Table of Content

15 February 2025, Volume 42 Issue 1 Previous Issue   

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Image Reconstruction Model Based on Improved Exponential Total Variation LI Yan, GUO Dinghui 2025, 42 (1):  1-12.  doi: 10.3969/j.issn.1005-3085.2025.01.001 Abstract ( 41 )   Save In this paper, exponential total variational reconstruction model is introduced into computed tomography reconstruction model to establish an improved exponential total variational reconstruction model (METV) which can perform gray transformation at low energy to properly suppress the step effect and avoid over-smoothing at high energy. The existence of the solution of the minimization problem corresponding to the improved model is proved by variational method. It is also verified by experiments that under the condition of adding mixed noise of different intensity, compared with TV and ETV models, the reconstructed image of METV model can be very close to the real image, and the obtained image edge structure is clearer. Related Articles | Metrics

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Six Order Mixed Compact Difference Schemes for Convection Diffusion Reaction Equations WANG Mingjing, TIAN Fang 2025, 42 (1):  13-31.  doi: 10.3969/j.issn.1005-3085.2025.01.002 Abstract ( 29 )   Save For the variable coefficient convection-diffusion reaction equation, three sixth-order hybrid compact difference schemes are constructed. Firstly, the high-order difference approximation operator of high-order derivatives is derived based on Taylor series expansion. Then, by using the truncation error residual correction method and the original model equation, three sixth-order hybrid compact difference schemes for solving the convection-diffusion reaction equation are obtained. Finally, typical numerical examples are selected to conduct numerical experiments to verify the accuracy of the proposed schemes. Related Articles | Metrics

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Solving Least Square Problem of Quaternion Stein Matrix Equation Based on $\mathcal{H}$-representation YUE Shufang, LI Ying, ZHAO Jianli 2025, 42 (1):  32-44.  Abstract ( 15 )   Save It mainly studies the least square solutions of quaternion Stein matrix equation. Firstly, by using the real representation method of quaternion matrix, the problem of solving quaternion matrix equation is transformed into the problem of solving corresponding real matrix equation. Secondly, according to the symmetric structural properties of the centrosymmetric (anti-centrosymmetric) matrix, using the $\mathcal{H}$-representation to extract independent elements and simplify the calculation, we give a new method for solving the least square centrosymmetric (anti-centrosymmetric) solution of the quaternion Stein matrix equation. Finally, the solution set of the least squares centrosymmetric (anti-centrosymmetric) solution of the equation and the necessary and sufficient conditions for the solution are given. The effectiveness of the method and results is demonstrated by numerical algorithms and examples. Related Articles | Metrics

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A Local Preconditioned SOR-like Method for Generalized Absolute Value Equations ZHANG Zhenzhu, LI Chaoqian 2025, 42 (1):  45- 58.  Abstract ( 18 )   Save Generalized absolute value equations play an important role in fields such as Economics and Engineering, and solving it has become one of the important problems in computational mathematics and optimization. Based on their equivalent forms and preconditioning techniques, we have conducted research on efficient algorithms for solving generalized absolute value equations, a local preconditioned SOR-like method is proposed. The convergence of this method is discussed. Numerical examples are also given to demonstrate that it outperforms some existing methods in some cases. Related Articles | Metrics

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New Type Projection Algorithm for Basis Pursuit Denoising Problem XUE Bing, ZHENG Zuokui 2025, 42 (1):  59-76.  Abstract ( 9 )   Save Basis pursuit de-noising (BPDN) problem is considered to be an important model encountered in the sparse signal reconstruction problem. A lot of numerical algorithms about solving the BPDN problems have been extensively developed, but the solving speed and accuracy are still need improved when the dimension increases greatly. Therefore, it is an important and challenging problem to construct an optimization algorithm with faster solution speed and higher accuracy for solving BPDN problems. Based on splitting the decision variable into two nonnegative auxiliary variables in the BPDN problems, and transform BPDN problems into linear complementarity problems. Based on a special iterative format, we present a new projection algorithm without any line search to find a suitable step size and computation of the subdifferential of the absolute value function, which needs only one value of the mapping per iteration and only one projection onto the nonnegative quadrant. At the same time, the global convergence of iterative sequences generated by the new algorithm is established in detail. Numerical experiments on the BPDN problems with different cases are also given to verify the effectiveness of the proposed method. Thus, the proposed new method improves the efficiency and accuracy of solving the high dimensional the BPDN problems, and have certain theoretical value and practical significance. Related Articles | Metrics

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A Production-inventory Model with Monitoring Window and Outsourcing Strategies and Its Properties under Demand Disruption WANG Mengzheng, WAN Zhong, CHU Shuhan 2025, 42 (1):  77-96.  Abstract ( 12 )   Save Production and inventory management often suffers from emergency events, which always lead to the phenomenon of ``stratification'' in market demand. By the mixed producing and outsourcing strategy, we propose a new production and inventory model with monitoring window from the perspective of manufacturers when an emergency event occurs during a fixed production period. With help of the monitoring strategy, the manufacturer determines a sudden change of demand rate. By building and solving the proposed production and inventory model defined by a system of differential equations, the analytical expressions of the productivity adjustment, the outsourcing time and the outsourcing quantity so that the supply matches the demand again. In case study, we apply the developed model and its theoretical properties to analyze impacts of COVID-19 on the production and inventory of small and medium enterprises, including the impacts of the demand fluctuation intensity, the size of monitoring window, and the producing and outsourcing structure. The results from the numerical simulation reveal a series of valuable practical managerial insights underlying the proposed model in this paper. Related Articles | Metrics

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Dynamic Mean-variance DC Pension Planning with a Minimum Guarantee under Stochastic Interest Rate and Inflation Environments KOU Mengke, CHANG Hao 2025, 42 (1):  97-113.  Abstract ( 17 )   Save In a defined contribution (DC) pension plan, the contribution rate is determined in advance and the pension payment depends on the contribution and investment return during the pension accumulation stage, and the investment risk is borne by the pension members themselves. In this situation, to realize the precise investment in pension funds and to improve the payment efficiency of pension funds has great theoretical and practical significance for relieving the current pension pressure. The interest rate model is described by the Cox-Ingersoll-Ross (CIR) dynamics. In addition, in order to keep the living standard of members, the terminal value of the pension plan should exceed a guarantee which serves as an annuity after retirement. By applying the principle of Lagrangian duality theorem and stochastic dynamic programming, the extended Hamilton-Jacobi-Bellman (HJB) equation is solved, we obtain the mean-variance efficient strategy and the efficient frontier explicitly. The result shows that the capital market line in the environment of the interest rate risk, the inflation risk and the salary risk is still a straight line in the mean-standard deviation plane. Related Articles | Metrics

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Construction and Simulation of Hydraulic Fracturing Model with Temperature Field in Deep Shale Gas Reservoirs ZOU Longqing, HE Yunbin, E Xuanji, LU Han 2025, 42 (1):  114-126.  Abstract ( 17 )   Save The deep shale gas reservoir has the geological characteristics of high temperature and high pressure, and the conventional fluid-structure coupling fracturing model cannot describe the effect of temperature field on fracture propagation. In this paper, based on some reasonable assumptions, a full three-dimensional thermo-fluid-solid coupling hydraulic fracturing model is constructed to describe the hydraulic fracture propagation process of deep shale gas reservoirs. Numerical experiments with finite volume discretization and implicit time discretization show that temperature has a significant effect on hydraulic fracture propagation. According to the results of numerical simulation experiments, the following conclusions are drawn: Compared with the conventional model, the fracture model considering temperature field is more difficult to crack and has greater fracturing difficulty; Higher bottom hole temperature makes it more difficult for fractures to expand, and there is a significant difference in fracture length between high temperature environment and normal temperature environment; The larger the coefficient of thermal expansion, the more significant the effect of bottom hole temperature on fracture propagation. Related Articles | Metrics

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Interval Number Ranking and Its Application Based on Different Risk Preferences and Irrational Behaviors of Decision Makers LI Huiyun, YE Guoju, LIU Wei, ZHAO Dafang, GUO Yating, SHI Fangfang 2025, 42 (1):  127-138.  Abstract ( 17 )   Save Based on the different attitudes of decision makers toward risk and the fact that decisions can be influenced by complex psychological mechanisms such as limited human rationality, this paper proposes two interval number ranking methods for the interval number ranking problem arising from the selection of decision options. First, a two-parameter app-roach is introduced to represent the risk preferences of the decision maker and to measure the concessions made by the decision maker for the goal, thus giving a full order to compare the number of intervals, and the parameters are selected by great entropy to make the ranking method scientific and reasonable. Then the prospect theory is introduced to reflect the influence of irrational psychology on decision making under uncertainty and a second method of ranking interval numbers is given. Finally, the existing interval number ranking methods are compared and analyzed with the method proposed in this paper through the existing cases, and it is verified that the first two-parameter method can contain the results obtained by the two existing methods listed in this paper after changing different parameters, so that the two-parameter method is more widely used; the second prospect theory method takes into account the psychological behavior of people when they face gains and losses, and the decision results are more in line with the reality. Related Articles | Metrics

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Optimal Asset Allocation and Life Annuity Payment Strategy under Cobb-Douglas Utility and Epstein-Zin Recursive Utility WANG Suxin, RONG Ximin, ZHAO Hui 2025, 42 (1):  139-158.  Abstract ( 13 )   Save Life annuity plays an important role in the withdrawal phase of pensions, and it can help people deal with longevity risks effectively. This paper considers a stochastic model for a life annuity plan in continuous time, where the initial value of the individual annuity \mbox{account} is determined in advance, while the annuity payments depend on the financial situation of the account. The annuity fund is allowed to invest in a risk-free asset and a risky asset. The fund manager can adjust the annuity payment level and charge management fees to ensure the stable operation of the plan. In the objective function, we aim to maximize the utility of the weighted product of the annuity payment adjustment and the management fee, which is taken in the form of Cobb-Douglas utility. By applying dynamic programming approach, we establish the corresponding Hamilton-Jacobi-Bellman equation and derive the optimal strategies and the value function explicitly. Furthermore, the Epstein-Zin recursive utility is considered as an extension and we find the elasticity of intertemporal substitution has a positive effect on the annuity payment adjustment and the management fee. Numerical examples are presented to illustrate the sensitivity of the optimal strategies to model parameters, and the corresponding economic explanations are given, which demonstrate that this annuity plan is sustainable and can provide stable annuity payment for participants. Related Articles | Metrics

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Dynamics and Synchronization of a Fractional-order Discrete Lozi Map LIANG Xuefeng 2025, 42 (1):  159-168.  Abstract ( 17 )   Save In the paper, a fractional-order Lozi map with discrete fractional calculus is analyzed. Firstly, dynamics of the map with different values of a parameter or a derivative order is studied. Hopf and Period-doubling bifurcations are observed. The map has the chaotic attractors with different topological structures. Secondly, when a system parameter and a derivative order are varied, bifurcations for the system are investigated and presented in a three-dimensional space. The dynamics behavior of the system changes from chaos to regular with an decrease of derivative orders, and changes from regular to chaos with an increase of derivative orders. Finally, the synchronization of the fractional-order discrete Lozi map is studied. The validity of the designed controllers is demonstrated by the numerical simulations. Related Articles | Metrics

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Perturbation and Stability of Approximate Oblique Dual g-frames in Hilbert Space JIA Lu, YANG Shouzhi 2025, 42 (1):  169-176.  Abstract ( 13 )   Save In this paper, we study the perturbation problem of g-frame in separable Hilbert space $\mathcal{H}$. The stability conditions of g-frame with approximate oblique dual are given, we also reconstructed the approximate oblique dual g-frame, an approximate oblique dual g-frame of higher approximation order is obtained. Related Articles | Metrics

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Bifurcation Analysis of a Subthalamic Nucleusg-globus Pallidus Network Model with Electromagnetic Induction YI Dan, ZHENG Yanhong, CHEN Guotai, ZENG Qiaoyun 2025, 42 (1):  177-187.  Abstract ( 18 )   Save Parkinson's disease is a movement disorder of the nervous system caused by the abnormal oscillations in cortical-basal ganglia circuits, and electromagnetic induction plays an important role in neuronal activities. In this paper, a subthalamic nucleus-globus pallidus network model with electromagnetic induction is proposed to analyze the dynamic mechanism of the Hopf bifurcation with the help of the magnetic flux variable. By analyzing the characteristic equations and the stability of the model, the conditions for the occurrence of Hopf bifurcation with time delay are obtained, and numerical simulation verifies the results of theoretical analysis. It is revealed that increasing synaptic transmission delay can induced oscillations. In addition, two-parameter bifurcation analysis shows that the increase of average magnetic flux $k$ has a certain elimination the system oscillation caused by synaptic transmission delay $T$ and synaptic connection weight $W_{CS}$. It is hoped that the results might have some help in understanding the role of electromagnetic induction in Parkinson's disease. Related Articles | Metrics

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Optimization Method of Electric Vehicle Fast Charging Station Site Selection and Capacity Determination Based on Ant Colony Algorithm WANG Honggang, CHEN Changlong, YU Zhou 2025, 42 (1):  188-198.  Abstract ( 14 )   Save With increasing awareness of ecological issues and diminishing reliance on fossil fuels, electric vehicles (EVs) have garnered widespread attention as a sustainable transportation solution. Electric vehicles are favored for their environmental friendliness, yet their limited energy storage capacity restricts driving range, making efficient energy utilization crucial. To ensure timely energy replenishment for electric vehicles, this paper presents an optimization method based on the ant colony algorithm for fast charging station location and capacity determination. This study takes into account factors such as real-time pricing, usage duration, critical peak pricing, and peak time rebates, aiming to devise an optimal charging pricing strategy. Based on this strategy, the ant colony optimization algorithm is applied to conduct an in-depth analysis of electric vehicle traffic and charging demand. By comprehensively considering construction costs, equipment procurement expenses, maintenance fees, and user driving costs, an optimization model for fast charging station location and capacity determination is constructed. The ant colony algorithm is then utilized to solve this model, yielding the optimal location and capacity configuration. Experimental results demonstrate that the proposed optimization method based on the ant colony algorithm exhibits superior comprehensive performance, making it suitable for practical application scenarios. Related Articles | Metrics