Radon transform is to use the speed difference between primary wave and multiple wave to focus the difference on different"points"or"lines"in Radon domain,so as to suppress multiple wave.However,th...Radon transform is to use the speed difference between primary wave and multiple wave to focus the difference on different"points"or"lines"in Radon domain,so as to suppress multiple wave.However,the limited migration aperture,discrete sampling,and AVO characteristics of seismic data all will weaken the focusing characteristics of Radon transform.In addition,the traditional Radon transform does not take into account the AVO characteristics of seismic data,and uses L1 Norm,the approximate form of L0 Norm,to improve the focusing characteristics of Radon domain,which requires a lot of computation.In this paper,we combine orthogonal polynomials with the parabolic Radon transform(PRT)and find that the AVO characteristics of seismic data can be fitted with orthogonal polynomial coefficients.This allows the problem to be transformed into the frequency domain by Fourier transform and introduces a new variable,lambda,combining frequency and curvature.Through overall sampling of lambda,the PRT operator only needs to be calculated once for each frequency,yielding higher computational efficiency.The sparse solution of PRT under the constraints of the smoothed L0 Norm(SL0)obtained by the steepest descent method and the gradient projection principle.Synthetic and real examples are given to demonstrate that the proposed method has This method has advantages in improving the Radon focusing characteristics than does the PRT based on L1 norm.展开更多
In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smoo...In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.展开更多
Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Eucl...Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.展开更多
Let P(t) be a product of(possibly repeated) linear factors over Q and K/Q an abelian extension. Under a strict condition, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the ...Let P(t) be a product of(possibly repeated) linear factors over Q and K/Q an abelian extension. Under a strict condition, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one for any smooth proper model of the variety over Q defined by P(t) = NK/Q(x).展开更多
We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded...We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.展开更多
Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means...Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.展开更多
基金funded by the National Natural Science Foundation of China(No.41774133)major national science and technology projects(No.2016ZX05024-003 and 2016ZX05026-002-002)the talent introduction project of China University of Petroleum(East China)(No.20180041)
文摘Radon transform is to use the speed difference between primary wave and multiple wave to focus the difference on different"points"or"lines"in Radon domain,so as to suppress multiple wave.However,the limited migration aperture,discrete sampling,and AVO characteristics of seismic data all will weaken the focusing characteristics of Radon transform.In addition,the traditional Radon transform does not take into account the AVO characteristics of seismic data,and uses L1 Norm,the approximate form of L0 Norm,to improve the focusing characteristics of Radon domain,which requires a lot of computation.In this paper,we combine orthogonal polynomials with the parabolic Radon transform(PRT)and find that the AVO characteristics of seismic data can be fitted with orthogonal polynomial coefficients.This allows the problem to be transformed into the frequency domain by Fourier transform and introduces a new variable,lambda,combining frequency and curvature.Through overall sampling of lambda,the PRT operator only needs to be calculated once for each frequency,yielding higher computational efficiency.The sparse solution of PRT under the constraints of the smoothed L0 Norm(SL0)obtained by the steepest descent method and the gradient projection principle.Synthetic and real examples are given to demonstrate that the proposed method has This method has advantages in improving the Radon focusing characteristics than does the PRT based on L1 norm.
文摘In freeform surface modelling, developable surfaces have much application value. But, in 3D space, there is not always a regular developable surface which interpolates the given boundary of an arbitrary piecewise smooth closed curve. In this paper, tensor product Bézier surfaces interpolating the closed curves are determined and the resulting surface is a minimum of the functional defined by the L2-integral norm of the Gaussian curvature. The Gaussian curvature of the surfaces is minimized by the method of solving nonlinear optimization problems. An improved approach trust-region form method is proposed. A simple application example is also given.
基金Project(JSPS.KAKENHI22560451) supported by the Japan Society for the Promotion of ScienceProject(69904003) supported by the National Natural Science Foundation of ChinaProject(YJ0267016) supported by the Advanced Ordnance Research Supporting Fund of China
文摘Let P（s, δ） be a sphere plant family described by the transfer function set where the coefficients of the denominator and numerator polynomials are affine in a real uncertain parameter vector δ satisfying the Euclidean norm constraint ｜｜δ｜｜〈δ. The concept of stabilizability radius of P（s, δ） is introduced which is the norm bound δs for δ such that every member plant of P（s, δ） is stabilizable if and only if ｜｜δ｜｜〈δs. The stabilizability radius can be simply interpreted as the ＇largest sphere＇ around the nominal plant P（s,θ） such that P（s, δ） is stabilizable. The numerical method and the analytical method are presented to solve the stabilizability radius calculation problem of the sphere plants.
文摘Let P(t) be a product of(possibly repeated) linear factors over Q and K/Q an abelian extension. Under a strict condition, we show that the Brauer-Manin obstruction to the Hasse principle and weak approximation is the only one for any smooth proper model of the variety over Q defined by P(t) = NK/Q(x).
基金supported by National Natural Science Foundation of China(Grant No.11071119)
文摘We discuss the relationship between the frequency and the growth of H-harmonic functions on the Heisenberg group.Precisely,we prove that an H-harmonic function must be a polynomial if its frequency is globally bounded.Moreover,we show that a class of H-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.
基金supported by the National Natural Science Foundation of China(Grant No.51175425)the Special Research Fund for the Doctoral Program of Higher Education of China(Grant No.20116102110003)
文摘Two revised regional importance measures(RIMs),that is,revised contribution to variance of sample mean(RCVSM)and revised contribution to variance of sample variance(RCVSV),are defined herein by using the revised means of sample mean and sample variance,which vary with the reduced range of the epistemic parameter.The RCVSM and RCVSV can be computed by the same set of samples,thus no extra computational cost is introduced with respect to the computations of CVSM and CVSV.From the plots of RCVSM and RCVSV,accurate quantitative information on variance reductions of sample mean and sample variance can be read because of reduced upper bound of the range of the epistemic parameter.For general form of quadratic polynomial output,the analytical solutions of the original and the revised RIMs are given.Numerical example is employed and results demonstrate that the analytical results are consistent and accurate.An engineering example is applied to testify the validity and rationality of the revised RIMs,which can give instructions to the engineers about how to reduce variance of sample mean and sample variance by reducing the range of epistemic parameters.
