Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time mi...Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.展开更多
In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic found...The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.展开更多
<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensio...<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>展开更多
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a gre...A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a great number of rotational spectra of even-even nu-clei in rare-earth and actinides region show that the formula is the best one among all two-pa-rameter formulas. It is pointed out that this formula can be applied to the spin assignment forsuperdeformed band.展开更多
The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement wi...The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.展开更多
Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual wo...Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles, three boundary integral equations which fit for arbitrary shapes, loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods.展开更多
The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which ...The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.展开更多
This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Ber...This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.展开更多
The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved li...The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.展开更多
In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)meth...In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions.As a result,a general set of second-order ordinary differential equations emerges,and by appropriately setting the stiffness of the end springs,one can easily study the dynamics of various systems with classical or non-classical bound-ary conditions.The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions,elastic support parameters,elastic foundation parameters and fluid mass ratios.The numerical model is validated by comparison with published data.It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elas-tic foundation.The pipe stability performance is very sensitive to the two elastic foundation parameters.Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the diver-gence.展开更多
基金supported by the Important National Science&Technology Specific Projects(No.2011ZX05019-003)the New Method and Technology Research Project of Geophysical Exploration of CNPC(No.2014A-3612)
文摘Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
文摘The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.
文摘<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
基金The project supported by the National Natural Scicnce Foundation of China CCAST (World Lab)
文摘A new two-parameter formula for the rotational spectra of well deformed nuclei isproposed. The formula is deduced from experimental level systematics and alternatively fromnuclear hydrodynamics. Comparisons with a great number of rotational spectra of even-even nu-clei in rare-earth and actinides region show that the formula is the best one among all two-pa-rameter formulas. It is pointed out that this formula can be applied to the spin assignment forsuperdeformed band.
文摘The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.
文摘Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles, three boundary integral equations which fit for arbitrary shapes, loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods.
基金Supported by the NNSF of China（70471057）Supported by the Natural Science Foundation of the Education Department of Shannxi Province（03JK065）
文摘The empirical Bayes test problem is considered for scale parameter of twoparameter exponential distribution under type-II censored data.By using wavelets estimation method,the EB test function is constructed,of which the asymptotic optimality and convergence rates are obtained.Finally,an example concerning the main result is given.
文摘This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.
文摘The two-parameter exponential distribution is proposed to be an underlying model,and prediction bounds for future observations are obtained by using Bayesian approach.Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type Ⅱ doubly censored samples.A numerical example is given to illustrate the procedures,prediction intervals are investigated via Monte Carlo method,and the accuracy of prediction intervals is presented.
文摘In this study,the vibration stability of fluid conveying pipe resting on two-parameter foundation is in-vestigated under four different elastic support boundary conditions.The harmonic differential quadrature(HDQ)method is applied to solve the governing vibration equation derived based on Euler–Bernoulli beam theory subject to the elastic foundation and boundary conditions.As a result,a general set of second-order ordinary differential equations emerges,and by appropriately setting the stiffness of the end springs,one can easily study the dynamics of various systems with classical or non-classical bound-ary conditions.The numerical simulations are conducted to study the pipe instability performance with respect to various boundary conditions,elastic support parameters,elastic foundation parameters and fluid mass ratios.The numerical model is validated by comparison with published data.It is found that the elastic support boundary conditions have significant effects on the stability of pipe resting on elas-tic foundation.The pipe stability performance is very sensitive to the two elastic foundation parameters.Larger fluid mass ratio enhances the pipe flutter stability performance but has no effects on the diver-gence.
