Cuiping Zhou, Shaobo Li, Cankun Xie, Panliang Yuan, Xiangfu Long
The snow ablation optimizer (SAO) is a meta-heuristic technique used to seek the best solution for sophisticated problems. In response to the defects in the SAO algorithm, which has poor search efficiency and is prone to getting trapped in local optima, this article suggests a multi-strategy improved (MISAO) snow ablation optimizer. It is employed in the unmanned aerial vehicle (UAV) path planning issue. To begin with, the tent chaos and elite reverse learning initialization strategies are merged to extend the diversity of the population; secondly, a greedy selection method is deployed to retain superior alternative solutions for the upcoming iteration; then, the Harris hawk (HHO) strategy is introduced to enhance the exploitation capability, which prevents trapping in partial ideals; finally, the red-tailed hawk (RTH) is adopted to perform the global exploration, which, enhances global optimization capability. To comprehensively evaluate MISAO’s optimization capability, a battery of digital optimization investigations is executed using 23 test functions, and the results of the comparative analysis show that the suggested algorithm has high solving accuracy and convergence velocity. Finally, the effectiveness and feasibility of the optimization path of the MISAO algorithm are demonstrated in the UAV path planning project.
{"title":"MISAO: A Multi-Strategy Improved Snow Ablation Optimizer for Unmanned Aerial Vehicle Path Planning","authors":"Cuiping Zhou, Shaobo Li, Cankun Xie, Panliang Yuan, Xiangfu Long","doi":"10.3390/math12182870","DOIUrl":"https://doi.org/10.3390/math12182870","url":null,"abstract":"The snow ablation optimizer (SAO) is a meta-heuristic technique used to seek the best solution for sophisticated problems. In response to the defects in the SAO algorithm, which has poor search efficiency and is prone to getting trapped in local optima, this article suggests a multi-strategy improved (MISAO) snow ablation optimizer. It is employed in the unmanned aerial vehicle (UAV) path planning issue. To begin with, the tent chaos and elite reverse learning initialization strategies are merged to extend the diversity of the population; secondly, a greedy selection method is deployed to retain superior alternative solutions for the upcoming iteration; then, the Harris hawk (HHO) strategy is introduced to enhance the exploitation capability, which prevents trapping in partial ideals; finally, the red-tailed hawk (RTH) is adopted to perform the global exploration, which, enhances global optimization capability. To comprehensively evaluate MISAO’s optimization capability, a battery of digital optimization investigations is executed using 23 test functions, and the results of the comparative analysis show that the suggested algorithm has high solving accuracy and convergence velocity. Finally, the effectiveness and feasibility of the optimization path of the MISAO algorithm are demonstrated in the UAV path planning project.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249192","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.
{"title":"Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces","authors":"Jagjeet Jakhar, Shalu Sharma, Jyotsana Jakhar, Majeed A. Yousif, Pshtiwan Othman Mohammed, Alina Alb Lupas, Nejmeddine Chorfi","doi":"10.3390/math12182868","DOIUrl":"https://doi.org/10.3390/math12182868","url":null,"abstract":"This manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lígia Henriques-Rodrigues, Frederico Caeiro, M. Ivette Gomes
The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.
{"title":"A New Class of Reduced-Bias Generalized Hill Estimators","authors":"Lígia Henriques-Rodrigues, Frederico Caeiro, M. Ivette Gomes","doi":"10.3390/math12182866","DOIUrl":"https://doi.org/10.3390/math12182866","url":null,"abstract":"The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous impulses. Specifically, the existence is derived through the Nehari manifold method, and the proof of multiplicity is based on Bonanno and Bisci’s critical point theorem, which does not require proof that the functional satisfies the Palais–Smale condition. Finally, to illustrate the obtained results, an example is provided.
{"title":"Solvability of a Class of Fractional Advection–Dispersion Coupled Systems","authors":"Yan Qiao, Tao Lu","doi":"10.3390/math12182873","DOIUrl":"https://doi.org/10.3390/math12182873","url":null,"abstract":"The purpose of this study is to provide some criteria for the existence and multiplicity of solutions for a class of fractional advection–dispersion coupled systems with nonlinear Sturm–Liouville conditions and instantaneous and non-instantaneous impulses. Specifically, the existence is derived through the Nehari manifold method, and the proof of multiplicity is based on Bonanno and Bisci’s critical point theorem, which does not require proof that the functional satisfies the Palais–Smale condition. Finally, to illustrate the obtained results, an example is provided.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249191","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Interdependent criteria play a crucial role in complex decision-making across various domains. Traditional methods often struggle to evaluate and prioritize criteria with intricate dependencies. This paper introduces a generalized method integrating the analytic network process (ANP), the decision-making trial and evaluation laboratory (DEMATEL), and the consistent fuzzy analytic hierarchy process (CFAHP) in a fuzzy environment. The Drazin inverse technique is applied to derive a fuzzy total priority matrix, and we normalize the row sum to achieve the steady-state fuzzy priorities. A numerical example in the information systems (IS) industry demonstrates the approach’s real-world applications. The proposed method derives narrower fuzzy spreads compared to the past fuzzy analytic network process (FANP) approaches, minimizing objective uncertainty. Total priority interdependent maps provide insights into complex technical and usability criteria relationships. Comparative analysis highlights innovations, including non-iterative convergence of the total priority matrix and the ability to understand interdependencies between criteria. The integration of the FANP’s network structure with the fuzzy DEMATEL’s influence analysis transcends the capabilities of either method in isolation, marking a significant methodological advancement. By addressing challenges such as parameter selection and mathematical complexity, this research offers new perspectives for future research and application in multi-attribute decision-making (MADM).
{"title":"A Generalized Method for Deriving Steady-State Behavior of Consistent Fuzzy Priority for Interdependent Criteria","authors":"Jih-Jeng Huang, Chin-Yi Chen","doi":"10.3390/math12182863","DOIUrl":"https://doi.org/10.3390/math12182863","url":null,"abstract":"Interdependent criteria play a crucial role in complex decision-making across various domains. Traditional methods often struggle to evaluate and prioritize criteria with intricate dependencies. This paper introduces a generalized method integrating the analytic network process (ANP), the decision-making trial and evaluation laboratory (DEMATEL), and the consistent fuzzy analytic hierarchy process (CFAHP) in a fuzzy environment. The Drazin inverse technique is applied to derive a fuzzy total priority matrix, and we normalize the row sum to achieve the steady-state fuzzy priorities. A numerical example in the information systems (IS) industry demonstrates the approach’s real-world applications. The proposed method derives narrower fuzzy spreads compared to the past fuzzy analytic network process (FANP) approaches, minimizing objective uncertainty. Total priority interdependent maps provide insights into complex technical and usability criteria relationships. Comparative analysis highlights innovations, including non-iterative convergence of the total priority matrix and the ability to understand interdependencies between criteria. The integration of the FANP’s network structure with the fuzzy DEMATEL’s influence analysis transcends the capabilities of either method in isolation, marking a significant methodological advancement. By addressing challenges such as parameter selection and mathematical complexity, this research offers new perspectives for future research and application in multi-attribute decision-making (MADM).","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.
{"title":"Absolute Monotonicity of Normalized Tail of Power Series Expansion of Exponential Function","authors":"Feng Qi","doi":"10.3390/math12182859","DOIUrl":"https://doi.org/10.3390/math12182859","url":null,"abstract":"In this work, the author reviews the origination of normalized tails of the Maclaurin power series expansions of infinitely differentiable functions, presents that the ratio between two normalized tails of the Maclaurin power series expansion of the exponential function is decreasing on the positive axis, and proves that the normalized tail of the Maclaurin power series expansion of the exponential function is absolutely monotonic on the whole real axis.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249148","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Haotian Yang, Pujie Jing, Zihan Wu, Lu Liu, Pengyan Liu
The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.
{"title":"SEAIS: Secure and Efficient Agricultural Image Storage Combining Blockchain and Satellite Networks","authors":"Haotian Yang, Pujie Jing, Zihan Wu, Lu Liu, Pengyan Liu","doi":"10.3390/math12182861","DOIUrl":"https://doi.org/10.3390/math12182861","url":null,"abstract":"The image integrity of real-time monitoring is crucial for monitoring crop growth, helping farmers and researchers improve production efficiency and crop yields. Unfortunately, existing schemes just focus on ground equipment and drone imaging, neglecting satellite networks in remote or extreme environments. Given that satellite internet features wide area coverage, we propose SEAIS, a secure and efficient agricultural image storage scheme combining blockchain and satellite networks. SEAIS presents the mathematical model of image processing and transmission based on satellite networks. Moreover, to ensure the integrity and authenticity of image data during pre-processing such as denoising and enhancement, SEAIS includes a secure agricultural image storage and verification method based on blockchain, homomorphic encryption, and zero-knowledge proof. Specifically, images are stored via IPFS, with hash values and metadata recorded on the blockchain, ensuring immutability and transparency. The simulation results show that SEAIS exhibits more stable and efficient processing times in extreme environments. Also, it maintains low on-chain storage overhead, enhancing scalability.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step changes observed in banded-TRL approaches when multiple Line standards are used. By introducing a bespoke weighting function that assigns phase-dependent weights to each Line standard, smoother transitions and improved S-parameter measurements can be achieved. Experimental validation using measurements of both 3.5 mm and Type-N devices demonstrates the effectiveness of the weighted-TRL method in eliminating discontinuities and calibration artifacts across a wide range of frequencies. The results reveal the improved calibration of S-parameters this approach can yield compared to traditional TRL calibration methods. The developed weighted-TRL calibration technique offers a significant advancement in metrology-grade measurements, enabling more precise characterization of high-frequency devices across broad frequency bands. By mitigating a key limitation of the TRL calibration, this method provides a valuable tool for enhancing the accuracy and reliability of VNA measurements for precision metrology applications.
本文介绍了一种应用于直通反射线路（TRL）校准技术的加权算法，以提高宽频带矢量网络分析仪（VNA）测量的准确性和可靠性。该方法解决了传统 TRL 校准的固有局限性，特别是在使用多个线路标准时，在带状 TRL 方法中观察到的阶跃变化。通过引入一个定制的加权函数，为每个线路标准分配与相位相关的权重，可以实现更平滑的转换和更好的 S 参数测量。通过对 3.5 毫米和 N 型器件的测量进行实验验证，证明了加权-TRL 方法在消除各种频率范围内的不连续性和校准伪影方面的有效性。结果表明，与传统的 TRL 校准方法相比，这种方法可以改进 S 参数的校准。所开发的加权-TRL 校准技术在计量级测量方面取得了重大进展，可在宽频带范围内对高频器件进行更精确的表征。通过缓解 TRL 校准的一个关键限制，该方法为提高精密计量应用中 VNA 测量的准确性和可靠性提供了宝贵的工具。
{"title":"Application of Weighting Algorithm for Enhanced Broadband Vector Network Analyzer Measurements","authors":"Sang-hee Shin, James Skinner","doi":"10.3390/math12182871","DOIUrl":"https://doi.org/10.3390/math12182871","url":null,"abstract":"A weighting algorithm for application in the Thru-Reflect-Line (TRL) calibration technique is presented to enhance the accuracy and reliability of vector network analyzer (VNA) measurements over broad frequency bands. The method addresses the inherent limitations of the traditional TRL calibration, particularly the step changes observed in banded-TRL approaches when multiple Line standards are used. By introducing a bespoke weighting function that assigns phase-dependent weights to each Line standard, smoother transitions and improved S-parameter measurements can be achieved. Experimental validation using measurements of both 3.5 mm and Type-N devices demonstrates the effectiveness of the weighted-TRL method in eliminating discontinuities and calibration artifacts across a wide range of frequencies. The results reveal the improved calibration of S-parameters this approach can yield compared to traditional TRL calibration methods. The developed weighted-TRL calibration technique offers a significant advancement in metrology-grade measurements, enabling more precise characterization of high-frequency devices across broad frequency bands. By mitigating a key limitation of the TRL calibration, this method provides a valuable tool for enhancing the accuracy and reliability of VNA measurements for precision metrology applications.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pshtiwan Othman Mohammed, Ravi P. Agarwal, Majeed A. Yousif, Eman Al-Sarairah, Alina Alb Lupas, Mohamed Abdelwahed
This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.
{"title":"Theoretical Results on Positive Solutions in Delta Riemann–Liouville Setting","authors":"Pshtiwan Othman Mohammed, Ravi P. Agarwal, Majeed A. Yousif, Eman Al-Sarairah, Alina Alb Lupas, Mohamed Abdelwahed","doi":"10.3390/math12182864","DOIUrl":"https://doi.org/10.3390/math12182864","url":null,"abstract":"This article primarily focuses on examining the existence and uniqueness analysis of boundary fractional difference equations in a class of Riemann–Liouville operators. To this end, we firstly recall the general solution of the homogeneous fractional operator problem. Then, the Green function to the corresponding fractional boundary value problems will be reconstructed, and homogeneous boundary conditions are used to find the unknown constants. Next, the existence of solutions will be studied depending on the fixed-point theorems on the constructed Green’s function. The uniqueness of the problem is also derived via Lipschitz constant conditions.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous elements x,y∈R, then x2∈P or yn∈P, for some positive integer n. Many examples and properties of Gwsq-primary ideals are given. Among several results, we compare Gwsq-primary ideals and other classical graded ideals such as graded strongly quasi primary ideals, graded weakly primary ideals and graded weakly 2-prime ideals etc.
本文将介绍并研究有级弱强准原初理想的概念。如果对于一些同质元素 x,y∈R 而言，当 0≠xy∈P 时，那么对于一些正整数 n 而言，x2∈P 或 yn∈P 时，我们称 R 的一个适当的有级理想 P 为有级弱强准原初（简称为 Gwsq-原初）理想。在几个结果中，我们比较了 Gwsq-原初理想和其他经典有级理想，如有级强准原初理想、有级弱原初理想和有级弱 2-prime 理想等。
{"title":"Graded Weakly Strongly Quasi-Primary Ideals over Commutative Graded Rings","authors":"Azzh Saad Alshehry, Rashid Abu-Dawwas, Basel Hawary","doi":"10.3390/math12182857","DOIUrl":"https://doi.org/10.3390/math12182857","url":null,"abstract":"In this article, we introduce and examine the concept of graded weakly strongly quasi primary ideals. A proper graded ideal P of R is said to be a graded weakly strongly quasi primary (shortly, Gwsq-primary) ideal if whenever 0≠xy∈P, for some homogeneous elements x,y∈R, then x2∈P or yn∈P, for some positive integer n. Many examples and properties of Gwsq-primary ideals are given. Among several results, we compare Gwsq-primary ideals and other classical graded ideals such as graded strongly quasi primary ideals, graded weakly primary ideals and graded weakly 2-prime ideals etc.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":null,"pages":null},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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