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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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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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Further Generalizations of Opial’s Inequality
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作者 戚征 《Acta Mathematica Sinica,English Series》 SCIE 1985年第3期196-200,共5页
Let C1[a,b] denote the set of all continuously differentiable functions on theclosed finite interval [a,b],and Iet AC [a,b] be the set of all absolutely continuousfunctions on [a,b].Z.Opial proved that if f∈C1[O,h],f... Let C1[a,b] denote the set of all continuously differentiable functions on theclosed finite interval [a,b],and Iet AC [a,b] be the set of all absolutely continuousfunctions on [a,b].Z.Opial proved that if f∈C1[O,h],f(O)-f(h)=0 andf(x)>0 when x∈(O,h),then 展开更多
关键词 In Further generalizations of Opial’s Inequality AO
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Electric-Field-Driven Generative Nanoimprinting for Tilted Metasurface Nanostructures
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作者 Yu Fan Chunhui Wang +6 位作者 Hongmiao Tian Xiaoming Chen Ben QLi Zhaomin Wang Xiangming Li Xiaoliang Chen Jinyou Shao 《Nano-Micro Letters》 2026年第1期290-305,共16页
Tilted metasurface nanostructures,with excellent physical properties and enormous application potential,pose an urgent need for manufacturing methods.Here,electric-field-driven generative-nanoimprinting technique is p... Tilted metasurface nanostructures,with excellent physical properties and enormous application potential,pose an urgent need for manufacturing methods.Here,electric-field-driven generative-nanoimprinting technique is proposed.The electric field applied between the template and the substrate drives the contact,tilting,filling,and holding processes.By accurately controlling the introduced included angle between the flexible template and the substrate,tilted nanostructures with a controllable angle are imprinted onto the substrate,although they are vertical on the template.By flexibly adjusting the electric field intensity and the included angle,large-area uniform-tilted,gradient-tilted,and high-angle-tilted nanostructures are fabricated.In contrast to traditional replication,the morphology of the nanoimprinting structure is extended to customized control.This work provides a cost-effective,efficient,and versatile technology for the fabrication of various large-area tilted metasurface structures.As an illustration,a tilted nanograting with a high coupling efficiency is fabricated and integrated into augmented reality displays,demonstrating superior imaging quality. 展开更多
关键词 Generative nanoimprinting Electric field assistance Tilted metasurface structures Large-area fabrication
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GENERALIZATIONS OF J-HOMOMORPHISM AND THE ROHLIN THEOREM
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作者 李贵松 《Chinese Science Bulletin》 SCIE EI CAS 1991年第1期7-11,共5页
Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, ... Ⅰ. INTRODUCTIONThroughout this note all manifolds are assumed to be compact,connected and differentiable. A theorem of Rohlin asserts that the first Pontrjagin class of a 4-manifold M is congruent to zero modulo 48, provided w<sub>1</sub>(M)=w<sub>2</sub> (M)=0. This result has been generalized to higher dimensions by Milnor and Kervaire. 展开更多
关键词 NORMAL BORDISM group GENERALIZED J-homomorphism GENERALIZED Rohlin theorem.
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Large language models for robotics:Opportunities,challenges,and perspectives 被引量:4
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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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Generative Artificial Intelligence and Its Applications in Cartography and GIS:an Exploratory Review 被引量:2
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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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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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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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Progress in the Understanding andModeling of Cavitation and Related Applications 被引量:1
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作者 Jianying Li DonglaiLi Tiefeng Li 《Fluid Dynamics & Materials Processing》 2025年第3期445-470,共26页
Hydrodynamic cavitation,as an efficient technique applied in many physical and chemical treatment methods,has been widely used by various industries and in several technological fields.Relevant generators,designed wit... Hydrodynamic cavitation,as an efficient technique applied in many physical and chemical treatment methods,has been widely used by various industries and in several technological fields.Relevant generators,designed with specific structures and parameters,can produce cavitation effects,thereby enabling effective treatment and reasonable transformation of substances.This paper reviews the design principles,performance,and practical applications associated with different types of cavitation generators,aiming to provide theoretical support for the optimization of these systems.It systematically analyzes the underpinning mechanisms and the various factors influencing the cavitation phenomena,also conducting a comparative analysis of the performance of different types of generators.Specific applications dealing with wastewater treatment,chemical reaction acceleration,and other fields are discussed together with the advantages,disadvantages,and applicability of each type of cavitation generator.We also explore research progress in areas such as cavitation stability,energy efficiency,and equipment design upgrades.The study concludes by forecasting the application prospects of intelligent design and computational fluid dynamics(CFD)in optimizing and advancing cavitation generators.It proposes new ideas for the further development of cavitation technology and highlights directions for its widespread future application. 展开更多
关键词 Cavitation effect cavitation generator wastewater treatment chemical reaction acceleration stability energy efficiency improvement
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