This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By u...This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.展开更多
Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significan...Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.展开更多
In this study,CiteSpace software is used to carry out visual analysis on the three-dimensional research literature on urban recreation space from the perspective of compact city theory in the past 20 years,exploring t...In this study,CiteSpace software is used to carry out visual analysis on the three-dimensional research literature on urban recreation space from the perspective of compact city theory in the past 20 years,exploring the scientific development trend and research hotspots in this field.The results show that the number of published documents shows a fluctuating upward trend,and the significant growth rate reflects the role of policy orientation in promoting the concept of compact city.The co-occurrence analysis of keywords reveals the research hotspots of“compact city”,“recreation space”and“urban park”,while the emergence of new keywords such as“vertical city”and“spatial justice”indicates the new trend of recent research.The cluster analysis and timeline map further show the evolution of research themes,with“compact city”being the largest cluster and having rich connections with other themes such as“urban design”and“urban park”.展开更多
In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） d...In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.展开更多
In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation...In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.展开更多
In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduce...In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.展开更多
This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function...This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.展开更多
A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.Th...A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.展开更多
Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coa...Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses.展开更多
We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into ...We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.展开更多
A series of related electrophysiology phenomena can be caused by the occurrence of interpolated ventricular premature contraction.In our recent three-dimensional Lorenz R-R scatter plot research,we found that atrioven...A series of related electrophysiology phenomena can be caused by the occurrence of interpolated ventricular premature contraction.In our recent three-dimensional Lorenz R-R scatter plot research,we found that atrioventricular node double path caused by interpolated ventricular premature contraction imprints a specifi c pattern on three-dimensional Lorenz plots generated from 24-hour Holter recordings.We found two independent subclusters separated from the interpolated premature beat precluster,the interpolated premature beat cluster,and the interpolated premature beat postcluster,respectively.Combined with use of the trajectory tracking function and the leap phenomenon,our results reveal the presence of the atrioventricular node double conduction path.展开更多
Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified f...Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified for the first time the scientific theory system of Fenlong Technology using three-dimensional space resources"Fenlong Agricultural Nature Theory"and the development of the relative"limits"of agricultural growth,which provides a huge power support and natural force for expanding human living spaces.Through inventing and creating a scientific and technological system of farming tools,farming machinery,farming modes,and magic weapons for cultivation,Fenlong Technology can increase grain,promote ecological development,and greatly expand the living spaces of the Chinese nation and achieve sustainable development.Using Fenlong Technology,China has expanded from the current single"cultivated land agriculture"to the"big pattern agriculture"of Fenlong"cultivated land+saline land+degraded grassland+marginal land+desertified land+river water",flexibly used 147 million ha of"three-dimensional space resources"of land,and the newly increased food,meat,and fish can feed 300 million to 400 million people,increased the water storage by 100 billion m^(3),and reduced the collection of groundwater by 20 million to 60 billion m^(3).展开更多
The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smooth...The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.展开更多
We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-finite von Neumann algebras and extend the Riesz type factorization to the semi-finite case.
Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(...Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.展开更多
This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means...This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.展开更多
The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle ...The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).展开更多
In the research of path planning for manipulators with many DOF, generally there is a problem in most traditional methods, which is that their computational cost (time and memory space) increases exponentially as DOF ...In the research of path planning for manipulators with many DOF, generally there is a problem in most traditional methods, which is that their computational cost (time and memory space) increases exponentially as DOF or resolution of the discrete configuration space increases. So this paper presents the collision-free trajectory planning for the space robot to capture a target based on the wavelet interpolation algorithm. We made wavelet sample on the desired trajectory of the manipulator’s end-effector to do trajectory planning by use of the proposed wavelet interpolation formula, and then derived joint vectors from the trajectory information of the end-effector based on the fixed-attitude-restrained generalized Jacobian matrix of multi-arm coordinated motion, so as to control the manipulator to capture a static body along the desired collision-free trajectory. The method overcomes the shortcomings of the typical methods, and the desired trajectory of the end-effector can be any kind of complex nonlinear curve. The algorithm is simple and highly effective and the real trajectory is close to the desired trajectory. In simulation, the planar dual-arm three DOF space robot is used to demonstrate the proposed method, and it shows that the algorithm is feasible.展开更多
文摘This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.
基金supported by the National Science Fund for Distinguished Young Scholars(42225107)the National Natural Science Foundation of China(42001326,42371414,42171409,and 42271419)+1 种基金the Natural Science Foundation of Guangdong Province of China(2022A1515012207)the Basic and Applied Basic Research Project of Guangzhou Science and Technology Planning(202201011539)。
文摘Three-dimensional(3D)urban structures play a critical role in informing climate mitigation strategies aimed at the built environment and facilitating sustainable urban development.Regrettably,there exists a significant gap in detailed and consistent data on 3D building space structures with global coverage due to the challenges inherent in the data collection and model calibration processes.In this study,we constructed a global urban structure(GUS-3D)dataset,including building volume,height,and footprint information,at a 500 m spatial resolution using extensive satellite observation products and numerous reference building samples.Our analysis indicated that the total volume of buildings worldwide in2015 exceeded 1×10^(12)m^(3).Over the 1985 to 2015 period,we observed a slight increase in the magnitude of 3D building volume growth(i.e.,it increased from 166.02 km3 during the 1985–2000 period to 175.08km3 during the 2000–2015 period),while the expansion magnitudes of the two-dimensional(2D)building footprint(22.51×10^(3) vs 13.29×10^(3)km^(2))and urban extent(157×10^(3) vs 133.8×10^(3)km^(2))notably decreased.This trend highlights the significant increase in intensive vertical utilization of urban land.Furthermore,we identified significant heterogeneity in building space provision and inequality across cities worldwide.This inequality is particularly pronounced in many populous Asian cities,which has been overlooked in previous studies on economic inequality.The GUS-3D dataset shows great potential to deepen our understanding of the urban environment and creates new horizons for numerous 3D urban studies.
基金Sponsored by the Project of Sichuan Landscape and Recreation Research Center(JGYQ2020037).
文摘In this study,CiteSpace software is used to carry out visual analysis on the three-dimensional research literature on urban recreation space from the perspective of compact city theory in the past 20 years,exploring the scientific development trend and research hotspots in this field.The results show that the number of published documents shows a fluctuating upward trend,and the significant growth rate reflects the role of policy orientation in promoting the concept of compact city.The co-occurrence analysis of keywords reveals the research hotspots of“compact city”,“recreation space”and“urban park”,while the emergence of new keywords such as“vertical city”and“spatial justice”indicates the new trend of recent research.The cluster analysis and timeline map further show the evolution of research themes,with“compact city”being the largest cluster and having rich connections with other themes such as“urban design”and“urban park”.
基金The National Basic Research Program of China under contract No. 2013CB430304the National High-Tech R&D Program of China under contract No. 2013AA09A505the National Natural Science Foundation of China under contract Nos 41030854,40906015,40906016,41106005 and 41176003
文摘In order to solve the so-called ＂bull-eye＂ problem caused by using a simple bilinear interpolation as an observational mapping operator in the cost function in the multigrid three-dimensional variational （3DVAR） data assimilation scheme, a smoothing term, equivalent to a penalty term, is introduced into the cost function to serve as a means of troubleshooting. A theoretical analysis is first performed to figure out what on earth results in the issue of ＂bull-eye＂, and then the meaning of such smoothing term is elucidated and the uniqueness of solution of the multigrid 3DVAR with the smoothing term added is discussed through the theoretical deduction for one-dimensional （1D） case, and two idealized data assimilation experiments （one- and two-dimensional （2D） cases）. By exploring the relationship between the smoothing term and the recursive filter theoretically and practically, it is revealed why satisfied analysis results can be achieved by using such proposed solution for the issue of the multigrid 3DVAR.
文摘The paper is given the interpolation of operators between weighted Hardy spaces and weighted L p spaces when w∈A 1 by Calderon Zygmund decomposition.
文摘In this article, the authors introduce some new Lorentz spaces for martingales, which are extensions of Hardy spaces of martingales. Then they discuss their basic properties, embedding relationships, and interpolation spaces between them, during which the use of rearrangement good-λ-inequality plays an important role.
基金supported by National Natural Science Foundation of China(Grant No.11201354)Hubei Province Key Laboratory of Systems Science in Metallurgical Process(Wuhan University of Science and Technology)(Y201321)National Natural Science Foundation of Pre-Research Item(2011XG005)
文摘In this paper, we apply function parameters to real interpolation of Lorentz- Orlicz martingale spaces. Some new interpolation theorems are formulated which generalize some known results in Lorentz spaces An introduced by Sharpley.
基金supported by National Natural Science Foundation of China(11871006,11671271)。
文摘This paper investigates the optimal Birkhoff interpolation and Birkhoff numbers of some function spaces in space L∞[-1,1]and weighted spaces Lp,ω[-1,1],1≤p<∞,with w being a continuous integrable weight function in(-1,1).We proved that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal.We also show that the Lagrange interpolation algorithms based on the zeros of some polynomials are optimal when the function values of the two endpoints are included in the interpolation systems.
基金supported by National Natural Science Funds for Young Scholar(No.50903027)the Natural Science Foundation of Hebei Province(No.E2010000058)Education Department Science Research Plan of Hebei Province(No.2007307).
文摘A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.
文摘Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses.
基金Project supported by the National Basic Research Program of China (Grant No. 2010CB327702)
文摘We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.
文摘A series of related electrophysiology phenomena can be caused by the occurrence of interpolated ventricular premature contraction.In our recent three-dimensional Lorenz R-R scatter plot research,we found that atrioventricular node double path caused by interpolated ventricular premature contraction imprints a specifi c pattern on three-dimensional Lorenz plots generated from 24-hour Holter recordings.We found two independent subclusters separated from the interpolated premature beat precluster,the interpolated premature beat cluster,and the interpolated premature beat postcluster,respectively.Combined with use of the trajectory tracking function and the leap phenomenon,our results reveal the presence of the atrioventricular node double conduction path.
基金Special Fund Project for Innovation Driven Development of Guangxi(Gui Ke AA17204037)Key Science and Technology Project of Guangxi(Gui Ke AA16380017)Team Project of Guangxi Academy of Agricultural Sciences(2015YT60).
文摘Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified for the first time the scientific theory system of Fenlong Technology using three-dimensional space resources"Fenlong Agricultural Nature Theory"and the development of the relative"limits"of agricultural growth,which provides a huge power support and natural force for expanding human living spaces.Through inventing and creating a scientific and technological system of farming tools,farming machinery,farming modes,and magic weapons for cultivation,Fenlong Technology can increase grain,promote ecological development,and greatly expand the living spaces of the Chinese nation and achieve sustainable development.Using Fenlong Technology,China has expanded from the current single"cultivated land agriculture"to the"big pattern agriculture"of Fenlong"cultivated land+saline land+degraded grassland+marginal land+desertified land+river water",flexibly used 147 million ha of"three-dimensional space resources"of land,and the newly increased food,meat,and fish can feed 300 million to 400 million people,increased the water storage by 100 billion m^(3),and reduced the collection of groundwater by 20 million to 60 billion m^(3).
文摘The interpolation spaces between Banach space valued martingale Hardy spaces, between Hardy and BMO spaces are identified respectively. Some results obtained here are connected closely with the convexity and smoothness of the Banach space which the martingales take values in.
基金partially supported by NSFC(11771372)K.N.Ospanov was partially supported by project AP05131557 of the Science Committee of Ministry of Education and Science of the Republic of Kazakhstan。
文摘We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-finite von Neumann algebras and extend the Riesz type factorization to the semi-finite case.
基金the French ANR project(ANR-19-CE40-0002)the Natural Science Foundation of China(12031004).
文摘Let M be a semifinite von Neumann algebra.We equip the associated noncommutative Lp-spaces with their natural operator space structure introduced by Pisier via complex interpolation.On the other hand,for L_(p),p(M)=(L_(∞)(M),L_(1)(M)_(1/p,p)be equipped with the operator space structure via real interpolation as defined by the second named author(J.Funct.Anal.139(1996),500–539).We show that Lp,p(M)=Lp(M)completely isomorphically if and only if M is finite dimensional.This solves in the negative the three problems left open in the quoted work of the second author.We also show that for 1<p<∞and 1≤q≤∞with p 6=q,(L_(∞)(M;l_(q)),L_(1)(M;l_(q)_(1/p,p)=L_(p)(M;l_(q)with equivalent norms,i.e.,at the Banach space level if and only if M is isomorphic,as a Banach space,to a commutative von Neumann algebra.Our third result concerns the following inequality:||(∑iixtq)^(1/q)||lp(M)≤||(∑iixit)^(1/q)||lp(M),for any finite sequence(xi)⊂L+p(M),where 0<r<q<∞and 0<p≤∞.If M is not isomorphic,as a Banach space,to a commutative von Meumann algebra,then this inequality holds if and only if p≥r.
基金Supported by the National Natural Science Foundation of China（liT61055） Supported by the Inner Mongolia Autonomous Region Natural Science Foundation of China（2017MS0123）
文摘This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality.
基金supported by the Innovation Research for the Postgrad-uates of Guangzhou University(2020GDJC-D06)supported by the National Natural Science Foundation of China(12071229)。
文摘The aim of this paper is to prove a new version of the Riesz-Thorin interpolation theorem on L^(P)(C,H).In the sense of Cullen-regular,we show Hadamard’s three-lines theorem by means of the Maximum modulus principle on a symmetric slice domain.In addition,two applications of the Riesz-Thorin theorem are presented.Finally,we investigate two kinds of Calderón’s complex interpolation methods in LP(C,H).
文摘In the research of path planning for manipulators with many DOF, generally there is a problem in most traditional methods, which is that their computational cost (time and memory space) increases exponentially as DOF or resolution of the discrete configuration space increases. So this paper presents the collision-free trajectory planning for the space robot to capture a target based on the wavelet interpolation algorithm. We made wavelet sample on the desired trajectory of the manipulator’s end-effector to do trajectory planning by use of the proposed wavelet interpolation formula, and then derived joint vectors from the trajectory information of the end-effector based on the fixed-attitude-restrained generalized Jacobian matrix of multi-arm coordinated motion, so as to control the manipulator to capture a static body along the desired collision-free trajectory. The method overcomes the shortcomings of the typical methods, and the desired trajectory of the end-effector can be any kind of complex nonlinear curve. The algorithm is simple and highly effective and the real trajectory is close to the desired trajectory. In simulation, the planar dual-arm three DOF space robot is used to demonstrate the proposed method, and it shows that the algorithm is feasible.
