Communications in Nonlinear Science and Numerical Simulation最新文献

筛选
英文 中文
Vibration control of wind turbine towers with the nonlinear tuned liquid damper considering the aero-elastic coupling behavior 考虑气动-弹性耦合特性的非线性调谐液体阻尼器风力发电塔的振动控制
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-17 DOI: 10.1016/j.cnsns.2025.109306
Zhenbo Lei , Gang Liu , Hui Wang , Mengzhu Li , Lixing Zhou , Tao Wang
{"title":"Vibration control of wind turbine towers with the nonlinear tuned liquid damper considering the aero-elastic coupling behavior","authors":"Zhenbo Lei ,&nbsp;Gang Liu ,&nbsp;Hui Wang ,&nbsp;Mengzhu Li ,&nbsp;Lixing Zhou ,&nbsp;Tao Wang","doi":"10.1016/j.cnsns.2025.109306","DOIUrl":"10.1016/j.cnsns.2025.109306","url":null,"abstract":"<div><div>Large-megawatts wind turbines with big-scale blade and tower have been rapidly upgraded and developed in the past several years, resulting in the more significant aero-elastic coupling vibrations between operating blade and tower structures. By means of the low design-cost, virtually maintenance-free and simpler frequency-tuning pattern, nonlinear tuned liquid dampers (TLDs) provide a promising means in controlling the vibrations of wind turbine tower. This paper considers the structural aero-elastic coupling behavior of wind turbine to evaluate the vibration control performance of nonlinear TLD synthetically. A dynamical aero-elastic coupling model of wind turbine is established by combining Euler-Lagrange equation with blade element momentum (BEM) method, and this model is validated by using the OpenFAST simulation tool. The stiffness and damping nonlinearities induced by the irregular liquid slope-deformation are considered to design a control system of nonlinear TLD, and the control performances of this nonlinear TLD for wind turbine tower are investigated and evaluated comprehensively. The theoretical and numerical analysis results indicated that the control capability of nonlinear TLD greatly depends on the aerodynamic damping of wind turbine under the different operation conditions, and it can provide the more outstanding contributions in controlling the dynamic responses of tower-top at side-side direction.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109306"},"PeriodicalIF":3.8,"publicationDate":"2025-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117903","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}
引用次数: 0
Consistently energy-stable decoupled method with second-order accuracy and lower density bounds for the incompressible fluid flows with variable density 变密度不可压缩流体流动的二阶精度低密度界一致能量稳定解耦方法
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-16 DOI: 10.1016/j.cnsns.2025.109303
Hanwen Zhang, Junxiang Yang
{"title":"Consistently energy-stable decoupled method with second-order accuracy and lower density bounds for the incompressible fluid flows with variable density","authors":"Hanwen Zhang,&nbsp;Junxiang Yang","doi":"10.1016/j.cnsns.2025.109303","DOIUrl":"10.1016/j.cnsns.2025.109303","url":null,"abstract":"<div><div>In this paper, we develop an energy-stable and linear numerical scheme for solving the incompressible fluid flows with variable density. To facilitate the construction of numerical method, two time-dependent auxiliary variables are introduced to recast the original governing equations into equivalent forms. Based on the equivalent equations, we present a semi-implicit time-marching scheme with second-order backward differentiation formula (BDF2), where the linear term and auxiliary variables are implicitly treated. Using a splitting technique, the proposed scheme can be easily solved in a totally decoupled manner. We analytically estimate the energy stability and the preservation of lower density bounds. In each time step, two simple correction steps are used to improve the energy consistency. Several numerical experiments are implemented to validate the accuracy, energy stability, and lower density bounds of the proposed method. Moreover, the Rayleigh–Taylor instability and incompressible flows with variable viscosity are simulated to further show the good capabilities.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109303"},"PeriodicalIF":3.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094137","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}
引用次数: 0
Self-sustainable chaotic dynamics of a liquid crystal elastomer pendulum in radial linear temperature fields 径向线性温度场中液晶弹性体摆的自持续混沌动力学
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-16 DOI: 10.1016/j.cnsns.2025.109338
Peibao Xu , Kuan Zhou , Xin Sun , Kai Li
{"title":"Self-sustainable chaotic dynamics of a liquid crystal elastomer pendulum in radial linear temperature fields","authors":"Peibao Xu ,&nbsp;Kuan Zhou ,&nbsp;Xin Sun ,&nbsp;Kai Li","doi":"10.1016/j.cnsns.2025.109338","DOIUrl":"10.1016/j.cnsns.2025.109338","url":null,"abstract":"<div><div>Self-sustainable chaotic systems based on liquid crystal elastomers can autonomously harvest energy from a steady external environment to sustain motion. Currently, chaotic pendulum system is usually induced by periodic stimuli and requires complex controllers, which limits its application scenarios. In this paper, a self-sustainable chaotic pendulum composed of a fiber and a mass sphere is designed under radial stimulation by introducing a steady radial linear temperature field. The corresponding nonlinear dynamic model is established to study its self-sustainable motion characteristics. The results of numerical calculation show that the liquid crystal elastomer pendulum system exhibits three distinct motion modes: periodic vibration, periodic swing and chaotic swing modes. The system compensates for the energy dissipated by damping using the net work done by the liquid crystal elastomer fiber in the linear temperature field, thus maintaining self-sustainable motion. Additionally, the paper explores the influence of system parameters on the motion behavior of the pendulum, and uses bifurcation diagrams to observe the changes in motion modes with parameter variations. It is worth emphasizing that this pendulum system can appear self-sustainable chaotic phenomenon in the position-independent driving mode. This research uncovers the thermodynamic self-sustainable motion law of the liquid crystal elastomer pendulum and proposes innovative applications in waste heat recovery, chaotic massage and chaotic heart simulation.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109338"},"PeriodicalIF":3.8,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117902","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}
引用次数: 0
Adaptive boundary vibration control for flexible manipulators under intermittent actuator failures 柔性机械臂间歇性故障下的自适应边界振动控制
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI: 10.1016/j.cnsns.2025.109300
Yongqiang Nai
{"title":"Adaptive boundary vibration control for flexible manipulators under intermittent actuator failures","authors":"Yongqiang Nai","doi":"10.1016/j.cnsns.2025.109300","DOIUrl":"10.1016/j.cnsns.2025.109300","url":null,"abstract":"<div><div>Investigating the suppression of intermittent elastic vibrations caused by actuator failures in flexible manipulators is both challenging and important, yet only limited studies have been reported. This paper proposes an adaptive boundary vibration control scheme to address this issue. First, intermittent jumps in failure parameters may lead to unbounded estimated parameters in the controller. To prevent this, a projection operator is employed to update the estimates, ensuring their boundedness as well as that of the parameter estimation errors. Second, since the derivatives of the estimation errors are undefined at failure times, a piecewise Lyapunov function incorporating the estimation errors is developed. This function demonstrates that all closed-loop signals are uniformly ultimately bounded (UUB) under the proposed control scheme. Furthermore, when the jump amplitudes of the Lyapunov function are sufficiently small and the time intervals between successive failures are sufficiently long, the steady-state performance in terms of angle tracking error and elastic deflection is enhanced. Third, based on the piecewise Lyapunov function, two explicit bounds for the angle tracking error and the elastic deflection are derived, showing that transient performance can be improved through appropriate selection of design constants. Finally, numerical simulations confirm the effectiveness and superiority of the proposed approach.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109300"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145157742","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}
引用次数: 0
Reconstruction of diblock copolymer melts with an EnKF-based restoration framework 基于enkf修复框架的二嵌段共聚物熔体重建
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI: 10.1016/j.cnsns.2025.109302
Wenxuan Xie , Jiachen Feng , Junseok Kim , Yibao Li
{"title":"Reconstruction of diblock copolymer melts with an EnKF-based restoration framework","authors":"Wenxuan Xie ,&nbsp;Jiachen Feng ,&nbsp;Junseok Kim ,&nbsp;Yibao Li","doi":"10.1016/j.cnsns.2025.109302","DOIUrl":"10.1016/j.cnsns.2025.109302","url":null,"abstract":"<div><div>Incomplete or damaged regions disrupt the consistency of numerical simulations, making both analysis and prediction challenging. In this study, we present an efficient and flexible restoration framework of reconstructed solution for diblock copolymer systems. A sixth-order nonlinear phase-field model is adopted to describe the restoration dynamics, where parameter estimation is essential for accurate restoration results. To address this challenge, the Ensemble Kalman Filter (EnKF) data assimilation method is employed to iteratively estimate optimal model parameters with partial observations sampled from the target diblock copolymer states to be reconstructed. The estimated parameters are then incorporated into the governing model to reconstruct the missing morphology. A series of twin experiments are conducted to systematically evaluate the effectiveness and robustness of the method under controlled settings. The results confirm that the EnKF-based restoration framework is capable of reliably restoring diblock structures even with complex reconstructed domains.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109302"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145094138","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}
引用次数: 0
Analysis of a discontinuous Galerkin pressure correction scheme for the Kelvin-Voigt equation Kelvin-Voigt方程的不连续Galerkin压力校正格式分析
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI: 10.1016/j.cnsns.2025.109263
Kushal Roy, Rajen Kumar Sinha
{"title":"Analysis of a discontinuous Galerkin pressure correction scheme for the Kelvin-Voigt equation","authors":"Kushal Roy,&nbsp;Rajen Kumar Sinha","doi":"10.1016/j.cnsns.2025.109263","DOIUrl":"10.1016/j.cnsns.2025.109263","url":null,"abstract":"<div><div>We formulate and analyze a discontinuous Galerkin pressure correction scheme for solving the Kelvin-Voigt. The proposed scheme is proven to be unconditionally stable. Convergence of the discrete velocity is established through a priori error estimates in <span><math><msup><mi>L</mi><mn>2</mn></msup></math></span> and <span><math><mrow><mi>D</mi><mi>G</mi></mrow></math></span> norms, and validating our findings through numerical experiments. The theoretical analysis confirms optimal convergence rates in the <span><math><mrow><mi>D</mi><mi>G</mi></mrow></math></span> norm, and optimal spatial accuracy in the <span><math><msup><mi>L</mi><mn>2</mn></msup></math></span> norm, though temporal accuracy appears suboptimal. Nevertheless, numerical experiments indicate that the scheme achieves optimal accuracy in both time and space.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109263"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145117913","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}
引用次数: 0
Quasi-synchronization of Takagi-Sugeno fuzzy heterogeneous stochastic delayed networks by aperiodically intermittent control based on discrete-time state observations 基于离散时间状态观测的非周期间歇控制Takagi-Sugeno模糊异质随机延迟网络的准同步
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI: 10.1016/j.cnsns.2025.109298
Zhiyuan Wen , Xiaofeng Xu , Ming Liu
{"title":"Quasi-synchronization of Takagi-Sugeno fuzzy heterogeneous stochastic delayed networks by aperiodically intermittent control based on discrete-time state observations","authors":"Zhiyuan Wen ,&nbsp;Xiaofeng Xu ,&nbsp;Ming Liu","doi":"10.1016/j.cnsns.2025.109298","DOIUrl":"10.1016/j.cnsns.2025.109298","url":null,"abstract":"<div><div>This article delves into the quasi-synchronization of Takagi-Sugeno fuzzy heterogeneous stochastic delayed networks (TSFHSDNs), in which an aperiodically intermittent control strategy incorporating time-varying control gains, driven by discrete-time state observations, is imposed on the networks. Compared with intermittent control strategies discussed in the existing literature, the proposed approach introduces control intervals that are determined by discrete-time state observations, enhancing the efficacy of the control process. Notably, the aperiodic nature of this intermittent control, based on discrete-time state feedback, alleviates the limitations imposed by periodicity that are characteristic of traditional intermittent control strategies. The incorporation of time-varying control gains offers the advantage of enabling the control strategy to adapt to the dynamic characteristics of the networks in real-time, thereby improving the flexibility and effectiveness of the control. Furthermore, the paper presents a robust and easily-verifiable theoretical framework for establishing the quasi-synchronization criterion of TSFHSDNs. Ultimately, the theoretical results are implemented in spring-mass-damper systems, accompanied by a numerical example to illustrate the practical relevance and efficacy of the theoretical findings.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109298"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145219433","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}
引用次数: 0
Adaptive actuator failure compensation control for uncalibrated eye-to-hand manipulators 无标定眼手机械手的自适应致动器故障补偿控制
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-15 DOI: 10.1016/j.cnsns.2025.109297
Can Yuan , Liang Yang , Xiuxiang Li , Guanyu Lai , Kairui Chen
{"title":"Adaptive actuator failure compensation control for uncalibrated eye-to-hand manipulators","authors":"Can Yuan ,&nbsp;Liang Yang ,&nbsp;Xiuxiang Li ,&nbsp;Guanyu Lai ,&nbsp;Kairui Chen","doi":"10.1016/j.cnsns.2025.109297","DOIUrl":"10.1016/j.cnsns.2025.109297","url":null,"abstract":"<div><div>The compensation for unknown time-varying actuator failures is rarely considered in the existing visual control schemes for robotic manipulators, which can result in a degradation of transient performance in practice when actuator failures take place. Based on such a consideration, this paper presents a visual fault-tolerant control method for uncalibrated eye-to-hand manipulators with possible time-varying actuator faults. To accommodate the deleterious impacts of actuator failures on transient performance, firstly an adaptive control method is developed to compensate for time-varying failures occurring in actuators. Then, a pseudo inverse of image Jacobian matrix is designed to transform image error into joint space of robotic manipulators so that the unknown failures and camera parameters are successfully linearized, based on which a parametrization form of uncertain dynamics can be derived successfully. Moreover, an adaptive mechanism is newly presented to achieve the unknown camera parameters estimation online. With the aid of the Lyapunov method, the asymptotic convergence of image errors can be proved strictly. Simulation results are presented to demonstrate the proposed scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109297"},"PeriodicalIF":3.8,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093942","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}
引用次数: 0
Predefined-time sliding mode trajectory tracking control for asymmetric underactuated surface vehicle with nonlinear disturbances 非对称欠驱动水面车辆非线性扰动的预定义时间滑模轨迹跟踪控制
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-14 DOI: 10.1016/j.cnsns.2025.109299
Chenliang Hao , Yana Yang , Jian Zhang , Guanglei Zhao
{"title":"Predefined-time sliding mode trajectory tracking control for asymmetric underactuated surface vehicle with nonlinear disturbances","authors":"Chenliang Hao ,&nbsp;Yana Yang ,&nbsp;Jian Zhang ,&nbsp;Guanglei Zhao","doi":"10.1016/j.cnsns.2025.109299","DOIUrl":"10.1016/j.cnsns.2025.109299","url":null,"abstract":"<div><div>In this paper, the predefined-time trajectory tracking problem of an asymmetric underactuated surface vehicle (AUSV) subject to external disturbances and model uncertainties is investigated. First, a new predefined-time disturbance observer (PTDO) is developed to estimate the compound disturbances accurately within a predefined time. Then, by employing coordinate transformations and cascaded system theory, the underactuation issue is addressed, and the tracking control problem of the AUSV is reformulated as a stabilization problem of two cascaded subsystems. Subsequently, two nonsingular predefined-time sliding mode control laws are designed for the two cascade subsystems. It is mathematically demonstrated that the tracking errors can converge in a predefined time. Meanwhile, the convergence time-bound is independent of the initial conditions of the system and can be predetermined within the physically allowable range as required. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109299"},"PeriodicalIF":3.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093943","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}
引用次数: 0
Self-triggered control for the convergence of n-person random evolutionary games [公式省略]人随机进化博弈收敛的自触发控制
IF 3.8 2区 数学
Communications in Nonlinear Science and Numerical Simulation Pub Date : 2025-09-14 DOI: 10.1016/j.cnsns.2025.109293
Xinling Li, Shihua Fu, Jianjun Wang, Fengxia Zhang
{"title":"Self-triggered control for the convergence of n-person random evolutionary games","authors":"Xinling Li,&nbsp;Shihua Fu,&nbsp;Jianjun Wang,&nbsp;Fengxia Zhang","doi":"10.1016/j.cnsns.2025.109293","DOIUrl":"10.1016/j.cnsns.2025.109293","url":null,"abstract":"<div><div>In this article, the self-triggered control scheme is designed to achieve the convergence of <span><math><mi>n</mi></math></span>-person random evolutionary games (REGs). Firstly, using the semi-tensor product (STP) of matrices, the <span><math><mi>n</mi></math></span>-person REG is converted to an algebraic form. Secondly, the control Lyapunov functions (CLFs) for the convergence problem of <span><math><mi>n</mi></math></span>-person REGs are presented, and an algorithm for the construction of a CLF is given. Moreover, a necessary and sufficient condition based on the CLF is proposed to detect whether an <span><math><mi>n</mi></math></span>-person REG can converge to a target profile with probability one. And a design scheme of state-feedback self-triggered controls (STCs) is established. Finally, an example is presented to illustrate the obtained results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109293"},"PeriodicalIF":3.8,"publicationDate":"2025-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145093944","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}
引用次数: 0
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信