焊缝跟踪精度对焊缝成形质量有很重要的影响,V型坡口是一种最常见的焊接接头。提出了一种提高激光视觉机器人跟踪V型坡口精度的软件措施,介绍了提取V型坡口中心亚像素级坐标的方法。采用多尺度的LOG(Laplacian of Gaussian)算子检测焊...焊缝跟踪精度对焊缝成形质量有很重要的影响,V型坡口是一种最常见的焊接接头。提出了一种提高激光视觉机器人跟踪V型坡口精度的软件措施,介绍了提取V型坡口中心亚像素级坐标的方法。采用多尺度的LOG(Laplacian of Gaussian)算子检测焊接坡口特征边缘,在分析图像灰度直方图的基础上选取适当的阈值进行二值化。用曲率极值的角点检测法从细化后的图像中提取焊接坡口中心点像素级图像坐标,然后对此点邻域的梯度值进行拉格朗日多项式插值求得亚像素级坐标。实验结果表明,该方法简单可行,能满足机器人焊缝跟踪的实时性要求。展开更多
In this paper,we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator △2u-a△u＋bu=Λρu,inΩRn,u｜Ω=uvΩ=0,where the constants a,b≥0.We obtain some estimates for the upper boun...In this paper,we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator △2u-a△u＋bu=Λρu,inΩRn,u｜Ω=uvΩ=0,where the constants a,b≥0.We obtain some estimates for the upper bounds of the （k＋1）-th eigenvalueΛ_k＋1 in terms of the first k eigenvalues.Moreover,these results contain some results for the biharmonic operator.展开更多
In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechani...In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.展开更多
Let P(∆)be a polynomial of the Laplace operator∆=n∑j=1∂^(2)∂x^(2)_(j) on R^(n).We prove the existence of a bounded right inverse of the differential operator P(∆)in the weighted Hilbert space with the Gaussian measur...Let P(∆)be a polynomial of the Laplace operator∆=n∑j=1∂^(2)∂x^(2)_(j) on R^(n).We prove the existence of a bounded right inverse of the differential operator P(∆)in the weighted Hilbert space with the Gaussian measure,i.e.,L^(2)(R^(n),e^(−|x|^(2))).展开更多
A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditi...A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<<dim(G).A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain.In this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so on.They give the general form of pre-processing matrix,theory and numerical test of GPA.The conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.展开更多
We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obt...We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.展开更多
In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are of...In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.展开更多
Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜...Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜·｜,dγ）, or the space （S, d, p）, where S - Rn×R＋ is the （ax ＋ b）-group, d is the left-invariant Riemannian metric and p is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces {Xs（Y））0〈s≤∞ and the BM0-type spaces {BM0（y, s）}0〈s≤∞. Let Hi（Y） be the known atomic Hardy space and L01（y） the subspace of f ∈ L1（Y） with integral 0. The authors prove that the dual space of Xs（Y） is SM0（Y,s） when s∈ （0, ∞）, Xs（Y） = H1（Y） when s ∈ （0, 1], and X∞（y） = L01（Y） （or L1（Y））. As applications, the authors show that if T is a linear operator bounded from H1 （Y） to L1 （Y） and from L1（y） to L1,∞（Y）, then for all r ∈ （1, ∞） and s ∈ （r, ∞], T is bounded from Xr（y） to the Lorentz space L1,8（y）, which applies to the Calderon-Zygmund operator on （Rn, ｜·｜,μ）, the imaginary powers of the 0rnstein-Uhlenbeck operator on （Rn, ｜·｜,dγ） and the spectral operator associated with the spectral multiplier on （S, d, p）. All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces.展开更多
We study the joint distributions of four random variables h(ω) (stopping time or optional time), location x(h), l(ω) (co-optional time) and location x(l) for Markov processes. Some distributions for d(≥3) -dimensio...We study the joint distributions of four random variables h(ω) (stopping time or optional time), location x(h), l(ω) (co-optional time) and location x(l) for Markov processes. Some distributions for d(≥3) -dimensional Brownian motion and the joint distribution of first exit and last exit locations for symmetric stable process are found.展开更多
Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detec...Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detect image edge. Vgroove center is extracted by corner detection of extremum curvature. Subpixel position is obtained by Lagarange polynomial interpolation algorithm. Experiment results show that the method is brief and applied, and is sufficient for the real time of robot welding by laser sensors.展开更多
Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, w...Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, where B is a Bn-operator. In this paper, we prove some generalization of this result which in particular yield-s some known polynomial inequalities as special. We also consider an operator Dαwhich maps a polynomial P（z） into DαP（z）：=nP（z）＋（α-z）P′（z） and obtain exten-sions and generalizations of a number of well-known Lq inequalities.展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
文摘焊缝跟踪精度对焊缝成形质量有很重要的影响,V型坡口是一种最常见的焊接接头。提出了一种提高激光视觉机器人跟踪V型坡口精度的软件措施,介绍了提取V型坡口中心亚像素级坐标的方法。采用多尺度的LOG(Laplacian of Gaussian)算子检测焊接坡口特征边缘,在分析图像灰度直方图的基础上选取适当的阈值进行二值化。用曲率极值的角点检测法从细化后的图像中提取焊接坡口中心点像素级图像坐标,然后对此点邻域的梯度值进行拉格朗日多项式插值求得亚像素级坐标。实验结果表明,该方法简单可行,能满足机器人焊缝跟踪的实时性要求。
基金supported by the National Natural Science Foundation of China(11001130)the NUST Research Funding(2010ZYTS064)supported by China Postdoctoral Science Foundation(20080430351)
文摘In this paper,we investigate the Dirichlet eigenvalue problem of fourth-order weighted polynomial operator △2u-a△u＋bu=Λρu,inΩRn,u｜Ω=uvΩ=0,where the constants a,b≥0.We obtain some estimates for the upper bounds of the （k＋1）-th eigenvalueΛ_k＋1 in terms of the first k eigenvalues.Moreover,these results contain some results for the biharmonic operator.
基金Project supported by the National Natural Science Foundation of China(Grant No.11775208)the Foundation for Young Talents at the College of Anhui Province,China(Grant Nos.gxyq2021210 and gxyq2019077)the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant Nos.KJ2020A0638 and 2022AH051586)。
文摘In our previous papers,the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics,and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform.The core function of the coordinate-momentum exchange operators in the addition law of fractional Fourier transform was analyzed too.In this paper,the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators(IWOP)are used to establish the entanglement fractional Fourier transform theory to the extent of quantum.A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.
文摘Let P(∆)be a polynomial of the Laplace operator∆=n∑j=1∂^(2)∂x^(2)_(j) on R^(n).We prove the existence of a bounded right inverse of the differential operator P(∆)in the weighted Hilbert space with the Gaussian measure,i.e.,L^(2)(R^(n),e^(−|x|^(2))).
基金supported by the Basic Research Plan on High Performance Computing of Institute of Software(No.ISCAS-PYFX-202302)the National Key R&D Program of China(No.2020YFB1709502)the Advanced Space Propulsion Laboratory of BICE and Beijing Engineering Research Center of Efficient and Green Aerospace Propulsion Technology(No.Lab ASP-2019-03)。
文摘A geometric intrinsic pre-processing algorithm(GPA for short)for solving largescale discrete mathematical-physical PDE in 2-D and 3-D case has been presented by Sun(in 2022–2023).Different from traditional preconditioning,the authors apply the intrinsic geometric invariance,the Grid matrix G and the discrete PDE mass matrix B,stiff matrix A satisfies commutative operator BG=GB and AG=GA,where G satisfies G^(m)=I,m<<dim(G).A large scale system solvers can be replaced to a more smaller block-solver as a pretreatment in real or complex domain.In this paper,the authors expand their research to 2-D and 3-D mathematical physical equations over more wide polyhedron grids such as triangle,square,tetrahedron,cube,and so on.They give the general form of pre-processing matrix,theory and numerical test of GPA.The conclusion that“the parallelism of geometric mesh pre-transformation is mainly proportional to the number of faces of polyhedron”is obtained through research,and it is further found that“commutative of grid mesh matrix and mass matrix is an important basis for the feasibility and reliability of GPA algorithm”.
基金supported by the Program for New Century Excellent Talents in University (Grant No. 06-0504)National Natural Science Foundation of China (Grant No. 10771153)
文摘We obtain some convergence properties concerning Faber polynomials and apply them to studying univalent functions with quasiconformal extensions. In particular, by introducing an operator on the usual l2 space, we obtain some new characterizations of quasiconformal extendablity and asymptotic conformality for univalent functions.
文摘In electrical circuit analysis, it is often necessary to find the set of all direct current （d.c.） operating points （either voltages or currents） of nonlinear circuits. In general, these nonlinear equations are often represented as polynomial systems. In this paper, we address the problem of finding the solutions of nonlinear electrical circuits, which are modeled as systems of n polynomial equations contained in an n-dimensional box. Branch and Bound algorithms based on interval methods can give guaranteed enclosures for the solution. However, because of repeated evaluations of the function values, these methods tend to become slower. Branch and Bound algorithm based on Bernstein coefficients can be used to solve the systems of polynomial equations. This avoids the repeated evaluation of function values, but maintains more or less the same number of iterations as that of interval branch and bound methods. We propose an algorithm for obtaining the solution of polynomial systems, which includes a pruning step using Bernstein Krawczyk operator and a Bernstein Coefficient Contraction algorithm to obtain Bernstein coefficients of the new domain. We solved three circuit analysis problems using our proposed algorithm. We compared the performance of our proposed algorithm with INTLAB based solver and found that our proposed algorithm is more efficient and fast.
基金Supported by National Natural Science Foundation of China （Grant No. 10871025）
文摘Let （y, d, dλ） be （Rn, ｜·｜,μ）, where ｜·｜ is the Euclidean distance, μ is a nonnegative Radon measure on Rn satisfying the polynomial growth condition, or the Gauss measure metric space （Rn, ｜·｜,dγ）, or the space （S, d, p）, where S - Rn×R＋ is the （ax ＋ b）-group, d is the left-invariant Riemannian metric and p is the right Haar measure on S with exponential growth. In this paper, the authors introduce and establish some properties of the atomic Hardy-type spaces {Xs（Y））0〈s≤∞ and the BM0-type spaces {BM0（y, s）}0〈s≤∞. Let Hi（Y） be the known atomic Hardy space and L01（y） the subspace of f ∈ L1（Y） with integral 0. The authors prove that the dual space of Xs（Y） is SM0（Y,s） when s∈ （0, ∞）, Xs（Y） = H1（Y） when s ∈ （0, 1], and X∞（y） = L01（Y） （or L1（Y））. As applications, the authors show that if T is a linear operator bounded from H1 （Y） to L1 （Y） and from L1（y） to L1,∞（Y）, then for all r ∈ （1, ∞） and s ∈ （r, ∞], T is bounded from Xr（y） to the Lorentz space L1,8（y）, which applies to the Calderon-Zygmund operator on （Rn, ｜·｜,μ）, the imaginary powers of the 0rnstein-Uhlenbeck operator on （Rn, ｜·｜,dγ） and the spectral operator associated with the spectral multiplier on （S, d, p）. All these results generalize the corresponding results of Sweezy, Abu-Shammala and Torchinsky on Euclidean spaces.
基金Project supported by the Chinese National Tian Yuan Science Foundation.
文摘We study the joint distributions of four random variables h(ω) (stopping time or optional time), location x(h), l(ω) (co-optional time) and location x(l) for Markov processes. Some distributions for d(≥3) -dimensional Brownian motion and the joint distribution of first exit and last exit locations for symmetric stable process are found.
基金This work is financially supported by National Nature Science Foundation of China (Grant No. 50175027).
文摘Subpixel accuracy for V-groove center in robot welding is researched and a software measure to increase the accuracy of seam tracking by laser is presented. LOG （ Laplacian of Gaussian ） operator is adopted to detect image edge. Vgroove center is extracted by corner detection of extremum curvature. Subpixel position is obtained by Lagarange polynomial interpolation algorithm. Experiment results show that the method is brief and applied, and is sufficient for the real time of robot welding by laser sensors.
文摘Let Pn be the class of polynomials of degree at most n. Rather and Shah [15] proved that if P∈Pn and P（z） 6=0 in｜z｜〈1, then for every R〉0 and 0≤q〈∞,｜B[P（Rz）]｜q≤｜RnB[zn]＋λ0｜q｜1＋zn｜q ｜P（z）｜q, where B is a Bn-operator. In this paper, we prove some generalization of this result which in particular yield-s some known polynomial inequalities as special. We also consider an operator Dαwhich maps a polynomial P（z） into DαP（z）：=nP（z）＋（α-z）P′（z） and obtain exten-sions and generalizations of a number of well-known Lq inequalities.
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘In this paper, we present several expansions of the symbolic operator （1 ＋E）^x. Moreover, we derive some series transforms formulas and the Newton generating functions of {f（k）}.
