Pub Date : 2026-04-01Epub Date: 2025-11-15DOI: 10.1016/j.matcom.2025.11.018
Shan Chen , Yuanzhao Ding
It is essential to comprehend and forecast animal migratory paths. Only with this knowledge will scientists be able to help conserve animals and better safeguard their habitats. Using the zebra migration as an example, this research simulates and interprets the evolution of zebra migration patterns using a revolutionary genetic algorithm method. With this technique, we discover that only when the zebra population size is quite large and the mutation rate is moderate does migratory route evolution go more smoothly. Future efforts to conserve animals will be greatly impacted by this paper's demonstration of the viability of employing a genetic algorithm to comprehend and enhance animal migration pathways.
{"title":"Feasibility study of using artificial intelligence to explore the process of zebra migration","authors":"Shan Chen , Yuanzhao Ding","doi":"10.1016/j.matcom.2025.11.018","DOIUrl":"10.1016/j.matcom.2025.11.018","url":null,"abstract":"<div><div>It is essential to comprehend and forecast animal migratory paths. Only with this knowledge will scientists be able to help conserve animals and better safeguard their habitats. Using the zebra migration as an example, this research simulates and interprets the evolution of zebra migration patterns using a revolutionary genetic algorithm method. With this technique, we discover that only when the zebra population size is quite large and the mutation rate is moderate does migratory route evolution go more smoothly. Future efforts to conserve animals will be greatly impacted by this paper's demonstration of the viability of employing a genetic algorithm to comprehend and enhance animal migration pathways.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 74-83"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-12-22DOI: 10.1016/S0378-4754(25)00539-7
{"title":"IMACS Calendar of Events","authors":"","doi":"10.1016/S0378-4754(25)00539-7","DOIUrl":"10.1016/S0378-4754(25)00539-7","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Page 367"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-12-22DOI: 10.1016/S0378-4754(25)00540-3
{"title":"News of IMACS","authors":"","doi":"10.1016/S0378-4754(25)00540-3","DOIUrl":"10.1016/S0378-4754(25)00540-3","url":null,"abstract":"","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Page 366"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145839819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-11-11DOI: 10.1016/j.matcom.2025.11.012
Jing Ren, Hao Sun, Panfei Sun
This paper investigates how corporate social responsibility, marginal costs, and market structure affect the stability of the Stackelberg equilibrium in mixed oligopolies. To achieve this, we develop dynamic mixed duopoly and triopoly models, showing that the Stackelberg equilibrium is locally asymptotically stable when the adjustment speed is below a threshold. The stability of the equilibrium is enhanced by increased marginal costs, stronger commitment to social responsibility, and the presence of a sophisticated follower in the triopoly setting. However, when the adjustment speed exceeds the threshold and the equilibrium becomes unstable, we introduce a control term into the dynamic model to restore stability. The implications of our analysis highlight the importance of firms avoiding excessive cost cutting in favor of innovation driven competition. Additionally, fostering social responsibility and moderate market competition plays a critical role in sustaining stable markets over the long term.
{"title":"Dynamic stability of Stackelberg equilibrium in mixed oligopolies: The role of social responsibility, marginal costs, and market structure","authors":"Jing Ren, Hao Sun, Panfei Sun","doi":"10.1016/j.matcom.2025.11.012","DOIUrl":"10.1016/j.matcom.2025.11.012","url":null,"abstract":"<div><div>This paper investigates how corporate social responsibility, marginal costs, and market structure affect the stability of the Stackelberg equilibrium in mixed oligopolies. To achieve this, we develop dynamic mixed duopoly and triopoly models, showing that the Stackelberg equilibrium is locally asymptotically stable when the adjustment speed is below a threshold. The stability of the equilibrium is enhanced by increased marginal costs, stronger commitment to social responsibility, and the presence of a sophisticated follower in the triopoly setting. However, when the adjustment speed exceeds the threshold and the equilibrium becomes unstable, we introduce a control term into the dynamic model to restore stability. The implications of our analysis highlight the importance of firms avoiding excessive cost cutting in favor of innovation driven competition. Additionally, fostering social responsibility and moderate market competition plays a critical role in sustaining stable markets over the long term.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 125-147"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580115","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-11-29DOI: 10.1016/j.matcom.2025.11.032
Andrés Fraguela , Carlos D. Ponce , Juan C. Hernández-Gómez , José M. Sigarreta
This paper develops a mathematical framework to estimate the average productivity of Aedes aegypti (Diptera: Culicidae) in artificial breeding sites, focusing on open household water-storage containers typical of areas with limited access to piped water. We introduce the effective larval displacement volume and, using data from a controlled experiment conducted under climatic conditions favorable for mosquito larval development, derive stage-specific carrying capacities as functions of container dimensions and water volume. The mosquito life cycle is represented by a dynamic population model with seven biologically grounded stages (egg, four larval instars, pupa, and adult) that incorporates nonlinear oviposition, asynchronous hatching, and density-dependent larval competition. Assuming favorable climatic conditions the model admits a unique, globally asymptotically stable equilibrium, so the equilibrium adult population provides a robust measure of breeding-site productivity. From this equilibrium we obtain a closed-form approximation for average adult productivity in terms of water-column height and container perimeter, and apply it to storage containers commonly used in Latin-America: buckets, plastic barrels, water tanks, and cement storage piles. The results indicate that productivity varies only weakly with container size, suggesting that consolidating stored water into a single large container, rather than several smaller ones, may reduce overall mosquito emergence. Because all estimates are derived under optimal environmental and water-quality conditions, they should be interpreted as upper bounds for productivity under less favorable or adverse settings, a distinction that is essential for real-world vector-control planning. Overall, the proposed approach offers an operational tool for quantifying productivity in domestic water-storage breeding sites.
{"title":"Maximum productivity of Aedes aegypti (Diptera: Culicidae) based on the dynamics of its aquatic state","authors":"Andrés Fraguela , Carlos D. Ponce , Juan C. Hernández-Gómez , José M. Sigarreta","doi":"10.1016/j.matcom.2025.11.032","DOIUrl":"10.1016/j.matcom.2025.11.032","url":null,"abstract":"<div><div>This paper develops a mathematical framework to estimate the average productivity of <em>Aedes aegypti</em> (Diptera: Culicidae) in artificial breeding sites, focusing on open household water-storage containers typical of areas with limited access to piped water. We introduce the effective larval displacement volume and, using data from a controlled experiment conducted under climatic conditions favorable for mosquito larval development, derive stage-specific carrying capacities as functions of container dimensions and water volume. The mosquito life cycle is represented by a dynamic population model with seven biologically grounded stages (egg, four larval instars, pupa, and adult) that incorporates nonlinear oviposition, asynchronous hatching, and density-dependent larval competition. Assuming favorable climatic conditions the model admits a unique, globally asymptotically stable equilibrium, so the equilibrium adult population provides a robust measure of breeding-site productivity. From this equilibrium we obtain a closed-form approximation for average adult productivity in terms of water-column height and container perimeter, and apply it to storage containers commonly used in Latin-America: buckets, plastic barrels, water tanks, and cement storage piles. The results indicate that productivity varies only weakly with container size, suggesting that consolidating stored water into a single large container, rather than several smaller ones, may reduce overall mosquito emergence. Because all estimates are derived under optimal environmental and water-quality conditions, they should be interpreted as upper bounds for productivity under less favorable or adverse settings, a distinction that is essential for real-world vector-control planning. Overall, the proposed approach offers an operational tool for quantifying productivity in domestic water-storage breeding sites.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 244-269"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-11-27DOI: 10.1016/j.matcom.2025.11.037
Qiu Peng , Manchun Tan , Mingbing Luo , Kai Wu
Synchronization is crucial for achieving coordinated dynamic behavior and improving operational efficiency in complex networks. This paper focuses on the practical finite-time bipartite synchronization (PFTBS) of fractional-order Takagi–Sugeno (T–S) fuzzy multilayer signed networks (FOTSFMSNs) with time-varying coupling weights. First, to reduce communication resource consumption and control costs, a fuzzy exponential dynamic event-triggered hybrid impulsive control method is designed by introducing the exponential decay function under the T–S fuzzy rule. Second, a graph-theoretic Lyapunov function with two time-varying coefficients is constructed, and corresponding fractional-order derivative rules are established. Using graph theory and a new practical fractional-order impulsive finite-time inequality, sufficient conditions for PFTBS are derived, and Zeno behavior is effectively excluded. Finally, numerical simulations are carried out on two FOTSFMSNs, one using fractional-order Chua’s chaotic circuit and the other using fractional-order power system as node dynamics. The numerical results confirm the effectiveness of the control method.
{"title":"Practical finite-time bipartite synchronization for fractional-order T–S fuzzy multilayer signed networks via dynamic event-triggered hybrid impulsive control","authors":"Qiu Peng , Manchun Tan , Mingbing Luo , Kai Wu","doi":"10.1016/j.matcom.2025.11.037","DOIUrl":"10.1016/j.matcom.2025.11.037","url":null,"abstract":"<div><div>Synchronization is crucial for achieving coordinated dynamic behavior and improving operational efficiency in complex networks. This paper focuses on the practical finite-time bipartite synchronization (PFTBS) of fractional-order Takagi–Sugeno (T–S) fuzzy multilayer signed networks (FOTSFMSNs) with time-varying coupling weights. First, to reduce communication resource consumption and control costs, a fuzzy exponential dynamic event-triggered hybrid impulsive control method is designed by introducing the exponential decay function under the T–S fuzzy rule. Second, a graph-theoretic Lyapunov function with two time-varying coefficients is constructed, and corresponding fractional-order derivative rules are established. Using graph theory and a new practical fractional-order impulsive finite-time inequality, sufficient conditions for PFTBS are derived, and Zeno behavior is effectively excluded. Finally, numerical simulations are carried out on two FOTSFMSNs, one using fractional-order Chua’s chaotic circuit and the other using fractional-order power system as node dynamics. The numerical results confirm the effectiveness of the control method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 297-322"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145693938","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-11-10DOI: 10.1016/j.matcom.2025.11.002
M.H. Derakhshan , H.R. Marasi , Pushpendra Kumar
In this paper, we propose an efficient hybrid numerical approach to obtain approximate solutions to the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators. This combined numerical approach includes two numerical approaches in time and space directions. The weighted and shifted Grünwald difference numerical method is used to approximate the fractional problem in the time direction, and the fractional compact numerical method is applied in the direction of the space variable. The stability and convergence analyses are studied for the proposed numerical approach. To show the effectiveness of the presented numerical method, some numerical examples are given, and the numerical results for these examples are plotted. Also, this numerical approach is compared with other methods.
{"title":"A numerical method for the solution of the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators","authors":"M.H. Derakhshan , H.R. Marasi , Pushpendra Kumar","doi":"10.1016/j.matcom.2025.11.002","DOIUrl":"10.1016/j.matcom.2025.11.002","url":null,"abstract":"<div><div>In this paper, we propose an efficient hybrid numerical approach to obtain approximate solutions to the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators. This combined numerical approach includes two numerical approaches in time and space directions. The weighted and shifted Grünwald difference numerical method is used to approximate the fractional problem in the time direction, and the fractional compact numerical method is applied in the direction of the space variable. The stability and convergence analyses are studied for the proposed numerical approach. To show the effectiveness of the presented numerical method, some numerical examples are given, and the numerical results for these examples are plotted. Also, this numerical approach is compared with other methods.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 230-243"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145624688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-10-17DOI: 10.1016/j.matcom.2025.10.020
Tamás Tóth-Katona , Dr. Péter Stumpf , Dr. Szabó Gergely
This paper introduces key equations for calculating the operating trajectories of the IPMSM and the electrical losses of the powertrain in steady-state. Based on these equations, the calculation of the so-called axis current map and steady-state efficiency map are introduced via a Newton–Raphson based method. The proposed steady-state calculations are validated through a dynamic simulation model with cascaded speed-current closed-loop control. Torque-current reference generation is also performed with the aforementioned Newton–Raphson based method. A clear novelty of this paper is the inclusion of both stator resistance and iron loss resistance in the calculation of reference currents. Additionally, we propose combining this algorithm with a time-variant 2DoF current controller to account for iron losses. The proposed combination improves dynamic behavior and accounts for losses. The steady-state calculations and the dynamic models presented align, proving to be reliable tools for estimating energy consumption and allowing the implementation of accurate reference torque tracking control algorithms.
{"title":"Steady-state and dynamic performance of IPMSM drive taking into account electric powertrain losses","authors":"Tamás Tóth-Katona , Dr. Péter Stumpf , Dr. Szabó Gergely","doi":"10.1016/j.matcom.2025.10.020","DOIUrl":"10.1016/j.matcom.2025.10.020","url":null,"abstract":"<div><div>This paper introduces key equations for calculating the operating trajectories of the IPMSM and the electrical losses of the powertrain in steady-state. Based on these equations, the calculation of the so-called <span><math><mrow><mi>d</mi><mi>q</mi></mrow></math></span> axis current map and steady-state efficiency map are introduced via a Newton–Raphson based method. The proposed steady-state calculations are validated through a dynamic simulation model with cascaded speed-current closed-loop control. Torque-current reference generation is also performed with the aforementioned Newton–Raphson based method. A clear novelty of this paper is the inclusion of both stator resistance and iron loss resistance in the calculation of reference currents. Additionally, we propose combining this algorithm with a time-variant 2DoF current controller to account for iron losses. The proposed combination improves dynamic behavior and accounts for losses. The steady-state calculations and the dynamic models presented align, proving to be reliable tools for estimating energy consumption and allowing the implementation of accurate reference torque tracking control algorithms.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 148-163"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-11-19DOI: 10.1016/j.matcom.2025.11.006
Zhidong Guo
Paper (Shokrollahi et al. [Mathematics and Computers in Simulation 226 (2024) 172-183]), addresses the pricing of geometric Asian options with jumps using a method analogous to that employed in non-jump scenarios. In this comment, based on the probability distribution of path variables, we will point out that the main conclusion of the paper is incorrect. More importantly, we aim to show that the conclusions drawn from non-jump models do not directly carry over to jump models when dealing with path-dependent options.
论文（Shokrollahi et al. [Mathematics and Computers in Simulation 226(2024) 172-183]），使用类似于非跳跃情景的方法，解决了具有跳跃的几何亚洲期权的定价问题。在这篇评论中，我们将根据路径变量的概率分布，指出本文的主要结论是不正确的。更重要的是，我们的目标是表明，当处理路径依赖选项时，从非跳跃模型得出的结论并不直接适用于跳跃模型。
{"title":"Comments on “Pricing Asian options under the mixed fractional Brownian motion with jumps”.","authors":"Zhidong Guo","doi":"10.1016/j.matcom.2025.11.006","DOIUrl":"10.1016/j.matcom.2025.11.006","url":null,"abstract":"<div><div>Paper (Shokrollahi et al. [Mathematics and Computers in Simulation 226 (2024) 172-183]), addresses the pricing of geometric Asian options with jumps using a method analogous to that employed in non-jump scenarios. In this comment, based on the probability distribution of path variables, we will point out that the main conclusion of the paper is incorrect. More importantly, we aim to show that the conclusions drawn from non-jump models do not directly carry over to jump models when dealing with path-dependent options.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 121-124"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145580213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-04-01Epub Date: 2025-12-08DOI: 10.1016/j.matcom.2025.12.004
Jian-hao Kang , Zhun Gou , Nan-jing Huang
This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer’s surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston’s stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton–Jacobi–Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.
{"title":"Equilibrium reinsurance and investment strategies for insurers with random risk aversion under Heston’s SV model","authors":"Jian-hao Kang , Zhun Gou , Nan-jing Huang","doi":"10.1016/j.matcom.2025.12.004","DOIUrl":"10.1016/j.matcom.2025.12.004","url":null,"abstract":"<div><div>This study employs expected certainty equivalents to explore the reinsurance and investment issue pertaining to an insurer that aims to maximize the expected utility while being subject to random risk aversion. The insurer’s surplus process is modeled approximately by a drifted Brownian motion, and the financial market is comprised of a risk-free asset and a risky asset with its price depicted by Heston’s stochastic volatility (SV) model. Within a game theory framework, a strict verification theorem is formulated to delineate the equilibrium reinsurance and investment strategies as well as the corresponding value function. Furthermore, through solving the pseudo Hamilton–Jacobi–Bellman (HJB) system, semi-analytical formulations for the equilibrium reinsurance and investment strategies and the associated value function are obtained under the exponential utility. Additionally, several numerical experiments are carried out to demonstrate the characteristics of the equilibrium reinsurance and investment strategies.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"242 ","pages":"Pages 343-365"},"PeriodicalIF":4.4,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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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