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A NEW PROOF OF THE WEAK(1,n/n-a)INEQUALITY FOR THE FRACTIONAL MAXIMAL OPERATORS
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作者 WANG Jie 《数学杂志》 2025年第3期213-217,共5页
In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,... In this paper,we provide an alternative proof of the weak type(1,n/n-a)inequality for the fractional maximal operators.By using the discretization technique,we can get the main result,which shows that the weak type(1,n/n-a)bound of M_(α)is at worst 2^(n-a).The weak type(1,n/n-a)bound of M_(α)can be estimated more directly and easily in this method,which is different from the usual ways. 展开更多
关键词 Hardy-Littlewood maximal operator fractional maximal operators Dirac deltas discrete method
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The Influence of Second Maximal Subgroups on the Structure of Group Class J_(pr)
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作者 Lin YANG Wei LIU +1 位作者 Shuqin DONG Hongwei BAO 《Journal of Mathematical Research with Applications》 2025年第5期629-636,共8页
In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the r... In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications. 展开更多
关键词 maximal subgroups second maximal subgroups group class J_(pr)
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Trend on Epimedium brevicornu Maxim in Two Decades(from 2003 to 2022):Bibliometric Analysis and Visualization
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作者 Lei ZHANG Zhaoxia JIN +7 位作者 Caixia ZHANG Jia SHI Manjia LI Wanying SU Yimin WANG Shuzhen WANG Feng HE Jinjun LUO 《Agricultural Biotechnology》 2025年第2期13-21,24,共10页
[Objectives]Epimedium brevicornu Maxim is a well-known plant having the concomitant function of both medicine and foodstuff with the bioactivity of anti-inflammatory and cardiovascular protection.It has important ther... [Objectives]Epimedium brevicornu Maxim is a well-known plant having the concomitant function of both medicine and foodstuff with the bioactivity of anti-inflammatory and cardiovascular protection.It has important therapeutic effects and health benefits for various chronic diseases.This study aimed to analyze the studies on E.brevicornu Maxim from 2003 to 2022 with bibliometric analysis.[Methods]Publications related to E.brevicornu Maxim was retrieved in Web of Science Core Collection(WoSCC)from January 1,2003 to November 19,2022,and analyzed in Microsoft Excle,CiteSpace,and VOSviewer.[Results]In total,1317 documents were extracted from the WoSCC database.The growth rate of the publications showed a rapid increase from 2017.China provided the most documents,and Chinese Academy of Medical Sciences,Fudan University and Chinese Academy of Sciences contributed more papers.Wang Ying from Chinese Academy of Sciences was the most productive author,and the Journal of Ethnopharmacology was the most co-cited journal.The words"icariin","activation","oxidative stress","apoptosis","proliferation","osteogenic differentiation"and"flavonoid"were frequently occurred in the abstract and title of articles.Cluster analysis of keywords demonstrated"hippocampal neuron","efficient production","liquid extraction","bone regeneration"and"leukemia cell growth"were the hot topics from 2003 to 2022.The focus of the research has changed from the liquid extraction of flavonoids to the inflammatory response and metabolism,while cognitive deficit has emerged as a recent research hotspot.[Conclusions]The research on E.brevicornu Maxim has been expanding,and more studies are related to signaling pathways and metabolism diseases. 展开更多
关键词 Citespace Epimedium brevicornu maxim Medicine food homology BIBLIOMETRICS VOSviewer
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Investigating maximal steered coherence under the common impacts of reservoir and noise
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作者 Ling-Ling Xing Huan Yang Gang Zhang 《Chinese Physics B》 2025年第5期230-235,共6页
Maximal steered coherence(MSC)is a noteworthy resource measure in the field of quantum information,and it is defined under the framework of coherence measure and the formalism of quantum steering ellipsoids(QSEs).Here... Maximal steered coherence(MSC)is a noteworthy resource measure in the field of quantum information,and it is defined under the framework of coherence measure and the formalism of quantum steering ellipsoids(QSEs).Here,we explore the MSC of a two-qubit X state under the common influences of reservoir and noise.The results disclose that the introduction of auxiliary qubits can give rise to enhancement of the MSC in both the strong and weak coupling regimes.Moreover,more auxiliary qubits can decrease the oscillation period of the MSC,and also suppress the oscillation amplitude of the MSC in the strong coupling regime.In contrast,the increases in auxiliary qubits result in the oscillation of the MSC for the setting of the initially weak coupling regime.Of particular interest is that the improvement effects of more auxiliary qubits on the MSC in the initially weak coupling regime are significantly stronger than that in the initially strong coupling regime. 展开更多
关键词 maximal steered coherence quantum steering ellipsoid RESERVOIR noise
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Machine vision and learning for evaluating different rancidity grades of Prunus mandshurica(Maxim.)Koehne
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作者 Yashun Wang Huirong Chen +3 位作者 Jianting Gong Yang Cui Huiqin Zou Yonghong Yan 《Journal of Traditional Chinese Medical Sciences》 2025年第2期287-296,共10页
Objective:To explore a rapid and accurate method for evaluating the quality of Prunus mandshurica(Maxim.)Koehne(P.mandshurica,Ku Xing Ren)during rancidity using machine vision and learning.Methods:Sensory evaluation a... Objective:To explore a rapid and accurate method for evaluating the quality of Prunus mandshurica(Maxim.)Koehne(P.mandshurica,Ku Xing Ren)during rancidity using machine vision and learning.Methods:Sensory evaluation and chemometrics were used to classify P.mandshurica quality grades after rancidity.Chemical indicators of the P.mandshurica quality change were determined to verify the ob-tained grades and support the subsequent modeling.The International Commission on Illumination color space was used to extract the color features of the P.mandshurica.Discrimination and prediction models based on color features combined with multiple machine learning algorithms were established using 10-fold cross-validation and external test set validation.Results:The P.mandshurica rancidity samples were allocated to three quality grades.The Bayes net model based on powder color successfully identified the P.mandshurica at different grades with an accuracy of 88.89%and 100%using two validations,and the naive Bayes model based on section color achieved the same accuracy with an receiver operating characteristic area of 0.979.The instance-based k-nearest neighbors model based on powder color performed best in predicting the amygdalin content[R^(2)=0.9801,mean absolute error(MAE)=0.2071,root mean squared error(RMSE)=0.4170],followed by the random com-mittee model in predicting the acid value(R^(2)=0.9580,MAE=1.5121,RMSE=1.9099)and the random forest model in predicting the peroxide value(R^(2)=0.8857,MAE=0.0027,RMSE=0.0035).Conclusion:This study demonstrates that color digitization analysis is a potential method for rapidly evaluating the quality of P.mandshurica across the rancidity process,providing a new reference for the quality assessment of traditional Chinese medicines. 展开更多
关键词 Quality evaluation Prunus mandshurica(maxim.)Koehne RANCIDITY Machine vision Machine learning
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Current Status,Problems and Countermeasures of Pesticide Registration on Zanthoxylum bungeanum Maxim.in China
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作者 Dexi CHEN Zhe ZHANG +5 位作者 Zhongquan HE Ronggang BAI Lingchao ZENG Huan LIU Hong ZHANG Qiyong LI 《Asian Agricultural Research》 2025年第7期26-29,35,共5页
To provide reference for the prevention and control of diseases,pests,and weeds on Zanthoxylum bungeanum Maxim.and the research and development of new pesticide registrations,this paper analyzes the quantity,variety s... To provide reference for the prevention and control of diseases,pests,and weeds on Zanthoxylum bungeanum Maxim.and the research and development of new pesticide registrations,this paper analyzes the quantity,variety structure,dosage forms,and toxicity of pesticides registered on Z.bungeanum in China.The analysis reveals a relatively low quantity of pesticide registrations on Z.bungeanum,with no herbicide registrations;suspension concentrates dominate the dosage forms,and pesticide toxicity is classified as low-toxicity or micro-toxicity;registered pesticides target only rust,anthracnose,scale insects,aphids,and spider mites,while plant growth regulators solely involve growth regulation and shoot control.Given the current status of limited and incomplete pesticide registrations targeting major diseases,pests,and weeds on Z.bungeanum,severe product homogenization,and unknown maximum residue limits,it is recommended to intensify efforts in pesticide registration on Z.bungeanum,actively research and apply green control technologies,strengthen technical training guidance and pesticide supervision enforcement,to promote the healthy development of the industry. 展开更多
关键词 Zanthoxylum bungeanum maxim. Pesticide registration Current situation Diseases and insect pests COUNTERMEASURES
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Analysis on Chemical Components of Meconopsis integrifolia(Maxim.)Franch Total Flavonoids by UPLC-Q-Exactive Orbitrap MS
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作者 Yifan TIAN Yuanlin KONG +5 位作者 Limin LI Zhengming YANG Chaoqin REN Yongcang ZHANG Yuan LIU Yanfei HUANG 《Medicinal Plant》 2025年第1期1-10,共10页
[Objectives]To analyze the chemical components of Meconopsis integrifolia(Maxim.)Franch total flavonoids(MITF).[Methods]The chemical components of MITF were identified by UPLC-Q-Exactive Orbitrap MS.The column was per... [Objectives]To analyze the chemical components of Meconopsis integrifolia(Maxim.)Franch total flavonoids(MITF).[Methods]The chemical components of MITF were identified by UPLC-Q-Exactive Orbitrap MS.The column was performed using ACQUITY UPLC HSS T3(100 mm×2.1 mm,1.8μm)with 0.1%formic acid water(A)-acetonitrile(B)with gradient elution at 30℃,injection volume of 2μL,and flow rate of 0.3 mL/min.Electrospray ion source adopted positive and negative ion detection mode with scanning range m/z 100-1000.[Results]A total of 93 compounds were identified from MITF,including 57 flavonoids,25 phenolic acids,9 alkaloids and 2 others.Among them,dimethoxytaxifolin was identified as a possible new compound by SciFinder search,and 67 compounds were first identified in M.integrifolia.[Conclusions]This study provides a scientific foundation for clarifying the material basis of the efficacy of M.integrifolia and improving the quality standards. 展开更多
关键词 Meconopsis integrifolia(maxim.)Franch UPLC-Q-Exactive Orbitrap MS Total flavonoids ALKALOIDS Phenolic acids
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The Boundedness of Hardy-Littlewood Maximal Operator Associated withψ-Rectangles
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作者 Jie ZHAO Canqin TANG +1 位作者 Kuikui LIU Suqing WU 《Journal of Mathematical Research with Applications》 2025年第4期488-500,共13页
In this paper,the authors establish the boundedness of Hardy-Littlewood maximal operators M^(ψ)associated withψ-rectangles on weighted Lebesgue spaces and on two kinds of Lorentz spaces with variable exponent,as wel... In this paper,the authors establish the boundedness of Hardy-Littlewood maximal operators M^(ψ)associated withψ-rectangles on weighted Lebesgue spaces and on two kinds of Lorentz spaces with variable exponent,as well as its corresponding Fefferman-Stein inequalities.All of these generalize the corresponding results in classical case. 展开更多
关键词 Hardy-Littlewood maximal operator Lorentz space variable exponent
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Sum-Rate Maximization in Active RIS-Assisted Multi-Antenna WPCN 被引量:2
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作者 Jiang Jie Lyu Bin +1 位作者 Chen Pengcheng Yang Zhen 《China Communications》 SCIE CSCD 2024年第6期23-39,共17页
In this paper,we propose an active reconfigurable intelligent surface(RIS)enabled hybrid relaying scheme for a multi-antenna wireless powered communication network(WPCN),where the active RIS is employed to assist both... In this paper,we propose an active reconfigurable intelligent surface(RIS)enabled hybrid relaying scheme for a multi-antenna wireless powered communication network(WPCN),where the active RIS is employed to assist both wireless energy transfer(WET)from the power station(PS)to energyconstrained users and wireless information transmission(WIT)from users to the receiving station(RS).For further performance enhancement,we propose to employ both transmit beamforming at the PS and receive beamforming at the RS.We formulate a sumrate maximization problem by jointly optimizing the RIS phase shifts and amplitude reflection coefficients for both the WET and the WIT,transmit and receive beamforming vectors,and network resource allocation.To solve this non-convex problem,we propose an efficient alternating optimization algorithm with the linear minimum mean squared error criterion,semidefinite relaxation(SDR)and successive convex approximation techniques.Specifically,the tightness of applying the SDR is proved.Simulation results demonstrate that our proposed scheme with 10 reflecting elements(REs)and 4 antennas can achieve 17.78%and 415.48%performance gains compared to the single-antenna scheme with 10 REs and passive RIS scheme with 100 REs,respectively. 展开更多
关键词 active reconfigurable intelligent surface BEAMFORMING sum-rate maximization wireless powered communication network
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CRB:A new rumor blocking algorithm in online social networks based on competitive spreading model and influence maximization 被引量:1
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作者 董晨 徐桂琼 孟蕾 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第8期588-604,共17页
The virtuality and openness of online social platforms make networks a hotbed for the rapid propagation of various rumors.In order to block the outbreak of rumor,one of the most effective containment measures is sprea... The virtuality and openness of online social platforms make networks a hotbed for the rapid propagation of various rumors.In order to block the outbreak of rumor,one of the most effective containment measures is spreading positive information to counterbalance the diffusion of rumor.The spreading mechanism of rumors and effective suppression strategies are significant and challenging research issues.Firstly,in order to simulate the dissemination of multiple types of information,we propose a competitive linear threshold model with state transition(CLTST)to describe the spreading process of rumor and anti-rumor in the same network.Subsequently,we put forward a community-based rumor blocking(CRB)algorithm based on influence maximization theory in social networks.Its crucial step is to identify a set of influential seeds that propagate anti-rumor information to other nodes,which includes community detection,selection of candidate anti-rumor seeds and generation of anti-rumor seed set.Under the CLTST model,the CRB algorithm has been compared with six state-of-the-art algorithms on nine online social networks to verify the performance.Experimental results show that the proposed model can better reflect the process of rumor propagation,and review the propagation mechanism of rumor and anti-rumor in online social networks.Moreover,the proposed CRB algorithm has better performance in weakening the rumor dissemination ability,which can select anti-rumor seeds in networks more accurately and achieve better performance in influence spread,sensitivity analysis,seeds distribution and running time. 展开更多
关键词 online social networks rumor blocking competitive linear threshold model influence maximization
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二分图中高效计算top-n maximalα-biclique的方法研究
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作者 唐东杭 吴进高 徐建 《软件工程》 2024年第9期43-49,共7页
针对当二分图中一类节点的数量固定时,如何搜索另一类型节点数量排序为前n的maximalα-biclique的问题,提出了一种基础搜索算法和一种基于共同邻居概念的改进搜索算法。在使用(1,α)-core剪枝方法加快搜索的算法基础上,基于共同邻居搜... 针对当二分图中一类节点的数量固定时,如何搜索另一类型节点数量排序为前n的maximalα-biclique的问题,提出了一种基础搜索算法和一种基于共同邻居概念的改进搜索算法。在使用(1,α)-core剪枝方法加快搜索的算法基础上,基于共同邻居搜索算法使用共同邻居的概念对算法进行了改进,该算法只遍历节点的二跳邻居,并利用节点顺序和最小阈值提高搜索效率。实验结果表明,两种算法都可以有效且高效地搜索节点数量排名为前n的maximalα-biclique。与基础搜索算法相比,基于共同邻居搜索算法的搜索效率提升了80%,在实际应用场景中更具优势。 展开更多
关键词 (1 α)-core maximalα-biclique 共同邻居 节点顺序
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VARIATIONAL ANALYSIS FOR THE MAXIMAL TIME FUNCTION IN NORMED SPACES
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作者 Ziyi ZHOU Yi JIANG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1696-1706,共11页
For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smalle... For a general normed vector space,a special optimal value function called a maximal time function is considered.This covers the farthest distance function as a special case,and has a close relationship with the smallest enclosing ball problem.Some properties of the maximal time function are proven,including the convexity,the lower semicontinuity,and the exact characterizations of its subdifferential formulas. 展开更多
关键词 maximal time function SUBDIFFERENTIAL normal cone nonsmooth analysis
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A Bitcoin Address Multi-Classification Mechanism Based on Bipartite Graph-Based Maximization Consensus
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作者 Lejun Zhang Junjie Zhang +4 位作者 Kentaroh Toyoda Yuan Liu Jing Qiu Zhihong Tian Ran Guo 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第4期783-800,共18页
Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services ope... Bitcoin is widely used as the most classic electronic currency for various electronic services such as exchanges,gambling,marketplaces,and also scams such as high-yield investment projects.Identifying the services operated by a Bitcoin address can help determine the risk level of that address and build an alert model accordingly.Feature engineering can also be used to flesh out labeled addresses and to analyze the current state of Bitcoin in a small way.In this paper,we address the problem of identifying multiple classes of Bitcoin services,and for the poor classification of individual addresses that do not have significant features,we propose a Bitcoin address identification scheme based on joint multi-model prediction using the mapping relationship between addresses and entities.The innovation of the method is to(1)Extract as many valuable features as possible when an address is given to facilitate the multi-class service identification task.(2)Unlike the general supervised model approach,this paper proposes a joint prediction scheme for multiple learners based on address-entity mapping relationships.Specifically,after obtaining the overall features,the address classification and entity clustering tasks are performed separately,and the results are subjected to graph-basedmaximization consensus.The final result ismade to baseline the individual address classification results while satisfying the constraint of having similarly behaving entities as far as possible.By testing and evaluating over 26,000 Bitcoin addresses,our feature extraction method captures more useful features.In addition,the combined multi-learner model obtained results that exceeded the baseline classifier reaching an accuracy of 77.4%. 展开更多
关键词 Bitcoin multi-service classification graph maximization consensus data security
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Continuity of truncated Hardy-Littlewood maximal function
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作者 WANG Yidong WU Jia YAN Dunyan 《中国科学院大学学报(中英文)》 CAS CSCD 北大核心 2024年第6期721-727,共7页
This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of... This paper focuses on the continuity of the truncated Hardy-Littlewood maximal function.We first show that the truncated Hardy-Littlewood maximal function is lower semi-continuous.Then by investigating the behavior of the truncated Hardy-Littlewood maximal function when the truncated parameterγchanges,we obtain an equivalent condition of the continuity of the truncated Hardy-Littlewood maximal function. 展开更多
关键词 Hardy-Littlewood maximal function TRUNCATION CONTINUITY truncated parameter
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Quantized Decoders that Maximize Mutual Information for Polar Codes
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作者 Zhu Hongfei Cao Zhiwei +1 位作者 Zhao Yuping Li Dou 《China Communications》 SCIE CSCD 2024年第7期125-134,共10页
In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete mem... In this paper,we innovatively associate the mutual information with the frame error rate(FER)performance and propose novel quantized decoders for polar codes.Based on the optimal quantizer of binary-input discrete memoryless channels(BDMCs),the proposed decoders quantize the virtual subchannels of polar codes to maximize mutual information(MMI)between source bits and quantized symbols.The nested structure of polar codes ensures that the MMI quantization can be implemented stage by stage.Simulation results show that the proposed MMI decoders with 4 quantization bits outperform the existing nonuniform quantized decoders that minimize mean-squared error(MMSE)with 4 quantization bits,and yield even better performance than uniform MMI quantized decoders with 5 quantization bits.Furthermore,the proposed 5-bit quantized MMI decoders approach the floating-point decoders with negligible performance loss. 展开更多
关键词 maximize mutual information polar codes QUANTIZATION successive cancellation decoding
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Hybrid Block Diagonalization Precoding for Multi-User Weighted Sum-Rate Maximization
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作者 Su Xiaofeng Jiang Yi 《China Communications》 SCIE CSCD 2024年第8期127-141,共15页
This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates ... This paper studies large-scale multi-input multi-output(MIMO)orthogonal frequency division multiplexing(OFDM)communications in a broadband frequency-selective channel,where a massive MIMO base station(BS)communicates with multiple users equipped with multi-antenna.We develop a hybrid precoding design to maximize the weighted sum-rate(WSR)of the users by optimizing the digital and the analog precoders alternately.For the digital part,we employ block-diagonalization to eliminate inter-user interference and apply water-filling power allocation to maximize the WSR.For the analog part,the optimization of the PSN is formulated as an unconstrained problem,which can be efficiently solved by a gradient descent method.Numerical results show that the proposed block-diagonal hybrid precoding algorithm can outperform the existing works. 展开更多
关键词 block-diagonal gradient descent hybrid precoding iterative optimization MIMO-OFDM MULTI-USER water-filling power allocation weighted sum-rate maximization
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Kinematic calibration under the expectation maximization framework for exoskeletal inertial motion capture system
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作者 QIN Weiwei GUO Wenxin +2 位作者 HU Chen LIU Gang SONG Tainian 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第3期769-779,共11页
This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters ... This study presents a kinematic calibration method for exoskeletal inertial motion capture (EI-MoCap) system with considering the random colored noise such as gyroscopic drift.In this method, the geometric parameters are calibrated by the traditional calibration method at first. Then, in order to calibrate the parameters affected by the random colored noise, the expectation maximization (EM) algorithm is introduced. Through the use of geometric parameters calibrated by the traditional calibration method, the iterations under the EM framework are decreased and the efficiency of the proposed method on embedded system is improved. The performance of the proposed kinematic calibration method is compared to the traditional calibration method. Furthermore, the feasibility of the proposed method is verified on the EI-MoCap system. The simulation and experiment demonstrate that the motion capture precision is significantly improved by 16.79%and 7.16%respectively in comparison to the traditional calibration method. 展开更多
关键词 human motion capture kinematic calibration EXOSKELETON gyroscopic drift expectation maximization(EM)
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PERIODIC SYSTEMS WITH TIME DEPENDENT MAXIMAL MONOTONE OPERATORS
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作者 Zhenhai LIU Nikolaos S.PAPAGEORGIOU 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1280-1300,共21页
We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the con... We consider a first order periodic system in R^(N),involving a time dependent maximal monotone operator which need not have a full domain and a multivalued perturbation.We prove the existence theorems for both the convex and nonconvex problems.We also show the existence of extremal periodic solutions and provide a strong relaxation theorem.Finally,we provide an application to nonlinear periodic control systems. 展开更多
关键词 periodic boundary condition time-dependent maximal monotone operator convex and nonconvex problems extremal solutions strong relaxation
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Maximal operators of pseudo-differential operators with rough symbols
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作者 Ramla Benhamoud ZHU Xiang-rong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第1期174-180,共7页
Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and ... Consider a pseudo-differential operator T_(a)f(x)=∫_(R^(n))e^(ix,ζ)a(x,ζ)f(ζ)dζwhere the symbol a is in the rough Hormander class L^(∞)S_(ρ)^(m)with m∈R andρ∈[0,1].In this note,when 1≤p≤2,if n(ρ-1)/p and a∈L^(∞)S_(ρ)^(m),then for any f∈S(R^(n))and x∈R^(n),we prove that M(T_(a)f)(x)≤C(M(|f|^(p))(x))^(1/p) where M is the Hardy-Littlewood maximal operator.Our theorem improves the known results and the bound on m is sharp,in the sense that n(ρ-1)/p can not be replaced by a larger constant. 展开更多
关键词 pseudo-differential operator rough Hormander class H-L maximal operator
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MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES
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作者 林孝盛 杨大春 +1 位作者 杨四辈 袁文 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期484-514,共31页
Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying som... Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new. 展开更多
关键词 Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function
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