中国科学院数学与系统科学研究院期刊网

01 August 2026, Volume 46 Issue 8
    

  • Select all
    |
  • CHEN Zuo, LI Dongmei, GUAN Jiancheng
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2460-2479. https://doi.org/10.12341/jssms250726
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Multidimensional system reduction is often converted to the equivalence between multivariate polynomial matrices and their Smith forms. This paper focuses on the unimodular equivalence of a class of multivariate polynomial matrices to their Smith forms. A criterion for the unimodular equivalence of such matrices and their Smith forms is proposed, with the result extended to non-square and rank-deficient cases. Finally, a general algorithm for reducing such matrices to their Smith forms is presented and an example is provided to illustrate the algorithm.
  • ZENG Zhongli, LIU Jinwang, WU Tao
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2480-2489. https://doi.org/10.12341/jssms250751
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    This paper studies the Smith form of polynomial matrices by using polynomial algebra isomorphism, discovers several new types of polynomial matrices, and characterizes the necessary and sufficient conditions for these new types of polynomial matrices to be equivalent to their Smith forms. These conditions can be judged by the theory and caculation of Gröbner bases,and there are corresponding algorithms.
  • LIU Jinwnag, WU Tao, GUAN Jiancheng, KANG Ying
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2490-2506. https://doi.org/10.12341/jssms250752
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    The equivalence of multidimensional systems is closely related to the equivalence and reduction of multivariate polynomial matrices, and the Smith form of matrices plays a key role in matrix equivalence. The problem of the equivalence of multivariate polynomial matrices to Smith form is very complex and this paper studies the problem of equivalence between quasi weak linear multivariate polynomial matrices and their Smith form, characterizes the sufficient and necessary conditions for this type of matrix to be equivalent to its Smith form, and provides corresponding algorithms.
  • QI Yue, XIA Xianwei, YAO Xiangmei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2507-2516. https://doi.org/10.12341/jssms250765
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    In 2021, Wang gave a systematic study on the parity of coefficients of classical mock theta functions. In 2022, a number of congruences modulo 4 for five mock theta functions have been proved by Chen and Garvan. Motivated by their works, we prove several new congruences modulo 4 and 8 for some Gordon and McIntosh's mock theta functions based on some identities involving mock theta functions and some results on congruences for the second-order mock theta function $A^{(2)}(q)$ due to Chen and Garvan. In particular, we confirm a conjecture on congruences modulo 8 for the second-order mock theta function $B^{(2)}(q)$.
  • ZENG Zhenbing, LU Jian, XU Yaochen
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2517-2547. https://doi.org/10.12341/jssms250799
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    It is known that the Heilbronn number of eight points in triangle is between 0.067789 and 0.067816, the eight points lie in certain small rectangular regions, respectively, and there are at most 11 minimal triangles in the optimal configuration. In this paper we prove that there are at least 8 minimal triangles through infinitesimal perturbation analysis and transformed the Heilbronn problem of eight points in triangle to 18 non-linear programming problems, where the constraints are bilinear polynomial inequalities. We get the solution to one of the 18 non-linear programming problems using symbolic computation in a minimal polynomial of degree 7, proved that the solutions of other 17 problems are not exceed this value, and finally determined the Heilbronn optimal arrangement of eight points in triangles.
  • MA Ying, WANG Juan, XU Changqing, YANG Xiaoguang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2548-2563. https://doi.org/10.12341/jssms250804
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Missing values are common in biomedical data and seriously affect the reliability of subsequent data analysis. This paper investigates the application of tensor completion to clinical data recovery. First, electronic health records are preprocessed, and interpolation and randomized singular value decomposition (rSVD) are employed under a matrix completion framework to analyze the limitations of matrix-based models. Subsequently, temporal information is incorporated to construct a third-order clinical data tensor. A nonnegative CP tensor completion (NCPC) algorithm, solved by a block coordinate descent strategy, is adopted for tensor recovery and compared with the simple low-rank tensor completion (SiLRTC) algorithm. Experiments are conducted on publicly available clinical datasets under different random missing ratios, and the reconstruction performance is evaluated using the Relative Squared Error (RSE). The experimental results show that tensor-based modeling exploits the multidimensional structure of clinical data more effectively than matrix-based approaches. Moreover, the NCPC algorithm consistently achieves lower reconstruction errors and better robustness than the SiLRTC algorithm across different missing rates. These results demonstrate that combining tensor modeling with nonnegative CP tensor completion provides an effective preprocessing approach for incomplete biomedical data and offers reliable support for subsequent clinical data analysis.
  • WANG Xiaoqiang, SUN Siyu, ZHENG Dabin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2564-2584. https://doi.org/10.12341/jssms250845
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Linear codes with few weights are widely used in various fields such as strongly regular graphs, secret sharing schemes, association schemes and authentication codes. The construction of linear codes with few weights and the determination of their weight distributions have always been an important research topic in error-correcting codes. In this paper, by selecting specific defining sets, this paper constructs two-weight, three-weight and four-weight linear codes with good parameters over finite fields with odd characteristic. By using some special exponential sums, the weight distributions of these linear codes are determined. The results generalize the corresponding results of Zhu and Xu (2017), Jian, et al. (2019) and Zheng, et al. (2021).
  • JIA Yanna, JIN Can, LIU Junjun
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2585-2597. https://doi.org/10.12341/jssms250491
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    This paper investigates the output regulation problem for uncertain variable-coefficient heat equations with matched boundary disturbances. The thermal system is governed by an uncertain parabolic partial differential equation (PDE) with mixed boundary conditions, characterized by unknown spatially varying diffusion coefficients and subject to smooth uncertain boundary disturbances that may potentially be unbounded in magnitude. We propose a robust control strategy that synergistically combines linear feedback design with the Twisting second-order sliding mode control algorithm, properly reformulated and integrated within an infinite-dimensional framework. The well-posedness of the closed-loop system, formulated as a differential inclusion, is established through maximal monotone operator theory. Furthermore, by employing a nonstandard Lyapunov functional and under the condition that the controller tuning parameters satisfy certain fundamental inequalities, we prove the global asymptotic stability of the closed-loop system in an appropriate Sobolev space. Numerical simulations in the experimental section validate the effectiveness of the proposed controller design.
  • XIONG Yongchang, YANG Yuyue, GUO Kun
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2598-2617. https://doi.org/10.12341/jssms250170
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    The rational allocation of basic education resources is essential to achieving educational equity and improving educational quality, while the enhancement of human capital is a core driving force for building a strong education system. Based on annual provincial panel data from 2000 to 2022, this paper employs fixed-effects models and difference-in-differences (DID) models to examine the effects of the accessibility, quality, and balanced allocation of basic education resources on human capital accumulation. The results show that the accessibility of basic education resources has a long-term positive effect on the stock of human capital, with the most significant effect observed at the junior high school stage. The effects of the quality of basic education resources on human capital quality vary across educational stages. The mechanism analysis indicates that high-quality education resources further enhance regional human capital quality by attracting inflows of highly educated individuals. The balanced allocation of basic education resources also plays a positive role in improving the structure of human capital, especially at the junior high school stage. In addition, the DID analysis further confirms the positive effect of policies promoting the balanced development of education on human capital accumulation.
  • YI Pingtao, WANG Shiye, LI Weiwei
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2618-2631. https://doi.org/10.12341/jssms241008
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    For the interval-type uncertainty group evaluation problem, a consensus-driven interval-based group evaluation method is proposed from the perspective of group consensus, using a possibility comparison approach and extending the stochastic aggregation solution algorithm. Firstly, the superiority matrix is used to measure the preference degree of different evaluators for the evaluated object under the same indicator, and the indicator weights are solved by the consensus differences among indicators; then, the overall preference degree of each evaluator for the evaluated object is solved to obtain the expert weights; finally, the Spearman rank correlation coefficient is used as the reference standard for consensus aggregation, identification of decision quality for a large amount of possibility judgement information, and aggregation of the solution, resulting in consensus-driven possibility ranking conclusion. This paper verifies the validity and applicability of the method by applying arithmetic examples, and further enriches and improves the theoretical and applied research of stochastic aggregation algorithm in group evaluation.
  • LIU Wenhua, TANG Xiaoling, SHI Luqing, LIN Yutong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2632-2647. https://doi.org/10.12341/jssms241024
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    This study investigates the effect of the digital economy on the high-quality development of the tourism industry, with a focus on its regional heterogeneity and spatial spillover effects. Using panel data from Chinese provinces spanning the period from 2015 to 2021, the study constructs indicators for the digital economy and high-quality tourism development, with the entropy method employed for indicator weighting. Through the application of a two-way fixed effects model, the findings indicate that the digital economy exerts a significant positive effect on the development of the tourism sector. Regional heterogeneity analysis reveals that digital technologies are more effectively integrated into the tourism industry in the eastern regions, whereas their application may be constrained in the remote areas of central and western regions. Moreover, analyses using the Moran's I index and the Spatial Durbin model highlight that the digital economy has a significant positive indirect effect and spatial spillover effects on the high-quality development of tourism. The empirical findings of this study provide valuable evidence for enhancing regional digitalization and promoting high-quality development in the tourism industry.
  • LIU Xinheng, YOU Taohong, YANG Taoning, YANG Xin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2648-2665. https://doi.org/10.12341/jssms250098
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Exchange-traded funds (ETF), as a burgeoning tool for index-based investment, have yet to be fully understood regarding their feedback effects from capital markets to the real economy and their influence on corporate behavior. This study examines A-share listed companies from 2011 to 2023, employing a fixed-effects model to empirically test how ETF ownership impacts corporate misconduct. The findings indicate that ETF ownership significantly curtails corporate violations, primarily due to ETFs exerting both resource and governance effects. Further heterogeneity tests reveal that the inhibitory effect of ETF ownership on corporate misconduct is more pronounced in samples with higher information asymmetry, more severe agency conflicts, and non-state-owned enterprises. This research aims to deepen the understanding of the real economic effects of ETF ownership and provides robust reference points for regulators in formulating policies to standardize the market behavior of institutional investors.
  • QIAN Hua, SUN Qian, LI Min, WEN Fenghua
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2666-2687. https://doi.org/10.12341/jssms250121
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    This study employs panel data from selected 278 Chinese prefecture-level cities (2012-2021) to construct a three-dimensional real estate health index incorporating price, structure, and speed, and applies a panel vector autoregression (PVAR) model to analyze pathways toward healthy real estate development driven by land finance transformation and economic structure optimization. Findings reveal that real estate health is a core driver of economic growth and sustainable land finance, with its enhancement significantly boosting land revenue (coefficient 2.4867, 1 % significance) and indirectly stimulating economic growth (coefficient 1.8646, 1 % significance). Regional heterogeneity is evident: Eastern regions leverage a “land finance + innovation industries” dual-driven mechanism, while western and northeastern areas require revitalizing idle land reserves and intelligent upgrades to activate resources. Industrial structure differences further shape transition trajectories-service-oriented cities should adopt “land finance + services” synergy, whereas industrial cities need to strengthen “land finance + manufacturing upgrading” integration. The study proposes regional differentiated policies, heterogeneous industrial coordination, technology-driven innovation, and institutional reforms to address the “real estate dependence-fiscal fragility-economic imbalance” cycle, offering theoretical and practical insights for sustainable urban development.
  • PENG Dinghong, BAI Wenjing, PENG Bo
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2688-2711. https://doi.org/10.12341/jssms240798
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Accurately measuring the coupling coordination degree between innovation factor allocation efficiency and innovation benefit is a key prerequisite for solving the dilemma of “high input, low benefit” of resource-based cities, promoting their green transformation and realizing sustainable development. Since the existing coupling coordination degree model is difficult to describe the nonlinear coupling and coordination effects of elements in innovative single-effect systems and effectively process dynamic information, an incentive combination radar chart model with reward and punishment features and guiding functions is proposed under the framework of the coupling and coordination degree model. Specifically, hesitant fuzzy sets are used to represent evaluation information. Based on the traditional radar map area model, the area, perimeter and eccentricity models of the excitation combined radar map are proposed to highlight the influence of the order of the indicators on the evaluation results and the function of the good and bad indicators. Then, the Mazziotta-Pareto Index composite incentive combination radar chart area, perimeter and eccentricity are utilized to comprehensively consider the coordination of the single-effect system and highlight the advantages and disadvantages. Subsequently, the deviation coefficient minimization model is used to calculate the coupling degree of the dual-effect system. Finally, the model is applied to five resource-based cities in Hebei Province to verify the effectiveness and superiority of the proposed model.
  • LIN Hui, JIAN Dan, LUO Qiang
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2712-2731. https://doi.org/10.12341/jssms250985
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Many practical problems in economics, management, engineering control, and artificial intelligence can be formulated directly or indirectly as unconstrained optimization problems, and the conjugate gradient method is one of the core algorithms for solving such large-scale problems. In this paper, we propose an improved Dai-Liao conjugate gradient method by modifying and truncating the Dai-Liao conjugate parameters and introducing a restart step into the search direction. Without relying on any line search conditions, the search direction generated by this method can satisfy the sufficient descent condition. Under standard assumptions, the strong convergence of the proposed method is proved. Numerical experiments on medium-large-scale problems from test collections such as CUTE show that the algorithm performs well. In addition, applying the method to image restoration and machine learning models further validate the effectiveness of the proposed method.
  • YAO Fengmin, LIN Jianing, WANG Liqing, SHENG Zhuo
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2732-2752. https://doi.org/10.12341/jssms250068
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    In the context of consumer skepticism about manufacturer's green design behavior, six closed-loop supply chain (CLSC) game models were constructed, considering whether the manufacturer applies blockchain and the differences in recycling entities. The impacts of consumer skepticism, unit introduction cost of blockchain and the step pricing parameters for smart recycling rewards on the recycling entities and blockchain introduction strategies within CLSC were analyzed. We find that an increase in consumer skepticism and the unit introduction cost of blockchain will reduce manufacturer's green design level, which may not always reduce market demand of new products, but is always detrimental to manufacturers' and retailers' profits. The green design may not always reduce total environmental impacts of new products and the changes in the recycling entities do not affect total environmental impacts of new products. While, the total environmental impacts of new products without blockchain application exceed that of those with blockchain application. When applying (not applying) blockchain, to maximize the profits, the manufacturer should entrust smart recycler to recycle (recycle by herself), and to maximize the volume of waste products recycling, the manufacturer should entrust smart (traditional) recycler to recycle. Moreover, smart recycler could adjust step pricing parameters and recycling price to maintain a stable recycling reward,while the increase in discard rate always works against the profitability of both manufacturer and smart recycler.
  • HE Zheng, ZHANG Tongjing, YANG Xiaohong
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2753-2770. https://doi.org/10.12341/jssms240675
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    In the platform ecosystem, platform enterprises and complementary enterprises work together to improve the efficiency of value co-creation. Because the level of effort of both sides can not be completely observed by each other, it will lead to bilateral moral hazard. Therefore, considering the factors such as platform governance ability, the external effect of the network, the embedding degree of the relationship, fairness preference, risk preference and so on, a multi-task principal-agent model is constructed, which is composed of platform enterprises and complementary enterprises under favorable and unfair conditions. The formal contract to maximize the value of both parties is explored. And the effects of various factors on the optimal effort level of the complementary enterprise, the optimal effort level of the platform enterprise to improve governance ability and the optimal income sharing ratio are analyzed. The conclusions of the study are as follows: The synergistic value, the degree of relationship embedding, and the enhancement of the pride intensity of complementary enterprises brought about by external network effects will increase the optimal effort level and optimal profit sharing ratio of complementary enterprises, while the enhancement of sympathy and jealousy intensity of complementary enterprises will reduce their optimal effort level and optimal profit sharing ratio. The research can help solve the bilateral moral hazard problem that arises between platform enterprises and complementary enterprises, reduce the negative impact of information asymmetry on the platform ecosystem, and thus improve the operational efficiency of the entire platform ecosystem.
  • LIU Yuanshan, XIA Yude, HUANG Jingxin
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2771-2781. https://doi.org/10.12341/jssms240416
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    The primary objective of this paper is to examine the challenges associated with optimization and tracking control in discrete-time multi-agent systems. First is to the optimal tracking control issue within the framework of a leader-follower multiagent system. Then, a novel approach based on policy iteration is introduced for calculating the control law and performance index. Meanwhile, the analysis of the convergence properties of this technique, ensuring its effectiveness in reaching optimal solutions, is also considered. To facilitate this, an Actor-Critic neural network framework is utilized to approximate the control law and iterative performance index function. The proposed approach enables the real-time implementation of the policy iteration method, eliminating the requirement for prior knowledge of the system's dynamics. This paper concludes with a series of simulation experiments that demonstrate the practicality and efficiency of the developed optimal tracking control strategies.
  • JIN Liang, HUANG He
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2782-2801. https://doi.org/10.12341/jssms240867
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    The existing literature has extensively demonstrated the significant value of technology adoption, but the interrelationship between fairness concerns, technology adoption, and their effects under asymmetric information has not been adequately studied. Under the background of asymmetric information and manufacturer's fairness concerns, we construct two game models before and after manufacturer adopts innovative technology. The impact of manufacturer's technology adoption decisions, the design of licensing contracts for innovative company, and equity concerns were investigated. The findings indicate that, regardless of the presence of fairness concerns, the manufacturer is motivated to adopt innovative technology and experience a “market expansion effect” only when their retained profits and the technological disparity with innovative company meets certain conditions. Moreover, the optimal licensing contract design for innovative company under asymmetric information includes both fixed fees and two-part tariff. Additionally, manufacturer's fairness concerns can increase their motivation for technology adoption, enhance social welfare, facilitate the redistribution of profits between manufacturer and innovative company, and mitigate the inequality in profit distribution between the two parties.
  • WAN Die, GUAN Peihua, SHU Taiyi
    Journal of Systems Science and Mathematical Sciences. 2026, 46(8): 2802-2816. https://doi.org/10.12341/jssms241047
    Abstract & Html ( ) Download PDF ( )   Knowledge map   Save
    Optimizing the business environment has been a significant initiative continuously promoted by China in recent years, aiming to drive the rapid development of new productive forces by enhancing resource allocation and stimulating market innovation vitality. This study takes the 2021 business environment innovation pilot city construction as a quasi-natural experiment to investigate the impact of the business environment on corporate innovation. The findings reveal that the pilot policies effectively stimulate local corporate innovation, and the promotion effect is more prominent among firms that are non-state-owned, with high institutional transaction costs, low degree of digital transformation, and high degree of development of the factor market in the host city. Mechanism analysis shows that the policies promote innovation through increasing market competition, alleviating financing constraints, and activating intellectual property trading markets in the pilot cities. Further results indicate that the promoting effect of the business environment on corporate innovation is mainly reflected in the “intensive margin” rather than the “extensive margin”, meaning that enterprises with prior patent applications are better positioned to leverage policy opportunities to enhance their innovation output. These findings contribute to the understanding of how the business environment influences micro-level enterprises and provide valuable insights for future policy optimization.