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ISOMORPHISMS OF VARIABLE HARDY SPACES ASSOCIATED WITH SCHRÖDINGER OPERATORS

Acta Mathematica Scientia 2021年第1期41卷 39-66页

作者： Junqiang ZHANG Dachun YANG School of Science China University of Mining and Technology-BeijingBeijing 100083China Laboratory of Mathematics and Complex Systems(Ministry of Education of China) School of Mathematical SciencesBeijing Normal UniversityBeijing 100875China

Let L:=-△+V be the Schrodinger operator on R^(n)with n≥3,where V is a non-negative potential satisfying△^(-1)(V)∈L^(∞)(R^(n)).Let w be an L-harmonic function,determined by V,satisfying that there exists a positive constantδsuch that,for any x∈Rn,0<δ≤w(x)≤*** that p(·):R^(n)→(0,1]is a variable exponent satisfying the globally log-Hölder continuous *** this article,the authors show that the mappings HL^(p)(·))(R^(n))■f■wf∈H^(p)(·)(R^(n))and HL^(p(·))(R^(n))■f■(-△)^(1/2)L^(-1/2)(f)∈H^(p(·))(R^(n))are isomorphisms between the variable Hardy spaces HL^(p(·))(R^(n)),associated with L,and the variable Hardy spaces H^(p(·))(R^(n)).

关键词： variable Hardy space Schrödinger operator L-harmonic function isomorphism atom

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Distributed Framework Construction for Affine Formation Control

arXiv

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arXiv 2025年

作者： Li, Huiming Chen, Hao Wang, Xiangke Li, Zhongkui Shen, Lincheng College of Intelligence Science and Technology National University of Defense Technology Changsha410073 China Laboratory of Science and Technology on Integrated Logistics Support National University of Defense Technology Changsha410073 China The State Key Laboratory for Turbulence and Complex Systems Department of Mechanics and Engineering Science College of Engineering Peking University Beijing100871 China

In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the formation or link/agent failures emerge. Motivated by this observation, we investigate the problem of constructing affine formation frameworks in three scenarios, including vertex addition, edge deletion and vertex deletion. Our approach starts from the original affine formation and uses geometric methods to locally adjust the structure of the weighted graph to describe the topology, so that the modified framework maintains the universal rigidity and affine localizability. Notably, the developed strategies only utilize local measurements and exhibit distributed characteristics, laying the foundation for applications in multi-agent systems. To demonstrate the compatibility with affine formation control proposals, we present a case study on affine formation tracking in a multi-UAV formation, demonstrating the effectiveness of our algorithms in constructing eligible frameworks in aforementioned scenarios. Moreover, a comparative simulations is also conducted to highlight the low time complexity of our distributed algorithm relative to the centralized optimization-based method. Copyright © 2025, The Authors. All rights reserved.

关键词： Rigidity

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Generate-on-Graph: Treat LLM as both Agent and KG for Incomplete Knowledge Graph Question Answering

Generate-on-Graph: Treat LLM as both Agent and KG for Incomp...

引用

2024 Conference on Empirical Methods in Natural Language Processing, EMNLP 2024

作者： Xu, Yao He, Shizhu Chen, Jiabei Wang, Zihao Song, Yangqiu Tong, Hanghang Liu, Guang Zhao, Jun Liu, Kang The Key Laboratory of Cognition and Decision Intelligence for Complex Systems Institute of Automation Chinese Academy of Sciences China School of Artificial Intelligence University of Chinese Academy of Sciences China The Hong Kong University of Science and Technology Hong Kong University of Illinois Urbana-Champaign United States Beijing Academy of Artificial Intelligence China

ISBN: (纸本)9798891761643

To address the issues of insufficient knowledge and hallucination in Large Language Models (LLMs), numerous studies have explored integrating LLMs with Knowledge Graphs (KGs).However, these methods are typically evaluated on conventional Knowledge Graph Question Answering (KGQA) with complete KGs, where all factual triples required for each question are entirely covered by the given *** such cases, LLMs primarily act as an agent to find answer entities within the KG, rather than effectively integrating the internal knowledge of LLMs and external knowledge sources such as *** fact, KGs are often incomplete to cover all the knowledge required to answer *** simulate these real-world scenarios and evaluate the ability of LLMs to integrate internal and external knowledge, we propose leveraging LLMs for QA under Incomplete Knowledge Graph (IKGQA), where the provided KG lacks some of the factual triples for each question, and construct corresponding *** handle IKGQA, we propose a training-free method called Generate-on-Graph (GoG), which can generate new factual triples while exploring ***, GoG performs reasoning through a Thinking-Searching-Generating framework, which treats LLM as both Agent and KG in *** results on two datasets demonstrate that our GoG outperforms all previous methods. © 2024 Association for Computational Linguistics.

关键词： Knowledge graph

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Lightweight and Covalent-Crosslinked Polybenzoxazine Aerogels for Fire Resistance and Thermal Insulation

SSRN

引用

SSRN 2024年

作者： Li, Liangjun Zhou, Jinlong Xiao, Yunyun Zeyu, Li Liu, Saihui Zhang, Sizhao Feng, Jian Science and Technology on Advanced Ceramic Fibers and Composites Laboratory College of Aerospace Science and Technology National University of Defense Technology Changsha410073 China International Institute for Innovation Jiangxi University of Science and Technology Jiangxi Nanchang330013 China Jiangxi Provincial Key Laboratory for Simulation and Modelling of Particulate Systems Jiangxi Nanchang330013 China

The rapid advancement of modern industry and aerospace has imposed demands on thermal insulators to possess not only efficient isolation but also multifunctionality. Polybenzoxazine (PBz) aerogels with several advantages have garnered considerable research interests in recent years. Nevertheless, PBz aerogels acquired from ambient pressure drying still confront the challenge of exhibiting relatively high densities and thermal conductivities. Herein, to enrich the category and provide ideas for overcoming the above plight, hexamethylene diisocyanate (HDI) was chosen as an additive to achieve the chemical modification of the PBz aerogels. The chemical structure characterization shown that a successful reaction was occurred between the isocyanates and the hydroxyl groups, forming a urethane-bridged structure between two PBz molecular chains. In this paper, the effect of introducing HDI on the physical and thermal insulation properties of the aerogels was investigated. The HDI-modified PBz (PBz-HDI) aerogels demonstrated lower densities (0.237–0.256 g·cm−3) and thermal conductivities (0.0354−0.0370 W·m−1·K−1) in comparison with the pristine aerogel. In addition, despite an observed reduction in the residual char yields in the PBz-HDI groups, the introduction of HDI has been demonstrated to not impact their superior intrinsic flame retardancy. Given such commendable properties, PBz-HDI aerogel is expected to be a promising candidate for thermal insulation and fire resistance applications in various domains. © 2024, The Authors. All rights reserved.

关键词： Thermal insulation

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Radar Signal Detection Based on Ambiguity Function and Deep Learning 2

Radar Signal Detection Based on Ambiguity Function and Deep ...

引用

2nd International Conference on Computer Engineering and Application, ICCEA 2021

作者： Lv, Fengrong Dong, Zeyu Wan, Tao Jiang, Kaili Fang, Xueli Zhang, Lei University of Electronic Science and Technology of China School of Information and Communication Engineering Chengdu China Key Laboratory of Complex Aviation Simulation System Beijing China

ISBN: (纸本)9781665426169

The ambiguity function describes the joint characteristics of the signal in the time domain and the frequency domain, and is usually used for signal recognition. The time domain and frequency domain distribution of noise is more spurious than the signal. Its ambiguity function can also reflect its characteristics. However, the direct use of the ambiguity function as the signal feature will increase the amount of calculation of the detection system, so slice it, which reduces the burden on the system for detecting signal information while preserving the information. At the same time, the radar signal detection based on neural network can avoid the influence of artificially setting the threshold on the detection performance of the system. So, we propose an algorithm for inputting the extracted fuzzy function slice sequence into a neural network to realize signal detection. simulation proves that when the signal-To-noise ratio of the received signal is very low, our proposed method still has a high detection probability. © 2021 IEEE.

关键词： Signal detection

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Assessing the effectiveness of the intervention measures of COVID-19 in China based on dynamical method

引用

Infectious Disease Modelling 2023年第1期8卷 159-171页

作者： Xiaomeng Wei Mingtao Li Xin Pei Zhiping Liu Juan Zhang Complex Systems Research Center Shanxi University030006ShanxiChina Shanxi Key Laboratory of Mathematical Techniques and Big Data Analysis on Disease Control and Prevention 030006ShanxiChina School of Mathematical Sciences Shanxi University030006ShanxiChina College of Mathematics Taiyuan University of Technology030024ShanxiChina School of Data Science and Technology North University of China030051ShanxiChina

Normalized interventions were implemented in different cities in China to contain the outbreak of COVID-19 before December ***,the differences in the intensity and timeliness of the implementations lead to differences in final size of the *** the outbreak of COVID-19 in three representative cities Xi'an,Zhengzhou and Yuzhou in January 2022,as examples,we develop a compartmental model to describe the spread of novel coronavirus and implementation of interventions to assess concretely the effectiveness of Chinese interventions and explore their impact on epidemic *** applying reported human confirmed cases to verify the rationality of the model,we apply the model to speculate transmission trend and length of concealed period at the initial spread phase of the epidemic(they are estimated as 10.5,7.8,8.2 days,respectively),to estimate the range of basic reproduction number(2.9,0.7,1.6),and to define two indexes(transmission rate vt and controlled rate vc)to evaluate the overall effect of the *** is shown that for Zhengzhou,vc is always more than v t with regular interventions,and Xi'an take 8 days to achieve vc>v t twice as long as Yuzhou,which can interpret the fact that the epidemic situation in Xi'an was more *** carrying out parameter values,it is concluded that in the early stage,strengthening the precision of close contact tracking and frequency of large-scale nucleic acid testing of non-quarantined population are the most effective on controlling the outbreaks and reducing final ***,if the close contact tracking strategy is sufficiently implemented,at the late stage largescale nucleic acid testing of non-quarantined population is not essential.

关键词： COVID-19 Close contact tracking Large-scale nucleic acid testing Dynamics The basic reproduction number Sensitivity analysis

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Radar Signal Modulation Recognition Based on Bispectrum Features and Deep learning 2

Radar Signal Modulation Recognition Based on Bispectrum Feat...

引用

2nd International Conference on Computer Engineering and Application, ICCEA 2021

作者： Dong, Zeyu Lv, Fengrong Wan, Tao Jiang, Kaili Fang, Xueli Zhang, Lei University of Electronic Science and Technology of China School of Information and Communication Engineering Chengdu China Key Laboratory of Complex Aviation Simulation System Beijing China

ISBN: (纸本)9781665426169

Signal bispectral transformation can not only suppress the influence of Gaussian white noise on signal modulation recognition, but also retain the signal amplitude and phase information. It is also used to extract the non-linear characteristics. Compared with other high-order spectra, bispectrum has a simple processing flow. However, the direct use of all bispectrum as signal features will lead to two-dimensional template matching, causing lots of calculations. Converting two-dimensional bispectrum into one-dimensional sequence, for example, extracting slice information of bispectrum, or using integral bispectrum apparently reduce the amount of data to be processed while retaining part of the bispectrum information. We input the extracted bispectral transformation of radar signals into the neural network to realize modulation recognition. The simulations validate our conclusions that our proposed methods still have a high recognition probability while SNR is low. © 2021 IEEE.

关键词： Template matching

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Semi-supervised Open-set Recognition of Radar Active Jamming

Semi-supervised Open-set Recognition of Radar Active Jamming

引用

2021 CIE International Conference on Radar, Radar 2021

作者： Li, Hao Fang, Xueli Zhang, Lei Kang, Hui Zhang, Wei School of Information and Communication Engineering University of Electronic Science and Technology of China Chengdu China Key Laboratory of Complex Aviation Simulation System Beijing China

ISBN: (纸本)9781665498142

With the emergence of various kinds of complex radar jamming, radar jamming intelligent recognition technology has increasingly become the key to electronic counter-counter measures. To achieve radar jamming open-set recognition with a small number of tagged samples, Generative adversarial network-based pseudolabeled convolutional neural network (GAN-PL-CNN) model is proposed in this paper. Firstly, radar jamming is modelled, and the radar jamming datasets with known and unknown types are established after time-frequency transformation and image processing. Then, the adaptive pseudolabeling method is used to achieve semi-supervised recognition of radar jamming by combining the learning capability of convolutional neural networks and the characteristics of pseudolabeling to increase labeled samples intelligently. Finally, generative adversarial networks are introduced to enhance the recognition ability of the model and the discrimination ability of the unknown type through the game between the generator and the discriminator in the iterative process. Experimental results show that the GAN-PL-CNN model achieves 89.7%-95.1% for known types and 30.7%-86.8% for unknown types at 3%-6% labeling rate. As the number of labeled samples increases, the recognition effect becomes better and has a greater ability to exclude unknown type. © 2021 IEEE.

关键词： convolutional neural network open-set recognition pseudo-label Radar active jamming

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A symmetry-based length model for characterizing the hypersonic boundary layer transition on a slender cone at moderate incidence

引用

Advances in Aerodynamics 2022年第1期4卷 546-568页

作者： Wei-Tao Bi Zhou Wei Ke-Xin Zheng Zhen-Su She State Key Laboratory for Turbulence and Complex Systems and Department of Mechanics and Engineering Science College of EngineeringPeking UniversityBeijing100871China Science and Technology on Scramjet Laboratory China Aerodynamics Research and Development CenterMianyang621000China State Key Laboratory of Aerodynamics China Aerodynamics Research and Development CenterMianyang621000China Computational Aerodynamics Institute China Aerodynamics Research and Development CenterMianyang621000China

The hypersonic boundary layer(HBL)transition on a slender cone at moderate incidence is studied via a symmetry-based length model:the SED-SL *** SED-SL specifies an analytic stress length function(which defines the eddy viscosity)describing a physically sound two-dimensional multi-regime structure of transitional boundary *** studies showed accurate predictions,especially on the drag coefficient,by the SED-SL for airfoil flows at different subsonic Mach numbers,Reynolds numbers and angles of ***,the SED-SL is extended to compute the hypersonic heat transfer on a 7∘half-angle straight cone at Mach numbers 6 and 7 and angles of attack from 0∘to 6∘.It is shown that a proper setting of the multi-regime structure with three parameters(i.e.a transition center,an after-transition near-wall eddy length,and a transition width quantifying transition overshoot)yields an accurate description of the surface heat fluxes measured in wind *** good agreements between simulations and measurements are obtained from windward to leeward side of the cone,implying the validity of the multi-regime description of the transition independent of instability *** is concluded that a unified description for the HBL transition of cone is found,and might offer a basis for developing a new transition model that is simultaneously of computational simplicity,sound physics and greater accuracy.

关键词： Hypersonic boundary layer transition Transition model Cone Heat flux

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Tracking control of motion control systems with disturbance observer based on high-order fully actuated system approach

Tracking control of motion control systems with disturbance ...

引用

Fully Actuated System Theory and Applications (CFASTA), Conference on

作者： Rongmei Li Xin Huo Aijing Wu Weizhen Liu Control and Simulation Center Harbin Institute of Technology Harbin P. R. China Shenzhen Key Laboratory of Control Theory and Intelligent Systems Southern University of Science and Technology Shenzhen China

ISBN: (数字)9798350373691

ISBN: (纸本)9798350373707

This paper investigates the tracking problem of motion control systems driven by permanent magnet synchronous motors (PMSMs) in the presence of unknown disturbances. In contrast to using the model of state space methods, this study adopts a different method by initially transforming the model of a motion control system driven by PMSM into a high-order fully actuated (HOFA) system. Subsequently, a controller is designed based on the HOFA system approach, and a closed-loop linear system with disturbances is obtained. To handle the impact of disturbances, a disturbance observer is employed to estimate the disturbance. The validity of the proposed algorithm is assessed through theoretical analysis, and a numerical simulation is also conducted to further support the findings, thereby underscoring the effectiveness of the proposed approach.

关键词： Linear systems Parameter estimation Tracking Aerospace electronics Control systems Permanent magnet motors Numerical simulation

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