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 is related to the similarity of operators of class , and then we give a sufficient condition for the existence of nontrivial hyperinvariant subspaces. These subspaces are the closure of for some singular inner functions . As an application, we prove that every
{"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Suppose that is a Banach algebra and is its enveloping dual Banach algebra, we show that is approximately contractible (approximately amenable) if has the same property. Also, we study the relation between the pseudoamenability of and the pseudoamenability of the second dual and we also characterize approximate biflatness and approximate biprojectivity of
{"title":"Enveloping Dual Banach Algebras and Approximate Properties","authors":"N. Razi, A. Pourabbas","doi":"10.1155/2024/6300080","DOIUrl":"https://doi.org/10.1155/2024/6300080","url":null,"abstract":"Suppose that <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> is a Banach algebra and <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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,-0.013,7.895,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"></path></g></svg> is its enveloping dual Banach algebra, we show that <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> is approximately contractible (approximately amenable) if <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)\"><use xlink:href=\"#g113-66\"></use></g></svg> has the same property. Also, we study the relation between the pseudoamenability of <svg height=\"11.5564pt\" style=\"vertical-align:-2.26807pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 26.2232 11.5564\" width=\"26.2232pt\" 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=\"#g113-71\"></use></g><g transform=\"matrix(.013,0,0,-0.013,7.895,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.393,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.528,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and the pseudoamenability of the second dual <svg height=\"10.1524pt\" style=\"vertical-align:-0.04990005pt\" version=\"1.1\" viewbox=\"-0.0498162 -10.1025 20.9329 10.1524\" width=\"20.9329pt\" 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=\"#g113-66\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,9.135,-5.741)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,14.695,-5.741)\"><use xlink:href=\"#g50-43\"></use></g></svg> and we also characterize approximate biflatness and approximate biprojectivity of <svg height=\"11.5564p","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574954","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 influence of consumer psychological effects on customer needs has become a normal state of product sales models in the consumer goods supply chain field. The literature lacks systematic research on the mechanism through which consumer psychological effects affect customer needs. On the basis of analyzing and sorting out the literature and viewpoints, this paper establishes a mathematical model to investigate how manufacturers design and plan product supply strategies based on nonessential demand patterns under three different sales models. Finally, by solving the mathematical model, the optimal production volume, the optimal commodity price, and the maximum profit that can be obtained by the manufacturer are obtained, and the correctness of the model is verified via numerical calculation. The study results explain the relationships among commodity costs, demand, and commodity pricing, which are significant for the study of consumer psychology and can further provide a beneficial reference for manufacturers in various industries.
{"title":"Mathematical Modelling of B2C Consumer Product Supply Strategy Based on Nonessential Demand Pattern","authors":"Zhiyi Zhuo, Shuhong Chen, Hong Yan","doi":"10.1155/2024/7711868","DOIUrl":"https://doi.org/10.1155/2024/7711868","url":null,"abstract":"The influence of consumer psychological effects on customer needs has become a normal state of product sales models in the consumer goods supply chain field. The literature lacks systematic research on the mechanism through which consumer psychological effects affect customer needs. On the basis of analyzing and sorting out the literature and viewpoints, this paper establishes a mathematical model to investigate how manufacturers design and plan product supply strategies based on nonessential demand patterns under three different sales models. Finally, by solving the mathematical model, the optimal production volume, the optimal commodity price, and the maximum profit that can be obtained by the manufacturer are obtained, and the correctness of the model is verified via numerical calculation. The study results explain the relationships among commodity costs, demand, and commodity pricing, which are significant for the study of consumer psychology and can further provide a beneficial reference for manufacturers in various industries.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140574952","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. Hussain, Hassan Ali, M. Usman, F. Zaman, Choonkil Park
The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D OSK), the Benjamin-Bona-Mahony (BBM), and the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The Exp (-ϕξ)-expansion method is used for new hyperbolic, trigonometric, rational, exponential, and polynomial function-based solutions. These solutions of the pseudo-parabolic class of partial differential equations (PDEs) studied here are new and novel and have not been reported in the literature. These solutions depict the hydrodynamics of various soliton shapes that can be utilized to study the nature of traveling wave solutions of other nonlinear PDE’s.
{"title":"Some New Families of Exact Solitary Wave Solutions for Pseudo-Parabolic Type Nonlinear Models","authors":"A. Hussain, Hassan Ali, M. Usman, F. Zaman, Choonkil Park","doi":"10.1155/2024/5762147","DOIUrl":"https://doi.org/10.1155/2024/5762147","url":null,"abstract":"The objective of the current study is to provide a variety of families of soliton solutions to pseudo-parabolic equations that arise in nonsteady flows, hydrostatics, and seepage of fluid through fissured material. We investigate a class of such equations, including the one-dimensional Oskolkov (1D OSK), the Benjamin-Bona-Mahony (BBM), and the Benjamin-Bona-Mahony-Peregrine-Burgers (BBMPB) equation. The Exp (-ϕξ)-expansion method is used for new hyperbolic, trigonometric, rational, exponential, and polynomial function-based solutions. These solutions of the pseudo-parabolic class of partial differential equations (PDEs) studied here are new and novel and have not been reported in the literature. These solutions depict the hydrodynamics of various soliton shapes that can be utilized to study the nature of traveling wave solutions of other nonlinear PDE’s.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140360880","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 the classroom teaching of Chinese international education (CIE), teachers will face different types of problems. Teachers should focus on each teaching link, identify key and difficult points, teach students in line with their aptitude, and emphasize communication with students to improve the classroom teaching quality in CIE. The classroom teaching quality evaluation of CIE in higher-education institutions is regarded as multiple-attribute decision-making (MADM). Recently, the EDAS and CRITIC model was employed to put forward the MADM. The double-valued neutrosophic sets (DVNSs) are employed as the optimal decision tool for expressing the uncertain data during the classroom teaching quality evaluation of CIE in higher-education institutions. In this paper, EDAS is founded for MADM under DVNSs. Then, the double-valued neutrosophic number EDAS (DVNN-EDAS) model is constructed for MADM. Finally, a numerical example for classroom teaching quality evaluation of CIE is employed to verify the DVNN-EDAS model. The main decision contribution of this study is that (1) the novel MADM technique is established in line with EDAS and CRITIC under DVNSs. (2) The objective weights are constructed through CRITIC. (3) A numerical example for classroom teaching quality evaluation of CIE in higher-education institutions in line with the DVNN-EDAS is constructed.
{"title":"Research on Classroom Teaching Quality Evaluation of Chinese International Education in Higher-Education Institutions Based on EDAS Method and Euclidean Distance","authors":"Wei Li, Jia Song, Gangling Liu","doi":"10.1155/2024/5577601","DOIUrl":"https://doi.org/10.1155/2024/5577601","url":null,"abstract":"In the classroom teaching of Chinese international education (CIE), teachers will face different types of problems. Teachers should focus on each teaching link, identify key and difficult points, teach students in line with their aptitude, and emphasize communication with students to improve the classroom teaching quality in CIE. The classroom teaching quality evaluation of CIE in higher-education institutions is regarded as multiple-attribute decision-making (MADM). Recently, the EDAS and CRITIC model was employed to put forward the MADM. The double-valued neutrosophic sets (DVNSs) are employed as the optimal decision tool for expressing the uncertain data during the classroom teaching quality evaluation of CIE in higher-education institutions. In this paper, EDAS is founded for MADM under DVNSs. Then, the double-valued neutrosophic number EDAS (DVNN-EDAS) model is constructed for MADM. Finally, a numerical example for classroom teaching quality evaluation of CIE is employed to verify the DVNN-EDAS model. The main decision contribution of this study is that (1) the novel MADM technique is established in line with EDAS and CRITIC under DVNSs. (2) The objective weights are constructed through CRITIC. (3) A numerical example for classroom teaching quality evaluation of CIE in higher-education institutions in line with the DVNN-EDAS is constructed.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140311206","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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