In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic inte...In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic integrals.展开更多
This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω i...This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.展开更多
This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential g...This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential growth of mobile devices and data traffic has substantially increased network congestion,particularly in urban areas and regions with limited terrestrial infrastructure.Our approach jointly optimizes unmanned aerial vehicle(UAV)trajectories and satellite-assisted offloading strategies to simultaneously maximize data throughput,minimize energy consumption,and maintain equitable resource distribution.The proposed RMAPPO framework incorporates recurrent neural networks(RNNs)to model temporal dependencies in UAV mobility patterns and utilizes a decentralized multi-agent reinforcement learning architecture to reduce communication overhead while improving system robustness.The proposed RMAPPO algorithm was evaluated through simulation experiments,with the results indicating that it significantly enhances the cumulative traffic offloading rate of nodes and reduces the energy consumption of UAVs.展开更多
Multi-organ-on-a-chip(MOOC)technology represents a pivotal direction in the organ-on-a-chip field,seeking to emulate the complex interactions of multiple human organs in vitro through microfluidic systems.This technol...Multi-organ-on-a-chip(MOOC)technology represents a pivotal direction in the organ-on-a-chip field,seeking to emulate the complex interactions of multiple human organs in vitro through microfluidic systems.This technology overcomes the limitations of traditional single-organ models,providing a novel platform for investigating complex disease mechanisms and evaluating drug efficacy and toxicity.Although it demonstrates broad application prospects,its development still faces critical bottlenecks,including inadequate physiological coupling between organs,short functional maintenance durations,and limited real-time monitoring capabilities.Contemporary research is advancing along three key directions,including functional coupling,sensor integration,and full-process automation systems,to propel the technology toward enhanced levels of physiological relevance and predictive accuracy.展开更多
China is carving out a distinctive development path which features urban-rural integration.This approach has not only yielded tangible results domestically but also drawn the attention of other countries.
Flexible electronics face critical challenges in achieving monolithic three-dimensional(3D)integration,including material compatibility,structural stability,and scalable fabrication methods.Inspired by the tactile sen...Flexible electronics face critical challenges in achieving monolithic three-dimensional(3D)integration,including material compatibility,structural stability,and scalable fabrication methods.Inspired by the tactile sensing mechanism of the human skin,we have developed a flexible monolithic 3D-integrated tactile sensing system based on a holey MXene paste,where each vertical one-body unit simultaneously functions as a microsupercapacitor and pressure sensor.The in-plane mesopores of MXene significantly improve ion accessibility,mitigate the self-stacking of nanosheets,and allow the holey MXene to multifunctionally act as a sensing material,an active electrode,and a conductive interconnect,thus drastically reducing the interface mismatch and enhancing the mechanical robustness.Furthermore,we fabricate a large-scale device using a blade-coating and stamping method,which demonstrates excellent mechanical flexibility,low-power consumption,rapid response,and stable long-term operation.As a proof-of-concept application,we integrate our sensing array into a smart access control system,leveraging deep learning to accurately identify users based on their unique pressing behaviors.This study provides a promising approach for designing highly integrated,intelligent,and flexible electronic systems for advanced human-computer interactions and personalized electronics.展开更多
Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understandi...Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understanding how best to preserve,build on its remarkable achievements,and develop its intellectual legacy.Critics such as Schumpeter and Taylor have long argued that the economic reasoning found in ancient China cannot compare with that of classical Greece or medieval Europe.Yet this view often reflects the narrow assumptions of mainstream economics,defining analysis almost entirely in terms of market exchange.As a result,it tends to overlook traditions built around statecraft,governance,and the management of economic order.A careful re-examination and Sino-Western comparative analysis of key thinkers-including Mencius,Guanzi,and Sima Qian-tells a different story.Rooted in China’s distinctive cultural and philosophical heritage,traditional Chinese economic thought not only contains the analytical dimensions(as defined by Schumpeter)but also displays a broader and more diverse set of economic reasoning.Notably,its systematic depth and intellectual precision were,in many respects,remarkably advanced.Therefore,advancing the construction of a Chinese school of economics in the new era under the framework of the“Second Integration”,i.e.,integrating the basic tenets of Marxism with China’s fine traditional culture,should,and indeed can draw essential insights from this analytical tradition.展开更多
Carbon-based air cathodes offer low cost,high electrical conductivity,and structural tunability.However,they suffer from limited catalytic activity and inefficient gas transport,and they typically rely on noble metal ...Carbon-based air cathodes offer low cost,high electrical conductivity,and structural tunability.However,they suffer from limited catalytic activity and inefficient gas transport,and they typically rely on noble metal additives or complex multilayer configurations.To tackle these issues,this study devised a self-activated integrated carbon-based air cathode.By integrating in situ catalytic site construction with structural optimization,the strategy not only induces the formation of oxygen functional groups(─C─OH,─C═O,─COOH),hierarchical pores,and uniformly distributed active sites,but also establishes a favorable electronic and mass-transport environment.Furthermore,the roll-pressing-based integrated design streamlines electrode construction,reinforces interfacial bonding,and significantly enhances mechanical stability.Density functional theory(DFT)calculations show that oxygen functional groups initiate hydrogen bonding interaction and promote charge enrichment,which improves the activity of the cathode and facilitates intermediate adsorption/desorption in oxygen reduction and evolution reactions processes.As a result,the integrated air cathode-based rechargeable zinc-air batteries(RZABs)achieve a high specific capacity of 811 mAh g^(-1).It also performs well in quasi-solid-state RZABs and silicon-air batteries systems across a wide temperature range,demonstrating strong adaptability and application potential.This study provides a scalable and cost-effective design strategy for high-performance carbon-based air cathodes,offering new insights into advancing durable and practical metal-air energy systems.展开更多
Photonic neural networks(PNNs)of sufficiently large physical dimensions and high operation accuracies are envisaged as ideal candidates for breaking the major bottlenecks in the current artificial intelligence archite...Photonic neural networks(PNNs)of sufficiently large physical dimensions and high operation accuracies are envisaged as ideal candidates for breaking the major bottlenecks in the current artificial intelligence architectures in terms of latency,energy efficiency,and computational power.To achieve this vision,it is of vital importance to scale up the PNNs while simultaneously reducing the high demand on the dimensions required by them.The underlying cause of this strategy is the enormous gap between the scales of photonic and electronic integrated circuits.Here,we demonstrate monolithically integrated optical convolutional processors on thin film lithium niobate(TFLN)that harness inherent parallelism in photonics to enable large-scale programmable convolution kernels and,in turn,greatly reduce the dimensions required by subsequent fully connected layers.Experimental validation achieves high classification accuracies of 96%(86%)on the MNIST(Fashion-MNIST)dataset and 84.6%on the AG News dataset while dramatically reducing the required subsequent fully connected layer dimensions to 196×10(from 784×10)and 175×4(from 800×4),respectively.Furthermore,our devices can be driven by commercial field-programmable gate array systems;a unique advantage in addition to their scalable channel number and kernel size.Our architecture provides a solution to build practical machine learning photonic devices.展开更多
Urinary tract infections(UTIs)are among the most prevalent pediatric bacterial infections,and undertreated episodes may lead to renal scarring,hypertension,or chronic kidney disease.Multidrug-resistant(MDR)Enterobacte...Urinary tract infections(UTIs)are among the most prevalent pediatric bacterial infections,and undertreated episodes may lead to renal scarring,hypertension,or chronic kidney disease.Multidrug-resistant(MDR)Enterobacterales have been increasingly reported in children,with higher rates in Asian and Middle Eastern settings than in high-income countries[1,2].展开更多
Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were appli...Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.展开更多
Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA ...Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.展开更多
Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. T...Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2...Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.展开更多
This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. T...This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.展开更多
基金Supported by the National Natural Science Foundation of China(11971142)the Natural Science Foundation of Zhejiang Province(LY19A010012)the key Scientific Research Projects of Hunan Provincial Department of Education in 2021(21A0526)。
文摘In the article,we provide a sharp lower bound for the weighted Lehmer mean of the complete p-elliptic integrals of the first and second kinds,which is the extension of the previous results for complete p-elliptic integrals.
文摘This paper considers the following Marcinkiewicz type integrals■which can be regarded as an extension of the classical Marcinkiewicz integral po introduced by Stein in[Trans Amer Math Soc,88(1958):159-172],where Ω is a homogeneous function of degree zero on R^(n)with mean value zero in the unit sphere S^(n-1),Under the assumption that Ω∈L^(∞)(S^(n-1)),the authors establish the L^(q)-estimate and weak(1,1)type estimate as well as the corresponding weighted estimates for po.s with 1<q<∞ and 0<β(q-1)n/q.Moreover,the bounds do not depend on β and the strong(q,q)type and weak(1,1)type estimates for the classical Marcinkiewicz integral po can be recovered from the above estimates of μΩ,β whenβ→0.
文摘This paper investigates the traffic offloading optimization challenge in Space-Air-Ground Integrated Networks(SAGIN)through a novel Recursive Multi-Agent Proximal Policy Optimization(RMAPPO)algorithm.The exponential growth of mobile devices and data traffic has substantially increased network congestion,particularly in urban areas and regions with limited terrestrial infrastructure.Our approach jointly optimizes unmanned aerial vehicle(UAV)trajectories and satellite-assisted offloading strategies to simultaneously maximize data throughput,minimize energy consumption,and maintain equitable resource distribution.The proposed RMAPPO framework incorporates recurrent neural networks(RNNs)to model temporal dependencies in UAV mobility patterns and utilizes a decentralized multi-agent reinforcement learning architecture to reduce communication overhead while improving system robustness.The proposed RMAPPO algorithm was evaluated through simulation experiments,with the results indicating that it significantly enhances the cumulative traffic offloading rate of nodes and reduces the energy consumption of UAVs.
基金supported by the Shenzhen Medical Research Fund(Grant No.A2303049)Guangdong Basic and Applied Basic Research(Grant No.2023A1515010647)+1 种基金National Natural Science Foundation of China(Grant No.22004135)Shenzhen Science and Technology Program(Grant No.RCBS20210706092409020,GXWD20201231165807008,20200824162253002).
文摘Multi-organ-on-a-chip(MOOC)technology represents a pivotal direction in the organ-on-a-chip field,seeking to emulate the complex interactions of multiple human organs in vitro through microfluidic systems.This technology overcomes the limitations of traditional single-organ models,providing a novel platform for investigating complex disease mechanisms and evaluating drug efficacy and toxicity.Although it demonstrates broad application prospects,its development still faces critical bottlenecks,including inadequate physiological coupling between organs,short functional maintenance durations,and limited real-time monitoring capabilities.Contemporary research is advancing along three key directions,including functional coupling,sensor integration,and full-process automation systems,to propel the technology toward enhanced levels of physiological relevance and predictive accuracy.
文摘China is carving out a distinctive development path which features urban-rural integration.This approach has not only yielded tangible results domestically but also drawn the attention of other countries.
基金supported by the National Natural Science Foundation of China(52272177,12204010)the Foundation for the Introduction of High-Level Talents of Anhui University(S020118002/097)+1 种基金the University Synergy Innovation Program of Anhui Province(GXXT-2023-066)the Scientific Research Project of Anhui Provincial Higher Education Institution(2023AH040008)。
文摘Flexible electronics face critical challenges in achieving monolithic three-dimensional(3D)integration,including material compatibility,structural stability,and scalable fabrication methods.Inspired by the tactile sensing mechanism of the human skin,we have developed a flexible monolithic 3D-integrated tactile sensing system based on a holey MXene paste,where each vertical one-body unit simultaneously functions as a microsupercapacitor and pressure sensor.The in-plane mesopores of MXene significantly improve ion accessibility,mitigate the self-stacking of nanosheets,and allow the holey MXene to multifunctionally act as a sensing material,an active electrode,and a conductive interconnect,thus drastically reducing the interface mismatch and enhancing the mechanical robustness.Furthermore,we fabricate a large-scale device using a blade-coating and stamping method,which demonstrates excellent mechanical flexibility,low-power consumption,rapid response,and stable long-term operation.As a proof-of-concept application,we integrate our sensing array into a smart access control system,leveraging deep learning to accurately identify users based on their unique pressing behaviors.This study provides a promising approach for designing highly integrated,intelligent,and flexible electronic systems for advanced human-computer interactions and personalized electronics.
基金supported by the National Social Science Fund of China(NSSFC):NSSFC Major Project“Exploration and Practice in the Development of Chinese Economics Since the Modern Era”(Grant No.17ZDA034)NSSFC Key Project“The Status and Value of Traditional Chinese Economic Thought”(Grant No.17AJL006)NSSFC General Project“The Transformation and Evolution of Chinese Economic Thought During the Republican Era”(Grant No.22BJL130).
文摘Does traditional Chinese economic thought possess genuine analytical rigor?This question lies at the heart of any serious evaluation of its theoretical value and historical significance.It also matters for understanding how best to preserve,build on its remarkable achievements,and develop its intellectual legacy.Critics such as Schumpeter and Taylor have long argued that the economic reasoning found in ancient China cannot compare with that of classical Greece or medieval Europe.Yet this view often reflects the narrow assumptions of mainstream economics,defining analysis almost entirely in terms of market exchange.As a result,it tends to overlook traditions built around statecraft,governance,and the management of economic order.A careful re-examination and Sino-Western comparative analysis of key thinkers-including Mencius,Guanzi,and Sima Qian-tells a different story.Rooted in China’s distinctive cultural and philosophical heritage,traditional Chinese economic thought not only contains the analytical dimensions(as defined by Schumpeter)but also displays a broader and more diverse set of economic reasoning.Notably,its systematic depth and intellectual precision were,in many respects,remarkably advanced.Therefore,advancing the construction of a Chinese school of economics in the new era under the framework of the“Second Integration”,i.e.,integrating the basic tenets of Marxism with China’s fine traditional culture,should,and indeed can draw essential insights from this analytical tradition.
基金funded by the National Nature Science Foundation of China(62264006,62574102)“Thousand Talents Program”of Yunnan Province for Young Talents,Innovative Research Teams(in Science and Technology)in the University of Yunnan Province(IRTSTYN),XingDian Talent Support Program for Young Talents,and Frontier Research Team of Kunming University 2023,The Basic Research Project of Yunnan Province(Nos.202201AU070022)+2 种基金Kunming University Talent Introduction Fund(Nos.YJL20024)Yunnan Province Education Department Scientific Research Fund Project(Nos.2024Y759)Undergraduate Innovation and Entrepreneurship Training Program Project of Yunnan Provincial(202411393005)。
文摘Carbon-based air cathodes offer low cost,high electrical conductivity,and structural tunability.However,they suffer from limited catalytic activity and inefficient gas transport,and they typically rely on noble metal additives or complex multilayer configurations.To tackle these issues,this study devised a self-activated integrated carbon-based air cathode.By integrating in situ catalytic site construction with structural optimization,the strategy not only induces the formation of oxygen functional groups(─C─OH,─C═O,─COOH),hierarchical pores,and uniformly distributed active sites,but also establishes a favorable electronic and mass-transport environment.Furthermore,the roll-pressing-based integrated design streamlines electrode construction,reinforces interfacial bonding,and significantly enhances mechanical stability.Density functional theory(DFT)calculations show that oxygen functional groups initiate hydrogen bonding interaction and promote charge enrichment,which improves the activity of the cathode and facilitates intermediate adsorption/desorption in oxygen reduction and evolution reactions processes.As a result,the integrated air cathode-based rechargeable zinc-air batteries(RZABs)achieve a high specific capacity of 811 mAh g^(-1).It also performs well in quasi-solid-state RZABs and silicon-air batteries systems across a wide temperature range,demonstrating strong adaptability and application potential.This study provides a scalable and cost-effective design strategy for high-performance carbon-based air cathodes,offering new insights into advancing durable and practical metal-air energy systems.
基金supported by the National Natural Science Foundation of China (Grant Nos.12192251,12334014,62335019,12134001,1230441812474378)+1 种基金the Quantum Science and Technology National Science and Technology Major Project(Grant No.2021ZD0301403)the Shanghai Municipal Science and Technology Major Project (Grant No.2019SHZDZX01)。
文摘Photonic neural networks(PNNs)of sufficiently large physical dimensions and high operation accuracies are envisaged as ideal candidates for breaking the major bottlenecks in the current artificial intelligence architectures in terms of latency,energy efficiency,and computational power.To achieve this vision,it is of vital importance to scale up the PNNs while simultaneously reducing the high demand on the dimensions required by them.The underlying cause of this strategy is the enormous gap between the scales of photonic and electronic integrated circuits.Here,we demonstrate monolithically integrated optical convolutional processors on thin film lithium niobate(TFLN)that harness inherent parallelism in photonics to enable large-scale programmable convolution kernels and,in turn,greatly reduce the dimensions required by subsequent fully connected layers.Experimental validation achieves high classification accuracies of 96%(86%)on the MNIST(Fashion-MNIST)dataset and 84.6%on the AG News dataset while dramatically reducing the required subsequent fully connected layer dimensions to 196×10(from 784×10)and 175×4(from 800×4),respectively.Furthermore,our devices can be driven by commercial field-programmable gate array systems;a unique advantage in addition to their scalable channel number and kernel size.Our architecture provides a solution to build practical machine learning photonic devices.
文摘Urinary tract infections(UTIs)are among the most prevalent pediatric bacterial infections,and undertreated episodes may lead to renal scarring,hypertension,or chronic kidney disease.Multidrug-resistant(MDR)Enterobacterales have been increasingly reported in children,with higher rates in Asian and Middle Eastern settings than in high-income countries[1,2].
文摘Aim To extend several fundamental theorems of conventional elasticity theory to quasicrystalelasticity theory. Methods The basic governing equations of quasicrystal elasticity theory and Gauss's theorem were applied in the derivation. Results and Conclusion The principle of virtual work, Betti's reciprocal theorem and the uniqueness theorem of quasicrystal elasticity theory are proud, and some conservative integrals in quasicrystal elasticty theory are obtained.
基金Supported by Inner Mongolia Natural Science Foundation(200711020112)Innovation Fundation of Inner Mongolia University of Science and Technology (2009NC064)~~
文摘Based on protein-DNA complex crystal structural data in up-to-date Nucleic Acid Database,the related parameters of DNA Kinetic Structure were investigated by Monte-Carlo Multiple Integrals on the base of modified DNA structure statistical mechanical model,and time complexity and precision were analyzed on the calculated results.
文摘Refer to the Hamiltonian system, first integrals of the Birkhoffian system can be found by using of the perfect differential method. Through these first integrals, the order of the Birkhoffian system can be reduced. Then according to the alternate of the coordinate, a kind of new partial differential operator was defined in order to hold the Birkhoff form. The result shows that the Birkhoffian system has generalized energy integrals and cyclic integrals. Furthermore, each integral can reduce the order of equations two degrees.
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
基金supported by the Natural Science Foundation of China(11701176,61673169,11301127,11626101,11601485)the Science and Technology Research Program of Zhejiang Educational Committee(Y201635325)
文摘We establish the monotonicity and convexity properties for several special functions involving the generalized elliptic integrals, and present some new analytic inequalities.
基金Supported by National 973 Project(G.19990751)the SEDF of China(20040027001)
文摘Let b = （b1,…,bm） be a finite family of locally integrable functions. Then, we introduce generalized higher commutator of Marcinkiwicz integral as follows：（ μΩ^b^→（f）（x）=（∫ 0^∞｜FΩ^b^→,t（f）（x）｜^2t/dt）^1/2,where（FΩ^b^→,t（f）（x）=1/t∫｜x-y｜≤t Ω（x-y）/｜x-y｜^n-1 Лj=1^m（bj（x）-bj（y））f（y）dy.）When（bj∈Aβj,1≤j≤m,0〈βj〈1∑j=1^mβj=β〈n）and Ω is homogeneous of degreezero and satisfies the cancelation condition, we prove that μΩ^b^→is bounded from L^p（R^n）to L^8（R^n）,where1〈p〈βand 1/s=1/p-β/n,Moreover,if Ω also satisties some L^q -Dini condition,then μΩ^b^→ isbounded from L^p（R^n）to Fp^β,∞（R^n）and on certain Hardy spaces.The article extends some known results.
基金Project supported by State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences and the National Natural Science Foundation of China （Grant Nos 10672143 and 10471145） and the Natural Science Foundation of Henan Province Government, China （Grant Nos 0311011400 and 0511022200）.
文摘This paper presents a discrete vaxiational principle and a method to build first-integrals for finite dimensional Lagrange-Maxwell mechanico-electrical systems with nonconservative forces and a dissipation function. The discrete variational principle and the corresponding Euler-Lagrange equations are derived from a discrete action associated to these systems. The first-integrals are obtained by introducing the infinitesimal transformation with respect to the generalized coordinates and electric quantities of the systems. This work also extends discrete Noether symmetries to mechanico-electrical dynamical systems. A practical example is presented to illustrate the results.
