301626","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}
Various divergence measure methods have been used in many applications of fuzzy set theory for calculating the discrimination between two objects. This paper aims to develop a novel divergence measure incorporated with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, along with the discussions of its properties. Since ambiguity or uncertainty is an inevitable characteristic of multi-criteria decision-making (MCDM) problems, the fuzzy concept is utilised to convert linguistic expressions into triangular fuzzy numbers. A numerical example of a staff performance appraisal is given to demonstrate suggested method's effectiveness and practicality. Outcomes from this study were compared with various MCDM techniques in terms of correlation coefficients and central processing unit (CPU) time. From the results, there is a slight difference in the ranking order between the proposed method and the other MCDM methods as all the correlation coefficient values are more than 0.9. It is also discovered that CPU time of the proposed method is the lowest compared to the other divergence measure techniques. Hence, the proposed method provides a more sensible and feasible solutions than its counterparts.
{"title":"A New Divergence Measure based on Fuzzy TOPSIS for Solving Staff Performance Appraisal","authors":"M. S. Saidin, Lee L. S., M. A. Bakar, M. Z. Ahmad","doi":"10.47836/mjms.16.3.14","DOIUrl":"https://doi.org/10.47836/mjms.16.3.14","url":null,"abstract":"Various divergence measure methods have been used in many applications of fuzzy set theory for calculating the discrimination between two objects. This paper aims to develop a novel divergence measure incorporated with the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, along with the discussions of its properties. Since ambiguity or uncertainty is an inevitable characteristic of multi-criteria decision-making (MCDM) problems, the fuzzy concept is utilised to convert linguistic expressions into triangular fuzzy numbers. A numerical example of a staff performance appraisal is given to demonstrate suggested method's effectiveness and practicality. Outcomes from this study were compared with various MCDM techniques in terms of correlation coefficients and central processing unit (CPU) time. From the results, there is a slight difference in the ranking order between the proposed method and the other MCDM methods as all the correlation coefficient values are more than 0.9. It is also discovered that CPU time of the proposed method is the lowest compared to the other divergence measure techniques. Hence, the proposed method provides a more sensible and feasible solutions than its counterparts.","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":"44648023","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. Senguttuvan, D. Mohankumar, R. Ganapathy, K. Karthikeyan
We have introduced a comprehensive subclass of analytic functions with respect to (j,k) - symmetric points. We have obtained the interesting coefficient bounds for the newly defined classes of functions. Further, we have extended the study using quantum calculus. Our main results have several applications, here we have presented only a few of them.
{"title":"Coefficient Inequalities of a Comprehensive Subclass of Analytic Functions With Respect to Symmetric Points","authors":"A. Senguttuvan, D. Mohankumar, R. Ganapathy, K. Karthikeyan","doi":"10.47836/mjms.16.3.03","DOIUrl":"https://doi.org/10.47836/mjms.16.3.03","url":null,"abstract":"We have introduced a comprehensive subclass of analytic functions with respect to (j,k) - symmetric points. We have obtained the interesting coefficient bounds for the newly defined classes of functions. Further, we have extended the study using quantum calculus. Our main results have several applications, here we have presented only a few of them.","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":"49662575","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}
For a field F, where any polynomial of degree two and three possess a root, we give an algorithm transforming any two-dimensional algebra over F to a "canonical form" in terms of structure constants of the algebra. A system of invariant conditions in form of equalities and non-equalities (inequalities) separating non-isomorphic two-dimensional algebras is given.
{"title":"Canonical Form Algorithm and Separating Systems for Two-Dimensional Algebras","authors":"Houida Ahmed, U. Bekbaev, I. Rakhimov","doi":"10.47836/mjms.16.3.02","DOIUrl":"https://doi.org/10.47836/mjms.16.3.02","url":null,"abstract":"For a field F, where any polynomial of degree two and three possess a root, we give an algorithm transforming any two-dimensional algebra over F to a \"canonical form\" in terms of structure constants of the algebra. A system of invariant conditions in form of equalities and non-equalities (inequalities) separating non-isomorphic two-dimensional algebras is given.","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":"43578081","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 investigate the vibrations of embankments by the singular Sturm-Liouville equations. At first, we create the mathematical form of the vibrations by the shear beam (SB) model (see [21]) and transform this given form to the Sturm-Liouville form with a singularity. Finally, we discuss the numerical solution to the considered problem using the variational iteration method.
{"title":"A Survey of the Earth Dams by Sturm-Liouville Equations - The Singular Case","authors":"A. Neamaty, Y. Khalili","doi":"10.47836/mjms.16.3.13","DOIUrl":"https://doi.org/10.47836/mjms.16.3.13","url":null,"abstract":"In this work, we investigate the vibrations of embankments by the singular Sturm-Liouville equations. At first, we create the mathematical form of the vibrations by the shear beam (SB) model (see [21]) and transform this given form to the Sturm-Liouville form with a singularity. Finally, we discuss the numerical solution to the considered problem using the variational iteration method.","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":"43608680","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 evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group.
{"title":"Algebraic representation of Three Qubit Quantum Circuit Problems","authors":"Chew K. Y., N. M. Shah, Chan K. T.","doi":"10.47836/mjms.16.3.10","DOIUrl":"https://doi.org/10.47836/mjms.16.3.10","url":null,"abstract":"The evolution of quantum states serves as good fundamental studies in understanding the quantum information systems which finally lead to the research on quantum computation. To carry out such a study, mathematical tools such as the Lie group and their associated Lie algebra is of great importance. In this study, the Lie algebra of su(8) is represented in a tensor product operation between three Pauli matrices. This can be realized by constructing the generalized Gell-Mann matrices and comparing them to the Pauli bases. It is shown that there is a one-to-one correlation of the Gell-Mann matrices with the Pauli basis which resembled the change of coordinates. Together with the commutator relations and the frequency analysis of the structure constant via the algebra, the Lie bracket operation will be highlighted providing insight into relating quantum circuit model with Lie Algebra. These are particularly useful when dealing with three-qubit quantum circuit problems which involve quantum gates that is derived from the SU(8) Lie group.","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":"48120486","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}
Image recognition includes the segmentation of image boundary geometrical features extraction and classification is used in the particular image database development. The ultimate challenge in this task is it is computationally expensive. This paper highlighted a CPU GPU architecture for image segmentation and features extraction processes of 125 images of Malaysian Herb Leaves. Two GPUs and three kernels are utilized in the CPU GPU platform using MATLAB software. Each of herb image has pixel dimensions 16161080. The segmentation process uses the Sobel operator which is then used to extract the boundary points. Finally seven geometrical features are extracted for each image. Both processes are first executed on the CPU alone before bringing it onto a CPU GPU platform to accelerate the computational performance. The results show that the developed CPU GPU platform has accelerated the computation process by a factor of 4.13. However the efficiency shows a decline which suggests that the processors utilization must be improved in the future to balance the load distribution.
{"title":"Performance of CPU GPU Parallel Architecture on Segmentation and Geometrical Features Extraction of Malaysian Herb Leaves","authors":"N. A. Hadi, S. Halim, N. Lazim, N. Alias","doi":"10.47836/mjms.16.2.12","DOIUrl":"https://doi.org/10.47836/mjms.16.2.12","url":null,"abstract":"Image recognition includes the segmentation of image boundary geometrical features extraction and classification is used in the particular image database development. The ultimate challenge in this task is it is computationally expensive. This paper highlighted a CPU GPU architecture for image segmentation and features extraction processes of 125 images of Malaysian Herb Leaves. Two GPUs and three kernels are utilized in the CPU GPU platform using MATLAB software. Each of herb image has pixel dimensions 16161080. The segmentation process uses the Sobel operator which is then used to extract the boundary points. Finally seven geometrical features are extracted for each image. Both processes are first executed on the CPU alone before bringing it onto a CPU GPU platform to accelerate the computational performance. The results show that the developed CPU GPU platform has accelerated the computation process by a factor of 4.13. However the efficiency shows a decline which suggests that the processors utilization must be improved in the future to balance the load distribution.","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":"48222225","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 foremost objective of this study is to reflect the behaviour of hybrid nanofluid towards a permeable porous medium, with consideration of second-order velocity slip and heat absorption impacts on the fluid flow. Two distinct fluids of copper (Cu) and aluminium oxide (Al2O3) are reviewed in this study to work out as a hybrid nanofluid flow. The equations of boundary layer flow in the form of partial differential equations are reduced to a system of ODEs by conducting a similarity transformation technique, and the findings that obtained from this study are presented in the respective tables and figures. The effects of involving parameters such as suction, porous medium permeability, heat absorption and second order velocity slip are perceived, as well as our intention in observing the impact of traditional nanofluid and hybrid nanofluid on the fluid flow. Our findings revealed that the hybrid Cu-Al2O3/water nanofluid performs well on the fluid flow behaviour against the mono Al2O3/water nanofluid. Moreover, the participating parameters of porous medium permeability, suction and nanoparticle volume fraction are said to improve the boundary layer thickness, while second-order velocity slip parameter is deemed to decay the fluid flow.
{"title":"Hybrid Nanofluid Flow in a Porous Medium with Second-Order Velocity Slip, Suction and Heat Absorption","authors":"S. A. Bakar, N. Arifin, N. Bachok, F. Ali","doi":"10.47836/mjms.16.2.06","DOIUrl":"https://doi.org/10.47836/mjms.16.2.06","url":null,"abstract":"The foremost objective of this study is to reflect the behaviour of hybrid nanofluid towards a permeable porous medium, with consideration of second-order velocity slip and heat absorption impacts on the fluid flow. Two distinct fluids of copper (Cu) and aluminium oxide (Al2O3) are reviewed in this study to work out as a hybrid nanofluid flow. The equations of boundary layer flow in the form of partial differential equations are reduced to a system of ODEs by conducting a similarity transformation technique, and the findings that obtained from this study are presented in the respective tables and figures. The effects of involving parameters such as suction, porous medium permeability, heat absorption and second order velocity slip are perceived, as well as our intention in observing the impact of traditional nanofluid and hybrid nanofluid on the fluid flow. Our findings revealed that the hybrid Cu-Al2O3/water nanofluid performs well on the fluid flow behaviour against the mono Al2O3/water nanofluid. Moreover, the participating parameters of porous medium permeability, suction and nanoparticle volume fraction are said to improve the boundary layer thickness, while second-order velocity slip parameter is deemed to decay the fluid flow.","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":"45344776","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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