Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"General decay anti-synchronization and H∞ anti-synchronization of derivative coupled delayed memristive neural networks with constant and delayed state coupling","authors":"","doi":"10.1016/j.cnsns.2024.108313","DOIUrl":"10.1016/j.cnsns.2024.108313","url":null,"abstract":"<div><p>In this article, we explore the general decay anti-synchronization (GDAS) and general decay <span><math><msub><mrow><mi>H</mi></mrow><mrow><mi>∞</mi></mrow></msub></math></span> anti-synchronization (GDHAS) of derivative coupled delayed memristive neural networks (DCDMNNs) with constant and delayed state coupling, respectively. To begin with, on account of the definitions of <span><math><mi>ψ</mi></math></span>-type function as well as <span><math><mi>ψ</mi></math></span>-type stability, we present the GDAS and GDHAS concepts for the considered DCDMNNs. What is more, several sufficient conditions are derived for reaching GDAS and GDHAS of DCDMNNs with constant and delayed state coupling by selecting correct Lyapunov functionals and devising a proper controller. Moreover, numerical simulations examples are provided to demonstrate the feasibility of the obtained conclusions.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142098329","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}

{"title":"Convergence of the Two Point Flux Approximation method and the fitted Two Point Flux Approximation method for options pricing with local volatility function","authors":"","doi":"10.1016/j.cnsns.2024.108291","DOIUrl":"10.1016/j.cnsns.2024.108291","url":null,"abstract":"<div><p>In this paper, we deal with numerical approximations for solving the Black–Scholes Partial Differential Equation (PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally of both stock price and time. In contrast to constant volatility or time-dependent volatility models for which analytical representations of the exact solution is known for European Call options, there is no analytical solution for local volatility. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called Fitted Two-Point Flux Approximation (FTPFA). The Fitted Two-Point Flux Approximation (FTPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero with the goal to handle the degeneracy of the PDE while the TPFA method is used on the rest of space domain. This combination yields our fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support theoretical results are provided.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S1007570424004763/pdfft?md5=0bcf7875ec168a4e9f16cbcf9e56fa9d&pid=1-s2.0-S1007570424004763-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142097873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"(αη)-contractive and (βχ)-contractive mapping based fixed point theorems in fuzzy bipolar metric spaces and application to nonlinear Volterra integral equations","authors":"","doi":"10.1016/j.cnsns.2024.108307","DOIUrl":"10.1016/j.cnsns.2024.108307","url":null,"abstract":"<div><p>In this paper, we introduce some novel concepts within the realm of fuzzy bipolar metric spaces, namely (<span><math><mrow><mi>α</mi><mi>η</mi></mrow></math></span>)-contractive type covariant mappings and contravariant mappings, and (<span><math><mrow><mi>β</mi><mi>χ</mi></mrow></math></span>)-contractive type covariant mappings. We establish some fixed point theorems that demonstrate both the existence and uniqueness of fixed points for (<span><math><mrow><mi>α</mi><mi>η</mi></mrow></math></span>)-contractive type covariant mappings and contravariant mappings, and for (<span><math><mrow><mi>β</mi><mi>χ</mi></mrow></math></span>)-contractive type covariant mappings in complete fuzzy bipolar metric spaces utilizing the triangular property. Additionally, to substantiate the findings, some illustrative examples and consequential outcomes are presented. Furthermore, the proven results serve to extend, generalize, and enhance the corresponding outcomes documented in existing literature. A practical application of these findings in the context of non-linear Volterra integral equations is demonstrated, solidifying and reinforcing the credibility of the established results. Overall, this paper contributes to the understanding of fixed point theory in the context of fuzzy bipolar metric spaces and highlights the significance of (<span><math><mrow><mi>α</mi><mi>η</mi></mrow></math></span>)-contractive mappings and (<span><math><mrow><mi>β</mi><mi>χ</mi></mrow></math></span>)-contractive mappings in this domain.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142098327","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}

{"title":"Semi-wavefront for a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay","authors":"","doi":"10.1016/j.cnsns.2024.108297","DOIUrl":"10.1016/j.cnsns.2024.108297","url":null,"abstract":"<div><p>This paper considers a Belousov–Zhabotinskii reaction–diffusion system with spatio-temporal delay. The spatio-temporal delay is modeled as the convolution of <span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> with a kernel function <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo></mrow><mo>≥</mo><mn>0</mn></mrow></math></span>, where <span><math><mrow><msub><mrow><mo>∫</mo></mrow><mrow><mi>R</mi></mrow></msub><msubsup><mrow><mo>∫</mo></mrow><mrow><mn>0</mn></mrow><mrow><mo>+</mo><mi>∞</mi></mrow></msubsup><mi>g</mi><mrow><mo>(</mo><mi>s</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mi>d</mi><mi>s</mi><mi>d</mi><mi>y</mi><mo>=</mo><mn>1</mn></mrow></math></span>. By constructing an auxiliary system, applying Schauder’s fixed point theorem, and using a limiting argument, we demonstrate that the model admits non-negative traveling wave solutions connecting the equilibrium <span><math><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></math></span> to some unknown positive steady states (also referred to as a semi-wavefront) when the wave speed satisfies <span><math><mrow><mi>c</mi><mo>≥</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup><mo>=</mo><mn>2</mn><msqrt><mrow><mn>1</mn><mo>−</mo><mi>r</mi></mrow></msqrt></mrow></math></span>. Moreover, no such semi-wavefront exists if <span><math><mrow><mi>c</mi><mo>&lt;</mo><msup><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>. It is noteworthy that the kernel function is not required to have compact support in this analysis.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088309","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}

{"title":"Secure pinning synchronization on aperiodic intermittent event-triggered control in discrete-time complex networks against multi-pattern link attacks","authors":"","doi":"10.1016/j.cnsns.2024.108303","DOIUrl":"10.1016/j.cnsns.2024.108303","url":null,"abstract":"<div><p>This paper investigates the problem of secure synchronization in aperiodic intermittent event-triggered pinning control for discrete-time complex networks (DCNs) against multi-pattern link attacks. Firstly, in order to reduce communication burden and control cost, a novel aperiodic intermittent event-triggered control (AIEC) with discontinuous characteristics is designed based on periodic sampling, where triggering instants are determined by the intermittent control (IC). Secondly, multiple pattern attack are modeled, as they can interrupt different edges and change the network topology. In addition, multi-pattern attacks for each link are independent and their impact on the coupling topology is analyzed. Thirdly, under destroyed network topology, this paper designs aperiodic intermittent event-triggered pinning control (AIEPC) by combining pinning control (PC) with the AIEC. Meanwhile, based on PC, the isolated node and pinned nodes form a like-directed spanning tree with an asymmetrical coupling matrix, where rooted at the isolated node and only directed connections between the isolated node and pinned nodes. Fourthly, using the segmentation analysis method and the inequality iteration technique, a sufficient condition for exponential synchronization of error system is obtained by considering the instants neighboring different intermittent control and attack intervals. Finally, a simulation example on Chua’s circuit network is provided to verify the validity of the theoretical results achieved in this paper.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058507","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}

{"title":"Dynamic event-triggered neuro-optimal control for uncertain nonlinear systems with unknown dead-zone constraint","authors":"","doi":"10.1016/j.cnsns.2024.108308","DOIUrl":"10.1016/j.cnsns.2024.108308","url":null,"abstract":"<div><p>In this article, we propose a dynamic event-triggered neuro-optimal control scheme (DETNOC) for uncertain nonlinear systems subject to unknown dead-zone and disturbances through the design of a composite control law. An integral sliding mode-based discontinuous control law is utilized to compensate for the effects of unknown dead-zone, disturbance, and a component of uncertainties. As a result, a system dynamics that evolves free of these effects during the sliding mode is obtained. Then, an adaptive dynamic programming-based dynamic event-triggered optimal control law is designed to stabilize the sliding mode dynamics with the help of critic-only neural network architecture. Finally, stability analysis of the closed-loop system is provided and the effectiveness of the developed DETNOC scheme is verified.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077487","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}

{"title":"Positive steady states in a two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity","authors":"","doi":"10.1016/j.cnsns.2024.108311","DOIUrl":"10.1016/j.cnsns.2024.108311","url":null,"abstract":"<div><p>– In this paper, we consider the following stationary two-species chemotaxis-competition system with signal-dependent diffusion and sensitivity <span><span><span>(0.1)</span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>Δ</mi><mi>u</mi><mo>=</mo><mi>λ</mi><mi>u</mi><mo>−</mo><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>b</mi><mi>u</mi><mi>v</mi><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mtext>div</mtext><mrow><mo>[</mo><mi>d</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>∇</mo><mi>v</mi><mo>+</mo><mi>χ</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mi>v</mi><mo>∇</mo><mi>w</mi><mo>]</mo></mrow><mo>=</mo><mi>μ</mi><mi>v</mi><mo>−</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>c</mi><mi>u</mi><mi>v</mi><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>3</mn></mrow></msub><mi>Δ</mi><mi>w</mi><mo>=</mo><mo>−</mo><mi>κ</mi><mi>w</mi><mo>+</mo><mi>τ</mi><mi>u</mi><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mi>v</mi><mo>=</mo><mi>w</mi><mo>=</mo><mn>0</mn><mo>,</mo></mtd><mtd><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>x</mi><mo>∈</mo><mi>∂</mi><mi>Ω</mi></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>in a bounded smooth domain <span><math><mrow><mi>Ω</mi><mo>⊂</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mspace></mspace><mrow><mo>(</mo><mi>N</mi><mo>≥</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, where <span><math><mrow><mi>λ</mi><mo>,</mo><mi>μ</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>d</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>,</mo><mi>κ</mi><mo>,</mo><mi>τ</mi></mrow></math></span> are positive constants, and <span><math><mrow><mrow><mo>(</mo><mi>d</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>,</mo><mi>χ</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>)</mo></mrow><mo>∈</mo><mtext>[</mtext><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>∞</mi><mtext>)</mtext><mo>]</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span> with <span><math><mrow><mi>d</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>,</mo><mi>χ</mi><mrow><mo>(</mo><mi>w</mi><mo>)</mo></mrow><mo>&gt;</mo><mn>0</mn></mrow></math></span> for all <span><math><mrow><mi>w</mi><mo>≥</mo><mn>0</mn></mrow></math></span>. Since there does not exist an immediate change variable that transforms (0.1) into a sem","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142049776","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}

{"title":"Studying the transient process of an intermittent control system from its response property","authors":"","doi":"10.1016/j.cnsns.2024.108309","DOIUrl":"10.1016/j.cnsns.2024.108309","url":null,"abstract":"<div><p>As we all know, the output of a system is affected by its input and response properties. When the input switches, there must exist a transient process in the output and this transient process is different for different systems due to their different response properties and different dynamic process. However, the response property and dynamic process have rarely been studied in the obtained achievements about the transient process of an intermittent control system. The obtained achievements cannot agree with the real physical process and cannot be applied to study the transient process in engineering.</p><p>By introducing the unit step function and taking the intermittent input signal as a piecewise signal, we have studied the transient process. Our research shows that the transient process is related to the response characteristics, historical dynamic information, and control parameters, which agrees well with the real system and can be applied to analyze and optimize the transient process in engineering. Some examples in our paper verify our theoretical achievements.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142058506","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}

{"title":"Control and stochastic dynamic behavior of Fractional Gaussian noise-excited time-delayed inverted pendulum system","authors":"","doi":"10.1016/j.cnsns.2024.108302","DOIUrl":"10.1016/j.cnsns.2024.108302","url":null,"abstract":"<div><p>In this paper, we investigate the control and dynamic behavior of the inverted pendulum system with time delay under fractional Gaussian noise excitation. For H=1/2 and H<span><math><mrow><mo>∈</mo><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mn>2</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span>, we analyze the stochastic dynamic characteristics of the system under Hopf bifurcation, utilizing time delay and noise intensity as bifurcation parameters, and validate the theoretical conclusions through numerical simulations. We also defined the engineering application range of angle and angular velocity under both asymptotically stable and periodic oscillation dynamic states. Furthermore, using the stochastic <span><math><mrow><mi>I</mi><mi>t</mi><mover><mrow><mi>o</mi></mrow><mrow><mo>ˆ</mo></mrow></mover></mrow></math></span> equation, we determined the values of time delay and noise intensity that satisfy the maximum engineering application range of angle and angular velocity, and verified their accuracy against the original equation. Additionally, we observed stochastic D-bifurcation and P-bifurcation arising from the combined effects of time delay and noise. Our results exhibit remarkable consistency between analytical and numerical findings, affirming the robustness of our approach and shedding light on the intricate dynamics of the system.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088306","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}

{"title":"Reduced-order reconstruction of discrete grey forecasting model and its application","authors":"","doi":"10.1016/j.cnsns.2024.108310","DOIUrl":"10.1016/j.cnsns.2024.108310","url":null,"abstract":"<div><p>Discrete grey forecasting models based on an accumulative operator have been widely used in many practical fields. With the development of grey forecasting models, it is a problem to be solved to further analyze internal mechanisms and unify the structures. This paper aims to reconstruct the model from a perspective of sequence characteristics and simplify the modeling steps under the condition of ensuring the accuracy of the model. First, this paper analyzes dynamic sequence evolution hidden and mines relationship between the structure and original sequence features contained in discrete grey forecasting model. Then, the reconstruction is carried out to prove the equivalence and quantitative relation between reduced-order model and original model. Under order recursive estimation, new parameters are addressed. Finally, theoretical correctness is verified by large-scale numerical simulation. Moreover, the reduced-order model is applied for prediction on the peak of battery incremental capacity and capacity degradation. Results show the effectiveness and superior prediction performance of the reduced-order model, where MAPEs of grey forecasting models have controlled under 4%.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142077486","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}