We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method,...We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.展开更多
CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.F...CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.For the consecutive micro-line segments interpolation,the velocities at the junction of two segments are the bottlenecks for the machining efficiency.This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode,which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision.A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining speed.The proposed algorithm has been implemented on Blue Sky NC System,and experimented in real material manufacturing.Compared with several existing algorithms,the current algorithm can improve the manufacturing time ranging from 50% to 180%,depending on the machining parameters,and also results in better machining quality.In addition,the algorithm also satisfies the need of real-time interpolation.展开更多
The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use o...The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.展开更多
A class of stochastic Besov spaces BpL^(2)(Ω;˙H^(α)(O)),1≤p≤∞andα∈[−2,2],is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du−Δudt=f(u)dt+dW(t),under the fol...A class of stochastic Besov spaces BpL^(2)(Ω;˙H^(α)(O)),1≤p≤∞andα∈[−2,2],is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du−Δudt=f(u)dt+dW(t),under the following conditions for someα∈(0,1]:||∫_(0)^(t)e−(t−s)^(A)dW(s)||L^(2)(Ω;L^(2)(O))≤C^(t^(α/2))and||∫_(0)^(t)e−(t−s)^(A)dW(s)||_B^(∞)L^(2)(Ω:H^(α)(O))≤C..The conditions above are shown to be satisfied by both trace-class noises(withα=1)and one-dimensional space-time white noises(withα=1/2).The latter would fail to satisfy the conditions withα=1/2 if the stochastic Besov norm||·||B∞L^(2)(Ω;˙H^(α)(O))is replaced by the classical Sobolev norm||·||L^(2)(Ω;˙Hα(O)),and this often causes reduction of the convergence order in the numerical analysis of the semilinear stochastic heat equation.In this paper,the convergence of a modified exponential Euler method,with a spectral method for spatial discretization,is proved to have orderαin both the time and space for possibly nonsmooth initial data in L^(4)(Ω;˙H^(β)(O))withβ>−1,by utilizing the real interpolation properties of the stochastic Besov spaces and a class of locally refined stepsizes to resolve the singularity of the solution at t=0.展开更多
We present a new high-payload joint reversible data-hiding scheme for encrypted images. Instead of embedding data in the encrypted image directly, the content owner first uses an interpolation technique to estimate wh...We present a new high-payload joint reversible data-hiding scheme for encrypted images. Instead of embedding data in the encrypted image directly, the content owner first uses an interpolation technique to estimate whether the location can be used for embedding and generates a location map before encryption. Next, the data hider embeds the additional data through flipping the most significant bits （MSBs） of the encrypted image according to the location map. At the receiver side, before extracting the additional data and reconstructing the image, the receiver decrypts the image first. Experimental results demonstrate that the proposed method can achieve real reversibility, which means data extraction and image recovery are free of error. Moreover, our scheme can embed more payloads than most existing reversible data hiding schemes in encrypted images.展开更多
In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real ...In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given. Keywords Martingale space, BMO space, Lorentz space, real interpolation, function parameter展开更多
We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal me...We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Г.展开更多
The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is： Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C（-∞,∞） satisfy ｜y｜= O（e^（1/2-δo）xk^2,...The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is： Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C（-∞,∞） satisfy ｜y｜= O（e^（1/2-δo）xk^2,） and ｜f（x）｜t= O（e^（1-εo ）x2^）. Then for any given point x ∈ R, we have limn→Hn,（f, x） = f（x）.展开更多
Background Petrochemical products possess a high risk of flammability,explosivity,and toxicity,making petrochemical accidents exceedingly destructive.Therefore,disaster analysis,prediction,and real-time simulations ha...Background Petrochemical products possess a high risk of flammability,explosivity,and toxicity,making petrochemical accidents exceedingly destructive.Therefore,disaster analysis,prediction,and real-time simulations have become important means of controlling and reducing accident hazards.Methods This study proposes a complete real-time simulation solution of gas diffusion with coordinate and concentration data,which was mainly aimed at simulating the types of harmful gas leakage and diffusion accidents in the petrochemical industry.The rendering effect was more continuous and accurate through grid homogenization and trilinear interpolation.This study presents a data processing and rendering parallelization process to enhance simulation efficiency.Gas concentration and fragment transparency were combined to synthesize transparent pixels in a scene.To ensure the approximate accuracy of the rendering effect,improve the efficiency of real-time rendering,and meet the requirement of intuitive perception using concentration data,a weighted blended order-independent transparency(OIT)with enhanced alpha weight is presented,which can provide a more intuitive perception of the hierarchical information of concentration data while preserving depth information.This study compares and analyzes three OIT algorithms-depth peeling,weighted blended OIT,and weighted blended OIT with enhanced alpha weight-in terms of rendering image quality,rendering time,required memory,and hierarchical information.Results Using weighted blended OIT with an enhanced alpha weight technique,the rendering time was shortened by 53.2%compared with that of the depth peeling algorithm,and the texture memory required was significantly smaller than that of the depth peeling algorithm.The rendering results of weighted blended OIT with an enhanced alpha weight were approximately accurate compared with those of the depth peeling algorithm as the ground truth,and there was no popping when surfaces passed through one another.Simultaneously,compared with weighted b展开更多
Tool path smoothing of linear commands is important to guarantee the high-order motion continuity of multi-axis motion control systems.The existing local tool path smoothing methods mainly construct symmetrical spline...Tool path smoothing of linear commands is important to guarantee the high-order motion continuity of multi-axis motion control systems.The existing local tool path smoothing methods mainly construct symmetrical splines at transition corners of linear segments.When the linear segments are short,the symmetrical splines must be shrunk to avoid overlapping,which gives rise to relatively high curvature and low machining efficiency.This paper proposes a tool-path smoothing algorithm for serial industrial robots with 6 rotary(6R)joints by constructing asymmetrical Pythagorean-hodograph(PH)splines.Firstly,symmetrical PH splines are initially constructed at transition corners to realize the third-order differential continuity of tool path position and tool orientation.Tool tip position smoothing errors are constrained by directly evaluating the control polygon length of spline according to the error tolerance in the workpiece coordinate system,while the tool orientation smoothing errors are constrained by adjusting control polygon length after converting tool orientation error to Euler angles using Jacobian matrix.Then asymmetrical splines are constructed by dealing with the spline overlapping problem,while guarantying the fully utilization of error tolerance to reduce spline curvature.The position and orientation are synchronized to the arc-length of the tool tip position to ensure the continuity of acceleration and jerk commands.The control points and arc-length of the constructed asymmetrical splines can all be solved analytically,which makes it suitable for on-line tool path smoothing.Experiments demonstrate that the proposed method achieves higher motion efficiency and lower tracking error than the existing symmetrical and asymmetrical tool path smoothing methods,which validates the advantages of the proposed method in high speed machining.展开更多
A simple way of interpolation for real time processing is pres -ented. For passive localization, the time delay between two signals can be determined by the peak of their cross-correlation. It is more efficient to est...A simple way of interpolation for real time processing is pres -ented. For passive localization, the time delay between two signals can be determined by the peak of their cross-correlation. It is more efficient to estimate a cross-correlation function by the inverse FFT of the cross-spectral density. The original smapling rate is usually very low to reduce computation. The sampling rate of the cross-correlation so computed is too low to estimate satisfactorily and an interpolation procedure is therefore needed. The interpolation by zero augmented spectrum is concise, fast and accurate. The results of the computer simulation and real nuderwater signal processing are given in the paper.展开更多
We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padr...We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.展开更多
A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit...A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit theory and digital filter design can also be re-duced to the solution of matrix rational interpolation problems[1—4].By means of thereachability and the observability indices of defined pairs of matrices,Antoulas,Ball,Kang and Willems solved the minimal matrix rational interpolation problem in[1].On展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11471042,11171027 and 11361020)the Alexander von Humboldt Foundation+1 种基金the Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20120003110003)the Fundamental Research Funds for Central Universities of China(Grant Nos.2013YB60 and 2014KJJCA10)
文摘We study the interpolation of Morrey-Campanato spaces and some smoothness spaces based on Morrey spaces, e. g., Besov-type and Triebel-Lizorkin-type spaces. Various interpolation methods, including the complex method, the ±-method and the Peetre-Gagliardo method, are studied in such a framework. Special emphasis is given to the quasi-Banach case and to the interpolation property.
基金supported by the National Key Basic Research Project of China (Grant Nos 2011CB302400)the National Natural Science Foundation of China (Grant Nos 60821002, 10871195, 10925105)+1 种基金Major National S&T Project "Advanced CNC Systems"CAS Project "MM Methods for Advanced CNC Systems"
文摘CNC machining plays an important role in mechanical manufacturing.A key issue is to improve the machining feedrate while keeping the machining precision and satisfying the acceleration constraints of the CNC machine.For the consecutive micro-line segments interpolation,the velocities at the junction of two segments are the bottlenecks for the machining efficiency.This paper proposes a multi-period turning method to improve the feedrate at the junctions using the linear acceleration and deceleration mode,which utilizes the maximal acceleration capabilities of the NC machine while satisfying the machining precision.A new and more efficient look-ahead method and a feedrate override method are also proposed to boast the global machining speed.The proposed algorithm has been implemented on Blue Sky NC System,and experimented in real material manufacturing.Compared with several existing algorithms,the current algorithm can improve the manufacturing time ranging from 50% to 180%,depending on the machining parameters,and also results in better machining quality.In addition,the algorithm also satisfies the need of real-time interpolation.
文摘The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.
基金supported by National Natural Science Foundation of China(Grant Nos.12071020,12131005 and U2230402)the Research Grants Council of Hong Kong(Grant No.Poly U15300519)an Internal Grant of The Hong Kong Polytechnic University(Grant No.P0038843,Work Programme:ZVX7)。
文摘A class of stochastic Besov spaces BpL^(2)(Ω;˙H^(α)(O)),1≤p≤∞andα∈[−2,2],is introduced to characterize the regularity of the noise in the semilinear stochastic heat equation du−Δudt=f(u)dt+dW(t),under the following conditions for someα∈(0,1]:||∫_(0)^(t)e−(t−s)^(A)dW(s)||L^(2)(Ω;L^(2)(O))≤C^(t^(α/2))and||∫_(0)^(t)e−(t−s)^(A)dW(s)||_B^(∞)L^(2)(Ω:H^(α)(O))≤C..The conditions above are shown to be satisfied by both trace-class noises(withα=1)and one-dimensional space-time white noises(withα=1/2).The latter would fail to satisfy the conditions withα=1/2 if the stochastic Besov norm||·||B∞L^(2)(Ω;˙H^(α)(O))is replaced by the classical Sobolev norm||·||L^(2)(Ω;˙Hα(O)),and this often causes reduction of the convergence order in the numerical analysis of the semilinear stochastic heat equation.In this paper,the convergence of a modified exponential Euler method,with a spectral method for spatial discretization,is proved to have orderαin both the time and space for possibly nonsmooth initial data in L^(4)(Ω;˙H^(β)(O))withβ>−1,by utilizing the real interpolation properties of the stochastic Besov spaces and a class of locally refined stepsizes to resolve the singularity of the solution at t=0.
基金Project supported by the National Natural Science Foundation of China （Nos. 61572089 and 61633005）, the Natural Science Foundation of Chongqing Science and Technology Commission （No. cstc2017jcyjBX0008）, the Chongqing Graduate Student Research Innovation Project （No. CY1317026）, and the Fundamental Research Funds for the Central Universities （Nos. 106112017CDJQJ188830 and 106112017CDJXY180005）
文摘We present a new high-payload joint reversible data-hiding scheme for encrypted images. Instead of embedding data in the encrypted image directly, the content owner first uses an interpolation technique to estimate whether the location can be used for embedding and generates a location map before encryption. Next, the data hider embeds the additional data through flipping the most significant bits （MSBs） of the encrypted image according to the location map. At the receiver side, before extracting the additional data and reconstructing the image, the receiver decrypts the image first. Experimental results demonstrate that the proposed method can achieve real reversibility, which means data extraction and image recovery are free of error. Moreover, our scheme can embed more payloads than most existing reversible data hiding schemes in encrypted images.
基金Supported by National Natural Science Foundation of China(Grant No.10871016)
文摘In this paper, we consider the real interpolation with a function parameter between martingale Hardy and BMO spaces. An interpolation theorem for martingale Hardy and BMO spaces is formulated. As an application, real interpolation between martingale Lorentz and BMO spaces is given. Keywords Martingale space, BMO space, Lorentz space, real interpolation, function parameter
基金The authors have been supported in part by the Spanish Ministerio de Educación y Ciencia(MTM2004-01888)
文摘We work with the abstract K and J interpolation method generated by a sequence lattice Г. We investigate the deviation of an interpolated operator from a given operator ideal by establishing formulae for the ideal measure of the interpolated operator in terms of the ideal measures of restrictions of the operator. Formulae are given in terms of the norms of the shift operators on Г.
基金Open Funds of State Key Laboratory of Oil and Gas Reservoir and Exploitation,Southwest Petroleum University(No.PCN0613)the Natural Foundation of Zhejiang Provincial Education Department (No.Kyg091206029)
文摘The present paper investigates the convergence of Hermite interpolation operators on the real line. The main result is： Given 0 〈 δo 〈 1/2, 0 〈 εo 〈 1. Let f ∈ C（-∞,∞） satisfy ｜y｜= O（e^（1/2-δo）xk^2,） and ｜f（x）｜t= O（e^（1-εo ）x2^）. Then for any given point x ∈ R, we have limn→Hn,（f, x） = f（x）.
基金Supported by National Key R&D Program of China (2020YFB1710400)。
文摘Background Petrochemical products possess a high risk of flammability,explosivity,and toxicity,making petrochemical accidents exceedingly destructive.Therefore,disaster analysis,prediction,and real-time simulations have become important means of controlling and reducing accident hazards.Methods This study proposes a complete real-time simulation solution of gas diffusion with coordinate and concentration data,which was mainly aimed at simulating the types of harmful gas leakage and diffusion accidents in the petrochemical industry.The rendering effect was more continuous and accurate through grid homogenization and trilinear interpolation.This study presents a data processing and rendering parallelization process to enhance simulation efficiency.Gas concentration and fragment transparency were combined to synthesize transparent pixels in a scene.To ensure the approximate accuracy of the rendering effect,improve the efficiency of real-time rendering,and meet the requirement of intuitive perception using concentration data,a weighted blended order-independent transparency(OIT)with enhanced alpha weight is presented,which can provide a more intuitive perception of the hierarchical information of concentration data while preserving depth information.This study compares and analyzes three OIT algorithms-depth peeling,weighted blended OIT,and weighted blended OIT with enhanced alpha weight-in terms of rendering image quality,rendering time,required memory,and hierarchical information.Results Using weighted blended OIT with an enhanced alpha weight technique,the rendering time was shortened by 53.2%compared with that of the depth peeling algorithm,and the texture memory required was significantly smaller than that of the depth peeling algorithm.The rendering results of weighted blended OIT with an enhanced alpha weight were approximately accurate compared with those of the depth peeling algorithm as the ground truth,and there was no popping when surfaces passed through one another.Simultaneously,compared with weighted b
基金supported by the Key Research and Development Plan(Grant No.2020YFB1710400)the National Natural Science Foundation of China(Grant No.52122512 and 52188102)the Natural Science Foundation of Hubei Province,China(Grant No.2021CFA075)。
文摘Tool path smoothing of linear commands is important to guarantee the high-order motion continuity of multi-axis motion control systems.The existing local tool path smoothing methods mainly construct symmetrical splines at transition corners of linear segments.When the linear segments are short,the symmetrical splines must be shrunk to avoid overlapping,which gives rise to relatively high curvature and low machining efficiency.This paper proposes a tool-path smoothing algorithm for serial industrial robots with 6 rotary(6R)joints by constructing asymmetrical Pythagorean-hodograph(PH)splines.Firstly,symmetrical PH splines are initially constructed at transition corners to realize the third-order differential continuity of tool path position and tool orientation.Tool tip position smoothing errors are constrained by directly evaluating the control polygon length of spline according to the error tolerance in the workpiece coordinate system,while the tool orientation smoothing errors are constrained by adjusting control polygon length after converting tool orientation error to Euler angles using Jacobian matrix.Then asymmetrical splines are constructed by dealing with the spline overlapping problem,while guarantying the fully utilization of error tolerance to reduce spline curvature.The position and orientation are synchronized to the arc-length of the tool tip position to ensure the continuity of acceleration and jerk commands.The control points and arc-length of the constructed asymmetrical splines can all be solved analytically,which makes it suitable for on-line tool path smoothing.Experiments demonstrate that the proposed method achieves higher motion efficiency and lower tracking error than the existing symmetrical and asymmetrical tool path smoothing methods,which validates the advantages of the proposed method in high speed machining.
文摘A simple way of interpolation for real time processing is pres -ented. For passive localization, the time delay between two signals can be determined by the peak of their cross-correlation. It is more efficient to estimate a cross-correlation function by the inverse FFT of the cross-spectral density. The original smapling rate is usually very low to reduce computation. The sampling rate of the cross-correlation so computed is too low to estimate satisfactorily and an interpolation procedure is therefore needed. The interpolation by zero augmented spectrum is concise, fast and accurate. The results of the computer simulation and real nuderwater signal processing are given in the paper.
文摘We discuss the definition and effectiveness of a Padé-type approximation to 2π-periodic finite Baire measures on [-π,π]. In the first two sections we recall the definitions and basic properties of the Padré-type approximants to harmonic functions in the unit disk and to L p -functions on the unit circle. Section 3 deals with the extension of these definitions and properties to a finite 2π-periodic Baire measure. Finally, section 4 is devoted to a study of the convergence of a sequence of such approximants, in the weak star topology of measures.
基金The works is supported by the National Natural Science Foundation of China(19871054)
文摘A variety of matrix rational interpolation problems include the partial realizationproblem for matrix power series and the minimal rational interpolation problem for generalmatrix functions.Several problems in circuit theory and digital filter design can also be re-duced to the solution of matrix rational interpolation problems[1—4].By means of thereachability and the observability indices of defined pairs of matrices,Antoulas,Ball,Kang and Willems solved the minimal matrix rational interpolation problem in[1].On
