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Some Generalizations of Monotonicity Condition and Applications 被引量:2
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作者 虞旦盛 周颂平 《数学进展》 CSCD 北大核心 2006年第6期755-757,共3页
0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the cond... 0 Introduction It is well known that there axe a great number of interesting results in Fourier analysis established by assuming monotonicity of coefficients, and many of them have been generalized by loosing the condition to quasi-monotonicity, O-regularly varying quasi-monotonicity, etc.. 展开更多
关键词 LIM Some generalizations of Monotonicity Condition and Applications
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Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws
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作者 Xian-Guo Geng Fei-Ying Guo Yun-Yun Zhai 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第5期70-73,共4页
With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positi... With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained. 展开更多
关键词 integrable generalizations positive flow and negative flow infinite conservation laws
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SOME GENERALIZATIONS ON THE BOUNDEDNESS OF BILINEAR OPERATORS
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作者 Li Xiaochun Lu Shanzhen Yang Dachun(Beijing Normal University, China) 《Analysis in Theory and Applications》 1997年第3期8-28,共21页
For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or ... For denote the Lebesgue space for and the Hardy space for p <1 In this paper, the authors study mapping properties of bilinear operators given by finite sums of the products of the standard fractional integrals or the standard fractional integral with the Calderon-Zygmund operator. The authors prove that such mapping properties hold if and only if these operators satisfy certain cancellation conditions. 展开更多
关键词 MATH SOME generalizations ON THE BOUNDEDNESS OF BILINEAR OPERATORS
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INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS GENERALIZATIONS
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作者 A.Shadrin 《Analysis in Theory and Applications》 1992年第3期51-61,共11页
The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies ... The following theorem is proved Theorem 1.Let q be a polynomial of degree n(qP_n)with n distinct zeroes lying in the interval[-1,1] and △'_q={-1}∪{τ_i:q'(τ_i)=0,i=1,n-1}∪{1}. If polynomial pP_n satisfies the inequality then for each k=1,n and any x[-1,1]its k-th derivative satisfies the inequality 丨p^(k)(x)丨≤max{丨q^((k))(x)丨,丨1/k(x^2-1)q^(k+1)(x)+xq^((k))(x)丨}. This estimate leads to the Markov inequality for the higher order derivatives of polynomials if we set q=T_n,where Tn is Chebyshev polynomial least deviated from zero. Some other results are established which gives evidence to the conjecture that under the conditions of Theorem 1 the inequality ‖p^((k))‖≤‖q^(k)‖holds. 展开更多
关键词 INTERPOLATION WITH LAGRANGE POLYNOMIALS A SIMPLE PROOF OF MARKOV INEQUALITY AND SOME OF ITS generalizations
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Generalizations of Euler Numbers and Euler Numbers of Higher Order 被引量:5
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作者 LUOQiu-ming QIFeng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2005年第1期54-58,共5页
The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler... The purpose of this paper is to define the generalized Euler numbers and the generalized Euler numbers of higher order, their recursion formula and some properties were established, accordingly Euler numbers and Euler numbers of higher order were extended. 展开更多
关键词 Euler numbers higher order Euler numbers generalized Euler numbers generalized higher order Euler numbers recursion formula
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GENERALIZATIONS OF THE SUZUKI AND KANNAN FIXED POINT THEOREMS IN G-CONE METRIC SPACES 被引量:1
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作者 Mohammad Sadegh Asgari Zohreh Abbasbigi 《Analysis in Theory and Applications》 2012年第3期248-262,共15页
In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in gener... In this paper we develop the Banach contraction principle and Kannan fixed point theorem on generalized cone metric spaces. We prove a version of Suzuki and Kannan type generalizations of fixed point theorems in generalized cone metric spaces. 展开更多
关键词 fixed point D-metric space 2-metric space generalized cone metric space Kannan mapping generalized Kannan mapping contractive mapping
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SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES 被引量:1
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作者 张石生 杨干山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1990年第11期1027-1034,共8页
The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the result... The purpose of this paper is to introduce the concept of generalized KKM mapping and to obtain some general version of the famous KKM theorem and Ky Fan's minimax inequality. As applications, we utilize the results presented in this paper to study the saddle . point problem and the existence problem of solutions for a class of quasi-variational inequalities. The results obtained in this paper extend and improve some recent results of[1-6] 展开更多
关键词 generalized KKM mapping upper-semicontinuous γ-diagonally quasi-convex saddle point
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Generalizations of Some Formulas of the Reciprocal Sum and Alternating Sum for Generalized Lucas Numbers
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作者 YE Xiao-li LIU Mai-xue 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2007年第1期99-103,共5页
The purpose of this article is to provide the inversion relationships between the reciprocal sum S(1, 2,…, m) and the alternating sum T(1, 2,…, m) for generalized Lucas numbers which generalizes the Melham's re... The purpose of this article is to provide the inversion relationships between the reciprocal sum S(1, 2,…, m) and the alternating sum T(1, 2,…, m) for generalized Lucas numbers which generalizes the Melham's results. 展开更多
关键词 generalized Lucas numbers reciprocal sum alternating sum
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Properties of Elliptic Integrals and Their Generalizations
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作者 ZHANGXiao-hui QIUSong-fiang 《杭州电子工业学院学报》 2004年第6期55-58,共4页
In this paper, a conjecture put forward by G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy in 1995 and concerning elliptic integrals is proved to be true, and some monotoneity and onvexity properties of certain combi... In this paper, a conjecture put forward by G. D. Anderson, S.-L. Qiu and M. K. Vamanamurthy in 1995 and concerning elliptic integrals is proved to be true, and some monotoneity and onvexity properties of certain combinations of generalized elliptic integrals are obtained. 展开更多
关键词 generalized ELLIPTIC INTEGRALS monotoneity CONVEXITY CONJECTURE proof
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Large language models for robotics:Opportunities,challenges,and perspectives 被引量:3
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作者 Jiaqi Wang Enze Shi +7 位作者 Huawen Hu Chong Ma Yiheng Liu Xuhui Wang Yincheng Yao Xuan Liu Bao Ge Shu Zhang 《Journal of Automation and Intelligence》 2025年第1期52-64,共13页
Large language models(LLMs)have undergone significant expansion and have been increasingly integrated across various domains.Notably,in the realm of robot task planning,LLMs harness their advanced reasoning and langua... Large language models(LLMs)have undergone significant expansion and have been increasingly integrated across various domains.Notably,in the realm of robot task planning,LLMs harness their advanced reasoning and language comprehension capabilities to formulate precise and efficient action plans based on natural language instructions.However,for embodied tasks,where robots interact with complex environments,textonly LLMs often face challenges due to a lack of compatibility with robotic visual perception.This study provides a comprehensive overview of the emerging integration of LLMs and multimodal LLMs into various robotic tasks.Additionally,we propose a framework that utilizes multimodal GPT-4V to enhance embodied task planning through the combination of natural language instructions and robot visual perceptions.Our results,based on diverse datasets,indicate that GPT-4V effectively enhances robot performance in embodied tasks.This extensive survey and evaluation of LLMs and multimodal LLMs across a variety of robotic tasks enriches the understanding of LLM-centric embodied intelligence and provides forward-looking insights towards bridging the gap in Human-Robot-Environment interaction. 展开更多
关键词 Large language models ROBOTICS Generative AI Embodied intelligence
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Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type 被引量:5
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作者 杨恩浩 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1990年第3期230-242,共13页
We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.A... We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched. 展开更多
关键词 Discrete generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type
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Development and application of rock rheological constitutive model considering dynamic stress field and seepage field 被引量:2
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作者 Yian Chen Guangming Zhao +2 位作者 Wensong Xu Shoujian Peng Jiang Xu 《International Journal of Mining Science and Technology》 2025年第3期467-482,共16页
The generalized rheological tests on sandstone were conducted under both dynamic stress and seepage fields.The results demonstrate that the rheological strain of the specimen under increased stress conditions is great... The generalized rheological tests on sandstone were conducted under both dynamic stress and seepage fields.The results demonstrate that the rheological strain of the specimen under increased stress conditions is greater than that under creep conditions,indicating that the dynamic stress field significantly influences the rheological behaviours of sandstone.Following the rheological tests,the number of small pores in the sandstone decreased,while the number of medium-sized pores increased,forming new seepage channels.The high initial rheological stress accelerated fracture compression and the closure of seepage channels,resulting in reduction in the permeability of sandstone.Based on the principles of generalized rheology and the experimental findings,a novel rock rheological constitutive model incorporating both the dynamic stress field and seepage properties has been developed.Numerical simulations of surrounding rock deformation in geotechnical engineering were carried out using a secondary development version of this model,which confirmed the applicability of the generalized rheological numerical simulation method.These results provide theoretical support for the long-term stability evaluation of engineering rock masses and for predicting the deformation of surrounding rock. 展开更多
关键词 Generalized rheological test Seepage-stress coupling Seepage properties Dynamic stress field Rheological constitutive model
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Improve Strategy for Transient Power Angle Stability Control of VSG Combining Frequency Difference Feedback and Virtual Impedance 被引量:2
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作者 Dianlang Wang Qi Yin +3 位作者 Haifeng Wang Jing Chen Hong Miao Yihan Chen 《Energy Engineering》 2025年第2期651-666,共16页
As the penetration rate of distributed energy increases,the transient power angle stability problem of the virtual synchronous generator(VSG)has gradually become prominent.In view of the situation that the grid impeda... As the penetration rate of distributed energy increases,the transient power angle stability problem of the virtual synchronous generator(VSG)has gradually become prominent.In view of the situation that the grid impedance ratio(R/X)is high and affects the transient power angle stability of VSG,this paper proposes a VSG transient power angle stability control strategy based on the combination of frequency difference feedback and virtual impedance.To improve the transient power angle stability of the VSG,a virtual impedance is adopted in the voltage loop to adjust the impedance ratio R/X;and the PI control feedback of the VSG frequency difference is introduced in the reactive powervoltage link of theVSGto enhance the damping effect.Thesecond-orderVSGdynamic nonlinearmodel considering the reactive power-voltage loop is established and the influence of different proportional integral(PI)control parameters on the system balance stability is analyzed.Moreover,the impact of the impedance ratio R/X on the transient power angle stability is presented using the equal area criterion.In the simulations,during the voltage dips with the reduction of R/X from 1.6 to 0.8,Δδ_(1)is reduced from 0.194 rad to 0.072 rad,Δf_(1)is reduced from 0.170 to 0.093 Hz,which shows better transient power angle stability.Simulation results verify that compared with traditional VSG,the proposedmethod can effectively improve the transient power angle stability of the system. 展开更多
关键词 Transient synchronous stability virtual synchronous generator impedance ratio
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Diffusion-based generative drug-like molecular editing with chemical natural language 被引量:1
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作者 Jianmin Wang Peng Zhou +6 位作者 Zixu Wang Wei Long Yangyang Chen Kyoung Tai No Dongsheng Ouyang Jiashun Mao Xiangxiang Zeng 《Journal of Pharmaceutical Analysis》 2025年第6期1215-1225,共11页
Recently,diffusion models have emerged as a promising paradigm for molecular design and optimization.However,most diffusion-based molecular generative models focus on modeling 2D graphs or 3D geom-etries,with limited ... Recently,diffusion models have emerged as a promising paradigm for molecular design and optimization.However,most diffusion-based molecular generative models focus on modeling 2D graphs or 3D geom-etries,with limited research on molecular sequence diffusion models.The International Union of Pure and Applied Chemistry(IUPAC)names are more akin to chemical natural language than the simplified molecular input line entry system(SMILES)for organic compounds.In this work,we apply an IUPAC-guided conditional diffusion model to facilitate molecular editing from chemical natural language to chemical language(SMILES)and explore whether the pre-trained generative performance of diffusion models can be transferred to chemical natural language.We propose DiffIUPAC,a controllable molecular editing diffusion model that converts IUPAC names to SMILES strings.Evaluation results demonstrate that our model out-performs existing methods and successfully captures the semantic rules of both chemical languages.Chemical space and scaffold analysis show that the model can generate similar compounds with diverse scaffolds within the specified constraints.Additionally,to illustrate the model’s applicability in drug design,we conducted case studies in functional group editing,analogue design and linker design. 展开更多
关键词 Diffusion model IUPAC Molecular generative model Chemical natural language Transformer
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Generative Artificial Intelligence and Its Applications in Cartography and GIS:an Exploratory Review 被引量:1
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作者 SUN Chenzhen LAN Tian +3 位作者 WU Zhiwei SHI Xing CHENG Donglin JIANG Songlin 《Journal of Geodesy and Geoinformation Science》 2025年第2期74-89,共16页
Since the release of ChatGPT in late 2022,Generative Artificial Intelligence(GAI)has gained widespread attention because of its impressive capabilities in language comprehension,reasoning,and generation.GAI has been s... Since the release of ChatGPT in late 2022,Generative Artificial Intelligence(GAI)has gained widespread attention because of its impressive capabilities in language comprehension,reasoning,and generation.GAI has been successfully applied across various aspects(e.g.,creative writing,code generation,translation,and information retrieval).In cartography and GIS,researchers have employed GAI to handle some specific tasks,such as map generation,geographic question answering,and spatiotemporal data analysis,yielding a series of remarkable results.Although GAI-based techniques are developing rapidly,literature reviews of their applications in cartography and GIS remain relatively limited.This paper reviews recent GAI-related research in cartography and GIS,focusing on three aspects:①map generation,②geographical analysis,and③evaluation of GAI’s spatial cognition abilities.In addition,the paper analyzes current challenges and proposes future research directions. 展开更多
关键词 generative artificial intelligence CARTOGRAPHY map generation geographical analysis spatial cognition
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Leveraging machine learning for accelerated materials innovation in lithium-ion battery:A review 被引量:1
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作者 Rushuai Li Wanyu Zhao +4 位作者 Ruimin Li Chaolun Gan Li Chen Zhitao Wang Xiaowei Yang 《Journal of Energy Chemistry》 2025年第7期44-62,共19页
As energy demands continue to rise in modern society,the development of high-performance lithium-ion batteries(LIBs)has become crucial.However,traditional research methods of material science face challenges such as l... As energy demands continue to rise in modern society,the development of high-performance lithium-ion batteries(LIBs)has become crucial.However,traditional research methods of material science face challenges such as lengthy timelines and complex processes.In recent years,the integration of machine learning(ML)in LIB materials,including electrolytes,solid-state electrolytes,and electrodes,has yielded remarkable achievements.This comprehensive review explores the latest applications of ML in predicting LIB material performance,covering the core principles and recent advancements in three key inverse material design strategies:high-throughput virtual screening,global optimization,and generative models.These strategies have played a pivotal role in fostering LIB material innovations.Meanwhile,the paper briefly discusses the challenges associated with applying ML to materials research and offers insights and directions for future research. 展开更多
关键词 Lithium-ion battery Machine learning Material screening Performance prediction Inverse design Generative model
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Generation of SARS-CoV-2 dual-target candidate inhibitors through 3D equivariant conditional generative neural networks 被引量:1
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作者 Zhong-Xing Zhou Hong-Xing Zhang Qingchuan Zheng 《Journal of Pharmaceutical Analysis》 2025年第6期1291-1310,共20页
Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)mutations are influenced by random and uncontrollable factors,and the risk of the next widespread epidemic remains.Dual-target drugs that synergistically act ... Severe acute respiratory syndrome coronavirus 2(SARS-CoV-2)mutations are influenced by random and uncontrollable factors,and the risk of the next widespread epidemic remains.Dual-target drugs that synergistically act on two targets exhibit strong therapeutic effects and advantages against mutations.In this study,a novel computational workflow was developed to design dual-target SARS-CoV-2 candidate inhibitors with the Envelope protein and Main protease selected as the two target proteins.The drug-like molecules of our self-constructed 3D scaffold database were used as high-throughput molecular docking probes for feature extraction of two target protein pockets.A multi-layer perceptron(MLP)was employed to embed the binding affinities into a latent space as conditional vectors to control conditional distribution.Utilizing a conditional generative neural network,cG-SchNet,with 3D Euclidean group(E3)symmetries,the conditional probability distributions of molecular 3D structures were acquired and a set of novel SARS-CoV-2 dual-target candidate inhibitors were generated.The 1D probability,2D joint probability,and 2D cumulative probability distribution results indicate that the generated sets are significantly enhanced compared to the training set in the high binding affinity area.Among the 201 generated molecules,42 molecules exhibited a sum binding affinity exceeding 17.0 kcal/mol while 9 of them having a sum binding affinity exceeding 19.0 kcal/mol,demonstrating structure diversity along with strong dual-target affinities,good absorption,distribution,metabolism,excretion,and toxicity(ADMET)properties,and ease of synthesis.Dual-target drugs are rare and difficult to find,and our“high-throughput docking-multi-conditional generation”workflow offers a wide range of options for designing or optimizing potent dual-target SARS-CoV-2 inhibitors. 展开更多
关键词 SARS-CoV-2 Dual-target drug 3D generative neural networks Drug design
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Complementary roles of glial cells in generating region-specific neuroinflammatory responses and phagocytosis in Parkinson’s disease
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作者 Leyre Ayerra Maria S.Aymerich 《Neural Regeneration Research》 SCIE CAS 2025年第10期2917-2918,共2页
Neuroinflammation is associated with Parkinson’s disease:Reactive gliosis and neuroinflammation are hallmarks of Parkinson’s disease(PD),a multisystem neurodegenerative disorder characterized by a progressive loss o... Neuroinflammation is associated with Parkinson’s disease:Reactive gliosis and neuroinflammation are hallmarks of Parkinson’s disease(PD),a multisystem neurodegenerative disorder characterized by a progressive loss of dopaminergic neurons.Neuroinflammation has long been considered a mere consequence of neuronal loss,but whether it promotes PD or is a key player in disease progression remains to be determined.Human leukocyte antigen. 展开更多
关键词 inflammation LEUKOCYTE generating
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Systematic experimental investigation on pressure build-up characteristics of water-jet injection into a molten LBE pool 被引量:1
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作者 Hao-Ran Huang Zi-Jian Deng +1 位作者 Song-Bai Cheng Jia-Yue Chen 《Nuclear Science and Techniques》 2025年第1期161-174,共14页
In the scenario of a steam generator tube rupture accident in a lead-cooled fast reactor,secondary circuit subcooled water under high pressure is injected into an ordinary-pressure primary vessel,where a molten lead-b... In the scenario of a steam generator tube rupture accident in a lead-cooled fast reactor,secondary circuit subcooled water under high pressure is injected into an ordinary-pressure primary vessel,where a molten lead-based alloy(typically pure lead or lead-bismuth eutectic(LBE))is used as the coolant.To clarify the pressure build-up characteristics under water-jet injection,this study conducted several experiments by injecting pressurized water into a molten LBE pool at Sun Yat-sen University.To obtain a further understanding,several new experimental parameters were adopted,including the melt temperature,water subcooling,injection pressure,injection duration,and nozzle diameter.Through detailed analyses,it was found that the pressure and temperature during the water-melt interaction exhibited a consistent variation trend with our previous water-droplet injection mode LBE experiment.Similarly,the existence of a steam explosion was confirmed,which typically results in a much stronger pressure build-up.For the non-explosion cases,increasing the injection pressure,melt-pool temperature,nozzle diameter,and water subcooling promoted pressure build-up in the melt pool.However,a limited enhancement effect was observed when increasing the injection duration,which may be owing to the continually rising pressure in the interaction vessel or the isolation effect of the generated steam cavity.Regardless of whether a steam explosion occurred,the calculated mechanical and kinetic energy conversion efficiencies of the melt were relatively small(not exceeding 4.1%and 0.7%,respectively).Moreover,the range of the conversion efficiency was similar to that of previous water-droplet experiments,although the upper limit of the jet mode was slightly lower. 展开更多
关键词 Lead-cooled fast reactor Steam generator tube rupture accident Pressure build-up characteristics Experimental study Pressure water-jet injection
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Research on Stock Price Prediction Method Based on the GAN-LSTM-Attention Model
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作者 Peng Li Yanrui Wei Lili Yin 《Computers, Materials & Continua》 SCIE EI 2025年第1期609-625,共17页
Stock price prediction is a typical complex time series prediction problem characterized by dynamics,nonlinearity,and complexity.This paper introduces a generative adversarial network model that incorporates an attent... Stock price prediction is a typical complex time series prediction problem characterized by dynamics,nonlinearity,and complexity.This paper introduces a generative adversarial network model that incorporates an attention mechanism(GAN-LSTM-Attention)to improve the accuracy of stock price prediction.Firstly,the generator of this model combines the Long and Short-Term Memory Network(LSTM),the Attention Mechanism and,the Fully-Connected Layer,focusing on generating the predicted stock price.The discriminator combines the Convolutional Neural Network(CNN)and the Fully-Connected Layer to discriminate between real stock prices and generated stock prices.Secondly,to evaluate the practical application ability and generalization ability of the GAN-LSTM-Attention model,four representative stocks in the United States of America(USA)stock market,namely,Standard&Poor’s 500 Index stock,Apple Incorporatedstock,AdvancedMicroDevices Incorporatedstock,and Google Incorporated stock were selected for prediction experiments,and the prediction performance was comprehensively evaluated by using the three evaluation metrics,namely,mean absolute error(MAE),root mean square error(RMSE),and coefficient of determination(R2).Finally,the specific effects of the attention mechanism,convolutional layer,and fully-connected layer on the prediction performance of the model are systematically analyzed through ablation study.The results of experiment show that the GAN-LSTM-Attention model exhibits excellent performance and robustness in stock price prediction. 展开更多
关键词 Stock price prediction generative adversarial network attention mechanism time-series prediction
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