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Centroid Hom-associative Algebras and Centroid Hom-Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第4期40卷 935-961页

作者： Yu Xiu BAI Leonid A.BOKUT Yu Qun CHEN Ze Rui ZHANG Department of mathematics Teaching Guangzhou Civil Aviation CollegeGuangzhou 510403P.R.China Sobolev institute of mathematics Novosibirsk 630090Russia Novosibirsk State University Novosibirsk 630090Russia school of Mathematical Sciences South China Normal UniversityGuangzhou 510631P.R.China

In this article,we construct free centroid hom-associative algebras and free centroid hom-Lie *** also construct some other relatively free centroid hom-associative algebras by applying the Gr?bner-Shirshov basis theory for(unital)centroid hom-associative ***,we prove that the"Poincaré-Birkhoff-Witt theorem"holds for certain type of centroid hom-Lie algebras over a field of characteristic 0,namely,every centroid hom-Lie algebra such that the eigenvectors of the mapβlinearly generates the whole algebra can be embedded into its universal enveloping centroid hom-associative algebra,and the linear basis of the universal enveloping algebra does not depend on the multiplication table of the centroid hom-Lie algebra under consideration.

关键词： Centroid hom-Lie algebra centroid hom-associative algebra Gr?bner-Shirshov basis

High-rate metal-free MXene microsupercapacitors on paper substrates

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Carbon Energy 2024年第5期6卷 94-104页

作者： Han Xue Po‐Han Huang Lee‐Lun Lai Yingchun Su Axel Strömberg Gaolong Cao Yuzhu Fan Sergiy Khartsev Mats Göthelid Yan‐Ting Sun Jonas Weissenrieder Kristinn BGylfason Frank Niklaus Jiantong Li school of Electrical Engineering and Computer Science KTH Royal Institute of TechnologyStockholmSweden school of Engineering Sciences KTH Royal Institute of TechnologyStockholmSweden

MXene is a promising energy storage material for miniaturized microbatteries and microsupercapacitors(MSCs).Despite its superior electrochemical performance,only a few studies have reported MXene-based ultrahigh-rate(>1000 mV s^(−1))on-paper MSCs,mainly due to the reduced electrical conductance of MXene films deposited on ***,ultrahigh-rate metal-free on-paper MSCs based on heterogeneous MXene/poly(3,4-ethylenedioxythiophene)-poly(styrenesulfonate)(PEDOT:PSS)-stack electrodes are fabricated through the combination of direct ink writing and femtosecond laser *** a footprint area of only 20 mm^(2),the on-paper MSCs exhibit excellent high-rate capacitive behavior with an areal capacitance of 5.7 mF cm^(−2)and long cycle life(>95%capacitance retention after 10,000 cycles)at a high scan rate of 1000 mV s^(−1),outperforming most of the present on-paper ***,the heterogeneous MXene/PEDOT:PSS electrodes can interconnect individual MSCs into metal-free on-paper MSC arrays,which can also be simultaneously charged/discharged at 1000 mV s^(−1),showing scalable capacitive *** heterogeneous MXene/PEDOT:PSS stacks are a promising electrode structure for on-paper MSCs to serve as ultrafast miniaturized energy storage components for emerging paper electronics.

关键词： direct ink writing femtosecond laser scribing MXene on-paper microsupercapacitors PEDOT:PSS ultrahigh rate capability

Effects of the initiation position on the damage and fracture characteristics of linear-charge blasting in rock

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International Journal of Minerals,Metallurgy and Materials 2024年第3期31卷 443-451页

作者： Chenxi Ding Renshu Yang Xiao Guo Zhe Sui Chenglong Xiao Liyun Yang school of Civil and Resource Engineering University of Science and Technology BeijingBeijing 100083China school of Mechanics and Civil Engineering China University of Mining and Technology(Beijing)Beijing 100083China school of mathematics and Physics University of Science and Technology BeijingBeijing 100083China State Key Lab of Explosion Science and Technology Beijing Institute of TechnologyBeijing 100081China

To study the effects of the initiation position on the damage and fracture characteristics of linear-charge blasting, blasting model experiments were conducted in this study using computed tomography scanning and three-dimensional reconstruction methods. The fractal damage theory was used to quantify the crack distribution and damage degree of sandstone specimens after blasting. The results showed that regardless of an inverse or top initiation, due to compression deformation and sliding frictional resistance, the plugging medium of the borehole is effective. The energy of the explosive gas near the top of the borehole is consumed. This affects the effective crushing of rocks near the top of the borehole, where the extent of damage to Sections Ⅰ and Ⅱ is less than that of Sections Ⅲ and Ⅳ. In addition, the analysis revealed that under conditions of top initiation, the reflected tensile damage of the rock at the free face of the top of the borehole and the compression deformation of the plug and friction consume more blasting energy, resulting in lower blasting energy efficiency for top initiation. As a result, the overall damage degree of the specimens in the top-initiation group was significantly smaller than that in the inverse-initiation group. Under conditions of inverse initiation, the blasting energy efficiency is greater, causing the specimen to experience greater damage. Therefore, in the engineering practice of rock tunnel cut blasting, to utilize blasting energy effectively and enhance the effects of rock fragmentation, using the inverse-initiation method is recommended. In addition, in three-dimensional(3D) rock blasting, the bottom of the borehole has obvious end effects under the conditions of inverse initiation, and the crack distribution at the bottom of the borehole is trumpet-shaped. The occurrence of an end effect in the 3D linear-charge blasting model experiment is related to the initiation position and the blocking condition.

关键词： blasting linear charge initiation position computed tomography three-dimensional reconstruction damage

Dynamic recrystallization mechanism, texture evolution development and mechanical characteristics of a Mg–8.7Gd–4.18Y–0.42Zr magnesium alloy by ECAP

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Progress in Natural Science:Materials International 2024年第02期34卷 376-388页

作者： Ling Zhang Yinglong Li school of Materials Science and Engineering Northeastern University school of Mechanical and Engineering Ningxia Institute of Science and Technology

Equal channel angle pressing is recognized for its ability to refine alloy grains and alter grain orientation, thereby achieve better mechanical performance of the magnesium alloy. This study investigates the microstructures,dynamic recrystallization mechanism, texture development, and mechanical performance of GW94K(Mg–8.7Gd–4.18Y–0.42Zr wt. %) Mg alloy following ECAP-4 passes at 400°C and 3 mm/min. Results show that when high-temperature deformation is undertaken, twin formation is suppressed while dislocation slip is facilitated, increasing dislocation density during deformation. Following ECAP deformation, the sample displayed higher fracture elongation, TYS, and UTS than the as-solutioned GW94K alloy. In particular, the GW94K alloy performed well mechanically after ECAP-4 passes, with an ultimate TYS of 231 MPa, an UTS of 290 MPa, and an elongation of 14.8 %. DDRX and shear bands induce CDRX, both of which are important in plastic deformation. as well as in modifying microstructure and grain orientation during ECAP deformation.

关键词： Equal channel angular pressing Dynamic recrystallization mechanism Mechanical performance Mg-Gd-Y-Zr alloy Magnesium alloy Texture development

SIRS epidemic modeling using fractional-ordered differential equations:Role of fear effect

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International Journal of Biomathematics 2024年第5期17卷 79-100页

作者： Shiv Mangal O.P.Misra Joydip Dhar school of mathematics and Allied Sciences Jiwaji University GwaliorMadhya PradeshIndia Department of mathematics Post Graduate College BinaMadhya PradeshIndia Department of Applied Sciences Atal Bihari Vajpayee-Indian Institute of Information Technology and Management GwaliorMadhya PradeshIndia

In this paper,an SIRS epidemic model using Grunwald-Letnikov fractional-order derivative is formulated with the help of a nonlinear system of fractional differential equations to analyze the effects of fear in the population during the outbreak of deadly infectious *** criteria for the spread or extinction of the disease are derived and discussed on the basis of the basic reproduction *** condition for the existence of Hopf bifurcation is discussed considering fractional order as a bifurcation ***,using the Grunwald-Letnikov approximation,the simulation is carried out to confirm the validity of analytic results *** the real data of COVID-19 in India recorded during the second wave from 15 May 2021 to 15 December 2021,we estimate the model parameters and find that the fractional-order model gives the closer forecast of the disease than the classical *** the analytical results and numerical simulations presented in this study suggest different policies for controlling or eradicating many infectious diseases.

关键词： SIRS epidemic model fear effect Mittag-Leffler function Hopf bifurcation parameter estimation

Navigation for autonomous vehicles via fast-stable and smooth reinforcement learning

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Science China(Technological Sciences) 2024年第2期67卷 423-434页

作者： ZHANG RuiXian YANG JiaNan LIANG Ye LU ShengAo DONG YiFei YANG BaoQing ZHANG LiXian school of Astronautics Harbin Institute of TechnologyHarbin 150001China

This paper investigates the navigation problem of autonomous vehicles based on reinforcement learning(RL)with both stability and smoothness *** introducing a data-based Lyapunov function,the stability criterion in mean cost is obtained,where the Lyapunov function has a property of fast ***,an off-policy RL algorithm is proposed to train safe policies,in which a more strict constraint is exerted in the framework of model-free RL to ensure the fast convergence of policy generation,in contrast with the existing RL merely with stability *** addition,by simultaneously introducing constraints on action increments and action distribution variations,the difference between the adjacent actions is effectively alleviated to ensure the smoothness of the obtained policy,instead of only seeking the similarity of the distributions of adjacent actions as commonly done in the past literature.A navigation task of a ground differentially driven mobile vehicle in simulations is adopted to demonstrate the superiority of the proposed algorithm on the fast stability and smoothness.

关键词： autonomous vehicles navigation reinforcement learning smoothness stability

Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

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Defence Technology（防务技术） 2024年第2期32卷 412-429页

作者： Wenxue Chen Yudong Hu Changsheng Gao Ruoming An school of Astronautics Harbin Institute of TechnologyHarbin 150001China

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost ***,the velocity control in such trajectory tracking guidance systems of missiles is *** our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking *** global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional ***,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid ***,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify *** obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

关键词： BP network neural Integral sliding mode control(ISMC) Missile defense Prescribed performance function(PPF) State observer Tracking guidance system

Three-Rigid-Body-Particle Modeling and Optimization of Trajectory and Posture for Alpine Skiing

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Journal of Systems Science & Complexity 2024年第2期37卷 581-608页

作者： ZHANG Yijia FEI Qing YAO Xiaolan SUN Jian ZHANG Yanjun CHEN Zhen school of Automation Beijing Institute of TechnologyBeijing 100081China

This paper presents a new study on modeling and optimization of trajectory and posture for the super-giant(SG)slalom of alpine *** is the first time that a Three-Rigid-Body-Particle model based on rigorous derivations and stability analysis is established to represent skiers trajectory and posture characteristics,as it is more accurate than the single-rigid-body model which is commonly used in existing *** addition,the Radau pseudospectral method is applied to solve the trajectory and posture optimization problem in order to obtain better skiing trajectory,skiing posture,and some key kinematic parameters of ***,this paper analyzes the effects of different body types,minimum turning radii,and flexor and extensor strength of knees and hip joint on skiing ***,based on the findings of the study,some advice about how to improve the performance of the SG slalom in view of science and technology is given to skiers and coaches for reference.

关键词： Alpine skiing modeling posture optimization Three-Rigid-Body-Particle model trajectory optimization

Multi-Robot Cooperative Localization:Time-Varying Unobservable Subspace Analysis and Consistent Algorithm Design

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Journal of Systems Science & Complexity 2024年第5期37卷 1937-1955页

作者： HAO Ning HE Fenghua YAO Yu school of Astronautics Harbin Institute of TechnologyHarbin 150000China

This paper investigates the problem of cooperative localization(CL)for a multi-robot system(MRS)under dynamic measurement topology,which involves a group of robots collectively estimating their poses with respect to a common reference frame using ego-motion measurements and robot-to-robot relative *** authors provide a theoretical analysis of the time-varying unobservable subspace and propose a consistent cooperative localization ***,the authors introduce the relative measurement graph(RMG)to represent the relative pose measurements obtained by the MRS at each ***,the authors derive the local observability matrix over a time *** equivalent relationship is established between the local observability matrix and the spectral matrices of the ***,the authors present a method for constructing the unobservable subspace based on the RMG under different topology *** on this analysis,the authors design a consistent cooperative localization algorithm that satisfies the constraints of the time-varying unobservable *** analytical optimal solution is derived for the constrained optimization *** Carlo numerical simulations are conducted to demonstrate the consistency and accuracy of the proposed method.

关键词： Consistency cooperative localization multi-robot system null space relative measurement graph time-varying unobservable subspace