We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
In the present paper, using the method of separating coupled physic quantity bypotential operator, we derive two special minmum principles in coupled thermoelastodynamics.
For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is ob...For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is obtained.展开更多
In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces...In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces VWLρП,φ（Ω） with bounded setΩ .展开更多
This paper studies the vapor pressure of water and precipitation situation in Lu'an Ground Station in Dabie Mountain area from 1979 to 1998.And the atmospheric perceivable water in Dabie Mountain can be calculated...This paper studies the vapor pressure of water and precipitation situation in Lu'an Ground Station in Dabie Mountain area from 1979 to 1998.And the atmospheric perceivable water in Dabie Mountain can be calculated by virtue of the empirical formula for atmospheric perceivable water.Besides,by analyzing the data,the seasonal changes of perceivable water in Dabie Mountain and the efficiency of precipitation of each weather system is acquired.The results show that there is a great potential for precipitation enhancement in Dabie Mountain.This paper introduces the processes and operation forms of precipitation enhancement for impounding water in reservoirs in Dabie Mountain region.展开更多
Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed.Meanwhile some related necessar...Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed.Meanwhile some related necessary and sufficient conditions are obtained展开更多
Let Ф be a non-negative locally integrable function on R^n and satisfy some weak growth conditions, define the potential type operator TФ by TФf（x）=∫R^n Ф（x-y）f（y）dy. The aim of this paper is to give severa...Let Ф be a non-negative locally integrable function on R^n and satisfy some weak growth conditions, define the potential type operator TФ by TФf（x）=∫R^n Ф（x-y）f（y）dy. The aim of this paper is to give several strong type and weak type weighted norm inequalities for the potential type operator TФ.展开更多
We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain...We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.展开更多
CONSPECTUS:Electrochemical devices are typically designed for operation over a narrow pH range and are constrained in the choice of catalysts and operating potentials by the pH environment of the electrodes.This is th...CONSPECTUS:Electrochemical devices are typically designed for operation over a narrow pH range and are constrained in the choice of catalysts and operating potentials by the pH environment of the electrodes.This is the result of a heretofore lack of a viable strategy to maintain pH gradients between the electrodes over practically significant time durations with only a minimal impact on the device performance.While bipolar interfaces are wellknown,they typically result in high junction potential losses that make them impractical in real-life systems.We have demonstrated a way to overcome this long-standing challenge using our tailormade,microscale bipolar interfaces,which allows the use of acidic electrolytes at one electrode and alkaline electrolytes at the other,without mixing over time.展开更多
In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator po...In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator potential V（x） ∈ C^1 （R^n, L （H1） ）, where L （H1 ） is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1（x）δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g（x） = （gij（x）） is the Riemannian matrix, while g^-1 （x） is the inverse of the matrix g（x）. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u ＋ V（x） u （x） = f（x） in the Hilbert space H where f（x） ∈ H as an application of the separation approach.展开更多
Low specific capacitances and/or limited working potential(≤4.5 V).of the prevalent carbon-based positive electrodes as the inborn bottleneck seriously hinder practical advancement of lithium-ion capacitors.Thus,brea...Low specific capacitances and/or limited working potential(≤4.5 V).of the prevalent carbon-based positive electrodes as the inborn bottleneck seriously hinder practical advancement of lithium-ion capacitors.Thus,breakthroughs in enhancement of both specific capacitances and upper cutoff potentials are enormously significant for high-energy density lithium-ion capacitors.Herein,we first meticulously design and scalably fabricate a commercializable fluorine-doped porous carbon material with competitive tap density,large active surface,appropriate aperture distribution,and promoted affinity with the electrolyte,rendering its abundant electroactive inter-/surface and rapid PF_(6)^(-)transport.Theoretical calculations authenticate that fluorine-doped porous carbon possesses lower PF_(6)^(-)adsorption energy and stronger interaction with PF_(6)^(-).Thanks to the remarkable structural/compositional superiority,when served as a positive electrode toward lithium-ion capacitors,the commercial-level fluorine-doped porous carbon showcases the record-breaking electrochemical properties within a wider working window of 2.5-5.0 V(vs Li/Li^(+))in terms of high-rate specific capacitances and long-duration stability,much superior to commercial activated carbon.More significantly,the 4.5 V-class graphite//fluorine-doped porous carbon lithium-ion capacitors are first constructed and manifest competitive electrochemical behaviors with long-cycle life,modest polarization,and large energy density.Our work provides a commendable positive paradigm and contributes a major step forward in next-generation lithium-ion capacitors and even other high-energy density metal-ion capacitors.展开更多
In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>...In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>）and HK<sub>q</sub><sup>α,P</sup>（ω<sub>1</sub>;ω<sub>2</sub>）,where ω<sub>1</sub>,ω<sub>2</sub> ∈A<sub>1</sub>-weight,1【q【∞, n（1-1/q）≤α【∞ and 0【p【∞.Then,using these new characterizations,they investigate the convergence of a bounded set in these spaces,and study the boundedness of some potential operators on these spaces.展开更多
基金Supported by the National Natural Science Foundation of China(Nos.10771049, 60773174)the Natural Science Foundation of Hebei Province (08M001)
文摘We derive some strong type and weak type weighted norm estimates which re- late the commutators of potential integral operators to the corresponding maximal operators in the context of spaces of homogeneous type.
文摘In the present paper, using the method of separating coupled physic quantity bypotential operator, we derive two special minmum principles in coupled thermoelastodynamics.
基金the National Natural Science Foundation of China (10771049 60773174)the Natural Science Foundation of Hebei Province (08M001)
文摘For the potential type operatorTФf（x）=∫RnФ（x-y）f（y）dy,where Ф is a non-negative locally integrable function on R^n and satisfies weak growth condition, a two-weight weak-type （p,q） inequality for TФ is obtained.
基金Supported by the Natural Science Foundation of Ningxia(Grant No.NZ15055)Institution of Higher Education Scientific Research Project in Ningxia(Grant No.NGY2017011)the National Natural Science Foundation of China(Grant Nos.11261041,11361044)
文摘In this paper we mainly give some characterizations for the boundedness of the weight Hardy operator, maximal operator, potential operator and singular integral operator on the vanishing generalized weak Morrey spaces VWLρП,φ（Ω） with bounded setΩ .
基金Supported by China Meteorological Administration (Provincial Figure Operation System Based on the New Generation Radar)The Program of Experimental Investigation on the Development and Utilization of Aerial Cloud Resource in Anhui Province
文摘This paper studies the vapor pressure of water and precipitation situation in Lu'an Ground Station in Dabie Mountain area from 1979 to 1998.And the atmospheric perceivable water in Dabie Mountain can be calculated by virtue of the empirical formula for atmospheric perceivable water.Besides,by analyzing the data,the seasonal changes of perceivable water in Dabie Mountain and the efficiency of precipitation of each weather system is acquired.The results show that there is a great potential for precipitation enhancement in Dabie Mountain.This paper introduces the processes and operation forms of precipitation enhancement for impounding water in reservoirs in Dabie Mountain region.
基金Supported in part by the National Natural Science Foundation of China (1 0 0 71 0 2 1 ) the Foundationfor University Key Teacher by MEC and Shanghai Priority Academic Discipline Foundation
文摘Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed.Meanwhile some related necessary and sufficient conditions are obtained
基金Foundation item： the Natural Science Foundation of Hebei Province （08M001） and the National Natural Science Foundation of China （Nos. 10771049,60773174）.
文摘Let Ф be a non-negative locally integrable function on R^n and satisfy some weak growth conditions, define the potential type operator TФ by TФf（x）=∫R^n Ф（x-y）f（y）dy. The aim of this paper is to give several strong type and weak type weighted norm inequalities for the potential type operator TФ.
文摘We derive a Hamiltonian formulation for two-dimensional nonlinear long waves between two bodies of immiscible fluid with a periodic bottom. From the formulation and using the Hamiltonian perturbation theory, we obtain effective Boussinesq equations that describe the motion of bidirectional long waves and unidirectional equations that are similar to the KdV equation for the case in which the bottom possesses short length scale. The computations for these results are performed in the framework of an asymptotic analysis of multiple scale operators.
基金support from the University of Texas at San Antonio through a startup grantsupport from the Advanced Research Projects Agency−Energy(ARPA-E)IGNIITE program,U.S.Department of Energy,under Award No.DE-AR0001930support from the University of Alabama,Tuscaloosa through a startup grant.
文摘CONSPECTUS:Electrochemical devices are typically designed for operation over a narrow pH range and are constrained in the choice of catalysts and operating potentials by the pH environment of the electrodes.This is the result of a heretofore lack of a viable strategy to maintain pH gradients between the electrodes over practically significant time durations with only a minimal impact on the device performance.While bipolar interfaces are wellknown,they typically result in high junction potential losses that make them impractical in real-life systems.We have demonstrated a way to overcome this long-standing challenge using our tailormade,microscale bipolar interfaces,which allows the use of acidic electrolytes at one electrode and alkaline electrolytes at the other,without mixing over time.
文摘In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu（x） = -△△u（x） ＋ V（x）u（x）,for all x ∈ R^n, in the Hilbert space H = L2（R^n,H1） with the operator potential V（x） ∈ C^1 （R^n, L （H1） ）, where L （H1 ） is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1（x）δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g（x） = （gij（x）） is the Riemannian matrix, while g^-1 （x） is the inverse of the matrix g（x）. Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u ＋ V（x） u （x） = f（x） in the Hilbert space H where f（x） ∈ H as an application of the separation approach.
基金support from the National Natural Science Foundation of China(Grant No.U22A20145,51904115,52072151,52171211,52102253,and 52271218)Jinan Independent Innovative Team(2020GXRC015)Major Program of Shandong Province Natural Science Foundation(ZR2023ZD43,ZR2021ZD05).
文摘Low specific capacitances and/or limited working potential(≤4.5 V).of the prevalent carbon-based positive electrodes as the inborn bottleneck seriously hinder practical advancement of lithium-ion capacitors.Thus,breakthroughs in enhancement of both specific capacitances and upper cutoff potentials are enormously significant for high-energy density lithium-ion capacitors.Herein,we first meticulously design and scalably fabricate a commercializable fluorine-doped porous carbon material with competitive tap density,large active surface,appropriate aperture distribution,and promoted affinity with the electrolyte,rendering its abundant electroactive inter-/surface and rapid PF_(6)^(-)transport.Theoretical calculations authenticate that fluorine-doped porous carbon possesses lower PF_(6)^(-)adsorption energy and stronger interaction with PF_(6)^(-).Thanks to the remarkable structural/compositional superiority,when served as a positive electrode toward lithium-ion capacitors,the commercial-level fluorine-doped porous carbon showcases the record-breaking electrochemical properties within a wider working window of 2.5-5.0 V(vs Li/Li^(+))in terms of high-rate specific capacitances and long-duration stability,much superior to commercial activated carbon.More significantly,the 4.5 V-class graphite//fluorine-doped porous carbon lithium-ion capacitors are first constructed and manifest competitive electrochemical behaviors with long-cycle life,modest polarization,and large energy density.Our work provides a commendable positive paradigm and contributes a major step forward in next-generation lithium-ion capacitors and even other high-energy density metal-ion capacitors.
文摘In this paper,the authors first establish some new real-variable characterizations of Herz- type Hardy spaces H<sub>q</sub><sup>α,p</sup>（ω<sub>1</sub>;ω<sub>2</sub>）and HK<sub>q</sub><sup>α,P</sup>（ω<sub>1</sub>;ω<sub>2</sub>）,where ω<sub>1</sub>,ω<sub>2</sub> ∈A<sub>1</sub>-weight,1【q【∞, n（1-1/q）≤α【∞ and 0【p【∞.Then,using these new characterizations,they investigate the convergence of a bounded set in these spaces,and study the boundedness of some potential operators on these spaces.
