The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies al...The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies all pairs of intersected fractures(the basic components composing the connectivity of a network),is one of its crucial procedures.This paper attempts to improve intersection analysis through parallel computing.Considering a seamless interfacing with other procedures in modeling,two algorithms are designed and presented,of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy.A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations.Moreover,the preferred application conditions for the two algorithms are also discussed.展开更多
Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critic...Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critical state line are selected in the analysis of cylindrical cavity expansion.Meanwhile, combining Rowe s flow rule and Bolton s simplification to stress-dilatancy relationship to reflect soil shear dilatancy and softening behavior, this paper analyzes the problem of cylindrical cavity expansion i...展开更多
AIM： To evaluate the use of short-duration transient visual evoked potentials（VEP） and color reflectivity discretization analysis（CORDA） in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.MET...AIM： To evaluate the use of short-duration transient visual evoked potentials（VEP） and color reflectivity discretization analysis（CORDA） in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS： The study included 136 eyes from 136 subjects： 49 eyes with glaucoma,45 glaucoma suspect eyes,and 42 healthy eyes.Subjects underwent Humphrey visual field（VF） testing,VEP testing,as well as peripapillary retinal nerve fiber layer optical coherence tomography imaging studies with post-acquisition CORDA applied.Statistical analysis was performed using means and ranges,ANOVA,post-hoc comparisons using Turkey＇s adjustment,Fisher＇s Exact test,area under the curve,and Spearman correlation coefficients.RESULTS： Parameters from VEP and CORDA correlated significantly with VF mean deviation（MD）（P〈0.05）.In distinguishing glaucomatous eyes from controls,VEP demonstrated area under the curve（AUC） values of 0.64-0.75 for amplitude and 0.67-0.81 for latency.The CORDA HR1 parameter was highly discriminative for glaucomatous eyes vs controls（AUC=0.94）.CONCLUSION： Significant correlations are found between MD and parameters of short-duration transient VEP and CORDA,diagnostic modalities which warrant further consideration in identifying glaucoma characteristics.展开更多
In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP（Rn1× … ×Rnk） of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive ...In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP（Rn1× … ×Rnk） of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators onHP（Rn1× … ×Rnk） and fromHP（Rn1× … ×Rnk）toLP（Rn1× … ×Rnk）.展开更多
The discrete excitation-emission-matrix fluorescence spectra (EEMS) at 12 excitation wavelengths (400, 430, 450, 460, 470, 490, 500, 510, 525, 550, 570, and 590 nm) and emission wavelengths ranging from 600-750 nm wer...The discrete excitation-emission-matrix fluorescence spectra (EEMS) at 12 excitation wavelengths (400, 430, 450, 460, 470, 490, 500, 510, 525, 550, 570, and 590 nm) and emission wavelengths ranging from 600-750 nm were determined for 43 phytoplankton species. A two-rank fluorescence spectra database was established by wavelet analysis and a fluorometric discrimination technique for determining phytoplankton population was developed. For laboratory simulatively mixed samples, the samples mixed from 43 algal species (the algae of one division accounted for 25%, 50%, 75%, 85%, and 100% of the gross biomass, respectively), the average discrimination rates at the level of division were 65.0%, 87.5%, 98.6%, 99.0%, and 99.1%, with average relative contents of 18.9%, 44.5%, 68.9%, 73.4%, and 82.9%, respectively; the samples mixed from 32 red tide algal species (the dominant species accounted for 60%, 70%, 80%, 90%, and 100% of the gross biomass, respectively), the average correct discrimination rates of the dominant species at the level of genus were 63.3%, 74.2%, 78.8%, 83.4%, and 79.4%, respectively. For the 81 laboratory mixed samples with the dominant species accounting for 75% of the gross biomass (chlorophyll), the discrimination rates of the dominant species were 95.1% and 72.8% at the level of division and genus, respectively. For the 12 samples collected from the mesocosm experiment in Maidao Bay of Qingdao in August 2007, the dominant species of the 11 samples were recognized at the division level and the dominant species of four of the five samples in which the dominant species accounted for more than 80% of the gross biomass were discriminated at the genus level; for the 12 samples obtained from Jiaozhou Bay in August 2007, the dominant species of all the 12 samples were recognized at the division level. The technique can be directly applied to fluorescence spectrophotometers and to the developing of an in situ algae fluorescence auto-analyzer for phytoplankton population.展开更多
The gecko's feet possess unique microstructures that enable strong adhesive forces when interacting with various surfaces.Understanding the interfacial forces generated by these microstructures is crucial for deci...The gecko's feet possess unique microstructures that enable strong adhesive forces when interacting with various surfaces.Understanding the interfacial forces generated by these microstructures is crucial for deciphering their adhesion mechanism.This study developed a contact mechanics model based on van der Waals forces and frictional self-locking effects,incorporating both the spatular pad and spatular shaft of the gecko’s foot microstructures.Building on this foundation,a discrete element simulation model was established using the bonding method to replicate the contact between the gecko's spatula and different surfaces.The dynamic adhesion and detaching processes under normal and tangential external forces were simulated,allowing for the analysis of variation curves of normal and tangential adhesion forces at different detaching angles.This provided insights into the directional adhesion mechanics of the gecko's spatula.Furthermore,a force measurement system was constructed using a multi-degree-of-freedom nano-manipulator and an atomic force microscope within a scanning electron microscope.This system was used to experimentally test the adhesion characteristics of the gecko’s foot microstructures,validating the accuracy of the proposed adhesion mechanics model.展开更多
The line of sight (LOS) wind velocity can be determined from the incoherent Doppler lidar backscattering signals. Noise and interference in the measurement greatly degrade the inversion accuracy. In this paper, we app...The line of sight (LOS) wind velocity can be determined from the incoherent Doppler lidar backscattering signals. Noise and interference in the measurement greatly degrade the inversion accuracy. In this paper, we apply the discrete wavelet denoising method by using biorthogonal wavelets and adopt a distance-dependent thresholds algorithm to improve the accuracy of wind velocity measurement by incoherent Doppler lidar. The noisy simulation data are processed and compared with the true LOS wind velocity. The results are compared by the evaluation of both the standard deviation and correlation coefficient. The results suggest that wavelet denoising with distance-dependent thresholds can considerably reduce the noise and interfering turbulence for wind lidar measurement.展开更多
The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cone...The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.展开更多
The results of a theoretical study on the influence of strength of interphase boundaries in metal-ceramic composite on macroscopical characteristics of composite response such as strength, deformation capacity, fractu...The results of a theoretical study on the influence of strength of interphase boundaries in metal-ceramic composite on macroscopical characteristics of composite response such as strength, deformation capacity, fracture energy and fracture pattern are presented. The study was conducted by means of computer-aided simulation by means of movable cellular automaton method taking account of a developed ＂mesoscopical＂ structural model of particle-reinforced composite. The strength of interphase boundaries is found to be a key structural factor determining not only the strength properties of metal-ceramic composite, but also the pattern and rate of fracture. The principles for achievement of the high-strength values of particle/binder interfaces in the metal-ceramic composition due to the formation of the wide transition zones （areas of variable chemical composition） at the interphase boundaries are discussed. Simulation results confirm that such transition zones provide a change in fracture mechanism and make the achievement of a high-strength and a high deformation capacity of metal-ceramic composite possible.展开更多
Climate change is having an increasing impact on coastal infrastructure,leading to more frequent and intensified wave activity,including higher waves driven by typhoons and abnormal sea conditions.Consequently,issues ...Climate change is having an increasing impact on coastal infrastructure,leading to more frequent and intensified wave activity,including higher waves driven by typhoons and abnormal sea conditions.Consequently,issues related to the stability of existing port structures,such as caissons,have become a significant concern.In particular,gravity-type caisson on the land side of coastal port structures require enhanced stability and safety.Gravity-type caissons,which resist external forces through their own weight,are highly vulnerable to functional failures,such as sliding displacement,triggered by abnormal waves shifting specific caissons.The destruction of caisson and quay walls can lead to substantial recovery costs,necessitating improvements in caisson stability to address the challenges posed by increased wave forces and changes in port logistics due to larger vessels.One approach to enhancing caisson stability is the use of long caissons.Long caisson is commonly used where a breakwater is needed to withstand wave action and distribute forces evenly along a length of breakwater.The construction of caissons faces challenges due to limitations on the size of individual units imposed by construction conditions,launching methods,and marine crane requirements.Therefore,connecting multiple caissons to form long caissons presents a viable alternative.This study suggested two connection methods for long caissons.The first method was a hemisphere caisson,which allows the connection parts to seat against each other under self-weight during construction.The second method was a displacement-allowing connection utilizing rubble(embedded rebar connection within riprap connection).This approach allows some displacement while employing rebar to resist excessive deformation,thereby dispersing the resulting wave forces to adjacent caissons.Performance comparisons between the developed connections and conventional gravity-type caissons were conducted using a finite element analysis model.The results indicate that the proposed connections demonstrate improved resistance to wave forces compared to traditional caissons without such connections.Further studies should include field applications and performance evaluations of various caisson sizes under different environmental and geological conditions.展开更多
Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the...Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.展开更多
Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper i...Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.展开更多
We apply discrete Littlewood Paley Stein theory, developed by Han and Lu, to establish Calderon Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hp for w C A∞ in both the one-parameter and t...We apply discrete Littlewood Paley Stein theory, developed by Han and Lu, to establish Calderon Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hp for w C A∞ in both the one-parameter and two-parameter cases.展开更多
基金supported by the National Basic Research Program of China(973 Program)(2010CB428801,2010CB428804)National High-tech R&D Program of China(863 Program)(2011AA050105)+1 种基金National Science Foundation of China(40972166)National Science and Technology Major Project of China(2011ZX 05060-005).
文摘The discrete fracture network model is a powerful tool for fractured rock mass fluid flow simulations and supports safety assessments of coal mine hazards such as water inrush.Intersection analysis,which identifies all pairs of intersected fractures(the basic components composing the connectivity of a network),is one of its crucial procedures.This paper attempts to improve intersection analysis through parallel computing.Considering a seamless interfacing with other procedures in modeling,two algorithms are designed and presented,of which one is a completely independent parallel procedure with some redundant computations and the other is an optimized version with reduced redundancy.A numerical study indicates that both of the algorithms are practical and can significantly improve the computational performance of intersection analysis for large-scale simulations.Moreover,the preferred application conditions for the two algorithms are also discussed.
基金Supported by National Natural Science Foundation of China (No. 50639010)PhD Start-up Research Fund of Northeast Dianli University (2010)
文摘Considering the effects of particle crushing and intermediate principal stress on material yielding strength, the spatial mobilization plane(SMP) yielding criterion and state parameter model including a general critical state line are selected in the analysis of cylindrical cavity expansion.Meanwhile, combining Rowe s flow rule and Bolton s simplification to stress-dilatancy relationship to reflect soil shear dilatancy and softening behavior, this paper analyzes the problem of cylindrical cavity expansion i...
文摘AIM： To evaluate the use of short-duration transient visual evoked potentials（VEP） and color reflectivity discretization analysis（CORDA） in glaucomatous eyes,eyes suspected of having glaucoma,and healthy eyes.METHODS： The study included 136 eyes from 136 subjects： 49 eyes with glaucoma,45 glaucoma suspect eyes,and 42 healthy eyes.Subjects underwent Humphrey visual field（VF） testing,VEP testing,as well as peripapillary retinal nerve fiber layer optical coherence tomography imaging studies with post-acquisition CORDA applied.Statistical analysis was performed using means and ranges,ANOVA,post-hoc comparisons using Turkey＇s adjustment,Fisher＇s Exact test,area under the curve,and Spearman correlation coefficients.RESULTS： Parameters from VEP and CORDA correlated significantly with VF mean deviation（MD）（P〈0.05）.In distinguishing glaucomatous eyes from controls,VEP demonstrated area under the curve（AUC） values of 0.64-0.75 for amplitude and 0.67-0.81 for latency.The CORDA HR1 parameter was highly discriminative for glaucomatous eyes vs controls（AUC=0.94）.CONCLUSION： Significant correlations are found between MD and parameters of short-duration transient VEP and CORDA,diagnostic modalities which warrant further consideration in identifying glaucoma characteristics.
文摘In this paper, we apply a discrete Littlewood-Paley analysis to obtain Hardy spaces HP（Rn1× … ×Rnk） of arbitrary number of parameters characterized by discrete Littlewood-Paley square function and derive the boundedness of singular integral operators onHP（Rn1× … ×Rnk） and fromHP（Rn1× … ×Rnk）toLP（Rn1× … ×Rnk）.
基金supported by National High-Tech Research and Development Program of China (863 Program)(No.2009AA063005)Natural Science Foundation of Shandong Province (No.ZR2009EM001)
文摘The discrete excitation-emission-matrix fluorescence spectra (EEMS) at 12 excitation wavelengths (400, 430, 450, 460, 470, 490, 500, 510, 525, 550, 570, and 590 nm) and emission wavelengths ranging from 600-750 nm were determined for 43 phytoplankton species. A two-rank fluorescence spectra database was established by wavelet analysis and a fluorometric discrimination technique for determining phytoplankton population was developed. For laboratory simulatively mixed samples, the samples mixed from 43 algal species (the algae of one division accounted for 25%, 50%, 75%, 85%, and 100% of the gross biomass, respectively), the average discrimination rates at the level of division were 65.0%, 87.5%, 98.6%, 99.0%, and 99.1%, with average relative contents of 18.9%, 44.5%, 68.9%, 73.4%, and 82.9%, respectively; the samples mixed from 32 red tide algal species (the dominant species accounted for 60%, 70%, 80%, 90%, and 100% of the gross biomass, respectively), the average correct discrimination rates of the dominant species at the level of genus were 63.3%, 74.2%, 78.8%, 83.4%, and 79.4%, respectively. For the 81 laboratory mixed samples with the dominant species accounting for 75% of the gross biomass (chlorophyll), the discrimination rates of the dominant species were 95.1% and 72.8% at the level of division and genus, respectively. For the 12 samples collected from the mesocosm experiment in Maidao Bay of Qingdao in August 2007, the dominant species of the 11 samples were recognized at the division level and the dominant species of four of the five samples in which the dominant species accounted for more than 80% of the gross biomass were discriminated at the genus level; for the 12 samples obtained from Jiaozhou Bay in August 2007, the dominant species of all the 12 samples were recognized at the division level. The technique can be directly applied to fluorescence spectrophotometers and to the developing of an in situ algae fluorescence auto-analyzer for phytoplankton population.
基金funded by The National Key R&D Program of China(2023YFC2205600)Open Project of Space Structure and Mechanism Technology Laboratory of China Aerospace Science and Technology Group Co.,Ltd.(YY-F805202312005)+1 种基金HIT Youth Scientist Laboratory Project,Postdoctoral Fellowship Program of CPSF(GZB20230259)the China Postdoctoral Science Foundation(2023TQ0133)(2023M731288).
文摘The gecko's feet possess unique microstructures that enable strong adhesive forces when interacting with various surfaces.Understanding the interfacial forces generated by these microstructures is crucial for deciphering their adhesion mechanism.This study developed a contact mechanics model based on van der Waals forces and frictional self-locking effects,incorporating both the spatular pad and spatular shaft of the gecko’s foot microstructures.Building on this foundation,a discrete element simulation model was established using the bonding method to replicate the contact between the gecko's spatula and different surfaces.The dynamic adhesion and detaching processes under normal and tangential external forces were simulated,allowing for the analysis of variation curves of normal and tangential adhesion forces at different detaching angles.This provided insights into the directional adhesion mechanics of the gecko's spatula.Furthermore,a force measurement system was constructed using a multi-degree-of-freedom nano-manipulator and an atomic force microscope within a scanning electron microscope.This system was used to experimentally test the adhesion characteristics of the gecko’s foot microstructures,validating the accuracy of the proposed adhesion mechanics model.
基金This work was supported by the National High Technology Research and Development Program of China (No. 2002AA135280)the National Natural Science Foundation of China (No. 60178017 and No. 40176011). S. Wu's e-mail address is shwu@orsi.ouc.edu.cn.
文摘The line of sight (LOS) wind velocity can be determined from the incoherent Doppler lidar backscattering signals. Noise and interference in the measurement greatly degrade the inversion accuracy. In this paper, we apply the discrete wavelet denoising method by using biorthogonal wavelets and adopt a distance-dependent thresholds algorithm to improve the accuracy of wind velocity measurement by incoherent Doppler lidar. The noisy simulation data are processed and compared with the true LOS wind velocity. The results are compared by the evaluation of both the standard deviation and correlation coefficient. The results suggest that wavelet denoising with distance-dependent thresholds can considerably reduce the noise and interfering turbulence for wind lidar measurement.
基金This work has been supported by US Army Research Office Grant(No.W911NF-15-1-0223)The Scientific and Technological Research Council of Turkey Grant(No.1059B191300653).
文摘The aim of this paper is to establish a fundamental theory of convex analysis for the sets and functions over a discrete domain.By introducing conjugate/biconjugate functions and a discrete duality notion for the cones over discrete domains,we study duals of optimization problems whose decision parameters are integers.In particular,we construct duality theory for integer linear programming,provide a discrete version of Slater’s condition that implies the strong duality and discuss the relationship between integrality and discrete convexity.
基金The investigation has been carried out within the SB RAS Program Ⅲ.20.2 for Basic Researchat partial financial support of the RFBR Grant No.11-08-12069-ofi-m-2011+1 种基金the Project No.5 of the Belarus NASSB RAS Program for Joint Basic Research
文摘The results of a theoretical study on the influence of strength of interphase boundaries in metal-ceramic composite on macroscopical characteristics of composite response such as strength, deformation capacity, fracture energy and fracture pattern are presented. The study was conducted by means of computer-aided simulation by means of movable cellular automaton method taking account of a developed ＂mesoscopical＂ structural model of particle-reinforced composite. The strength of interphase boundaries is found to be a key structural factor determining not only the strength properties of metal-ceramic composite, but also the pattern and rate of fracture. The principles for achievement of the high-strength values of particle/binder interfaces in the metal-ceramic composition due to the formation of the wide transition zones （areas of variable chemical composition） at the interphase boundaries are discussed. Simulation results confirm that such transition zones provide a change in fracture mechanism and make the achievement of a high-strength and a high deformation capacity of metal-ceramic composite possible.
基金supported by Basic Science Research Program through the National Research Foundation of Korea(NRF)funded by the Ministry of Education(Nos.RS-2023-00212586 and RS-2024-00348557)the Korea Maritime&Ocean University Research Fund in 2024.
文摘Climate change is having an increasing impact on coastal infrastructure,leading to more frequent and intensified wave activity,including higher waves driven by typhoons and abnormal sea conditions.Consequently,issues related to the stability of existing port structures,such as caissons,have become a significant concern.In particular,gravity-type caisson on the land side of coastal port structures require enhanced stability and safety.Gravity-type caissons,which resist external forces through their own weight,are highly vulnerable to functional failures,such as sliding displacement,triggered by abnormal waves shifting specific caissons.The destruction of caisson and quay walls can lead to substantial recovery costs,necessitating improvements in caisson stability to address the challenges posed by increased wave forces and changes in port logistics due to larger vessels.One approach to enhancing caisson stability is the use of long caissons.Long caisson is commonly used where a breakwater is needed to withstand wave action and distribute forces evenly along a length of breakwater.The construction of caissons faces challenges due to limitations on the size of individual units imposed by construction conditions,launching methods,and marine crane requirements.Therefore,connecting multiple caissons to form long caissons presents a viable alternative.This study suggested two connection methods for long caissons.The first method was a hemisphere caisson,which allows the connection parts to seat against each other under self-weight during construction.The second method was a displacement-allowing connection utilizing rubble(embedded rebar connection within riprap connection).This approach allows some displacement while employing rebar to resist excessive deformation,thereby dispersing the resulting wave forces to adjacent caissons.Performance comparisons between the developed connections and conventional gravity-type caissons were conducted using a finite element analysis model.The results indicate that the proposed connections demonstrate improved resistance to wave forces compared to traditional caissons without such connections.Further studies should include field applications and performance evaluations of various caisson sizes under different environmental and geological conditions.
基金supported by the NSF of USA(Grant No.DMS0901761)supported by NNSF of China(Grant Nos.10971228and11271209)Natural Science Foundation of Nantong University(Grant No.11ZY002)
文摘Though the theory of Triebel-Lizorkin and Besov spaces in one-parameter has been developed satisfactorily, not so much has been done for the multiparameter counterpart of such a theory. In this paper, we introduce the weighted Triebel-Lizorkin and Besov spaces with an arbitrary number of parameters and prove the boundedness of singular integral operators on these spaces using discrete Littlewood-Paley theory and Calderon＇s identity. This is inspired by the work of discrete Littlewood- Paley analysis with two parameters of implicit dilations associated with the flag singular integrals recently developed by Han and Lu [12]. Our approach of derivation of the boundedness of singular integrals on these spaces is substantially different from those used in the literature where atomic decomposition on the one-parameter Triebel-Lizorkin and Besov spaces played a crucial role. The discrete Littlewood-Paley analysis allows us to avoid using the atomic decomposition or deep Journe＇s covering lemma in multiparameter setting.
基金supported partly by NSF of China (No. 10571015)SRFDP of China (No. 20050027025)+2 种基金supported by the U.S. NSF (Grant DMS No. 0500853)supported partly by NSF of China (No. 10771054)supported by NSF of China (No, 10811120558)
文摘Though the theory of one-parameter Triebel-Lizorkin and Besov spaces has been very well developed in the past decades, the multi-parameter counterpart of such a theory is still absent. The main purpose of this paper is to develop a theory of multi-parameter Triebel-Lizorkin and Besov spaces using the discrete Littlewood-Paley-Stein analysis in the setting of implicit multi-parameter structure. It is motivated by the recent work of Han and Lu in which they established a satisfactory theory of multi-parameter Littlewood-Paley-Stein analysis and Hardy spaces associated with the flag singular integral operators studied by Muller-Ricci-Stein and Nagel-Ricci-Stein. We also prove the boundedness of flag singular integral operators on Triebel-Lizorkin space and Besov space. Our methods here can be applied to develop easily the theory of multi-parameter Triebel-Lizorkin and Besov spaces in the pure product setting.
文摘We apply discrete Littlewood Paley Stein theory, developed by Han and Lu, to establish Calderon Zygmund decompositions and interpolation theorems on weighted Hardy spaces Hp for w C A∞ in both the one-parameter and two-parameter cases.
