A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. By means of matrix method, numerical schemes are proved to be unconditionally stable and convergent with order . The validity of the proposed numerical scheme is verified by numerical experiments.
{"title":"An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models","authors":"Zeshan Qiu","doi":"10.1155/2024/6710903","DOIUrl":"https://doi.org/10.1155/2024/6710903","url":null,"abstract":"A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. By means of matrix method, numerical schemes are proved to be unconditionally stable and convergent with order <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 35.65 13.8595\" width=\"35.65pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.387,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,13.885,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,20.167,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,28.019,0)\"></path></g></svg><span></span><span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"38.506183799999995 -11.5914 16.394 13.8595\" width=\"16.394pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.556,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,45.264,-5.741)\"><use xlink:href=\"#g50-51\"></use></g><g transform=\"matrix(.013,0,0,-0.013,50.21,0)\"></path></g></svg>.</span></span> The validity of the proposed numerical scheme is verified by numerical experiments.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193021","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field and give upper and lower bounds. Also, we give some relations between this concept and commutativity degree, capability, and Schur multiplier.
{"title":"On the Exterior Degree of a Finite-Dimensional Lie Algebra","authors":"Afsaneh Shamsaki, Mohsen Parvizi, Ahmad Erfanian","doi":"10.1155/2024/5596170","DOIUrl":"https://doi.org/10.1155/2024/5596170","url":null,"abstract":"In this paper, we define the exterior degree for a finite-dimensional Lie algebra over the field <svg height=\"14.1623pt\" style=\"vertical-align:-5.47421pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.68809 11.2755 14.1623\" width=\"11.2755pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.097,3.132)\"></path></g></svg> and give upper and lower bounds. Also, we give some relations between this concept and commutativity degree, capability, and Schur multiplier.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141195082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris
In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.
{"title":"Study of Hybrid Problems under Exponential Type Fractional-Order Derivatives","authors":"Mohammed S. Abdo, Sahar Ahmed Idris, M. Daher Albalwi, Tomadir Ahmed Idris","doi":"10.1155/2024/2274198","DOIUrl":"https://doi.org/10.1155/2024/2274198","url":null,"abstract":"In this investigation, we develop a theory for the hybrid boundary value problem for fractional differential equations subject to three-point boundary conditions, including the antiperiodic hybrid boundary condition. On suggested problems, the third-order Caputo–Fabrizio derivative is the fractional operator applied. In this regard, the corresponding hybrid fractional integral equation is obtained by the Caputo–Fabrizio operator’s properties with the Green function’s aid. Then, we apply Dhage’s nonlinear alternative to the Schaefer type to prove the existence results. Finally, two examples are provided to confirm the validity of our main results.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Dong Guo, Huo Tang, Jun Zhang, Qingbing Xu, Zongtao Li
Suppose that is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional and for the class
{"title":"Hankel Determinants for the Logarithmic Coefficients of a Subclass of Close-to-Star Functions","authors":"Dong Guo, Huo Tang, Jun Zhang, Qingbing Xu, Zongtao Li","doi":"10.1155/2024/1315252","DOIUrl":"https://doi.org/10.1155/2024/1315252","url":null,"abstract":"Suppose that <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 36.9885 11.5564\" width=\"36.9885pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.659,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,21.515,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,26.013,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.253,0)\"></path></g></svg> is a class of close-to-star functions. In this paper, we investigated the estimate of Zalcman functional on the logarithmic coefficients and the third Hankel determinant for the class <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 36.9885 11.5564\" width=\"36.9885pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-20\"></use></g><g transform=\"matrix(.013,0,0,-0.013,9.659,0)\"><use xlink:href=\"#g198-21\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.515,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.013,0)\"><use xlink:href=\"#g113-50\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.253,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> with the determinant entry of logarithmic coefficients. Also, we obtained the sharp bounds of Zalcman functional <svg height=\"13.639pt\" style=\"vertical-align:-4.35067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.116 13.639\" width=\"34.116pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,5.031,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,9.463,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,11.619,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,16.59,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.088,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.441,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <svg height=\"13.639pt\" style=\"vertical-align:-4.35067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.116 13.639\" width=\"34.116pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-75\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,5.031,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,9.463,3.132)\"><use xlink:href=\"#g50-45\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,11.62,3.132)\"><use xlink:href=\"#g50-52\"></use></g><g transform=\"matrix(.013,0,0,-0.013,16.59,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.088,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,29.441,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> for the class <span><svg height=\"11.5564pt\" style=","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the conditions for the existence and uniqueness of solutions in a nonlinear system of sequential fractional differential equations using the Liouville–Caputo type with varying orders. This system is enriched by nonlocal coupled integral boundary conditions. The desired outcomes are attained by employing traditional fixed-point theorems. It is essential to emphasize that the fixed-point approach proves to be an effective method for establishing the existence of solutions in boundary value problems. Furthermore, we provide constructed examples to illustrate the obtained results.
{"title":"Existence Results for the System of Fractional-Order Sequential Integrodifferential Equations via Liouville–Caputo Sense","authors":"Muath Awadalla, Manigandan Murugesan, Subramanian Muthaiah, Jihan Alahmadi","doi":"10.1155/2024/6889622","DOIUrl":"https://doi.org/10.1155/2024/6889622","url":null,"abstract":"We investigate the conditions for the existence and uniqueness of solutions in a nonlinear system of sequential fractional differential equations using the Liouville–Caputo type with varying orders. This system is enriched by nonlocal coupled integral boundary conditions. The desired outcomes are attained by employing traditional fixed-point theorems. It is essential to emphasize that the fixed-point approach proves to be an effective method for establishing the existence of solutions in boundary value problems. Furthermore, we provide constructed examples to illustrate the obtained results.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Masoomeh Hezarjaribi Dastaki, Hamid Rasouli, Hasan Barzegar
In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free -act over a monoid is topologically dense injective if and only if is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.
{"title":"Characterizing Topologically Dense Injective Acts and Their Monoid Connections","authors":"Masoomeh Hezarjaribi Dastaki, Hamid Rasouli, Hasan Barzegar","doi":"10.1155/2024/2966461","DOIUrl":"https://doi.org/10.1155/2024/2966461","url":null,"abstract":"In this paper, we explore the concept of topologically dense injectivity of monoid acts. It is shown that topologically dense injective acts constitute a class strictly larger than the class of ordinary injective ones. We determine a number of acts satisfying topologically dense injectivity. Specifically, any strongly divisible as well as strongly torsion free <span><svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 6.25863 8.8423\" width=\"6.25863pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>act over a monoid <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 6.25863 8.8423\" width=\"6.25863pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-84\"></use></g></svg> is topologically dense injective if and only if <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 6.25863 8.8423\" width=\"6.25863pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-84\"></use></g></svg> is a left reversible monoid. Furthermore, we establish a counterpart of the Skornjakov criterion and also identify a class of acts satisfying the Baer criterion for topologically dense injectivity. Lastly, some homological classifications for monoids by means of this type of injectivity of monoid acts are also provided.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141172097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.
{"title":"Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems","authors":"Haiyan Li, Yuheng Guo, Min Wang","doi":"10.1155/2024/6167434","DOIUrl":"https://doi.org/10.1155/2024/6167434","url":null,"abstract":"Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Noura Alhouiti, Soumendu Roy, Santu Dey, Fatemah Mofarreh, Akram Ali, Yanlin Li
This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow. Here, we have delineated the conditions for conformal Ricci-Bourguignon soliton to be expanding, steady, or shrinking. We have studied certain curvature conditions on the spacetime that admit conformal Ricci-Bourguignon soliton. We have also discussed conformal Ricci-Bourguignon soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid, and radiation era.
{"title":"Geometric Classifications of Perfect Fluid Space-Time Admit Conformal Ricci-Bourguignon Solitons","authors":"Noura Alhouiti, Soumendu Roy, Santu Dey, Fatemah Mofarreh, Akram Ali, Yanlin Li","doi":"10.1155/2024/6674726","DOIUrl":"https://doi.org/10.1155/2024/6674726","url":null,"abstract":"This paper is dedicated to the study of the geometric composition of a perfect fluid space-time with a conformal Ricci-Bourguignon soliton, which is the extended version of the soliton to the Ricci-Bourguignon flow. Here, we have delineated the conditions for conformal Ricci-Bourguignon soliton to be expanding, steady, or shrinking. We have studied certain curvature conditions on the spacetime that admit conformal Ricci-Bourguignon soliton. We have also discussed conformal Ricci-Bourguignon soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid, and radiation era.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we introduce the concept of weakly semiprime ideals and weakly -systems in noncommutative rings. We establish the equivalence between an ideal being a weakly semiprime ideal and being a weakly -system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.
{"title":"A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings","authors":"Alaa Abouhalaka","doi":"10.1155/2024/9142090","DOIUrl":"https://doi.org/10.1155/2024/9142090","url":null,"abstract":"In this paper, we introduce the concept of weakly semiprime ideals and weakly <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.6501 6.1673\" width=\"6.6501pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg>-</span>systems in noncommutative rings. We establish the equivalence between an ideal <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.15071 8.68572\" width=\"8.15071pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g></svg> being a weakly semiprime ideal and <svg height=\"8.98583pt\" style=\"vertical-align:-0.3499308pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 29.8029 8.98583\" width=\"29.8029pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.057,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,21.593,0)\"><use xlink:href=\"#g113-81\"></use></g></svg> being a weakly <span><svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 6.6501 6.1673\" width=\"6.6501pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-111\"></use></g></svg>-</span>system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.
拓扑指数（TI）是表示分子网络整体化学结构的数字。在定量结构-活性关系（QSAR）和定量结构-性质关系（QSPR）研究中，拓扑指数有助于预测分子物质的生物活性。距离描述符与化学物质的各种化学和物理属性相关联，如熔点和凝固点、应变能、稳定性、温度、体积、密度和压力。文献中有多种基于距离的描述符，但在测量分子化合物的化学特性方面，基于连接的 TI 被认为比基于度的 TI 更有效。本研究主要针对最重要的化学结构类型，即菱形硅酸盐和菱形氧化物网络，计算基于连接的 TI。最后，我们根据计算结果对这些结构进行了比较。
{"title":"On the Comparative Analysis among Topological Indices for Rhombus Silicate and Oxide Structures","authors":"Aqsa Sattar, Muhammad Javaid, Mamo Abebe Ashebo","doi":"10.1155/2024/2773913","DOIUrl":"https://doi.org/10.1155/2024/2773913","url":null,"abstract":"A topological index (TI) is a numeric digit that signalizes the whole chemical structure of a molecular network. TIs are helpful in predicting the bioactivity of molecular substances in investigations of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR). TIs correlate various chemical and physical attributes of chemical substances such as melting and freezing point, strain energy, stability, temperature, volume, density, and pressure. There are several distance-based descriptors available in the literature, but connection-based TIs are considered more effective than degree-based TIs in measuring the chemical characteristics of molecular compounds. The present study focuses on computing the connection-based TIs for the most significant type of chemical structures, namely, rhombus silicate and rhombus oxide networks. At the end, we compare these structures on the basis of their computed result.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141149964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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