{"title":"ANFIS-Enhanced M/M/2 Queueing Model Investigation in Heterogeneous Server Systems with Catastrophe and Restoration","authors":"Indumathi P, Karthikeyan K","doi":"10.37256/cm.5220243977","DOIUrl":"https://doi.org/10.37256/cm.5220243977","url":null,"abstract":"<jats:p/>","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141340646","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 study explores the spectral Galerkin approach to solving the space-time Schrödinger, wave, Airy, and beam equations. In order to facilitate the creation of a semi-analytical approximation solution, it uses polynomial bases that are formed from a linear combination of Jacobi polynomials (JPs) in both spatial and temporal dimensions. By using these polynomials to expand the exact solution, the paper hopes to satisfy the homogeneous starting and Dirichlet boundary requirements. Notably, the Jacobi Galerkin (JG) method exhibits exponential convergence rates if the solution is sufficiently smooth. This result emphasizes the JG approach' s potential as an effective numerical solution method, which has promise for a variety of applications in other domains where these equations occur, such as quantum mechanics, acoustics, optics, and structural mechanics.
{"title":"Review on Jacobi-Galerkin Spectral Method for Linear PDEs in Applied Mathematics","authors":"R. Hafez, Y. H. Youssri","doi":"10.37256/cm.5220244768","DOIUrl":"https://doi.org/10.37256/cm.5220244768","url":null,"abstract":"This study explores the spectral Galerkin approach to solving the space-time Schrödinger, wave, Airy, and beam equations. In order to facilitate the creation of a semi-analytical approximation solution, it uses polynomial bases that are formed from a linear combination of Jacobi polynomials (JPs) in both spatial and temporal dimensions. By using these polynomials to expand the exact solution, the paper hopes to satisfy the homogeneous starting and Dirichlet boundary requirements. Notably, the Jacobi Galerkin (JG) method exhibits exponential convergence rates if the solution is sufficiently smooth. This result emphasizes the JG approach' s potential as an effective numerical solution method, which has promise for a variety of applications in other domains where these equations occur, such as quantum mechanics, acoustics, optics, and structural mechanics.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141345387","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 hypersoft set theory is an extension of soft set theory. The complex non-linear diophantine fuzzy set is a hybrid fuzzy extension that serves as a generalization of the q-rung linear diophantine fuzzy set and the complex linear diophantine fuzzy set. In this paper, to tackle multi-sub-attributed real-world situations under complex non-linear diophantine fuzzy ambiance, the concept of complex q-rung linear diophantine fuzzy hypersoft set is proposed along with its score and accuracy function. Also, the idea of lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is proposed in this paper, along with some of its basic algebraic operations. Furthermore, a highly effective algorithm using lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is provided for handling multi-attributed decision-making issues exquisitely, along with an illustrative example in the field of vertical farming. Then, a comparative analysis between the proposed and current notions is provided to demonstrate the superiority and benefits of the suggested concepts over the current ones.
{"title":"A Hybrid Fuzzy Extension and Its Application in Multi-Attribute Decision Making","authors":"AN. Surya, J. Vimala, K. A. Banu","doi":"10.37256/cm.5220244390","DOIUrl":"https://doi.org/10.37256/cm.5220244390","url":null,"abstract":"The hypersoft set theory is an extension of soft set theory. The complex non-linear diophantine fuzzy set is a hybrid fuzzy extension that serves as a generalization of the q-rung linear diophantine fuzzy set and the complex linear diophantine fuzzy set. In this paper, to tackle multi-sub-attributed real-world situations under complex non-linear diophantine fuzzy ambiance, the concept of complex q-rung linear diophantine fuzzy hypersoft set is proposed along with its score and accuracy function. Also, the idea of lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is proposed in this paper, along with some of its basic algebraic operations. Furthermore, a highly effective algorithm using lattice ordered complex q-rung linear diophantine fuzzy hypersoft set is provided for handling multi-attributed decision-making issues exquisitely, along with an illustrative example in the field of vertical farming. Then, a comparative analysis between the proposed and current notions is provided to demonstrate the superiority and benefits of the suggested concepts over the current ones.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141373845","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 pervasive need for cloud-hosted application services has resulted from the widespread use of cloud data centers. Not only that, but there has been a dramatic increase in the resource demands of current applications, especially in data-intensive businesses. This has resulted in an increase in the number of cloud servers made available, which has increased energy usage and prompted environmental concerns. Only partially do the difficulties of scalability and adaptability in cloud resource management get addressed by conventional heuristics and reinforcement learning-based techniques. Many existing works overlook the interdependencies between host temperature, task resource usage, and scheduling decisions. Especially in contexts with fluctuating resource demands, this results in poor scalability and an upsurge in computing resource requirements. The study recommended a holistic resource management strategy based on resource scheduling for enduring cloud computing as a solution to these restrictions. Energy, thermal, and cooling models are all taken into account in the proposed model, which expresses the optimization of data center energy efficiency as a multi-objective scheduling issue. To generate optimal scheduling decisions and approximate the quality of service (QoS) for a given system state, the model employs cat-based swarm optimization as a surrogate model. Using the China Ocean Shipping Company (COSCO) framework, we conducted experiments that demonstrate cloud service orchestrator (CSO)’s superior performance compared to state-of-the-art baselines in terms of energy ingesting, makespan, and execution overhead in both simulated and real-world cloud environments.
{"title":"CSO-based Efficient Resource Management for Sustainable Cloud Computing","authors":"K. Shanmugam, Satyam K, T. Rajasekhar","doi":"10.37256/cm.5220242700","DOIUrl":"https://doi.org/10.37256/cm.5220242700","url":null,"abstract":"The pervasive need for cloud-hosted application services has resulted from the widespread use of cloud data centers. Not only that, but there has been a dramatic increase in the resource demands of current applications, especially in data-intensive businesses. This has resulted in an increase in the number of cloud servers made available, which has increased energy usage and prompted environmental concerns. Only partially do the difficulties of scalability and adaptability in cloud resource management get addressed by conventional heuristics and reinforcement learning-based techniques. Many existing works overlook the interdependencies between host temperature, task resource usage, and scheduling decisions. Especially in contexts with fluctuating resource demands, this results in poor scalability and an upsurge in computing resource requirements. The study recommended a holistic resource management strategy based on resource scheduling for enduring cloud computing as a solution to these restrictions. Energy, thermal, and cooling models are all taken into account in the proposed model, which expresses the optimization of data center energy efficiency as a multi-objective scheduling issue. To generate optimal scheduling decisions and approximate the quality of service (QoS) for a given system state, the model employs cat-based swarm optimization as a surrogate model. Using the China Ocean Shipping Company (COSCO) framework, we conducted experiments that demonstrate cloud service orchestrator (CSO)’s superior performance compared to state-of-the-art baselines in terms of energy ingesting, makespan, and execution overhead in both simulated and real-world cloud environments.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368439","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}
Our manuscript puts forward two novel fuzzy proximal contractive conditions. First, we present two variants of fuzzy α-proximal quasi-H-contractions and establish optimal coincidence point outcomes for these contractions in fuzzy metric space. This manuscript’s second part proposes the fuzzy ψ-contraction for a multivalued mapping equipped with fuzzy weak P-property and achieves the best proximity point outcome in strong fuzzy metric space. The findings of this study broaden and generalize some existing research results.
{"title":"Fuzzy Metric Spaces: Optimizing Coincidence and Proximity Points","authors":"K. S. Wong, Z. Salleh, H. Akhadkulov","doi":"10.37256/cm.5220242655","DOIUrl":"https://doi.org/10.37256/cm.5220242655","url":null,"abstract":"Our manuscript puts forward two novel fuzzy proximal contractive conditions. First, we present two variants of fuzzy α-proximal quasi-H-contractions and establish optimal coincidence point outcomes for these contractions in fuzzy metric space. This manuscript’s second part proposes the fuzzy ψ-contraction for a multivalued mapping equipped with fuzzy weak P-property and achieves the best proximity point outcome in strong fuzzy metric space. The findings of this study broaden and generalize some existing research results.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140368808","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. H. Arnous, A. Biswas, Y. Yıldırım, A. Alshomrani
This paper investigates the significance of the dispersive concatenation model, incorporating the Kerr law of self-phase modulation in the presence of white noise. Our methodology relies on the enhanced direct algebraic method for integration. We reveal that intermediate solutions are expressed in terms of Jacobi's elliptic functions, leading to soliton solutions as the modulus of ellipticity approaches unity. This discovery culminates in the emergence of a diverse range of optical solitons. Our findings contribute novelty to the existing literature by offering insights into the behavior of optical solitons within the dispersive concatenation model, presenting a significant advancement in understanding this complex phenomenon.
{"title":"Optical Solitons with Dispersive Concatenation Model Having Multiplicative White Noise by the Enhanced Direct Algebraic Method","authors":"A. H. Arnous, A. Biswas, Y. Yıldırım, A. Alshomrani","doi":"10.37256/cm.5220244123","DOIUrl":"https://doi.org/10.37256/cm.5220244123","url":null,"abstract":"This paper investigates the significance of the dispersive concatenation model, incorporating the Kerr law of self-phase modulation in the presence of white noise. Our methodology relies on the enhanced direct algebraic method for integration. We reveal that intermediate solutions are expressed in terms of Jacobi's elliptic functions, leading to soliton solutions as the modulus of ellipticity approaches unity. This discovery culminates in the emergence of a diverse range of optical solitons. Our findings contribute novelty to the existing literature by offering insights into the behavior of optical solitons within the dispersive concatenation model, presenting a significant advancement in understanding this complex phenomenon.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140377007","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 orthogonal operators defined as similarity transformations on Euclidean space E can also be considered as group actions on the Clifford Algebra. In this paper, we investigate the finite subgroup of Euclidian space E of Geometric Algebra over a finite dimension vector space E. The hierarchy of the finite subgroups of Clifford Algebra C(E) is depicted through the lattice structure and we discussed the group action of these subgroups on the vector space E. Further, we shall address the number of non-trivial finite subgroups, Normal subgroups, and subnormal series of the subgroup of Clifford Algebra C(E) constructed over the vector space E by performing group action over the subgroup of Clifford Algebra C(E).
定义为欧几里得空间 E 上相似性变换的正交算子也可视为克利福德代数上的群作用。本文研究了有限维向量空间 E 上几何代数欧几里得空间 E 的有限子群。我们通过网格结构描绘了克利福德代数 C(E) 有限子群的层次，并讨论了这些子群对向量空间 E 的群作用。此外，我们还将讨论通过对 Clifford Algebra C(E) 子群进行群作用，在向量空间 E 上构建的 Clifford Algebra C(E) 子群的非琐有限子群、正常子群和子正常数列的数量。
{"title":"Application of Clifford Algebra on Group Theory","authors":"Farooqhusain Inamdar, Hasan S. N.","doi":"10.37256/cm.5220243921","DOIUrl":"https://doi.org/10.37256/cm.5220243921","url":null,"abstract":"The orthogonal operators defined as similarity transformations on Euclidean space E can also be considered as group actions on the Clifford Algebra. In this paper, we investigate the finite subgroup of Euclidian space E of Geometric Algebra over a finite dimension vector space E. The hierarchy of the finite subgroups of Clifford Algebra C(E) is depicted through the lattice structure and we discussed the group action of these subgroups on the vector space E. Further, we shall address the number of non-trivial finite subgroups, Normal subgroups, and subnormal series of the subgroup of Clifford Algebra C(E) constructed over the vector space E by performing group action over the subgroup of Clifford Algebra C(E).","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140387320","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 special type of soluble model corresponding to a coupled molecular and nuclear Hamiltonians H, the so-called generalized Friedrichs model, is considered. We aim to determine and provide the most important properties of the well-known Faddeev operator corresponding to H accommodating a number of discrete eigenvalues. Furthermore, we provide a formula for counting the multiplicity of discrete eigenvalues of H.
本文考虑了与耦合分子和核汉密尔顿H相对应的一种特殊类型的可溶模型，即所谓的广义弗里德里希模型。我们的目的是确定并提供与 H 相对应的著名的法迪夫算子的最重要性质，该算子包含若干离散特征值。此外，我们还提供了一个计算 H 离散特征值多重性的公式。
{"title":"On the Eigenvalues of a Soluble Model of Coupled Molecular and Nuclear Hamiltonians","authors":"T. Rasulov, E. Dilmurodov","doi":"10.37256/cm.5120242728","DOIUrl":"https://doi.org/10.37256/cm.5120242728","url":null,"abstract":"In this paper, a special type of soluble model corresponding to a coupled molecular and nuclear Hamiltonians H, the so-called generalized Friedrichs model, is considered. We aim to determine and provide the most important properties of the well-known Faddeev operator corresponding to H accommodating a number of discrete eigenvalues. Furthermore, we provide a formula for counting the multiplicity of discrete eigenvalues of H.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140218396","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 numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.
{"title":"Impact of Local Thermal Non-Equilibrium and Gravity Fluctuations on the Onset of a Darcy-Brinkman Porous Convection","authors":"G. Y. H., Manjunatha N, N. H, R. Udhayakumar","doi":"10.37256/cm.5120244240","DOIUrl":"https://doi.org/10.37256/cm.5120244240","url":null,"abstract":"The numerical investigation of the Darcy-Brinkman convective problem with gravity fluctuations in a Local Thermal Nonequilibrium (LTNE) model is conducted. Utilizing linear stability analysis, the convective problem is explored, and the numerical values of the Rayleigh and wave numbers for onset convection are computed through the one-term Galerkin approach. Three distinct types of gravity fluctuations (linear, parabolic, and exponential) are considered. The results show the Darcy number and gravity parameter delay the onset of convection. The porosity-scald conductivity ratio and interface heat transfer coefficient have a significant effect on the stability of the configuration. Graphical representations depict the effects of various parameters, highlighting the significant impacts of incorporating gravity fluctuations and non-equilibrium conditions in determining convection stability thresholds.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140214342","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 article, we use a new technique called conformable fractional reduced differential transform (CFRDT) with Adomian decomposition to estimate the solution of one and two-dimensional time-fractional partial linear and nonlinear differential equations with initial values. We explain the convergence analysis of this technique. The obtained results illustrate that the novel method is efficient and easy to use to find approximate solutions for the time-fractional partial differential equations (PDEs). Thus, the suggested method has a significant impact on how engineering, physics, and other disciplines solve fractional PDEs. Furthermore, we analyze the solution of problems with a 2D or 3D graphical representation by using Mathematica software.
{"title":"Solving Nonlinear Time-Fractional Partial Differential Equations Using Conformable Fractional Reduced Differential Transform with Adomian Decomposition Method","authors":"R. S. Teppawar, R. N. Ingle, R. A. Muneshwar","doi":"10.37256/cm.5120242463","DOIUrl":"https://doi.org/10.37256/cm.5120242463","url":null,"abstract":"In this article, we use a new technique called conformable fractional reduced differential transform (CFRDT) with Adomian decomposition to estimate the solution of one and two-dimensional time-fractional partial linear and nonlinear differential equations with initial values. We explain the convergence analysis of this technique. The obtained results illustrate that the novel method is efficient and easy to use to find approximate solutions for the time-fractional partial differential equations (PDEs). Thus, the suggested method has a significant impact on how engineering, physics, and other disciplines solve fractional PDEs. Furthermore, we analyze the solution of problems with a 2D or 3D graphical representation by using Mathematica software.","PeriodicalId":504505,"journal":{"name":"Contemporary Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140222598","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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