Kamran, Ujala Gul, Fahad M. Alotaibi, K. Shah, T. Abdeljawad
Laplace transform has been used for solving differential equations of fractional order either PDEs or ODEs. However, using the Laplace transform sometimes leads to solutions in Laplace space that are not readily invertible to the real domain by analytical techniques. Therefore, numerical inversion techniques are then used to convert the obtained solution from Laplace domain into time domain. Various famous methods for numerical inversion of Laplace transform are based on quadrature approximation of Bromwich integral. The key features are the contour deformation and the choice of the quadrature rule. In this work, the Gauss–Hermite quadrature method and the contour integration method based on the trapezoidal and midpoint rule are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to different types of fractional differential equations, numerical accuracy, computational efficiency, and ease of programming and implementation. The performance and efficiency of the methods are demonstrated with the help of figures and tables. It is observed that the proposed methods converge rapidly with optimal accuracy without any time instability.
{"title":"Computational Approach for Differential Equations with Local and Nonlocal Fractional-Order Differential Operators","authors":"Kamran, Ujala Gul, Fahad M. Alotaibi, K. Shah, T. Abdeljawad","doi":"10.1155/2023/6542787","DOIUrl":"https://doi.org/10.1155/2023/6542787","url":null,"abstract":"Laplace transform has been used for solving differential equations of fractional order either PDEs or ODEs. However, using the Laplace transform sometimes leads to solutions in Laplace space that are not readily invertible to the real domain by analytical techniques. Therefore, numerical inversion techniques are then used to convert the obtained solution from Laplace domain into time domain. Various famous methods for numerical inversion of Laplace transform are based on quadrature approximation of Bromwich integral. The key features are the contour deformation and the choice of the quadrature rule. In this work, the Gauss–Hermite quadrature method and the contour integration method based on the trapezoidal and midpoint rule are tested and evaluated according to the criteria of applicability to actual inversion problems, applicability to different types of fractional differential equations, numerical accuracy, computational efficiency, and ease of programming and implementation. The performance and efficiency of the methods are demonstrated with the help of figures and tables. It is observed that the proposed methods converge rapidly with optimal accuracy without any time instability.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"88 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75876427","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}
<jats:p>Topological indices are numerical quantities associated with the molecular graph of a chemical structure. These indices are used to predict various properties of chemical structures. Imbalance-based analysis is an advanced technique used for chemical compounds with irregular characteristics. The molecular graphs of zigzag benzenoid systems <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mi>Z</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </mfenced> </math> </jats:inline-formula> and rhombic benzenoid systems <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mfenced open="(" close=")" separators="|"> <mrow> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </mrow> </mfenced> </math> </jats:inline-formula> are inherently irregular. Therefore, applying the imbalance technique to these molecular structures plays an important role in predicting different properties. In this paper, we calculate sixteen irregularity indices for both <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <msub> <mrow> <mi>Z</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </math> </jats:inline-formula> and <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"> <msub> <mrow> <mi>R</mi> </mrow> <mrow> <mi>p</mi> </mrow> </msub> </math> </jats:inline-formula> systems. By examining these indices, we aim to provide insights into the properties of these structures and ultimately contribute to a
{"title":"Analysis of Zigzag and Rhombic Benzenoid Systems via Irregularity Indices","authors":"M. Awais, Zulfiqar Ahmed, W. Khalid, E. Bonyah","doi":"10.1155/2023/4833683","DOIUrl":"https://doi.org/10.1155/2023/4833683","url":null,"abstract":"<jats:p>Topological indices are numerical quantities associated with the molecular graph of a chemical structure. These indices are used to predict various properties of chemical structures. Imbalance-based analysis is an advanced technique used for chemical compounds with irregular characteristics. The molecular graphs of zigzag benzenoid systems <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> and rhombic benzenoid systems <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> are inherently irregular. Therefore, applying the imbalance technique to these molecular structures plays an important role in predicting different properties. In this paper, we calculate sixteen irregularity indices for both <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>Z</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> and <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula> systems. By examining these indices, we aim to provide insights into the properties of these structures and ultimately contribute to a","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"79 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75839286","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}
Shahid Zaman, M. Salman, Asad Ullah, S. Ahmad, Mohammed Salaheldeen Abdelgader Abas
Topological characterization of 3D molecular structures is an emerging study area in theoretical and computational chemistry. These structural descriptors are used in a variety of domains, including chemical graph theory, drug delivery, and nanomaterial characterization. Quantitative structural descriptors can be used to characterize the chemical and physical properties of a given compound. Topological indices of molecular graphs are numerical quantities that allow us to collect information about the chemical structure and reveal its hidden qualities without performing experiments. Due to the low cost of implementation, zeolite networks are considered popular chemical networks. Zeolites are widely used networks with applications in chemistry, medicine, and commercial production owing to their excellent chemical features. The sodalite network is composed of a very unique type of zeolite framework called sodalite. It is a three-dimensional network of interconnected cages and tunnels that provide an ideal environment for a wide range of chemical and physical processes. This paper deals with the sodalite material network’s degree-based and reverse degree-based irregularity indices. These indices provide a quantitative measure of the irregular behaviour of the sodalite material network. It can be used to identify areas of the network where irregular behaviour is occurring and to compare different networks to determine which is more irregular. Additionally, these indices can be used to monitor changes in irregularity over time, allowing us to measure the impact of any interventions that are implemented.
{"title":"Three-Dimensional Structural Modelling and Characterization of Sodalite Material Network concerning the Irregularity Topological Indices","authors":"Shahid Zaman, M. Salman, Asad Ullah, S. Ahmad, Mohammed Salaheldeen Abdelgader Abas","doi":"10.1155/2023/5441426","DOIUrl":"https://doi.org/10.1155/2023/5441426","url":null,"abstract":"Topological characterization of 3D molecular structures is an emerging study area in theoretical and computational chemistry. These structural descriptors are used in a variety of domains, including chemical graph theory, drug delivery, and nanomaterial characterization. Quantitative structural descriptors can be used to characterize the chemical and physical properties of a given compound. Topological indices of molecular graphs are numerical quantities that allow us to collect information about the chemical structure and reveal its hidden qualities without performing experiments. Due to the low cost of implementation, zeolite networks are considered popular chemical networks. Zeolites are widely used networks with applications in chemistry, medicine, and commercial production owing to their excellent chemical features. The sodalite network is composed of a very unique type of zeolite framework called sodalite. It is a three-dimensional network of interconnected cages and tunnels that provide an ideal environment for a wide range of chemical and physical processes. This paper deals with the sodalite material network’s degree-based and reverse degree-based irregularity indices. These indices provide a quantitative measure of the irregular behaviour of the sodalite material network. It can be used to identify areas of the network where irregular behaviour is occurring and to compare different networks to determine which is more irregular. Additionally, these indices can be used to monitor changes in irregularity over time, allowing us to measure the impact of any interventions that are implemented.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73814054","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}
Muhammad Kamran, Muhammad Farman, Seyma Ozon Yildirim, Sadik Delen, I. Naci Cangul, Maria Akram, M. Pandit
Chemical graph theory is currently expanding the use of topological indices to numerically encode chemical structure. The prediction of the characteristics provided by the chemical structure of the molecule is a key feature of these topological indices. The concepts from graph theory are presented in a brief discussion of one of its many applications to chemistry, namely, the use of topological indices in quantitative structure-activity relationship (QSAR) studies and quantitative structure-property relationship (QSPR) studies. This study uses the M-polynomial approach, a newly discovered technique, to determine the topological indices of the medication fenofibrate. With the use of degree-based topological indices, we additionally construct a few novel degree based topological descriptors of fenofibrate structure using M-polynomial. When using M-polynomials in place of degree-based indices, the computation of the topological indices can be completed relatively quickly. The topological indices are also plotted. Using M-polynomial, we compute novel formulas for the modified first Zagreb index, modified second Zagreb index, first and second hyper Zagreb indices, SK index, S K 1 index, S K 2 index, modified Albertson index, redefined first Zagreb index, and degree-based topological indices.
{"title":"Novel Degree-Based Topological Descriptors of Fenofibrate Using M-Polynomial","authors":"Muhammad Kamran, Muhammad Farman, Seyma Ozon Yildirim, Sadik Delen, I. Naci Cangul, Maria Akram, M. Pandit","doi":"10.1155/2023/2037061","DOIUrl":"https://doi.org/10.1155/2023/2037061","url":null,"abstract":"Chemical graph theory is currently expanding the use of topological indices to numerically encode chemical structure. The prediction of the characteristics provided by the chemical structure of the molecule is a key feature of these topological indices. The concepts from graph theory are presented in a brief discussion of one of its many applications to chemistry, namely, the use of topological indices in quantitative structure-activity relationship (QSAR) studies and quantitative structure-property relationship (QSPR) studies. This study uses the M-polynomial approach, a newly discovered technique, to determine the topological indices of the medication fenofibrate. With the use of degree-based topological indices, we additionally construct a few novel degree based topological descriptors of fenofibrate structure using M-polynomial. When using M-polynomials in place of degree-based indices, the computation of the topological indices can be completed relatively quickly. The topological indices are also plotted. Using M-polynomial, we compute novel formulas for the modified first Zagreb index, modified second Zagreb index, first and second hyper Zagreb indices, SK index, \u0000 \u0000 S\u0000 \u0000 \u0000 K\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 \u0000 index, \u0000 \u0000 S\u0000 \u0000 \u0000 K\u0000 \u0000 \u0000 2\u0000 \u0000 \u0000 \u0000 index, modified Albertson index, redefined first Zagreb index, and degree-based topological indices.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"143 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76975595","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}
Let be a ring with involution having a nontrivial symmetric idempotent element . If is any appropriate multiplicative generalized reverse CE-derivation of with involution , then under some suitable restrictions on , is centrally-extended additive.
Muhammad Usman Ghani, M. Inc., Faisal Sultan, M. Cancan, A. Houwe
The connection of Zagreb polynomials and Zagreb indices to chemical graph theory is a bifurcation of mathematical chemistry, which has had a crucial influence on the development of chemical sciences. Nowadays, the study of topological indices has become a vast effective research area in chemical graph theory. In this article, we add up eight different Zagreb polynomials for the Silicate Network and Silicate Chain Network. From these Zagreb polynomials, we catch up on degree-based Zagreb indices. We also provide a graphical representation of the outcome that describes the dependence of topological indices on the given parameters of polynomial structure.
{"title":"Computation of Zagreb Polynomial and Indices for Silicate Network and Silicate Chain Network","authors":"Muhammad Usman Ghani, M. Inc., Faisal Sultan, M. Cancan, A. Houwe","doi":"10.1155/2023/9722878","DOIUrl":"https://doi.org/10.1155/2023/9722878","url":null,"abstract":"The connection of Zagreb polynomials and Zagreb indices to chemical graph theory is a bifurcation of mathematical chemistry, which has had a crucial influence on the development of chemical sciences. Nowadays, the study of topological indices has become a vast effective research area in chemical graph theory. In this article, we add up eight different Zagreb polynomials for the Silicate Network and Silicate Chain Network. From these Zagreb polynomials, we catch up on degree-based Zagreb indices. We also provide a graphical representation of the outcome that describes the dependence of topological indices on the given parameters of polynomial structure.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"14 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80480285","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 studies the asymptotic stability of global solutions of the three-dimensional nonisentropic compressible Navier–Stokes equations, where the initial data satisfy the “well-prepared” initial conditions, and the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively, based on the incompressible limit of global solutions. With the uniform estimates with respect to both the Mach number ε and time t , we prove the exponentially asymptotic stability for global solutions of both the compressible Navier–Stokes equations and its limiting incompressible equations.
{"title":"Asymptotic Stability of Global Solutions to Non-isentropic Navier–Stokes Equations","authors":"Qingliu Li, Dandan Ren, Xinfeng Liang","doi":"10.1155/2023/7374955","DOIUrl":"https://doi.org/10.1155/2023/7374955","url":null,"abstract":"This paper studies the asymptotic stability of global solutions of the three-dimensional nonisentropic compressible Navier–Stokes equations, where the initial data satisfy the “well-prepared” initial conditions, and the velocity field and temperature satisfy the Dirichlet boundary condition and convective boundary condition, respectively, based on the incompressible limit of global solutions. With the uniform estimates with respect to both the Mach number \u0000 \u0000 ε\u0000 \u0000 and time \u0000 \u0000 t\u0000 \u0000 , we prove the exponentially asymptotic stability for global solutions of both the compressible Navier–Stokes equations and its limiting incompressible equations.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88680167","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. G. Hassan, TranThi KieuVan, Shuangyin Liu, Harish Garg, Munawar Hassan, Shafqat Iqbal
The precise estimates about finance, atmospheric science, power sector, industries, agriculture, and other science help governments and institutions economically in making the relevant policies regarding import-export, demand, consumption, storage, and local industries. Due to the uncertainty and nondeterministic behavior of data series with respect to time, the foremost challenge is to develop and identify the practical method to handle the above stated complex issues. As an illustration, this study presented an analysis of a new fuzzy time-series (FTS) approach and comparison with traditional forecasting models for prediction of gram pulse production. Taking into consideration the theory of fuzzy sets, FTS, fuzzy rules, triangular membership functions, distance measures, and modified weighted average method, a robust and effective fuzzy rules-based methodology was developed for the prediction of time-series data regarding crop production and share prices. Conventional statistical forecasting methods such as Holt’s linear trend, Holt’s exponential trend, and Holt’s damped exponential trend models were also applied on time-series data for comparison. To identify the primacy of modeling and forecasting, the techniques of root mean squared error (RMSE) and mean absolute error (MAE) were used as a criterion. The numerical values of RMSE and MAE such as 106.51 and 74.8897 clearly demonstrated that the proposed fuzzy rules-based method is robust for forecasting of production and market share prices in the environment of uncertainty.
{"title":"A Novel First-Order Fuzzy Rules-Based Forecasting System Using Distance Measures Approach for Financial Market Forecasting","authors":"S. G. Hassan, TranThi KieuVan, Shuangyin Liu, Harish Garg, Munawar Hassan, Shafqat Iqbal","doi":"10.1155/2023/8027664","DOIUrl":"https://doi.org/10.1155/2023/8027664","url":null,"abstract":"The precise estimates about finance, atmospheric science, power sector, industries, agriculture, and other science help governments and institutions economically in making the relevant policies regarding import-export, demand, consumption, storage, and local industries. Due to the uncertainty and nondeterministic behavior of data series with respect to time, the foremost challenge is to develop and identify the practical method to handle the above stated complex issues. As an illustration, this study presented an analysis of a new fuzzy time-series (FTS) approach and comparison with traditional forecasting models for prediction of gram pulse production. Taking into consideration the theory of fuzzy sets, FTS, fuzzy rules, triangular membership functions, distance measures, and modified weighted average method, a robust and effective fuzzy rules-based methodology was developed for the prediction of time-series data regarding crop production and share prices. Conventional statistical forecasting methods such as Holt’s linear trend, Holt’s exponential trend, and Holt’s damped exponential trend models were also applied on time-series data for comparison. To identify the primacy of modeling and forecasting, the techniques of root mean squared error (RMSE) and mean absolute error (MAE) were used as a criterion. The numerical values of RMSE and MAE such as 106.51 and 74.8897 clearly demonstrated that the proposed fuzzy rules-based method is robust for forecasting of production and market share prices in the environment of uncertainty.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"203 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89014701","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}
Shahzaib Ashraf, Muhammad Ijaz, Muhammad Naeem, S. Abdullah, Lula Babole Alphonse-Roger
The main objective of the present study is to evaluate the multicriteria group decision-making problem in risk management for technological innovation projects (TIPs) under dual-probabilistic linguistic information. The suggested approach is based on an enhanced dual probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (DPL-VIKOR) technique to assess risk management in TIP employing probabilistic linguistic information. The conventional VIKOR approach is incapable of dealing with the complexity and difficulty of risk assessment in TIP. Therefore, we incorporated the information included in the dual probabilistic linguistic term set. In DPL-VIKOR, we investigated the relationship between the positive ideal solution (PIS) of the alternative and the negative ideal solution (NIS). To deal with the multicriteria group decision-making problem of risk assessment in TIP, we proposed the extended DPL-VIKOR approach rather than the traditional VIKOR method. We compared the findings to those of several decision-making problem techniques and examined the effectiveness and reliability, as well as advantages of the proposed approach. From the comparison and sensitivity analysis, we conclude that the proposed method is more reliable and effective for evaluating the best alternative in risk management problems for TIP.
{"title":"Extended DPL-VIKOR Method for Risk Assessment of Technological Innovation Using Dual Probabilistic Linguistic Information","authors":"Shahzaib Ashraf, Muhammad Ijaz, Muhammad Naeem, S. Abdullah, Lula Babole Alphonse-Roger","doi":"10.1155/2023/7570984","DOIUrl":"https://doi.org/10.1155/2023/7570984","url":null,"abstract":"The main objective of the present study is to evaluate the multicriteria group decision-making problem in risk management for technological innovation projects (TIPs) under dual-probabilistic linguistic information. The suggested approach is based on an enhanced dual probabilistic linguistic-vise kriterijumska optimizacija kompromisno resenje (DPL-VIKOR) technique to assess risk management in TIP employing probabilistic linguistic information. The conventional VIKOR approach is incapable of dealing with the complexity and difficulty of risk assessment in TIP. Therefore, we incorporated the information included in the dual probabilistic linguistic term set. In DPL-VIKOR, we investigated the relationship between the positive ideal solution (PIS) of the alternative and the negative ideal solution (NIS). To deal with the multicriteria group decision-making problem of risk assessment in TIP, we proposed the extended DPL-VIKOR approach rather than the traditional VIKOR method. We compared the findings to those of several decision-making problem techniques and examined the effectiveness and reliability, as well as advantages of the proposed approach. From the comparison and sensitivity analysis, we conclude that the proposed method is more reliable and effective for evaluating the best alternative in risk management problems for TIP.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90010346","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}
Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This additive category has a minimal exact structure and thus a notion of simple systems as those systems have no subsystems apart from zero and themselves. The so-called single-input systems are proven to be exactly the simple systems in the category of reachable systems over vector spaces. The category is also proven to be semisimple in objects because every reachable linear system is decomposed in a finite parallel gathering of simple systems. Hence, decomposition result is fulfilled for linear systems and feedback morphisms, but category of reachable linear systems is not abelian semisimple because it is not balanced and hence fails to be abelian. Finally, it is conjectured that the category of linear systems and feedback actions is in fact semiabelian; some threads to find the result and consequences are also given.
{"title":"Natural Factorization of Linear Control Systems through Parallel Gathering of Simple Systems","authors":"M. Carriegos","doi":"10.1155/2023/7963973","DOIUrl":"https://doi.org/10.1155/2023/7963973","url":null,"abstract":"Linear systems over vector spaces and feedback morphisms form an additive category taking into account the parallel gathering of linear systems. This additive category has a minimal exact structure and thus a notion of simple systems as those systems have no subsystems apart from zero and themselves. The so-called single-input systems are proven to be exactly the simple systems in the category of reachable systems over vector spaces. The category is also proven to be semisimple in objects because every reachable linear system is decomposed in a finite parallel gathering of simple systems. Hence, decomposition result is fulfilled for linear systems and feedback morphisms, but category of reachable linear systems is not abelian semisimple because it is not balanced and hence fails to be abelian. Finally, it is conjectured that the category of linear systems and feedback actions is in fact semiabelian; some threads to find the result and consequences are also given.","PeriodicalId":43667,"journal":{"name":"Muenster Journal of Mathematics","volume":"22 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81321661","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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