In this paper, we delve into the intricate connections between the numerical ranges of specific operators and their transformations using a convex function. Furthermore, we derive inequalities related to the numerical radius. These relationships and inequalities are built upon well-established principles of convexity, which are applicable to non-negative real numbers and operator inequalities. To be more precise, our investigation yields the following outcome: consider the operators <svg height="8.68572pt" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 9.2729 8.68572" width="9.2729pt" 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> and <span><svg height="8.68572pt" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 7.94191 8.68572" width="7.94191pt" 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> both of which are positive and have spectra within the interval <span><svg height="11.439pt" style="vertical-align:-2.15067pt" version="1.1" viewbox="-0.0498162 -9.28833 17.706 11.439" width="17.706pt" 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,-0.013,4.485,0)"></path></g><g transform="matrix(.013,0,0,-0.013,14.742,0)"></path></g></svg><span></span><span><svg height="11.439pt" style="vertical-align:-2.15067pt" version="1.1" viewbox="19.835183800000003 -9.28833 17.521 11.439" width="17.521pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,19.885,0)"></path></g><g transform="matrix(.013,0,0,-0.013,32.693,0)"></path></g></svg>,</span></span> denoted as <svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 25.6752 11.5564" width="25.6752pt" 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,-0.013,7.347,0)"></path></g><g transform="matrix(.013,0,0,-0.013,11.845,0)"><use xlink:href="#g113-66"></use></g><g transform="matrix(.013,0,0,-0.013,20.98,0)"></path></g></svg> and <span><svg height="11.5564pt" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 24.3442 11.5564" width="24.3442pt" 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="#g113-240"></use></g><g transform="matrix(.013,0,0,-0.013,7.347,0)"><use xlink:href="#g113-41"></use></g><g transform="matrix(.013,0,0,-0.013,11.845,0)"><use xlink:href="#g113-67"></use></g><g transform="matrix(.013,0,0,-0.013,19.658,0)"><use xlink:href="#g113-42"></use></g></svg>.</span> In addition, let us introduce two monotone contin
{"title":"Certain Inequalities Related to the Generalized Numeric Range and Numeric Radius That Are Associated with Convex Functions","authors":"Feras Bani-Ahmad, M. H. M. Rashid","doi":"10.1155/2024/4087305","DOIUrl":"https://doi.org/10.1155/2024/4087305","url":null,"abstract":"In this paper, we delve into the intricate connections between the numerical ranges of specific operators and their transformations using a convex function. Furthermore, we derive inequalities related to the numerical radius. These relationships and inequalities are built upon well-established principles of convexity, which are applicable to non-negative real numbers and operator inequalities. To be more precise, our investigation yields the following outcome: consider the operators <svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 9.2729 8.68572\" width=\"9.2729pt\" 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> and <span><svg height=\"8.68572pt\" style=\"vertical-align:-0.0498209pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 7.94191 8.68572\" width=\"7.94191pt\" 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> both of which are positive and have spectra within the interval <span><svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 17.706 11.439\" width=\"17.706pt\" 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,-0.013,4.485,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,14.742,0)\"></path></g></svg><span></span><span><svg height=\"11.439pt\" style=\"vertical-align:-2.15067pt\" version=\"1.1\" viewbox=\"19.835183800000003 -9.28833 17.521 11.439\" width=\"17.521pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,19.885,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.693,0)\"></path></g></svg>,</span></span> denoted as <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 25.6752 11.5564\" width=\"25.6752pt\" 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,-0.013,7.347,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.845,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,20.98,0)\"></path></g></svg> and <span><svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 24.3442 11.5564\" width=\"24.3442pt\" 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=\"#g113-240\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.347,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,11.845,0)\"><use xlink:href=\"#g113-67\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.658,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span> In addition, let us introduce two monotone contin","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"60 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140839548","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}
Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou
The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.
{"title":"The Weak (Gorenstein) Global Dimension of Coherent Rings with Finite Small Finitistic Projective Dimension","authors":"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou","doi":"10.1155/2024/4896819","DOIUrl":"https://doi.org/10.1155/2024/4896819","url":null,"abstract":"The small finitistic dimension of a ring is determined as the supremum projective dimensions among modules with finite projective resolutions. This paper seeks to establish that, for a coherent ring <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.28119 8.8423\" width=\"8.28119pt\" 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> with a finite weak (resp. Gorenstein) global dimension, the small finitistic dimension of <svg height=\"8.8423pt\" style=\"vertical-align:-0.2064009pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 8.28119 8.8423\" width=\"8.28119pt\" 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=\"#g113-83\"></use></g></svg> is equal to its weak (resp. Gorenstein) global dimension. Consequently, we conclude some new characterizations for (Gorenstein) von Neumann and semihereditary rings.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"39 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613029","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}
Abdelkader Segres, Ahmed Bachir, Sid Ahmed Ould Ahmed Mahmoud
In the present paper, we first show that the existence of the solutions of the operator equation <span><svg height="10.3089pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -10.1025 40.024 10.3089" width="40.024pt" 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,-0.0091,6.136,-5.741)"></path></g><g transform="matrix(.013,0,0,-0.013,12.215,0)"></path></g><g transform="matrix(.013,0,0,-0.013,20.678,0)"></path></g><g transform="matrix(.013,0,0,-0.013,32.393,0)"></path></g></svg><span></span><svg height="10.3089pt" style="vertical-align:-0.2063999pt" version="1.1" viewbox="43.6061838 -10.1025 10.133 10.3089" width="10.133pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,43.656,0)"></path></g></svg></span> is related to the similarity of operators of class <span><svg height="11.927pt" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 15.8622 11.927" width="15.8622pt" 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="#g113-68"></use></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><use xlink:href="#g50-50"></use></g><g transform="matrix(.0091,0,0,-0.0091,13.051,3.132)"></path></g></svg>,</span> and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of <svg height="12.7178pt" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 42.6255 12.7178" width="42.6255pt" 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,-0.013,4.823,0)"></path></g><g transform="matrix(.013,0,0,-0.013,10.413,0)"></path></g><g transform="matrix(.013,0,0,-0.013,17.59,0)"></path></g><g transform="matrix(.013,0,0,-0.013,25.157,0)"></path></g><g transform="matrix(.013,0,0,-0.013,29.655,0)"></path></g><g transform="matrix(.013,0,0,-0.013,37.94,0)"></path></g></svg> for some singular inner functions <span><svg height="9.39034pt" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.69399 9.39034" width="7.69399pt" 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="#g113-253"></use></g></svg>.</span> As an application, we prove that every <span><svg height="11.927pt" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 18.1457 11.927" width="18.1457pt" 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="#g113-68"></use></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><use xlink:href="#g50-50"></use></g><g transform="matrix(.0091,0
{"title":"Similarity of : Operators and the Hyperinvariant Subspace Problem","authors":"Abdelkader Segres, Ahmed Bachir, Sid Ahmed Ould Ahmed Mahmoud","doi":"10.1155/2024/9943902","DOIUrl":"https://doi.org/10.1155/2024/9943902","url":null,"abstract":"In the present paper, we first show that the existence of the solutions of the operator equation <span><svg height=\"10.3089pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.1025 40.024 10.3089\" width=\"40.024pt\" 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,-0.0091,6.136,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.215,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.678,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,32.393,0)\"></path></g></svg><span></span><svg height=\"10.3089pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"43.6061838 -10.1025 10.133 10.3089\" width=\"10.133pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,43.656,0)\"></path></g></svg></span> is related to the similarity of operators of class <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 15.8622 11.927\" width=\"15.8622pt\" 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=\"#g113-68\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.619,3.132)\"><use xlink:href=\"#g50-50\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,13.051,3.132)\"></path></g></svg>,</span> and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 42.6255 12.7178\" width=\"42.6255pt\" 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,-0.013,4.823,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,10.413,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,17.59,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,25.157,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.655,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,37.94,0)\"></path></g></svg> for some singular inner functions <span><svg height=\"9.39034pt\" style=\"vertical-align:-3.42943pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.69399 9.39034\" width=\"7.69399pt\" 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=\"#g113-253\"></use></g></svg>.</span> As an application, we prove that every <span><svg height=\"11.927pt\" style=\"vertical-align:-3.291101pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.6359 18.1457 11.927\" width=\"18.1457pt\" 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=\"#g113-68\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.619,3.132)\"><use xlink:href=\"#g50-50\"></use></g><g transform=\"matrix(.0091,0","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613030","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 study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers. With the help of the properties obtained in this study, we defined a number sequence containing the new type of Leonardo numbers created by choosing the coefficients from the bicomplex numbers. Furthermore, we gave the relationship of this newly defined sequence with the Fibonacci sequence. We also provided some important identities in the literature provided by the elements of this sequence described in this paper.
{"title":"On the Leonardo Sequence via Pascal-Type Triangles","authors":"Serpil Halıcı, Sule Curuk","doi":"10.1155/2024/9352986","DOIUrl":"https://doi.org/10.1155/2024/9352986","url":null,"abstract":"In this study, we discussed the Leonardo number sequence, which has been studied recently and caught more attention. We used Pascal and Hosoya-like triangles to make it easier to examine the basic properties of these numbers. With the help of the properties obtained in this study, we defined a number sequence containing the new type of Leonardo numbers created by choosing the coefficients from the bicomplex numbers. Furthermore, we gave the relationship of this newly defined sequence with the Fibonacci sequence. We also provided some important identities in the literature provided by the elements of this sequence described in this paper.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"63 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140590587","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}
The world economy is affected by fluctuations in the price of crude oil, making precise and effective forecasting of crude oil prices essential. In this study, we propose a combined forecasting scheme, which combines a quadratic decomposition and optimized support vector regression (SVR). In the decomposition part, the original crude oil price series are first decomposed using empirical modal decomposition (CEEMDAN), and then the residuals of the first decomposition (RES) are decomposed using variational modal decomposition (VMD). Additionally, this work proposes to optimize the support vector regression model (SVR) by the seagull optimization algorithm (SOA). Ultimately, the empirical investigation created the feature-variable system and predicted the filtered features. By computing evaluation indices like MAE, MSE, , and MAPE and validating using Brent and WTI crude oil spot, the prediction errors of the CEEMDAN -RES.-VMD -SOA-SVR combination prediction model presented in this paper are assessed and compared with those of the other twelve comparative models. The empirical evidence shows that the combination model being proposed in this paper outperforms the other related comparative models and improves the accuracy of the crude oil price forecasting model.
{"title":"A Crude Oil Spot Price Forecasting Method Incorporating Quadratic Decomposition and Residual Forecasting","authors":"Yonghui Duan, Ziru Ming, Xiang Wang","doi":"10.1155/2024/6652218","DOIUrl":"https://doi.org/10.1155/2024/6652218","url":null,"abstract":"The world economy is affected by fluctuations in the price of crude oil, making precise and effective forecasting of crude oil prices essential. In this study, we propose a combined forecasting scheme, which combines a quadratic decomposition and optimized support vector regression (SVR). In the decomposition part, the original crude oil price series are first decomposed using empirical modal decomposition (CEEMDAN), and then the residuals of the first decomposition (RES) are decomposed using variational modal decomposition (VMD). Additionally, this work proposes to optimize the support vector regression model (SVR) by the seagull optimization algorithm (SOA). Ultimately, the empirical investigation created the feature-variable system and predicted the filtered features. By computing evaluation indices like MAE, MSE, <span><svg height=\"11.7978pt\" style=\"vertical-align:-0.2063999pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 13.2276 11.7978\" width=\"13.2276pt\" 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,-0.0091,8.151,-5.741)\"></path></g></svg>,</span> and MAPE and validating using Brent and WTI crude oil spot, the prediction errors of the CEEMDAN -RES.-VMD -SOA-SVR combination prediction model presented in this paper are assessed and compared with those of the other twelve comparative models. The empirical evidence shows that the combination model being proposed in this paper outperforms the other related comparative models and improves the accuracy of the crude oil price forecasting model.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"70 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574942","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}
The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one-kind mean values related to Dedekind sums and give some interesting identities for them.
{"title":"Some New Identities Related to Dedekind Sums Modulo a Prime","authors":"Jiayuan Hu","doi":"10.1155/2024/8844153","DOIUrl":"https://doi.org/10.1155/2024/8844153","url":null,"abstract":"The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one-kind mean values related to Dedekind sums and give some interesting identities for them.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"70 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574951","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}
The Hyers–Ulam stability of multi-coefficients Pexider additive functional inequalities in Banach spaces is investigated. In order to do this, the fixed point method and the direct method are used.
{"title":"The Stability of Multi-Coefficients Pexider Additive Functional Inequalities in Banach Spaces","authors":"Yang Liu, Gang Lyu, Yuanfeng Jin, Jiangwei Yang","doi":"10.1155/2024/6931488","DOIUrl":"https://doi.org/10.1155/2024/6931488","url":null,"abstract":"The Hyers–Ulam stability of multi-coefficients Pexider additive functional inequalities in Banach spaces is investigated. In order to do this, the fixed point method and the direct method are used.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"26 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602868","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}
M. Mukherjee, D. Pal, S. K. Mahato, Ebenezer Bonyah, Ali Akbar Shaikh
This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.
{"title":"Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay","authors":"M. Mukherjee, D. Pal, S. K. Mahato, Ebenezer Bonyah, Ali Akbar Shaikh","doi":"10.1155/2024/2708546","DOIUrl":"https://doi.org/10.1155/2024/2708546","url":null,"abstract":"This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"69 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574877","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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