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Judging the Normativity of PAF Based on TFN and NAN
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作者 LI Zhiqiang BAO Jinsong +1 位作者 LIU Tianyuan WANG Jiacheng 《Journal of Shanghai Jiaotong university(Science)》 EI 2020年第5期569-577,共9页
The normativity of workers'actions during producing has a great impact on the quality of the products and the safety of the operation process.Previous studies mainly focused on the normativity of each single produ... The normativity of workers'actions during producing has a great impact on the quality of the products and the safety of the operation process.Previous studies mainly focused on the normativity of each single producing action instead of considering the normativity of continuous producing actions,which is defined as producing action flow(PAF)in this paper,during operation process.For this issue,a normativity judging method based on two-LSTM fusion network(TFN)and normativity-aware attention network(NAN)is proposed.First,TFN is designed to detect and recognize the producing actions based on skeleton sequences of a worker during complete operation process,and PAF data in sequential form are obtained.Then.NAN is built to allocate difTerent levels of attention to each producing action within the sequence of PAF.and by this means,an efficient normativity judging is conducted.The combustor surface cleaning(CSC)process of rocket engine is taken as the experimental case,and the CSC-Action2D dataset is established for evaluation.Experiment results show the high performance of TFN and NAN.demonstrating the effectiveness of the proposed method for PAF normativity judging. 展开更多
关键词 producing action normativity sequential model attention mechanism deep learning
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有限群的幂自同构与子群格
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作者 郭秀云 王俊新 《数学进展》 北大核心 2025年第2期357-378,共22页
群与格是现代数学中两个最基本的研究对象.本文主要介绍群的幂自同构与群的子群格之间的相互关联,以及近年来围绕群的幂自同构与群的子群格方面人们所取得的一些新的研究成果.我们将从有限群的幂自同构与有限群的结构,有限群的norm、Wie... 群与格是现代数学中两个最基本的研究对象.本文主要介绍群的幂自同构与群的子群格之间的相互关联,以及近年来围绕群的幂自同构与群的子群格方面人们所取得的一些新的研究成果.我们将从有限群的幂自同构与有限群的结构,有限群的norm、Wielandt-子群以及Wielandt-子群链与有限群的结构,有限群的子群格与有限群的结构,有限群的二极大子群、弱二极大子群与有限群的结构等四个方面来阐述.同时,一些可以进一步研究的问题被提出. 展开更多
关键词 幂自同构 子群格 NORM Wielandt-子群链 极大子群 二极大子群 弱二极大子群 Pálfy-Pudlák问题
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Infrared small target detection algorithm via partial sum of the tensor nuclear norm and direction residual weighting
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作者 SUN Bin XIA Xing-Ling +1 位作者 FU Rong-Guo SHI Liang 《红外与毫米波学报》 北大核心 2025年第2期277-288,共12页
Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small targe... Aiming at the problem that infrared small target detection faces low contrast between the background and the target and insufficient noise suppression ability under the complex cloud background,an infrared small target detection method based on the tensor nuclear norm and direction residual weighting was proposed.Based on converting the infrared image into an infrared patch tensor model,from the perspective of the low-rank nature of the background tensor,and taking advantage of the difference in contrast between the background and the target in different directions,we designed a double-neighborhood local contrast based on direction residual weighting method(DNLCDRW)combined with the partial sum of tensor nuclear norm(PSTNN)to achieve effective background suppression and recovery of infrared small targets.Experiments show that the algorithm is effective in suppressing the background and improving the detection ability of the target. 展开更多
关键词 infrared small target detection infrared patch tensor model partial sum of the tensor nuclear norm direction residual weighting
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Rational Presupposition, Normativity and Pluralist Expression: A Cross-Cultural Perspective on the Universality of Philosophy
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作者 Cheng Lesong 黄德远 《Social Sciences in China》 2022年第1期88-103,共16页
The question of the universality of philosophy is highlighted when seen from a cross-cultural perspective,for it reveals the tension between particularity and universality,as well as the connotations of the universali... The question of the universality of philosophy is highlighted when seen from a cross-cultural perspective,for it reveals the tension between particularity and universality,as well as the connotations of the universality of philosophy.In terms of philosophical activities concerned with the content of Chinese life experience,the universality of philosophy,the particularity of Chinese thought,and the uniqueness of Chinese expression together constitute a persistent theoretical tension.We distinguish the universality of philosophy from universal philosophy;the former stems from the universal presupposition of rational capacity and points to the richness and pluralism of the empirical world while maintaining a dynamic balance between universality and pluralism in normative attitudes of discourse practice and conceptual activity.From the perspective of cultural subjectivity,it is necessary to avoid misleading views that equate the universality of philosophy with Western philosophy;moreover,normativity cannot be understood as specific censorship rules.The universality of philosophy requires a sense of boundaries and a normative attitude that will ensure that people from different contexts can enter into dialogue on the basis of rational ability and construct a space for dialogue and understanding.The concern for diverse objects based on the richness of experience gives philosophical concepts and arguments pluralist differences that encompass cultural differences and autonomy at the level of expression.All in all,it is only on the basis of the universality of philosophy that we can understand the normative requirements of philosophical activities and the pluralism of cross-cultural philosophical reflection. 展开更多
关键词 universality of philosophy universal philosophy presupposition of rational capacity normativity
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Ecological Assessment of Physicochemical Pollution of Wadi Sebou(Gharb,Morocco)
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作者 Habiby El Moctar Fatimetou Salma +9 位作者 Brahim Ahmed Dick Ilyass Laazar Ettaki Jalal Aalama Fatima Hraira Thami Hammouali Kamal Maaroufi Manal Echayeb Hajar Fariri Khalid Belghyti Driss 《Journal of Environmental & Earth Sciences》 2025年第6期351-369,共19页
In Morocco,hydrological and hydrobiological surveys of wadis,river and stream are rare.In this research,we plan to attempt to characterize the physico-chemistry of surface waters of sixteen stations sampled at the lev... In Morocco,hydrological and hydrobiological surveys of wadis,river and stream are rare.In this research,we plan to attempt to characterize the physico-chemistry of surface waters of sixteen stations sampled at the level of the Sebou basin during the period 2013-2023.The diagnosis showed that this natural watercourse is highly enriched in oce-anic salts.A large fluctuation in the chemical nature of the waters was recorded,as well as electrical conductivity(EC),which oscillates between 629 and 22,766μS/cm.Hydrogen Potential ranges from 8.01 to 8.79 while remaining basic.Nitrate(NO3-)concentrations range from a maximum of 886.9 mg/l to a minimum of 0.24 mg/l.Similarly,the am-monium concentration varies from 0.04 to 15.34 mg/l.It was also noted that the waters were very rich in chloride ions(860.27 to 145.55 mg/l),in sodium Na+ion(51 to 2,530 mg/l),in sulfate ions SO4--(441.4 to 37.62 mg/l),in calcium ions Ca2+(97.6 to 1,072.8 mg/l)and in magnesium ions Mg2+(631.2 to 17.28 mg/l)which explains the high hardness of these waters.The concentrations of potassium ions(K+)range from 2.54 to 17.55 mg/l.The high alkalinity is due to the high concentrations of bicarbonate ions(75.64 to 362.34 mg/l).Our study concludes that the waters of the Sebou re-main below the irrigation threshold authorized by Moroccan law when moving away from its Atlantic estuary.They are too degraded and we suggest that urban and industrial wastewater be pre-treated as a priority to reduce natural environment. 展开更多
关键词 Watercourse Physicochemistry Norme QUALITY Sebou Kenitra Morocco
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Bayesian Network Reconstruction and Iterative Divergence Problem Solving Method Based on Norm Minimization
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作者 Kuo Li Aimin Wang +2 位作者 Limin Wang Yuetan Zhao Xinyu Zhu 《Computer Modeling in Engineering & Sciences》 2025年第4期617-637,共21页
A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values.This method achieves... A Bayesian network reconstruction method based on norm minimization is proposed to address the sparsity and iterative divergence issues in network reconstruction caused by noise and missing values.This method achieves precise adjustment of the network structure by constructing a preliminary random network model and introducing small-world network characteristics and combines L1 norm minimization regularization techniques to control model complexity and optimize the inference process of variable dependencies.In the experiment of game network reconstruction,when the success rate of the L1 norm minimization model’s existence connection reconstruction reaches 100%,the minimum data required is about 40%,while the minimum data required for a sparse Bayesian learning network is about 45%.In terms of operational efficiency,the running time for minimizing the L1 normis basically maintained at 1.0 s,while the success rate of connection reconstruction increases significantly with an increase in data volume,reaching a maximum of 13.2 s.Meanwhile,in the case of a signal-to-noise ratio of 10 dB,the L1 model achieves a 100% success rate in the reconstruction of existing connections,while the sparse Bayesian network had the highest success rate of 90% in the reconstruction of non-existent connections.In the analysis of actual cases,the maximum lift and drop track of the research method is 0.08 m.The mean square error is 5.74 cm^(2).The results indicate that this norm minimization-based method has good performance in data efficiency and model stability,effectively reducing the impact of outliers on the reconstruction results to more accurately reflect the actual situation. 展开更多
关键词 Bayesian norm minimization network reconstruction iterative divergence SPARSITY
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Generative Artificial Intelligence in Judicial Applications:Functions,Risks,and Controls
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作者 Hong Wenxiao 《Contemporary Social Sciences》 2025年第1期142-155,共14页
The application of generative artificial intelligence(GAI)in the judicial domain represents an innovative approach to achieving digital justice.GAI’s functionalities are primarily exhibited in the enhancement of judi... The application of generative artificial intelligence(GAI)in the judicial domain represents an innovative approach to achieving digital justice.GAI’s functionalities are primarily exhibited in the enhancement of judicial efficiency,improving the accuracy and fairness of adjudications,promoting the uniform application of the law,and enhancing transparency and engagement in judicial processes.However,these advancements are accompanied by potential risks and challenges in technology,adjudication,and ethics.It is thus essential to strengthen privacy protection during the processing and transmission of data,ensure data security and confidentiality,and establish and refine clear legal norms regarding the roles,responsibilities,and legal obligations of GAI in judicial settings.In addition,ethical guidelines that delineate the behavioral boundaries and value orientations of GAI need to be formulated.Collectively,these elements can form a trinary model of technical controls,legal norms,and ethical constraints,to facilitate the modernization and intelligent development of the judicial system. 展开更多
关键词 GAI application functions RISKS technical controls legal norms ethical constraints
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Commentary on“International norms for adult handgrip strength:A systematic review of data on 2.4 million adults aged 20 to 100+years from 69 countries and regions”
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作者 Barbara E.Ainsworth Zhining Zhou 《Journal of Sport and Health Science》 2025年第4期40-42,共3页
In the December 2025 issue of the Journal of Sport and Health Science,Tomkinson et al.^(1)present international norms for adult handgrip strength(HGS)developed from a systematic review of 100 studies with 2.4 million ... In the December 2025 issue of the Journal of Sport and Health Science,Tomkinson et al.^(1)present international norms for adult handgrip strength(HGS)developed from a systematic review of 100 studies with 2.4 million adults aged 20 to 100+years from 69 countries and regions.Twenty-eight interna-tional handGRIP Strength(iGRIPS)researchers contributed to the study. 展开更多
关键词 handgrip strength systematic review ADULTS international norms
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Schweizer-Sklar T-Norm Operators for Picture Fuzzy Hypersoft Sets: Advancing Suistainable Technology in Social Healthy Environments
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作者 Xingsi Xue Himanshu Dhumras +2 位作者 Garima Thakur Rakesh Kumar Bajaj Varun Shukla 《Computers, Materials & Continua》 2025年第7期583-606,共24页
Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain informat... Ensuring a sustainable and eco-friendly environment is essential for promoting a healthy and balanced social life.However,decision-making in such contexts often involves handling vague,imprecise,and uncertain information.To address this challenge,this study presents a novel multi-criteria decision-making(MCDM)approach based on picture fuzzy hypersoft sets(PFHSS),integrating the flexibility of Schweizer-Sklar triangular norm-based aggregation operators.The proposed aggregation mechanisms—weighted average and weighted geometric operators—are formulated using newly defined operational laws under the PFHSS framework and are proven to satisfy essential mathematical properties,such as idempotency,monotonicity,and boundedness.The decision-making model system-atically incorporates both benefit and cost-type criteria,enabling more nuanced evaluations in complex social or environmental decision problems.To enhance interpretability and practical relevance,the study conducts a sensitivity analysis on the Schweizer-Sklar parameter(Δ).The results show that varyingΔaffects the strictness of aggregation,thereby influencing the ranking stability of alternatives.A comparative analysis with existing fuzzy and hypersoft-based MCDM methods confirms the robustness,expressiveness,and adaptability of the proposed approach.Notably,the use of picture fuzzy sets allows for the inclusion of positive,neutral,and negative memberships,offering a richer representation of expert opinions compared to traditional models.A case study focused on green technology adoption for environmental sustainability illustrates the real-world applicability of the proposed method.The analysis confirms that the approach yields consistent and interpretable results,even under varying degrees of decision uncertainty.Overall,this work contributes an efficient and flexible MCDM tool that can support decision-makers in formulating policies aligned with sustainable and socially responsible outcomes. 展开更多
关键词 Hypersoft set picture fuzzy set Schweizer-Sklar norms aggregation operators DECISION-MAKING green technology adoption
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International Norms for Lethal Autonomous Weapon Systems:Divergences among Major Countries
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作者 Chen Genfeng Sun Xuefeng 《Contemporary International Relations》 2025年第2期19-36,共18页
Lethal autonomous weapon systems(LAWS)have become a prominent issue in global security governance.However,significant divergences remain among the world's major countries regarding their regulation:some support re... Lethal autonomous weapon systems(LAWS)have become a prominent issue in global security governance.However,significant divergences remain among the world's major countries regarding their regulation:some support restrictions,while others oppose any binding rules,and there are also countries adopting a neutral stance,though their choices are subject to external pressure.In the foreseeable future,the deployment of LAWS will increase further,raising the risk of arms races,with international support for regulating these weapons gaining strength.Yet,establishing legally binding international rules within the United Nations(UN)framework remains a distant prospect.Given this backdrop,China should continue to actively participate in international norms setting concerning LAWS under UN auspices and deepen coordination and cooperation with other countries towards more applicable norms and global governance frameworks. 展开更多
关键词 international norm international security lethal autonomous weapon system major country
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Table manners
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作者 Maria Chiu 《空中英语教室(初级版.大家说英语)》 2025年第10期21-24,52,53,56,共7页
Table manners are important in manycultures.Inmost countries,youwait untileveryone has food before eating.Youalso don't put your elbows on the table.It's not polite to eat too fast.And youshouldn't talk wi... Table manners are important in manycultures.Inmost countries,youwait untileveryone has food before eating.Youalso don't put your elbows on the table.It's not polite to eat too fast.And youshouldn't talk with food in yourmouth orchew with your mouth open. 展开更多
关键词 eating etiquette cultural norms table manners
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A Total Variational Image Denoising Model Coupled with a New Non-local Edge Extractor and a Level Set Curvature Gradient
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作者 Zhou Han Xianchun Zhou +1 位作者 Binxin Tang Siqi Lu 《Instrumentation》 2025年第2期47-59,共13页
To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the infl... To solve the problem of false edges in a flat region of l_(1)norm total variational TV model,an edge extractor based on non-local idea is proposed in this paper.The new edge extractor can effectively suppress the influence of noise and extract the edge information of the image.The new edge extractor is used as the adaptive function and the weighting function of the l_(p) norm variational model to control the noise reduction ability of the model,and a new model 1 is obtained.Considering that the new model 1 only uses the gradient mode as the image feature operator,which is insufficient to express the image texture information,a new level set curvature gradient variational model 2 combined with the edge extractor is proposed.The new model 2 uses the idea of minimum curvature of the level set of clear images to obtain noise reduction images.By coupling new model 1 and new model 2 to smooth the noise and protect more textures,a new Non-local level set denoising model(NLSDM)for image noise reduction is obtained.The experimental results show that compared with the noise reduction model,the new model has significantly improved the peak signal-to-noise ratio and structural similarity,and the effect of noise reduction and edge preservation is better. 展开更多
关键词 TV model the l_(p)norm NONLOCAL pfunction level set curvature term of regularization
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Sobolev space norm regularized full waveform inversion for ultrasound computed tomography
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作者 Panpan Li Yubing Li +2 位作者 Chang Su Zeyuan Dong Weijun Lin 《Chinese Physics B》 2025年第5期444-456,共13页
Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this... Full waveform inversion(FWI)is a complex data fitting process based on full wavefield modeling,aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution.However,this process is highly nonlinear and ill-posed,therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging.We propose a multiscale frequency–domain full waveform inversion(FDFWI)framework for ultrasound computed tomography(USCT)imaging of biological tissues,which innovatively incorporates Sobolev space norm regularization for enhancement of prior information.Specifically,we investigate the effect of different types of hyperparameter on the imaging quality,during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term.This strategy reduces reliance on predefined hyperparameters,ensuring robust inversion performance.The inversion results from both numerical and experimental tests(i.e.,numerical breast,thigh,and ex vivo pork-belly tissue)demonstrate the effectiveness of our regularized FWI strategy.These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging. 展开更多
关键词 full waveform inversion Sobolev space norm regularization ultrasound computed tomography
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APPLICATION OF THE MINIMAL NORM TENSOR PRINCIPLE IN MOBIUS GEOMETRY
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作者 XING Jin-xiong GONG Yi-fan 《数学杂志》 2025年第3期205-212,共8页
This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere.By implementing the minimum norm tensor principle,we rigorously estimate the squared norm o... This paper addresses Pinching problems in Möbius geometry for hypersurfaces with Möbius isotropy in the unit sphere.By implementing the minimum norm tensor principle,we rigorously estimate the squared norm of the quadratic gradient term associated with the Möbius second fundamental form.This analysis yields a critical inequality governing the geometric config-uration.Leveraging this inequality,we subsequently prove a Pinching theorem characterizing the eigenvalues of the Blaschke tensor. 展开更多
关键词 minimal norm tensor Möbius second fundamental form HYPERSURFACE
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Channel Estimation for Reconfigurable Intelligent Surface Aided Multiuser Millimeter-Wave/THz Systems 被引量:2
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作者 Chu Hongyun Pan Xue Li Baijiang 《China Communications》 SCIE CSCD 2024年第3期91-103,共13页
It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only b... It is assumed that reconfigurable intelligent surface(RIS)is a key technology to enable the potential of mmWave communications.The passivity of the RIS makes channel estimation difficult because the channel can only be measured at the transceiver and not at the RIS.In this paper,we propose a novel separate channel estimator via exploiting the cascaded sparsity in the continuously valued angular domain of the cascaded channel for the RIS-enabled millimeter-wave/Tera-Hz systems,i.e.,the two-stage estimation method where the cascaded channel is separated into the base station(BS)-RIS and the RIS-user(UE)ones.Specifically,we first reveal the cascaded sparsity,i.e.,the sparsity exists in the hybrid angular domains of BS-RIS and the RIS-UEs separated channels,to construct the specific sparsity structure for RIS enabled multi-user systems.Then,we formulate the channel estimation problem using atomic norm minimization(ANM)to enhance the proposed sparsity structure in the continuous angular domains,where a low-complexity channel estimator via Alternating Direction Method of Multipliers(ADMM)is proposed.Simulation findings demonstrate that the proposed channel estimator outperforms the current state-of-the-arts in terms of performance. 展开更多
关键词 atomic norm minimization cascaded channel estimation convex optimization mmWave/THz reconfigurable intelligent surface(RIS) sparsity
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Suppression of seismic random noise by deep learning combined with stationary wavelet packet transform 被引量:1
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作者 Fan Hua Wang Dong-Bo +2 位作者 Zhang Yang Wang Wen-Xu Li Tao 《Applied Geophysics》 SCIE CSCD 2024年第4期740-751,880,共13页
Many traditional denoising methods,such as Gaussian filtering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis too... Many traditional denoising methods,such as Gaussian filtering,tend to blur and lose details or edge information while reducing noise.The stationary wavelet packet transform is a multi-scale and multi-band analysis tool.Compared with the stationary wavelet transform,it can suppress high-frequency noise while preserving more edge details.Deep learning has significantly progressed in denoising applications.DnCNN,a residual network;FFDNet,an efficient,fl exible network;U-NET,a codec network;and GAN,a generative adversative network,have better denoising effects than BM3D,the most popular conventional denoising method.Therefore,SWP_hFFDNet,a random noise attenuation network based on the stationary wavelet packet transform(SWPT)and modified FFDNet,is proposed.This network combines the advantages of SWPT,Huber norm,and FFDNet.In addition,it has three characteristics:First,SWPT is an eff ective featureextraction tool that can obtain low-and high-frequency features of different scales and frequency bands.Second,because the noise level map is the input of the network,the noise removal performance of diff erent noise levels can be improved.Third,the Huber norm can reduce the sensitivity of the network to abnormal data and enhance its robustness.The network is trained using the Adam algorithm and the BSD500 dataset,which is augmented,noised,and decomposed by SWPT.Experimental and actual data processing results show that the denoising eff ect of the proposed method is almost the same as those of BM3D,DnCNN,and FFDNet networks for low noise.However,for high noise,the proposed method is superior to the aforementioned networks. 展开更多
关键词 random noise stationary wavelet packet transform deep learning noise level map Huber norm
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Constructing river ethics: A new paradigm for the harmonious coexistence between humans and rivers 被引量:2
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作者 Guoying Li 《River》 2024年第3期221-224,共4页
River ethics encompasses the values,moral principles,and behavioral norms that govern and regulate the relationship between humans and rivers.Constructing rivers ethics breaks through the traditional ethical dimension... River ethics encompasses the values,moral principles,and behavioral norms that govern and regulate the relationship between humans and rivers.Constructing rivers ethics breaks through the traditional ethical dimension that is limited to interpersonal judgment and extends the moral relationship from solely between humans to between humans and river life.China's eco-civilization drive elucidates that harmony between humans and rivers are the core concept of constructing river ethics.This paper discusses the values,foundation,moral principles,and behavioral norms of river ethics,and forms the theoretical framework of river ethics. 展开更多
关键词 behavioral norms China's eco-civilization drive moral codes rights of rivers river ethics river health and life river values
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THE BSE PROPERTY FOR SOME VECTOR-VALUED BANACH FUNCTION ALGEBRAS
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作者 Fatemeh ABTAHI Ali REJALI Farshad SAYAF 《Acta Mathematica Scientia》 SCIE CSCD 2024年第5期1945-1954,共10页
In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the ... In this paper,X is a locally compact Hausdorff space and A is a Banach algebra.First,we study some basic features of C0(X,A)related to BSE concept,which are gotten from A.In particular,we prove that if C0(X,A)has the BSE property then A has so.We also establish the converse of this result,whenever X is discrete and A has the BSE-norm property.Furthermore,we prove the same result for the BSE property of type I.Finally,we prove that C0(X,A)has the BSE-norm property if and only if A has so. 展开更多
关键词 BSE algebras BSE-function BSE norm multiplier algebra SEMISIMPLE without order
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REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS
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作者 Xiaohui LI Meiqi LIU Chunyuan DENG 《Acta Mathematica Scientia》 SCIE CSCD 2024年第4期1229-1243,共15页
In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm ineq... In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value. 展开更多
关键词 NORM orthogonal projection positive operator SPECTRAL block operator valued matrix
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