In this paper, we introduce F-b-metric space (function weighted b-metric space) as a generalization of the F-metric space (the function weighted metric space). We also propose and prove some topological properties of the F-b-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.
{"title":"Some results in function weighted b-metric spaces","authors":"B. Nurwahyu, N. Aris, Firman","doi":"10.3934/math.2023417","DOIUrl":"https://doi.org/10.3934/math.2023417","url":null,"abstract":"<abstract> <p>In this paper, we introduce <italic>F</italic>-<italic>b</italic>-metric space (function weighted <italic>b</italic>-metric space) as a generalization of the <italic>F</italic>-metric space (the function weighted metric space). We also propose and prove some topological properties of the <italic>F</italic>-<italic>b</italic>-metric space, the theorems of fixed point and the common fixed point for the generalized expansive mappings, and an application on dynamic programing.</p> </abstract>","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183280","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 investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.
This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document}$begin{equation*}left{begin{aligned}&u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*}$ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lamé equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.
{"title":"Orbital stability of periodic standing waves of the coupled Klein-Gordon-Zakharov equations","authors":"Qiuying Li, Xiaoxiao Zheng, Zhenguo Wang","doi":"10.3934/math.2023430","DOIUrl":"https://doi.org/10.3934/math.2023430","url":null,"abstract":"This paper investigates the orbital stability of periodic standing waves for the following coupled Klein-Gordon-Zakharov equations begin{document} $ begin{equation*} left{ begin{aligned} &u_{tt}-u_{xx}+u+alpha uv+beta|u|^{2}u = 0, &v_{tt}-v_{xx} = (|u|^{2})_{xx}, end{aligned} right. end{equation*} $ end{document} where $alpha>0$ and $beta$ are two real numbers and $alpha>beta$. Under some suitable conditions, we show the existence of a smooth curve positive standing wave solutions of dnoidal type with a fixed fundamental period L for the above equations. Further, we obtain the stability of the dnoidal waves for the coupled Klein-Gordon-Zakharov equations by applying the abstract stability theory and combining the detailed spectral analysis given by using Lam'{e} equation and Floquet theory. When period $Lrightarrowinfty$, dnoidal type will turn into sech-type in the sense of limit. In such case, we can obtain stability of sech-type standing waves. In particular, $beta = 0$ is advisable, we still can show the the stability of the dnoidal type and sech-type standing waves for the classical Klein-Gordon-Zakharov equations.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70183834","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 deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.
{"title":"Stability analysis and convergence rate of a two-step predictor-corrector approach for shallow water equations with source terms","authors":"R. T. Alqahtani, J. Ntonga, E. Ngondiep","doi":"10.3934/math.2023465","DOIUrl":"https://doi.org/10.3934/math.2023465","url":null,"abstract":"This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the $ L^{2} $-norm. A wide set of numerical examples confirm the theoretical results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186038","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 vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.
如果$ G $中的每个顶点在$ S $中至少有两个相邻顶点，则图$ G $的顶点集$ S $称为双共支配集。$ G $的双总支配数$ gamma_{times 2, t}(G) $是$ G $中所有双总支配集的最小基数。设$ G square H $表示图$ G $和$ H $的笛卡尔积。本文讨论了路径笛卡尔积的双总支配数。我们确定了$ i = 2, 3 $的$ gamma_{times 2, t}(P_isquare P_n) $值，并给出了$ i geq 4 $的$ gamma_{times 2, t}(P_isquare P_n) $的下界和上界。
{"title":"Double total domination number of Cartesian product of paths","authors":"Linyu Li, Jun Yue, Xia Zhang","doi":"10.3934/math.2023479","DOIUrl":"https://doi.org/10.3934/math.2023479","url":null,"abstract":"A vertex set $ S $ of a graph $ G $ is called a double total dominating set if every vertex in $ G $ has at least two adjacent vertices in $ S $. The double total domination number $ gamma_{times 2, t}(G) $ of $ G $ is the minimum cardinality over all the double total dominating sets in $ G $. Let $ G square H $ denote the Cartesian product of graphs $ G $ and $ H $. In this paper, the double total domination number of Cartesian product of paths is discussed. We determine the values of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i = 2, 3 $, and give lower and upper bounds of $ gamma_{times 2, t}(P_isquare P_n) $ for $ i geq 4 $.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70186508","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 quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.
{"title":"Cubic B-Spline method for the solution of the quadratic Riccati differential equation","authors":"O. Ala'yed, B. Batiha, Diala Alghazo, F. Ghanim","doi":"10.3934/math.2023483","DOIUrl":"https://doi.org/10.3934/math.2023483","url":null,"abstract":"The quadratic Riccati equations are first-order nonlinear differential equations with numerous applications in various applied science and engineering areas. Therefore, several numerical approaches have been derived to find their numerical solutions. This paper provided the approximate solution of the quadratic Riccati equation via the cubic b-spline method. The convergence analysis of the method is discussed. The efficiency and applicability of the proposed approach are verified through three numerical test problems. The obtained results are in good settlement with the exact solutions. Moreover, the numerical results indicate that the proposed cubic b-spline method attains a superior performance compared with some existing methods.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70187140","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}
S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara
Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding "patient zero" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.
{"title":"A space-time model for analyzing contagious people based on geolocation data using inverse graphs","authors":"S. Merino, Juergen Doellner, Javier Martínez, F. Guzmán, R. Guzmán, Juan De Dios Lara","doi":"10.3934/math.2023516","DOIUrl":"https://doi.org/10.3934/math.2023516","url":null,"abstract":"Mobile devices provide us with an important source of data that capture spatial movements of individuals and allow us to derive general mobility patterns for a population over time. In this article, we present a mathematical foundation that allows us to harmonize mobile geolocation data using differential geometry and graph theory to identify spatial behavior patterns. In particular, we focus on models programmed using Computer Algebra Systems and based on a space-time model that allows for describing the patterns of contagion through spatial movement patterns. In addition, we show how the approach can be used to develop algorithms for finding \"patient zero\" or, respectively, for identifying the selection of candidates that are most likely to be contagious. The approach can be applied by information systems to evaluate data on complex population movements, such as those captured by mobile geolocation data, in a way that analytically identifies, e.g., critical spatial areas, critical temporal segments, and potentially vulnerable individuals with respect to contact events.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188826","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}
Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.
{"title":"Discrete Erlang-2 distribution and its application to leukemia and COVID-19","authors":"Mohamed Ahmed Mosilhy","doi":"10.3934/math.2023520","DOIUrl":"https://doi.org/10.3934/math.2023520","url":null,"abstract":"Via the survival discretization method, this research revealed a novel discrete one-parameter distribution known as the discrete Erlang-2 distribution (DE2). The new distribution has numerous surprising improvements over many conventional discrete distributions, particularly when analyzing excessively dispersed count data. Moments and moments-generating functions, a few descriptive measures (central tendency and dispersion), monotonicity of the probability mass function, and the hazard rate function are just a few of the statistical aspects of the postulated distribution that have been developed. The single parameter of the DE2 distribution was estimated via the maximum likelihood technique. Real-world datasets, leukemia and COVID-19, were applied to analyze the effectiveness of the recommended distribution.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70188894","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 era of modern portfolio theory began with the revolutionary approach by Harry Markowitz in 1952. However, several drawbacks of the model have rendered it impractical to be used in reality. Thus, various modifications have been done to refine the classical model, including concerns about risk measures, trading practices and computational efficiency. On the other hand, Islamic finance is proven to be a viable alternative to the conventional system following its outstanding performance during the financial crisis in 2008. This emerging sector has gained a lot of attention from investors and economists due to its significantly increasing impact on today's economy, corresponding to globalization and a demand for a sustainable investment strategy. A comprehensive literature review of the notable conventional and Islamic models is done to aid future research and development of portfolio optimization, particularly for Islamic investment. Additionally, the study provides a concisely detailed overview of the principles of Islamic finance to prepare for the future development of an Islamic finance model. Generally, this study outlines the comprehensive features of portfolio optimization models over the decades, with an attempt to classify and categorize the advantages and drawbacks of the existing models. The trend of portfolio optimization modelling can be captured by gathering and recording the problems and solutions of the reviewed models.
{"title":"A review on portfolio optimization models for Islamic finance","authors":"Doong Toong Lim, K. Goh, Y. Sim","doi":"10.3934/math.2023523","DOIUrl":"https://doi.org/10.3934/math.2023523","url":null,"abstract":"The era of modern portfolio theory began with the revolutionary approach by Harry Markowitz in 1952. However, several drawbacks of the model have rendered it impractical to be used in reality. Thus, various modifications have been done to refine the classical model, including concerns about risk measures, trading practices and computational efficiency. On the other hand, Islamic finance is proven to be a viable alternative to the conventional system following its outstanding performance during the financial crisis in 2008. This emerging sector has gained a lot of attention from investors and economists due to its significantly increasing impact on today's economy, corresponding to globalization and a demand for a sustainable investment strategy. A comprehensive literature review of the notable conventional and Islamic models is done to aid future research and development of portfolio optimization, particularly for Islamic investment. Additionally, the study provides a concisely detailed overview of the principles of Islamic finance to prepare for the future development of an Islamic finance model. Generally, this study outlines the comprehensive features of portfolio optimization models over the decades, with an attempt to classify and categorize the advantages and drawbacks of the existing models. The trend of portfolio optimization modelling can be captured by gathering and recording the problems and solutions of the reviewed models.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189076","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 goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (alpha, beta, gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.
本文的目的是介绍一类新的广义非扩张算子，称为$ (alpha, beta, gamma) $ -非扩张映射。进一步研究了一般Banach空间中这些映射的一些相关性质。此外，在$ K $ -迭代技术中使用的算子估计不动点并检查其行为。此外，还提供了两个示例来支持我们的主要结果。数值结果清楚地表明$ K $ -迭代方法在使用这类新算子时收敛速度更快。最后，我们使用$ K $型迭代方法解决了Hilbert空间上的变分不等式问题。
{"title":"Iterative schemes for numerical reckoning of fixed points of new nonexpansive mappings with an application","authors":"K. Ullah, Junaid Ahmad, H. Hammad, R. George","doi":"10.3934/math.2023543","DOIUrl":"https://doi.org/10.3934/math.2023543","url":null,"abstract":"The goal of this manuscript is to introduce a new class of generalized nonexpansive operators, called $ (alpha, beta, gamma) $-nonexpansive mappings. Furthermore, some related properties of these mappings are investigated in a general Banach space. Moreover, the proposed operators utilized in the $ K $-iterative technique estimate the fixed point and examine its behavior. Also, two examples are provided to support our main results. The numerical results clearly show that the $ K $-iterative approach converges more quickly when used with this new class of operators. Ultimately, we used the $ K $-type iterative method to solve a variational inequality problem on a Hilbert space.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"31 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70189874","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 traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.
{"title":"Pricing of vulnerable options based on an uncertain CIR interest rate model","authors":"Guiwen Lv, Ping Xu, Yanxue Zhang","doi":"10.3934/math.2023563","DOIUrl":"https://doi.org/10.3934/math.2023563","url":null,"abstract":"The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70190904","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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