Ge You, Hao Guo, Abd Alwahed Dagestani, Ibrahim Alnafrah
To reduce the economic losses caused by debt evasion amongst lost-link borrowers (LBs) and improve the efficiency of finding information on LBs, this paper focuses on the cross-platform information collaborative search optimization problem for LBs. Given the limitations of platform/system heterogeneity, data type diversity, and the complexity of collaborative control in cross-platform information search for LBs, a collaborative search model for LBs’ information based on multi-agent technology is proposed. Additionally, a multi-agent Q-learning algorithm for the collaborative scheduling of multi-search subtasks is designed. We use the Q-learning algorithm based on function approximation to update the description model of the LBs. The multi-agent collaborative search problem is transformed into a reinforcement learning problem by defining search states, search actions, and reward functions. The results indicate that: (i) this model greatly improves the comprehensiveness and accuracy of the search for key information of LBs compared with traditional search engines; (ii) during searching for the information of LBs, the agent is more inclined to search on platforms and data types with larger environmental rewards, and the multi-agent Q-learning algorithm has a stronger ability to acquire information value than the transition probability matrix algorithm and the probability statistical algorithm for the same number of searches; (iii) the optimal search times of the multi-agent Q-learning algorithm are between 14 and 100. Users can flexibly set the number of searches within this range. It is significant for improving the efficiency of finding key information related to LBs.
{"title":"Collaborative Search Model for Lost-Link Borrowers Information Based on Multi-Agent Q-Learning","authors":"Ge You, Hao Guo, Abd Alwahed Dagestani, Ibrahim Alnafrah","doi":"10.3390/axioms12111033","DOIUrl":"https://doi.org/10.3390/axioms12111033","url":null,"abstract":"To reduce the economic losses caused by debt evasion amongst lost-link borrowers (LBs) and improve the efficiency of finding information on LBs, this paper focuses on the cross-platform information collaborative search optimization problem for LBs. Given the limitations of platform/system heterogeneity, data type diversity, and the complexity of collaborative control in cross-platform information search for LBs, a collaborative search model for LBs’ information based on multi-agent technology is proposed. Additionally, a multi-agent Q-learning algorithm for the collaborative scheduling of multi-search subtasks is designed. We use the Q-learning algorithm based on function approximation to update the description model of the LBs. The multi-agent collaborative search problem is transformed into a reinforcement learning problem by defining search states, search actions, and reward functions. The results indicate that: (i) this model greatly improves the comprehensiveness and accuracy of the search for key information of LBs compared with traditional search engines; (ii) during searching for the information of LBs, the agent is more inclined to search on platforms and data types with larger environmental rewards, and the multi-agent Q-learning algorithm has a stronger ability to acquire information value than the transition probability matrix algorithm and the probability statistical algorithm for the same number of searches; (iii) the optimal search times of the multi-agent Q-learning algorithm are between 14 and 100. Users can flexibly set the number of searches within this range. It is significant for improving the efficiency of finding key information related to LBs.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"1 14","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819391","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 relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain.
{"title":"Geometrically Non-Linear Plane Elasticity Problem in the Area of an Angular Boundary Cut-Out","authors":"Lyudmila Frishter","doi":"10.3390/axioms12111030","DOIUrl":"https://doi.org/10.3390/axioms12111030","url":null,"abstract":"A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress–strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"60 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135933536","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 article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust ε-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond–Weir-type robust dual problem. Moreover, we also investigate robust ε-quasi converse-like duality properties between them.
{"title":"On Mond–Weir-Type Robust Duality for a Class of Uncertain Fractional Optimization Problems","authors":"Xiaole Guo","doi":"10.3390/axioms12111029","DOIUrl":"https://doi.org/10.3390/axioms12111029","url":null,"abstract":"This article is focused on the investigation of Mond–Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond–Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust ε-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond–Weir-type robust dual problem. Moreover, we also investigate robust ε-quasi converse-like duality properties between them.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"17 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135973584","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}
We propose and study a class of discrete-time commensalism systems with additive Allee effects on the host species. First, the single species with additive Allee effects is analyzed for existence and stability, then the existence of fixed points of discrete systems is given, and the local stability of fixed points is given by characteristic root analysis. Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. Furthermore, this paper used the hybrid chaos method to control the chaos that occurs in the flip bifurcation of the system. Finally, the analysis conclusions were verified by numerical simulations. Compared with the continuous system, the similarities are that both species’ densities decrease with increasing Allee values under the weak Allee effect and that the host species hastens extinction under the strong Allee effect. Further, when the birth rate of the benefited species is low and the time is large enough, the benefited species will be locally asymptotically stabilized. Thus, our new finding is that both strong and weak Allee effects contribute to the stability of the benefited species under certain conditions.
{"title":"Dynamics Analysis of a Discrete-Time Commensalism Model with Additive Allee for the Host Species","authors":"Yanbo Chong, Ankur Jyoti Kashyap, Shangming Chen, Fengde Chen","doi":"10.3390/axioms12111031","DOIUrl":"https://doi.org/10.3390/axioms12111031","url":null,"abstract":"We propose and study a class of discrete-time commensalism systems with additive Allee effects on the host species. First, the single species with additive Allee effects is analyzed for existence and stability, then the existence of fixed points of discrete systems is given, and the local stability of fixed points is given by characteristic root analysis. Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. Furthermore, this paper used the hybrid chaos method to control the chaos that occurs in the flip bifurcation of the system. Finally, the analysis conclusions were verified by numerical simulations. Compared with the continuous system, the similarities are that both species’ densities decrease with increasing Allee values under the weak Allee effect and that the host species hastens extinction under the strong Allee effect. Further, when the birth rate of the benefited species is low and the time is large enough, the benefited species will be locally asymptotically stabilized. Thus, our new finding is that both strong and weak Allee effects contribute to the stability of the benefited species under certain conditions.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"3 7","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135974808","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}
Kadda Maazouz, Moussa Daif Allah Zaak, Rosana Rodríguez-López
This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional calculus and Krasnoselskii’s fixed-point theorem. Moreover, the Ulam–Hyers–Rassias stability of the nonlinear fractional pantograph equation is analyzed. To conclude this paper, we provide an example illustrating our findings and approach.
{"title":"Existence and Uniqueness Results for a Pantograph Boundary Value Problem Involving a Variable-Order Hadamard Fractional Derivative","authors":"Kadda Maazouz, Moussa Daif Allah Zaak, Rosana Rodríguez-López","doi":"10.3390/axioms12111028","DOIUrl":"https://doi.org/10.3390/axioms12111028","url":null,"abstract":"This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional calculus and Krasnoselskii’s fixed-point theorem. Moreover, the Ulam–Hyers–Rassias stability of the nonlinear fractional pantograph equation is analyzed. To conclude this paper, we provide an example illustrating our findings and approach.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"73 2-4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135271232","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 paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution.
{"title":"Excess Lifetime Extropy of Order Statistics","authors":"Mansour Shrahili, Mohamed Kayid","doi":"10.3390/axioms12111024","DOIUrl":"https://doi.org/10.3390/axioms12111024","url":null,"abstract":"This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"77 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135871241","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 study, we utilize the properties of the Sumudu transform (SuT) and combine it with the homotopy perturbation method to address the time fractional Navier-Stokes equation. We introduce a new technique called the homotopy perturbation Sumudu transform Strategy (HPSuTS), which combines the SuT with the homotopy perturbation method using He’s polynomials. This approach proves to be powerful and practical for solving various linear and nonlinear fractional partial differential equations (FPDEs) in scientific and engineering fields. We demonstrate the efficiency and simplicity of this method through examples, showcasing its ability to approximate solutions for FPDEs. Additionally, we compare the numerical results obtained using this technique for different values of alpha, showing that as the value moves from a fractional order to an integer order, the solution becomes increasingly similar to the exact solution. Furthermore, we provide the tabular representations of the solution for each example.
{"title":"An Approach for Approximating Analytical Solutions of the Navier-Stokes Time-Fractional Equation Using the Homotopy Perturbation Sumudu Transform’s Strategy","authors":"Sajad Iqbal, Francisco Martínez","doi":"10.3390/axioms12111025","DOIUrl":"https://doi.org/10.3390/axioms12111025","url":null,"abstract":"In this study, we utilize the properties of the Sumudu transform (SuT) and combine it with the homotopy perturbation method to address the time fractional Navier-Stokes equation. We introduce a new technique called the homotopy perturbation Sumudu transform Strategy (HPSuTS), which combines the SuT with the homotopy perturbation method using He’s polynomials. This approach proves to be powerful and practical for solving various linear and nonlinear fractional partial differential equations (FPDEs) in scientific and engineering fields. We demonstrate the efficiency and simplicity of this method through examples, showcasing its ability to approximate solutions for FPDEs. Additionally, we compare the numerical results obtained using this technique for different values of alpha, showing that as the value moves from a fractional order to an integer order, the solution becomes increasingly similar to the exact solution. Furthermore, we provide the tabular representations of the solution for each example.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135872459","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}
We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.
{"title":"Properties of Various Entropies of Gaussian Distribution and Comparison of Entropies of Fractional Processes","authors":"Anatoliy Malyarenko, Yuliya Mishura, Kostiantyn Ralchenko, Yevheniia Anastasiia Rudyk","doi":"10.3390/axioms12111026","DOIUrl":"https://doi.org/10.3390/axioms12111026","url":null,"abstract":"We consider five types of entropies for Gaussian distribution: Shannon, Rényi, generalized Rényi, Tsallis and Sharma–Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135869571","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}
Gabriela M. Rodrigues, Edwin M. M. Ortega, Gauss M. Cordeiro
Regression analysis can be appropriate to describe a nonlinear relationship between the response variable and the explanatory variables. This article describes the construction of a partially linear regression model with two systematic components based on the exponentiated odd log-logistic normal distribution. The parameters are estimated by the penalized maximum likelihood method. Simulations for some parameter settings and sample sizes empirically prove the accuracy of the estimators. The superiority of the proposed regression model over other regression models is shown by means of agronomic experimentation data. The predictive performance of the new model is compared with two machine learning techniques: decision trees and random forests. These methods achieved similar prediction performance, i.e., none stands out as a better predictor. In this sense, the objective of the research is to choose the best method. If the objective is only predictive, the decision tree can be used due to its simplicity. For inference purposes, the regression model is recommended, which can provide much more information regarding the relationship of the variables under study.
{"title":"New Partially Linear Regression and Machine Learning Models Applied to Agronomic Data","authors":"Gabriela M. Rodrigues, Edwin M. M. Ortega, Gauss M. Cordeiro","doi":"10.3390/axioms12111027","DOIUrl":"https://doi.org/10.3390/axioms12111027","url":null,"abstract":"Regression analysis can be appropriate to describe a nonlinear relationship between the response variable and the explanatory variables. This article describes the construction of a partially linear regression model with two systematic components based on the exponentiated odd log-logistic normal distribution. The parameters are estimated by the penalized maximum likelihood method. Simulations for some parameter settings and sample sizes empirically prove the accuracy of the estimators. The superiority of the proposed regression model over other regression models is shown by means of agronomic experimentation data. The predictive performance of the new model is compared with two machine learning techniques: decision trees and random forests. These methods achieved similar prediction performance, i.e., none stands out as a better predictor. In this sense, the objective of the research is to choose the best method. If the objective is only predictive, the decision tree can be used due to its simplicity. For inference purposes, the regression model is recommended, which can provide much more information regarding the relationship of the variables under study.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"92 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135809320","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}
Mikhail Kolev, Nikolay Netov, Iveta Nikolova, Irina Naskinova, Velika Kuneva, Marian Milev
The proposed paper is devoted to presenting and analyzing a kinetic model describing the development of autoimmune disorders. The proposed model is a nonlinear system of differential equations that considers the biological activity of the interacting populations. The main characteristics of autoimmune diseases are taken into account. Preliminaries to the research area are provided. The modeling problem is discretized and solved approximately. The numerical results illustrate typical outcomes of autoimmune diseases.
{"title":"On a Mathematical Model of a General Autoimmune Disease","authors":"Mikhail Kolev, Nikolay Netov, Iveta Nikolova, Irina Naskinova, Velika Kuneva, Marian Milev","doi":"10.3390/axioms12111021","DOIUrl":"https://doi.org/10.3390/axioms12111021","url":null,"abstract":"The proposed paper is devoted to presenting and analyzing a kinetic model describing the development of autoimmune disorders. The proposed model is a nonlinear system of differential equations that considers the biological activity of the interacting populations. The main characteristics of autoimmune diseases are taken into account. Preliminaries to the research area are provided. The modeling problem is discretized and solved approximately. The numerical results illustrate typical outcomes of autoimmune diseases.","PeriodicalId":53148,"journal":{"name":"Axioms","volume":"42 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136022547","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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