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Strong Laws of Large Numbers for Sequences of Blockwise m-Dependent and Sub-Orthogonal Random Variables under Sublinear Expectations 被引量:1
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作者 Jialiang FU 《Journal of Mathematical Research with Applications》 2026年第1期103-118,共16页
In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random vari... In this paper,we establish some strong laws of large numbers,which are for nonindependent random variables under the framework of sublinear expectations.One of our main results is for blockwise m-dependent random variables,and another is for sub-orthogonal random variables.Both extend the strong law of large numbers for independent random variables under sublinear expectations to the non-independent case. 展开更多
关键词 sublinear expectations strong law of large numbers blockwise m-dependent suborthogonal random variables
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Global Existence and Blow-up of Solutions for Fourth-order Parabolic Equation with p(x)-Laplacian and Variable Exponents
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作者 YANG Chunxiao YU Lifei DUAN Chenyan 《数学进展》 北大核心 2026年第1期221-239,共19页
In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence... In this paper,we consider the fourth-order parabolic equation with p(x)Laplacian and variable exponent source ut+∆^(2)u−div(|■u|^(p(x)−2■u))=|u|^(q(x))−1u.By applying potential well method,we obtain global existence,asymptotic behavior and blow-up of solutions with initial energy J(u_(0))≤d.Moreover,we estimate the upper bound of the blow-up time for J(u_(0))≤0. 展开更多
关键词 fourth-order parabolic equation variable exponent source global existence asymptotic behavior BLOW-UP
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Study of Beam Scan with Variable Linear Polarisation Directions of Antenna Arrays Using MMIC T/R Modules
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作者 李镇 邓次平 《Journal of Beijing Institute of Technology》 EI CAS 1992年第1期24-30,共7页
The beam scan with variable linear polarization directions of antenna arrays using MM/C transmit-receive (T/R) modules is explored. It is shown that the beam scan and the polarizations of electric fields can be contro... The beam scan with variable linear polarization directions of antenna arrays using MM/C transmit-receive (T/R) modules is explored. It is shown that the beam scan and the polarizations of electric fields can be controlled simultaneously if the forms of module arrangement are chosen properly and the amplitudes and the phases of array excitation are determined by the method presented in this article. Moreover, the calculations of the amplitudes and the phases of array excitation are simplified greatly while using the bounded conditions properly, and the desired beam sweep rate is achieved. 展开更多
关键词 millimeter waves antenna array scanning antenna/variable polarization
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Discrete-Rate Adaptive Modulation with Variable Threshold for Distributed Antenna System in the Presence of Imperfect CSI 被引量:3
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作者 YU Xiangbin TAN Wenting +1 位作者 WU Binbin LI Yang 《China Communications》 SCIE CSCD 2014年第A01期31-39,共9页
Discrete-rate adaptive modulation (AM) scheme for distributed antenna system (DAS) with imperfect channel state information (CSI) is developed, and the corresponding performance is investigated in composite Rayl... Discrete-rate adaptive modulation (AM) scheme for distributed antenna system (DAS) with imperfect channel state information (CSI) is developed, and the corresponding performance is investigated in composite Rayleigh channel. Subject to target bit error rate (BER) constraint, an improved fixed switching threshold (FST) for the AM scheme is presented by means of tightly-approximate BER expression, and it can avoid the performance loss fxom conventional FST. Based on the imperfect CSI, the variable switching threshold (VST) is derived by utilizing the maximum a posteriori method. This VST includes the improved FST as a special case, and may lower the impact of estimation error on the performance. By the switching thresholds, the spectrum efficiency (SE) and average BER of the system are respectively derived, and resulting closed- form expressions are attained. With these expressions, the system performance can be effectively evaluated. Simulation results show that the derived theoretical SE and BER can match the simulations well. Moreover, the AM with the presented FST has higher SE than that with the conventional one, and the AM with VST can tolerate the large estimation error while maintaining the target BER. 展开更多
关键词 distributed antenna system adaptive modulation imperfect estimation variable thresholds
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Prediction of microstructure evolution of ZK61 alloy during hot spinning by internal state variable model 被引量:3
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作者 Jin-qi PAN Wen-cong ZHANG +3 位作者 Jian-lei YANG Song-hui WANG Yong WU Huan LI 《Transactions of Nonferrous Metals Society of China》 2025年第1期126-142,共17页
An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of t... An internal state variable(ISV)model was established according to the experimental results of hot plane strain compression(PSC)to predict the microstructure evolution during hot spinning of ZK61 alloy.The effects of the internal variables were considered in this ISV model,and the parameters were optimized by genetic algorithm.After validation,the ISV model was used to simulate the evolution of grain size(GS)and dynamic recrystallization(DRX)fraction during hot spinning via Abaqus and its subroutine Vumat.By comparing the simulated results with the experimental results,the application of the ISV model was proven to be reliable.Meanwhile,the strength of the thin-walled spun ZK61 tube increased from 303 to 334 MPa due to grain refinement by DRX and texture strengthening.Besides,some ultrafine grains(0.5μm)that played an important role in mechanical properties were formed due to the proliferation,movement,and entanglement of dislocations during the spinning process. 展开更多
关键词 internal state variable model hot spinning ZK61 alloy finite element simulation texture evolution
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Numerical Methods for Boundary Value Problems in Variable Coefficient Ordinary Differential Equations 被引量:1
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作者 ZHAO Ting-ting CAI Wei-yun 《Chinese Quarterly Journal of Mathematics》 2025年第3期295-303,共9页
In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error... In order to solve the problem of the variable coefficient ordinary differen-tial equation on the bounded domain,the Lagrange interpolation method is used to approximate the exact solution of the equation,and the error between the numerical solution and the exact solution is obtained,and then compared with the error formed by the difference method,it is concluded that the Lagrange interpolation method is more effective in solving the variable coefficient ordinary differential equation. 展开更多
关键词 variable coefficient ordinary differential equations Lagrange interpolation Difference methods
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Optimizing Fine-Tuning in Quantized Language Models:An In-Depth Analysis of Key Variables
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作者 Ao Shen Zhiquan Lai +1 位作者 Dongsheng Li Xiaoyu Hu 《Computers, Materials & Continua》 SCIE EI 2025年第1期307-325,共19页
Large-scale Language Models(LLMs)have achieved significant breakthroughs in Natural Language Processing(NLP),driven by the pre-training and fine-tuning paradigm.While this approach allows models to specialize in speci... Large-scale Language Models(LLMs)have achieved significant breakthroughs in Natural Language Processing(NLP),driven by the pre-training and fine-tuning paradigm.While this approach allows models to specialize in specific tasks with reduced training costs,the substantial memory requirements during fine-tuning present a barrier to broader deployment.Parameter-Efficient Fine-Tuning(PEFT)techniques,such as Low-Rank Adaptation(LoRA),and parameter quantization methods have emerged as solutions to address these challenges by optimizing memory usage and computational efficiency.Among these,QLoRA,which combines PEFT and quantization,has demonstrated notable success in reducing memory footprints during fine-tuning,prompting the development of various QLoRA variants.Despite these advancements,the quantitative impact of key variables on the fine-tuning performance of quantized LLMs remains underexplored.This study presents a comprehensive analysis of these key variables,focusing on their influence across different layer types and depths within LLM architectures.Our investigation uncovers several critical findings:(1)Larger layers,such as MLP layers,can maintain performance despite reductions in adapter rank,while smaller layers,like self-attention layers,aremore sensitive to such changes;(2)The effectiveness of balancing factors depends more on specific values rather than layer type or depth;(3)In quantization-aware fine-tuning,larger layers can effectively utilize smaller adapters,whereas smaller layers struggle to do so.These insights suggest that layer type is a more significant determinant of fine-tuning success than layer depth when optimizing quantized LLMs.Moreover,for the same discount of trainable parameters,reducing the trainable parameters in a larger layer is more effective in preserving fine-tuning accuracy than in a smaller one.This study provides valuable guidance for more efficient fine-tuning strategies and opens avenues for further research into optimizing LLM fine-tuning in resource-constrained environments. 展开更多
关键词 Large-scale Language Model Parameter-Efficient Fine-Tuning parameter quantization key variable trainable parameters experimental analysis
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Equilibrium Strategies in M/M/1 Retrial Queues with Variable Service Rate
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作者 LIU Yuanyuan YAN Zhaozeng YANG Qin 《应用概率统计》 北大核心 2025年第3期448-466,共19页
We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponen... We consider a single server constant retrial queue,in which a state-dependent service policy is used to control the service rate.Customer arrival follows Poisson process,while service time and retrial time are exponential distributions.Whenever the server is available,it admits the retrial customers into service based on a first-come first-served rule.The service rate adjusts in real-time based on the retrial queue length.An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario.Furthermore,we investigate the impact of parameters on the social optimal threshold.The effectiveness of the results is illustrated by two examples. 展开更多
关键词 variable service rate retrial queues real-time adaptability equilibrium strategies ALGORITHM
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A novel approach to visual image encryption:2D hyperchaos,variable Josephus,and 3D diffusion 被引量:1
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作者 Yan Hong Xinyan Duan +2 位作者 Jingming Su Zhaopan Wang Shihui Fang 《Chinese Physics B》 2025年第4期335-352,共18页
With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and po... With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and poor encryption efficiency.To enhance performance,this paper proposes a new encryption algorithm designed to optimize parallel processing and adapt to images of varying sizes and colors.The method begins by using SHA-384 to extract the hash value of the plaintext image,which is then processed to determine the chaotic system’s initial value and block size.The image is padded and divided into blocks for further processing.A novel two-dimensional infinite collapses hyperchaotic map(2DICHM)is employed to generate the intra-block scrambling sequence,while an improved variable Joseph traversal sequence is used for inter-block scrambling.After removing the padding,3D forward and backward shift diffusions,controlled by the 2D-ICHM sequences,are applied to the scrambled image,producing the ciphertext.Simulation results demonstrate that the proposed algorithm outperforms others in terms of entropy,anti-noise resilience,correlation coefficient,robustness,and encryption efficiency. 展开更多
关键词 SHA-384 two-dimensional infinite collapses hyperchaotic map(2D-ICHM) variable Joseph traversal 3D forward shift diffusion
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Variable stiffness design optimization of fiber-reinforced composite laminates with regular and irregular holes considering fiber continuity for additive manufacturing 被引量:1
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作者 Yi LIU Zunyi DUAN +6 位作者 Chunping ZHOU Yuan SI Chenxi GUAN Yi XIONG Bin XU Jun YAN Jihong ZHU 《Chinese Journal of Aeronautics》 2025年第3期334-354,共21页
Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design o... Fiber-reinforced composites are an ideal material for the lightweight design of aerospace structures. Especially in recent years, with the rapid development of composite additive manufacturing technology, the design optimization of variable stiffness of fiber-reinforced composite laminates has attracted widespread attention from scholars and industry. In these aerospace composite structures, numerous cutout panels and shells serve as access points for maintaining electrical, fuel, and hydraulic systems. The traditional fiber-reinforced composite laminate subtractive drilling manufacturing inevitably faces the problems of interlayer delamination, fiber fracture, and burr of the laminate. Continuous fiber additive manufacturing technology offers the potential for integrated design optimization and manufacturing with high structural performance. Considering the integration of design and manufacturability in continuous fiber additive manufacturing, the paper proposes linear and nonlinear filtering strategies based on the Normal Distribution Fiber Optimization (NDFO) material interpolation scheme to overcome the challenge of discrete fiber optimization results, which are difficult to apply directly to continuous fiber additive manufacturing. With minimizing structural compliance as the objective function, the proposed approach provides a strategy to achieve continuity of discrete fiber paths in the variable stiffness design optimization of composite laminates with regular and irregular holes. In the variable stiffness design optimization model, the number of candidate fiber laying angles in the NDFO material interpolation scheme is considered as design variable. The sensitivity information of structural compliance with respect to the number of candidate fiber laying angles is obtained using the analytical sensitivity analysis method. Based on the proposed variable stiffness design optimization method for complex perforated composite laminates, the numerical examples consider the variable stiffness design optimization of typical non-perforated and perforated composite laminates with circular, square, and irregular holes, and systematically discuss the number of candidate discrete fiber laying angles, discrete fiber continuous filtering strategies, and filter radius on structural compliance, continuity, and manufacturability. The optimized discrete fiber angles of variable stiffness laminates are converted into continuous fiber laying paths using a streamlined process for continuous fiber additive manufacturing. Meanwhile, the optimized non-perforated and perforated MBB beams after discrete fiber continuous treatment, are manufactured using continuous fiber co-extrusion additive manufacturing technology to verify the effectiveness of the variable stiffness fiber optimization framework proposed in this paper. 展开更多
关键词 variable stiffness composite laminates Discrete material interpolation scheme Normal distribution fiber optimization Discrete fiber continuous filtering strategy Additive manufacturing of composite laminates
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Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of i.i.d.Random Variables under Sublinear Expectations
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作者 XU Mingzhou CHENG Kun 《应用概率统计》 北大核心 2025年第3期339-352,共14页
The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the... The complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space is studied.By moment inequality and truncation methods,we establish the equivalent conditions of complete convergence for weighted sums of sequences of independent,identically distributed random variables under sublinear expectation space.The results complement the corresponding results in probability space to those for sequences of independent,identically distributed random variables under sublinear expectation space. 展开更多
关键词 complete convergence weighted sums i.i.d.random variables sublinear expectation
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Improving the uniformity of RF-plasma density by a humped variable-gap spiral antenna
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作者 徐旭 李林森 +2 位作者 刘峰 周前红 梁荣庆 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第11期4242-4246,共5页
This paper develops a humped spiral antenna of top inductively coupled plasma with variable gap. Comparing with planar spiral antennae, it investigates the performance of humped spiral antennae in the calculated elect... This paper develops a humped spiral antenna of top inductively coupled plasma with variable gap. Comparing with planar spiral antennae, it investigates the performance of humped spiral antennae in the calculated electromagnetic configurations and experimental results. It finds that the humped antenna has the improved uniformity of plasma density in the radial direction and the decreased electron temperature in the top inductively coupled plasma. By experimental and theoretical analyses, the plasma performance in the case of humped antennae is considered to be the combined results of the uniform electromagnetic configurations and the depressed capacitively coupling effect. 展开更多
关键词 inductively coupled plasma Langmuir probe planar antenna density uniformity
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Micro-mechanical damage simulation of 2.5D woven variable thickness composites
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作者 Nan WANG Haitao CUI +3 位作者 Hongjian ZHANG Yaoming FU Gangjin HUANG Shuangqi LYU 《Chinese Journal of Aeronautics》 2025年第7期168-184,共17页
With the application of 2.5D Woven Variable Thickness Composites(2.5DWVTC)in aviation and other fields,the issue of strength failure in this composite type has become a focal point.First,a three-step modeling approach... With the application of 2.5D Woven Variable Thickness Composites(2.5DWVTC)in aviation and other fields,the issue of strength failure in this composite type has become a focal point.First,a three-step modeling approach is proposed to rapidly construct full-scale meso-finite element models for Outer Reduction Yarn Woven Composites(ORYWC)and Inner Reduction Yarn Woven Composites(IRYWC).Then,six independent damage variables are identified:yarn fiber tension/compression,yarn matrix tension/compression,and resin matrix tension/compression.These variables are utilized to establish the constitutive equation of woven composites,considering the coupling effects of microscopic damage.Finally,combined with the Hashin failure criterion and von Mises failure criterion,the strength prediction model is implemented in ANSYS using APDL language to simulate the strength failure process of 2.5DWVTC.The results show that the predicted stiffness and strength values of various parts of ORYWC and IRYWC are in good agreement with the relevant test results. 展开更多
关键词 Constitutive equation 2.5D woven variable thickness composites Damage variables Finite element models Modeling approach Strength prediction model
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Complete f-Moment Convergence for Sung’s Type Weighted Sums of Negatively Superadditive Dependent Random Variables
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作者 HU Xueping WANG Liuliu +1 位作者 HU Ke XU Zhonghao 《应用概率统计》 北大核心 2025年第4期585-601,共17页
In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergen... In this paper,by utilizing the Marcinkiewicz-Zygmund inequality and Rosenthal-type inequality of negatively superadditive dependent(NSD)random arrays and truncated method,we investigate the complete f-moment convergence of NSD random variables.We establish and improve a general result on the complete f-moment convergence for Sung’s type randomly weighted sums of NSD random variables under some general assumptions.As an application,we show the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors. 展开更多
关键词 Marcinkiewicz-Zygmund inequality Rosenthal-type inequality Sung’s type randomly weighted sums negatively superadditive dependent random variables complete f-moment convergence
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Distributional Solutions to Nonlinear Elliptic Equations with Variable Exponents and Degenerate Coercivity
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作者 Zhongqing LI 《Journal of Mathematical Research with Applications》 2025年第6期789-799,共11页
We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-orde... We investigate a class of elliptic equations with an L^(1)source in the framework of variable exponent spaces.A key characteristic of these equations is the coexistence of a degenerate coercivity term and a lower-order convection term.By employing innovative integralbased test functions,we derive the necessary a priori estimates.To prove the convergence of solutions to the degenerate coercivity problem,we adopt a method that combines monotonicity and truncation techniques.This approach allows us to demonstrate that the gradient sequences converge almost everywhere. 展开更多
关键词 elliptic equations degenerate coercivity variable exponents
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COMMUTATOR ESTIMATES FOR VECTOR FIELDS ON BESOV SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY
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作者 BenMahmoud SALAH 《Acta Mathematica Scientia》 2025年第3期771-788,共18页
In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator esti... In this paper we present certain bilinear estimates for commutators on Besov spaces with variable smoothness and integrability,and under no vanishing assumptions on the divergence of vector fields.Such commutator estimates are motivated by the study of well-posedness results for some models in incompressible fuid mechanics. 展开更多
关键词 COMMUTATOR vector fields Besov space variable exponent
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Multi-agent System Cooperative Control of Autonomous Vehicle Chassis Based on Scenario-driven Hybrid-DMPC with Variable Topology
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作者 Yuxing Li Yingfeng Cai +2 位作者 Yubo Lian Xiaoqiang Sun Long Chen 《Chinese Journal of Mechanical Engineering》 2025年第5期156-175,共20页
The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achiev... The development of chassis active safety control technology has improved vehicle stability under extreme conditions.However,its cross-system and multi-functional characteristics make the controller difficult to achieve cooperative goals.In addition,the chassis system,which has high complexity,numerous subsystems,and strong coupling,will also lead to low computing efficiency and poor control effect of the controller.Therefore,this paper proposes a scenario-driven hybrid distributed model predictive control algorithm with variable control topology.This algorithm divides multiple stability regions based on the vehicle’s β−γ phase plane,forming a mapping relationship between the control structure and the vehicle’s state.A control input fusion mechanism within the transition domain is designed to mitigate the problems of system state oscillation and control input jitter caused by switching control structures.Then,a distributed state-space equation with state coupling and input coupling characteristics is constructed,and a weighted local agent cost function in quadratic programming is derived.Through cost coupling,local agents can coordinate global performance goals.Finally,through Simulink/CarSim joint simulation and hardware-in-the-loop(HIL)test,the proposed algorithm is validated to improve vehicle stability while ensuring trajectory tracking accuracy and has good applicability for multi-objective coordinated control.This paper combines the advantages of distributed MPC and decentralized MPC,achieving a balance between approximating the global optimal results and the solution’s efficiency. 展开更多
关键词 Autonomous vehicle Distributed control Multi-agent system Hybrid-DMPC variable topology
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Influence of ambient geochemical and microbiological variables on the bacterial diversity in a cold seep ecosystem in North Indian Ocean
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作者 Delcy R.Nazareth Maria Judith Gonsalves Nitisha Sangodkar 《Geoscience Frontiers》 2025年第3期153-163,共11页
Cold seeps are oases for biological communities on the sea floor around hydrocarbon emission pathways.Microbial utilization of methane and other hydrocarbons yield products that fuel rich chemosynthetic communities at... Cold seeps are oases for biological communities on the sea floor around hydrocarbon emission pathways.Microbial utilization of methane and other hydrocarbons yield products that fuel rich chemosynthetic communities at these sites.One such site in the cold seep ecosystem of Krishna-Godavari basin(K-G basin)along the east coast of India,discovered in Feb 2018 at a depth of 1800 m was assessed for its bacterial diversity.The seep bacterial communities were dominated by phylum Proteobacteria(57%),Firmicutes(16%)and unclassified species belonging to the family Helicobacteriaceae.The surface sediments of the seep had maximum OTUs(operational taxonomic units)(2.27×10^(3))with a Shannon alpha diversity index of 8.06.In general,environmental parameters like total organic carbon(p<0.01),sulfate(p<0.001),sulfide(p<0.05)and methane(p<0.01)were responsible for shaping the bacterial community of the cold seep ecosystem in the K-G Basin.Environmental parameters play a significant role in changing the bacterial diversity richness between different cold seep environments in the oceans. 展开更多
关键词 SEDIMENTS Environmental variables PROTEOBACTERIA Cold seep ecosystem Organic matter
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Design of a Bio-inspired Extensible Continuum Manipulator with Variable Stiffness
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作者 Dongbao Sui Sikai Zhao +3 位作者 Tianshuo Wang Yubin Liu Yanhe Zhu Jie Zhao 《Journal of Bionic Engineering》 2025年第1期181-194,共14页
This paper presents a continuum manipulator inspired by the anatomical characteristics of the elephant trunk.Specifically,the manipulator mimics the conoid profile of the elephant trunk,which helps to enhance its stre... This paper presents a continuum manipulator inspired by the anatomical characteristics of the elephant trunk.Specifically,the manipulator mimics the conoid profile of the elephant trunk,which helps to enhance its strength.The design features two concentric parts:inner pneumatically actuated bellows and an outer tendon-driven helical spring.The tendons control the omnidirectional bending of the manipulator,while the fusion of the pneumatic bellows with the tendon-driven spring results in an antagonistic actuation mechanism that provides the manipulator with variable stiffness and extensibility.This paper presents a new design for extensible manipulator and analyzes its stiffness and motion characteristics.Experimental results are consistent with theoretical analysis,thereby demonstrating the validity of the theoretical approach and the versatile practical mechanical properties of the continuum manipulator.The impressive extensibility and variable stiffness of the manipulator were further demonstrated by performing a pin-hole assembly task. 展开更多
关键词 Bioinspired robots Continuum robots Soft robotics variable stiffness
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Stress wave scaling theory of bar with variable cross-section
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作者 Xumeng Ren Shujuan Hou Xu Han 《Acta Mechanica Sinica》 2025年第10期165-178,共14页
The coconut structure exhibits inherent impact resistance,with the macroscopically ordered distribution of variable crosssection fibers in its husk playing a crucial role in stress wave propagation and scaling.Inspire... The coconut structure exhibits inherent impact resistance,with the macroscopically ordered distribution of variable crosssection fibers in its husk playing a crucial role in stress wave propagation and scaling.Inspired by the natural structure and fibers,this study proposes a stress wave propagation model for a variable cross-section bar considering viscous effects.A theoretical model for stress wave propagation in a fusiform-shaped bar with variable cross-section is established,elucidating the stress wave scaling effect observed in coconut fibers.Additionally,a quasi-one-dimensional method for analyzing and measuring stress wave propagation is introduced,and an experimental setup is assembled.Experimental validation of the stress wave scaling effect confirms the theory’s accuracy for stress wave scaling in variable cross-section bars.This research provides theoretical guidance and measurement methods for the design of space landers,automobile anti-collision beams,stress wave collectors,and scalers,as well as for impact testing of macro and micro materials and the design of sustainable plant-based materials for impact protection. 展开更多
关键词 Stress wave variable cross-section Scaling effect Coconut fiber IMPACT
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