期刊：
Journal of Computational and Applied Mathematics,2026年475:116998 ISSN：0377-0427
通讯作者：
Pengcheng Xie
作者机构：
[Lin Li; Yuheng Zhou] School of Mathematics and Physics, University of South China, Hengyang, China;[Pengcheng Xie] Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, 94720, CA, USA;[Huiyuan Li] State Key Laboratory of Computer Science/Laboratory of Parallel Computing, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
通讯机构：
[Pengcheng Xie] A;Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, 94720, CA, USA
摘要：
Numerous practical problems give rise to nonlinear differential equations that may exhibit multiple nontrivial solutions relevant to applications. Efficiently computing these solutions is crucial for a profound understanding of these problems and enhancing various applications. Therefore, the development of a numerical method capable of finding multiple solutions efficiently is imperative. Additionally, the provision of an efficient iteration process is vital for promptly obtaining multiple solutions. In the current paper, we introduce a novel algorithm for identifying multiple solutions of semilinear elliptic systems, where the trust region Levenberg–Marquardt method, combined with the deflation technique, is designed to compute multiple solutions for the first time. Based on several numerical experiments, our algorithm demonstrates efficacy in efficiently identifying multiple solutions, even when the nonlinear term appearing in these equations involves solely the first derivative. Moreover, we validate the efficiency of our algorithm and unveil previously undiscovered solutions in the existing literature
Numerous practical problems give rise to nonlinear differential equations that may exhibit multiple nontrivial solutions relevant to applications. Efficiently computing these solutions is crucial for a profound understanding of these problems and enhancing various applications. Therefore, the development of a numerical method capable of finding multiple solutions efficiently is imperative. Additionally, the provision of an efficient iteration process is vital for promptly obtaining multiple solutions. In the current paper, we introduce a novel algorithm for identifying multiple solutions of semilinear elliptic systems, where the trust region Levenberg–Marquardt method, combined with the deflation technique, is designed to compute multiple solutions for the first time. Based on several numerical experiments, our algorithm demonstrates efficacy in efficiently identifying multiple solutions, even when the nonlinear term appearing in these equations involves solely the first derivative. Moreover, we validate the efficiency of our algorithm and unveil previously undiscovered solutions in the existing literature
作者：
Tongliang Zhang;Lijing Zheng*;Hengtai Wang;Jie Peng;Yanjun Li
期刊：
Finite Fields and Their Applications,2026年110:102743 ISSN：1071-5797
通讯作者：
Lijing Zheng
作者机构：
College of Science, North China University of Science and Technology, Tangshan, Hebei, 063000, China;Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan, Hebei, 063000, China;[Lijing Zheng; Hengtai Wang] School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, China;[Jie Peng] Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China;[Yanjun Li] Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui, 233030, China
通讯机构：
[Lijing Zheng] S;School of Mathematics and Physics, University of South China, Hengyang, Hunan, 421001, China
摘要：
Let q = 2 m . In a recent paper [34] , Zhang and Zheng investigated several classes of permutation pentanomials of the form ϵ 0 x d 0 + L ( ϵ 1 x d 1 + ϵ 2 x d 2 ) over F q 3 ( d 0 = 1 , 2 , 4 ) with a certain linearized polynomial L ( x ) . They applied the multivariate method and specific techniques to analyze the number of solutions of certain equations, and proposed an open problem: the permutation property of some pentanomials of this form remains unproven. In this paper, inspired by the idea of [12] , we further characterize the permutation property of such pentanomials over F q 3 ( d 0 = 1 , 2 , 4 ) . The techniques presented in this paper will be useful for investigating more new classes of permutation polynomials.
Let q = 2 m . In a recent paper [34] , Zhang and Zheng investigated several classes of permutation pentanomials of the form ϵ 0 x d 0 + L ( ϵ 1 x d 1 + ϵ 2 x d 2 ) over F q 3 ( d 0 = 1 , 2 , 4 ) with a certain linearized polynomial L ( x ) . They applied the multivariate method and specific techniques to analyze the number of solutions of certain equations, and proposed an open problem: the permutation property of some pentanomials of this form remains unproven. In this paper, inspired by the idea of [12] , we further characterize the permutation property of such pentanomials over F q 3 ( d 0 = 1 , 2 , 4 ) . The techniques presented in this paper will be useful for investigating more new classes of permutation polynomials.
作者：
Nan Li;Xianzhe Duan*;Jiawei Wang;Nadia Cheemaa;Hafiza Tasneem Nazish;...
期刊：
Progress in Nuclear Energy,2026年191:106104 ISSN：0149-1970
通讯作者：
Xianzhe Duan
作者机构：
[Nan Li] School of Resource and Environment and Safety Engineering, University of South China, Hengyang, 421001, China;Hunan Key Laboratory of the Rare Metal Minerals Exploitation and Geological Disposal of Wastes, Hengyang, 421001, China;National Key Laboratory for Nuclear Facility Decommissioning and Ecological Restoration, Hengyang, 421001, China;[Jiawei Wang] Beijing Research Institute of Uranium Geology, Beijing, 100029, China;School of Mathematics and Physics, University of South China, Hengyang, 421001, China
通讯机构：
[Xianzhe Duan] S;School of Resource and Environment and Safety Engineering, University of South China, Hengyang, 421001, China<&wdkj&>Hunan Key Laboratory of the Rare Metal Minerals Exploitation and Geological Disposal of Wastes, Hengyang, 421001, China<&wdkj&>National Key Laboratory for Nuclear Facility Decommissioning and Ecological Restoration, Hengyang, 421001, China
摘要：
Radionuclide pollution, driven by the rapid development of nuclear energy, has emerged as a critical environmental concern. Effectively managing radioactive nuclide pollutants to mitigate their impact on the ecological environment and human health is an urgent challenge. Bentonite, a naturally occurring mineral, is known for its strong adsorption capacity due to its unique mineral composition and structure, showing significant potential in nuclear waste management and environmental remediation. Its TOT layered structure, high ion exchange capacity, and large surface area enable effective adsorption of various radioactive nuclides, such as uranium (U), strontium-90 ( 90 Sr), cesium-137 ( 137 Cs), and selenium-79 ( 79 Se), playing a vital role in water pollution remediation and nuclear waste isolation. However, its adsorption performance is influenced by inherent physical-chemical properties and environmental conditions. Radiation exposure, especially from ionizing radiation (alpha, beta, and gamma), can significantly alter bentonite's structure, reducing its adsorption capacity, swelling behavior, and long-term stability. Significant advancements have been made in modifying bentonite. Modification techniques such as acid-base treatment, composite material enhancement, surface functionalization, and the addition of radiation-shielding additives have improved bentonite's adaptability and performance. This study reviews the current state of bentonite and its modified derivatives for radionuclide adsorption, examines their adsorption mechanisms and modification strategies, analyzes influencing factors, and explores potential applications in future nuclear waste management and environmental remediation. By optimizing its adsorption behavior and modification technologies, bentonite is expected to provide safer, more efficient, and sustainable solutions for controlling radioactive pollution, contributing to global nuclear pollution governance.
Radionuclide pollution, driven by the rapid development of nuclear energy, has emerged as a critical environmental concern. Effectively managing radioactive nuclide pollutants to mitigate their impact on the ecological environment and human health is an urgent challenge. Bentonite, a naturally occurring mineral, is known for its strong adsorption capacity due to its unique mineral composition and structure, showing significant potential in nuclear waste management and environmental remediation. Its TOT layered structure, high ion exchange capacity, and large surface area enable effective adsorption of various radioactive nuclides, such as uranium (U), strontium-90 ( 90 Sr), cesium-137 ( 137 Cs), and selenium-79 ( 79 Se), playing a vital role in water pollution remediation and nuclear waste isolation. However, its adsorption performance is influenced by inherent physical-chemical properties and environmental conditions. Radiation exposure, especially from ionizing radiation (alpha, beta, and gamma), can significantly alter bentonite's structure, reducing its adsorption capacity, swelling behavior, and long-term stability. Significant advancements have been made in modifying bentonite. Modification techniques such as acid-base treatment, composite material enhancement, surface functionalization, and the addition of radiation-shielding additives have improved bentonite's adaptability and performance. This study reviews the current state of bentonite and its modified derivatives for radionuclide adsorption, examines their adsorption mechanisms and modification strategies, analyzes influencing factors, and explores potential applications in future nuclear waste management and environmental remediation. By optimizing its adsorption behavior and modification technologies, bentonite is expected to provide safer, more efficient, and sustainable solutions for controlling radioactive pollution, contributing to global nuclear pollution governance.
摘要：
This paper presents a Respiratory Syncytial Virus (RSV) epidemic model for a continuous human population of super-spreading infected individuals. The model uses a generalized fractal-fractional derivative with the Mittag-Leffler function to analyze transmission, considering different infection stages, and demonstrates the effectiveness of certain individuals as viral spreaders. Using linear growth and Lipschitz requirements, the study determines the existence, uniqueness, positiveness, and boundedness of a proposed fractional-order system in order to assess its viability. The global stability of equilibrium points is verified by the Lyapunov function, and the effects of the model's parameters are investigated through sensitivity analysis. To comprehend the model's behavior and create preventative measures for infected people, a numerical simulation of its activity is also carried out. By offering a more realistic depiction of virus behavior at various dimensions and population effects, the fractal-fractional model enhances comprehension and forecasts. The results highlight the importance of fractional order and its fitting function in the model by demonstrating how input parameters affect the dynamic behavior of RSV infection. Such an investigation will aid in understanding the behavior of the RSV and develop prevention measures for infected individuals.
作者机构：
[Qian, Shengyou; Zou, Xiao; Chang, Shuai; Ju, Fangfang; Gong, Jinru; Tian, Feng; Lei, Weirui; Qian, SY] Hunan Normal Univ, Sch Phys & Elect, Changsha 410081, Peoples R China.;[Hu, Jiwen] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Zhai, Jintao] Hunan Univ, Coll Comp Sci & Elect Engn, Changsha 410012, Peoples R China.
通讯机构：
[Zou, X; Ju, FF; Qian, SY ] H;Hunan Normal Univ, Sch Phys & Elect, Changsha 410081, Peoples R China.
关键词：
AP;Flow and heat transfer;Focused ultrasound;Porous media
摘要：
Focused ultrasound has been widely used for the thermotherapy of soft tissue lesions. In this process, non-Fourier heat conduction and porous medium theory has to be considered because of non-homogeneous media. The study estimates the effects of the temperature lag and porous medium on the plaque ablation and drug treatment by focused ultrasound (FU). This study integrated TWMBT with the porous media heat transfer equation to characterize the internal temperature distribution within atherosclerotic plaque (AP) during FU application. The coupling equations are solved with finite element method. This paper focuses on the effects of porosity, permeability, and attenuation coefficient on the temperature and flow rate within the AP. The results consider artery wall thickness on heating of AP by FU. In addition, this study qualitatively analyzed the differences among the Pennes, TWMBT, and porous media heat conduction equations. The results show that the temperature responses of biological tissues exhibits lagging behaviors, which are inherently related to the physical time scale. Because of the disparities in the physical characteristics of the target and surrounding tissues, fluid flow within AP can have an impact on the distribution of tissue temperature, the direction of flow between solid tissues is determined by the permeability coefficient and ultrasonic intensity. The permeability coefficient, frequency and attenuation coefficient have a significant effect on the fluid flow within AP. Both heat dissipation and heat convergence are characteristics of fluid flow within the tissue, the focal location and the physical property parameters may affect the fluid heat dissipation and heat collection properties within the tissue. Furthermore, the temperature peak may not occur at the focus. The model can provide an analytical template for different types of precise thermal ablation AP, including radiofrequency ablation, microwave therapy, and laser ablation besides FU ablation, and can also provide a case for adjunctive drug transport.
Focused ultrasound has been widely used for the thermotherapy of soft tissue lesions. In this process, non-Fourier heat conduction and porous medium theory has to be considered because of non-homogeneous media. The study estimates the effects of the temperature lag and porous medium on the plaque ablation and drug treatment by focused ultrasound (FU). This study integrated TWMBT with the porous media heat transfer equation to characterize the internal temperature distribution within atherosclerotic plaque (AP) during FU application. The coupling equations are solved with finite element method. This paper focuses on the effects of porosity, permeability, and attenuation coefficient on the temperature and flow rate within the AP. The results consider artery wall thickness on heating of AP by FU. In addition, this study qualitatively analyzed the differences among the Pennes, TWMBT, and porous media heat conduction equations. The results show that the temperature responses of biological tissues exhibits lagging behaviors, which are inherently related to the physical time scale. Because of the disparities in the physical characteristics of the target and surrounding tissues, fluid flow within AP can have an impact on the distribution of tissue temperature, the direction of flow between solid tissues is determined by the permeability coefficient and ultrasonic intensity. The permeability coefficient, frequency and attenuation coefficient have a significant effect on the fluid flow within AP. Both heat dissipation and heat convergence are characteristics of fluid flow within the tissue, the focal location and the physical property parameters may affect the fluid heat dissipation and heat collection properties within the tissue. Furthermore, the temperature peak may not occur at the focus. The model can provide an analytical template for different types of precise thermal ablation AP, including radiofrequency ablation, microwave therapy, and laser ablation besides FU ablation, and can also provide a case for adjunctive drug transport.
作者机构：
[Song, Jiayin; Li, Junzhe; Li, Hao; Zeng, Sheng] School of Resources Environment and Safety Engineering, University of South China, Hengyang 421001, China;[Sun, Bing] School of Civil Engineering, University of South China, Hengyang 421001, China;[Cai, Qiue] School of Mathematics and Physics, University of South China, Hengyang 421001, China
通讯机构：
[Sheng Zeng] S;School of Resources Environment and Safety Engineering, University of South China, Hengyang 421001, China
摘要：
Mineral dissolution and erosion during the leaching of uranium-bearing sandstone have profound effects on the evolution of pore structure and uranium leaching rate. X-ray diffraction (XRD), scanning electron microscopy (SEM), and nuclear magnetic resonance (NMR) techniques were used to characterise mineral changes and pore structure evolution in samples. The results indicate that during the in situ leaching process, feldspar was transformed into clay minerals and quartz. Dolomite and calcite completely dissolved and formed a large amount of Ca 2+ , which increased the content of CaSO 4 . The CaSO 4 and MgSiO 3 precipitated particles formed in the reaction blocked the pores or migrated with the leaching solution, and the porosity of the sandstone initially decreased and then increased. Furthermore, the pores were divided into micropores, mesopores, and macropores, and combined with NMR fractal theory, it was found that the pore structure of sandstone exhibited multifractal characteristics. The obtained pore fractal dimension had a positive correlation with quartz, dolomite, calcite, and feldspar contents, whereas the other mineral components showed a negative correlation. This study provides a theoretical reference for understanding the mechanism of pore plugging and optimising the deplugging process in acid leaching for uranium extraction.
Mineral dissolution and erosion during the leaching of uranium-bearing sandstone have profound effects on the evolution of pore structure and uranium leaching rate. X-ray diffraction (XRD), scanning electron microscopy (SEM), and nuclear magnetic resonance (NMR) techniques were used to characterise mineral changes and pore structure evolution in samples. The results indicate that during the in situ leaching process, feldspar was transformed into clay minerals and quartz. Dolomite and calcite completely dissolved and formed a large amount of Ca 2+ , which increased the content of CaSO 4 . The CaSO 4 and MgSiO 3 precipitated particles formed in the reaction blocked the pores or migrated with the leaching solution, and the porosity of the sandstone initially decreased and then increased. Furthermore, the pores were divided into micropores, mesopores, and macropores, and combined with NMR fractal theory, it was found that the pore structure of sandstone exhibited multifractal characteristics. The obtained pore fractal dimension had a positive correlation with quartz, dolomite, calcite, and feldspar contents, whereas the other mineral components showed a negative correlation. This study provides a theoretical reference for understanding the mechanism of pore plugging and optimising the deplugging process in acid leaching for uranium extraction.
作者机构：
[Lin, Wenbin; Li, Jie] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Lv, Hongkui; Huang, Jiajun] Chinese Acad Sci, Inst High Energy Phys, Key Lab Particle Astrophys, Beijing 100049, Peoples R China.;[Lv, Hongkui] TIANFU Cosm Ray Res Ctr, Chengdu, Sichuan, Peoples R China.;[Lin, Wenbin; Liu, Yang] Univ South China, Sch Comp Sci, Hengyang 421001, Peoples R China.;[Huang, Jiajun] Univ Chinese Acad Sci, Beijing, Peoples R China.
通讯机构：
[Li, J ] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
期刊：
Mathematical Methods in the Applied Sciences,2025年48(5):5768-5780 ISSN：0170-4214
通讯作者：
Chen, HW
作者机构：
[Chen, Huiwen; Ouyang, Zigen; Xu, Xiaoliang] Univ South China, Sch Math & Phys, Hengyang, Hunan, Peoples R China.;[Chen, Huiwen; Ouyang, Zigen] Univ South China, Hunan Key Lab Math Modeling & Sci Comp, Hengyang, Hunan, Peoples R China.
通讯机构：
[Chen, HW ] U;Univ South China, Sch Math & Phys, Hengyang, Hunan, Peoples R China.;Univ South China, Hunan Key Lab Math Modeling & Sci Comp, Hengyang, Hunan, Peoples R China.
关键词：
critical point theory;existence and multiplicity;ground state solution;local superlinear condition;periodic discrete nonlinear Schr & ouml;dinger equation
摘要：
Consider the nonlinear difference equations of the form & Laplacetrf;u=fm(u),m is an element of & Zopf;$$ \mathit{\mathcal{L}u}={f}_m(u),\kern0.3em m\in \mathbb{Z} $$, where & Laplacetrf;$$ \mathcal{L} $$ is a Jacobi operator given by & Laplacetrf;um=amum+1+am-1um-1+bmum$$ \mathcal{L}{u}_m={a}_m{u}_{m+1}+{a}_{m-1}{u}_{m-1}+{b}_m{u}_m $$ for m is an element of & Zopf;,am$$ m\in \mathbb{Z},\kern0.3em \left\{{a}_m\right\} $$ and bm$$ \left\{{b}_m\right\} $$ are real valued T$$ T $$-periodic sequences, and f:& Zopf;x & Ropf;->& Ropf;$$ f:\mathbb{Z}\times \mathbb{R}\to \mathbb{R} $$. Applying critical point theory and a new analytical method, we obtain that the above problem has ground state solutions and infinitely many geometrically distinct solutions under the local superlinear condition limx ->infinity integral 0xfm(t)dt|x|2=infinity$$ {\lim}_{verbarxverbar\to \infty}\frac{\int_0<^>x{f}_m(t) dt}{{\left|x\right|}<^>2}=\infty $$ uniformly in m is an element of D$$ m\in D $$ for some set D subset of & Zopf;$$ D\subset \mathbb{Z} $$ instead of the global superlinear condition limx ->infinity integral 0xfm(t)dt|x|2=infinity$$ {\lim}_{verbarxverbar\to \infty}\frac{\int_0<^>x{f}_m(t) dt}{{\left|x\right|}<^>2}=\infty $$ uniformly in m is an element of & Zopf;$$ m\in \mathbb{Z} $$.
作者机构：
[Wang, Hongyong] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Ou, Chunhua] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
通讯机构：
[Ou, CH ] M;Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada.
关键词：
Lotka-Volterra competition system;gap formation;forced pulsating waves;spreading dynamics;shifting media
摘要：
We study the propagation dynamics of a Lotka-Volterra competition system in which one growth rate behaves like a monotonically decreasing wave profile that shifts with a given speed and is also periodic in the first spatial variable, while the other growth rate behaves similarly, except that its profile is monotonically increasing with respect to the shifting variable. Furthermore, both growth functions are assumed to be sign-changed, which implies that the environments in which the species live switch spatially from 'good' regions (suitable for survival) to 'bad' regions (not suitable for survival) and vice versa. We reveal that the model admits a forced pulsating wave only when the forced speed lies within a finite interval (c & lowast;,c(& lowast;)) that contains zero. Biologically, this corresponds to the formation of a shifting cline. Moreover, we find that c(& lowast;)<0 and c(& lowast;)>0 can be calculated in terms of the Fisher-KPP speeds related to the linearized equations of each species. By applying a sliding technique, we show that the forced pulsating wave is unique. We also prove that the forced pulsating wave is Lyapunov-stable. Finally, the spreading dynamics of spatial gap formation in the two species are also investigated when the forced wave speed is either less than c(& lowast;) or greater that c(& lowast;). We employ a novel approach to demonstrate how the species invade in response to a shifting environment.
期刊：
Nuclear Engineering and Design,2025年433:113872 ISSN：0029-5493
通讯作者：
Liu, HL
作者机构：
[Liu, Hongliang; Ouyang, Zigen; Liu, Wangheng] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Zeng, Wenjie] Univ South China, Sch Nucl Sci & Technol, Hengyang 421001, Peoples R China.;[Liu, Hua] Univ South China, Sch Elect Engn, Hengyang 421001, Peoples R China.
通讯机构：
[Liu, HL ] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Adaptive learning observer;Radial basis function neural networks;Fixed-time fault-tolerant control;Control rod drive mechanism faults;Load following for modular high-temperature;gas-cooled reactor
摘要：
Load following of the Modular High-Temperature Gas-Cooled Reactor (MHTGR) under Control Rod Drive Mechanism (CRDM) faults and disturbances remains a major challenge. This paper focuses on proposing a fixed-time fault-tolerant control method for this issue without considering the sensitivities associated with parameter setting. Firstly, to reconstruct some unmeasurable states of the MHTGR and the values of CRDM faults, an adaptive learning observer is established. Based on the learning characteristic of Radial Basis Function Neural Networks (RBFNN), the lumped uncertainties can be approximated. And then a fixed-time fault-tolerant controller is developed to ensure that the actual load output of the MHTGR actually tracks the expected output power within a fixed time, which can be determined through the system and controller parameters. Finally, simulations under two operational conditions demonstrate the control method is effective and feasible to the MHTGR system under disturbance and CRDM faults.
Load following of the Modular High-Temperature Gas-Cooled Reactor (MHTGR) under Control Rod Drive Mechanism (CRDM) faults and disturbances remains a major challenge. This paper focuses on proposing a fixed-time fault-tolerant control method for this issue without considering the sensitivities associated with parameter setting. Firstly, to reconstruct some unmeasurable states of the MHTGR and the values of CRDM faults, an adaptive learning observer is established. Based on the learning characteristic of Radial Basis Function Neural Networks (RBFNN), the lumped uncertainties can be approximated. And then a fixed-time fault-tolerant controller is developed to ensure that the actual load output of the MHTGR actually tracks the expected output power within a fixed time, which can be determined through the system and controller parameters. Finally, simulations under two operational conditions demonstrate the control method is effective and feasible to the MHTGR system under disturbance and CRDM faults.
作者机构：
[Lin, Wenbin; Jiang, Chunhua; Yang, Bo; Lin, WB] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Yang, Bo] Chinese Acad Sci, Purple Mt Observ, Nanjing 210023, Peoples R China.
通讯机构：
[Lin, WB ] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.
关键词：
Black holes;Regular Simpson-Visser black-bounce spacetime;Periastron advance
摘要：
In this paper, we present the second post-Newtonian solution for the quasi-Keplerian motion of a test particle in the regular Simpson-Visser black-bounce spacetime which has a bounce parameter $a$. The obtained solution is formulated in terms of the orbital energy, angular momentum, and the bounce parameter of the black hole. We explicitly analyze the leading effects of the bounce parameter, which has dimensions of length, on the test particle's orbit, including the periastron advance and orbital period. Then, we apply this model to the precessing motion of OJ 287 and determine the upper limits of the dimensionless bounce parameter as $a/m =3.45\pm 0.01$, where $m$ is the mass of the regular black hole. Compared with the bound given by the periastron advance of star S2, our bound on $a/m$ is reduced by one order of magnitude, although our upper limit of $a$ still needs further improvement.
作者机构：
[Lin, Wenbin; Lin, WB] Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;[Lin, Wenbin; Lin, WB] Southwest Jiaotong Univ, Sch Phys Sci & Technol, Chengdu 610031, Peoples R China.
通讯机构：
[Lin, WB ] U;Univ South China, Sch Math & Phys, Hengyang 421001, Peoples R China.;Southwest Jiaotong Univ, Sch Phys Sci & Technol, Chengdu 610031, Peoples R China.
关键词：
post-Newtonian approximation;gravitomagnetic field;second gravitational potential;spherically-symmetric system
摘要：
We prove that the post-Newtonian time-dependent metric of the self-gravitating and collapsing infinitely-thin spherical shell does satisfy Einstein field equations to the corresponding order. Meanwhile, the leading-order components of the thin spherical shell's energy-momentum tensor are recovered.
作者机构：
[Wenbin Lin] School of Mathematics and Physics, University of South China, Hengyang, China;[Zhixin Sun] School of Computer Science, University of South China, Hengyang, China
会议名称：
2025 5th International Conference on Artificial Intelligence and Industrial Technology Applications (AIITA)
会议时间：
28 March 2025
会议地点：
Xi'an, China
会议论文集名称：
2025 5th International Conference on Artificial Intelligence and Industrial Technology Applications (AIITA)
关键词：
Four-Player Military Chess;Neural-Guided MCTS;Imperfect-Information Games;Multi-Agent Strategy
摘要：
This paper introduces Deep Monte Carlo (DMC), a neural-enhanced algorithm designed for mastering Four-Player Military Chess, a complex imperfect-information game characterized by dynamic alliances and hierarchical combat mechanics. The proposed framework integrates three key components through a lightweight multi-branch neural network: a 17×17×8 tensor encoding spatial unit distributions, terrain features, and multi-scale threat maps; a 64-dimensional action vector representing move parameters and combat outcomes; and an 8-step historical sequence processed via bidirectional LSTM for temporal reasoning. These inputs are fused through convolutional blocks and attention mechanisms to drive Monte Carlo Tree Search (MCTS) optimization. Key innovations include a railway path validation algorithm enabling efficient route planning, an action masking layer ensuring 98.3% legal move compliance, and a history compression technique that reduces LSTM computation overhead by 45%. Extensive evaluation across 100,000 adversarial matches demonstrates DMC's superiority, achieving an 84.7% win rate against rule-based MCTS-Basic agents and 98.2% against random agents.
期刊：
Mechanics of Solids,2025年60(3):2085-2099 ISSN：0025-6544
通讯作者：
Yan, XJ;Xu, Feng;Guo, CQ
作者机构：
[Yan, Xuejin; Yan, XJ] Univ South China, Sch Civil Engn, Hengyang 421001, Hunan, Peoples R China.;[Xu, Feng; Xu, F; Guo, Changqing] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Yan, XJ ; Xu, F; Guo, CQ ] U;Univ South China, Sch Civil Engn, Hengyang 421001, Hunan, Peoples R China.;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
fluid-conveying pipe;base excitation;impact vibration response;Pasternak base
摘要：
When the fluid-conveying pipe is buried on the surface of the base, it will not only suffer from rigid impact damage caused by base excitation and surrounding gravel, but also be affected by the characteristics of the base, which makes safety accidents extremely likely to occur during the operation of the fluid-conveying pipe. Based on the Hamilton principle, a mathematical model of simply supported fluid-conveying pipe structures with a rigid constraint on the Pasternak base under base excitation is established. The Galerkin method is used to discretize the equation of motion, and the NDFS algorithm is employed to solve the system of equations. The influence is discussed in terms of the base excitation frequency, internal flow rate, and the viscoelastic coefficient of the pipe on the model. Bifurcation diagrams, phase diagrams, Poincaré maps, and time-history curves under various parameters are used to analyze the impact vibration response of the fluid-conveying pipe system. The research shows that: grazing impact usually occurs when the system’s motion state changes under impact vibration, and at a lower base excitation frequency, grazing impact will induce incomplete chatter-impact vibration in the system; there is a particular dynamic law in the evolution between quasi-periodic motion and single-period non-impact vibration on the Poincaré map; the increase in the equivalent linear spring stiffness K and shear stiffness KG of the Pasternak base is beneficial for resisting the unstable factors caused by base excitation. The findings of this study provide theoretical support for the optimal design, operation maintenance, and safety assurance of fluid-conveying pipes on the Pasternak base.
摘要：
The dynamic behavior of fluid-conveying pipes can lead to significant safety hazards when subjected to impact vibrations, influenced by complex operational environments such as base excitations, distributed follower forces, and support looseness. A model for the impact vibration of a simply supported, rigidly constrained fluid-conveying pipe is established based on Hamilton's principle under the combined effects of base excitations and distributed follower forces. The Galerkin method and the NDFs (variable-order numerical differentiation formulas) algorithm are employed for discretizing and solving the equation, respectively. The influences of parameters on the model are discussed under the actions of the base excitation frequency, magnitude of distributed follower forces, and fluid velocity. The evolutionary pathways within the model the periodic motions, quasi-periodic motions, chaos are captured by the analysis of bifurcation diagrams, phase diagrams, Poincar & eacute; maps, and time-history curves. So are unique behaviors to rigid impacts such as chatter vibrations and wiping contacts, and the stable focus on the Poincar & eacute; map mutates into an attractor with a shape resembling a plum blossom under multi-source excitation. The research reveals that Plum blossom attractors provide critical transition markers for analyzing vibration evolution from stable focus to attracting circles. Low base excitation frequencies trigger chatter-impact vibrations. The findings of this study provide a theoretical basis for the engineering parameter settings or safe operation of fluid-conveying pipes under multi-source excitation.
期刊：
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS,2025年2025(64) ISSN：1072-6691
通讯作者：
Liu, HL
作者机构：
[Zhou, Yao; Liu, Hongliang; Liu, HL] Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
通讯机构：
[Liu, HL ] U;Univ South China, Sch Math & Phys, Hengyang 421001, Hunan, Peoples R China.
关键词：
Singular perturbed;second order delay lattice system;uniform attractor;upper semicontinuity;continuous process;almost periodic function
摘要：
. In this article, we consider the upper semicontinuity of the uniform attractors for the singular perturbed second order nonautonomous delay lattice systems driven by the almost periodic forces as the coefficient of second order derivative term tends to zero under the Hausdorff semidistance. First we prove the existence of uniform attractors for the second order and the corresponding first order nonautonomous delay lattice systems. Then we establish some prior uniform estimations of solutions. Finally we study the upper semicontinuity of the uniform attractors as the coefficient of second order derivative term tends to zero which showing the relationship between the uniform attractors for second order and the corresponding first order nonautonomous delay lattice systems.
摘要：
Physical field simulations demand efficient mesh deformation and adaptive refinement methods. This paper proposes a systematical method tailored to the specific needs of simulations. Interpolation-based methods are preferred for large-scale mesh deformation due to computational efficiency. Improving the inverse distance weighted method by introducing auxiliary nodes using the sub-mesh. A node smoothing algorithm based on layered mesh is also devised to enhance mesh deformation ability. Optimizing the convergence criterion greatly reduces computation time. To improve element quality after deformation and meet the requirement for iterative refinement of mesh in simulation, a mesh refinement method is proposed. To address challenges in inserting nodes into narrow spaces, a novel algorithm is developed, which integrates the boundary constraints with the longest-edge propagation path. The co-optimization of surface and tetrahedral meshes is achieved through an algorithm based on size-field and an improved surface priority insertion strategy. A boundary edge priority algorithm is proposed to preserve the fitness between mesh and geometry. Flow field examples demonstrate the method’s effectiveness in mesh deformation and the optimization of poor-quality elements. Electromagnetic simulation results show that, compared to commercial software, the method significantly reduces the number of elements after refinement while maintaining solver accuracy.
Physical field simulations demand efficient mesh deformation and adaptive refinement methods. This paper proposes a systematical method tailored to the specific needs of simulations. Interpolation-based methods are preferred for large-scale mesh deformation due to computational efficiency. Improving the inverse distance weighted method by introducing auxiliary nodes using the sub-mesh. A node smoothing algorithm based on layered mesh is also devised to enhance mesh deformation ability. Optimizing the convergence criterion greatly reduces computation time.
To improve element quality after deformation and meet the requirement for iterative refinement of mesh in simulation, a mesh refinement method is proposed. To address challenges in inserting nodes into narrow spaces, a novel algorithm is developed, which integrates the boundary constraints with the longest-edge propagation path. The co-optimization of surface and tetrahedral meshes is achieved through an algorithm based on size-field and an improved surface priority insertion strategy. A boundary edge priority algorithm is proposed to preserve the fitness between mesh and geometry. Flow field examples demonstrate the method’s effectiveness in mesh deformation and the optimization of poor-quality elements. Electromagnetic simulation results show that, compared to commercial software, the method significantly reduces the number of elements after refinement while maintaining solver accuracy.
摘要：
In practical engineering, the unilateral gap constraint impact vibration in fluid-conveying pipes is a critical concern, often arising from constraint loosening or the presence of barriers around the pipe. These factors can significantly affect the service life and safety reliability of the pipes. A tension and compression anisotropy spring with rapidly increasing restoring force in compression but almost zero restoring force in tension is proposed to simulate the unilateral gap constraint, model a fluid-conveying pipe with a Pfluger column. Its reliability is also verified based on the bifurcation phase diagram comparison between the small and large stiffness conditions. Subsequently, we establish a vibration mechanics analysis model for the cantilever fluid-conveying pipe under foundation excitation to assess the effects of basic excitation frequency, fluid velocity, distributed follower force, position coordinate of unilateral gap constraint, and the viscoelastic coefficient on the impact vibration stability of the fluid-conveying pipe. Our findings reveal that when the period-doubling bifurcation sequence is interrupted by Bare-grazing bifurcation, the system directly transitions into chaotic vibration or induces a new period-doubling bifurcation sequence, followed by re-entry into chaotic vibration. These results provide valuable insights into the intricate dynamics of fluid-conveying pipes under foundation excitation, offering a deeper understanding of the impact of various parameters on the pipe's vibration.
In practical engineering, the unilateral gap constraint impact vibration in fluid-conveying pipes is a critical concern, often arising from constraint loosening or the presence of barriers around the pipe. These factors can significantly affect the service life and safety reliability of the pipes. A tension and compression anisotropy spring with rapidly increasing restoring force in compression but almost zero restoring force in tension is proposed to simulate the unilateral gap constraint, model a fluid-conveying pipe with a Pfluger column. Its reliability is also verified based on the bifurcation phase diagram comparison between the small and large stiffness conditions. Subsequently, we establish a vibration mechanics analysis model for the cantilever fluid-conveying pipe under foundation excitation to assess the effects of basic excitation frequency, fluid velocity, distributed follower force, position coordinate of unilateral gap constraint, and the viscoelastic coefficient on the impact vibration stability of the fluid-conveying pipe. Our findings reveal that when the period-doubling bifurcation sequence is interrupted by Bare-grazing bifurcation, the system directly transitions into chaotic vibration or induces a new period-doubling bifurcation sequence, followed by re-entry into chaotic vibration. These results provide valuable insights into the intricate dynamics of fluid-conveying pipes under foundation excitation, offering a deeper understanding of the impact of various parameters on the pipe's vibration.
