Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was...Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.展开更多
A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations...A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.展开更多
Several parameters are needed to describe the converted-wave （C-wave） moveout in processing multi-component seismic data, because of asymmetric raypaths and anisotropy. As the number of parameters increases, the con...Several parameters are needed to describe the converted-wave （C-wave） moveout in processing multi-component seismic data, because of asymmetric raypaths and anisotropy. As the number of parameters increases, the converted wave data processing and analysis becomes more complex. This paper develops a new moveout equation with two parameters for C-waves in vertical transverse isotropy （VTI） media. The two parameters are the C-wave stacking velocity （Vc2） and the squared velocity ratio （7v,i） between the horizontal P-wave velocity and C-wave stacking velocity. The new equation has fewer parameters, but retains the same applicability as previous ones. The applicability of the new equation and the accuracy of the parameter estimation are checked using model and real data. The form of the new equation is the same as that for layered isotropic media. The new equation can simplify the procedure for C-wave processing and parameter estimation in VTI media, and can be applied to real C-wave processing and interpretation. Accurate Vc2 and Yvti can be deduced from C-wave data alone using the double-scanning method, and the velocity ratio model is suitable for event matching between P- and C-wave data.展开更多
Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derive...Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.展开更多
Based on the conduction and transformation of the thermal infrared radiative transfer equation of water target,a twinchannel difference model(DM) was proposed to improve the calibration precision by conquering the lim...Based on the conduction and transformation of the thermal infrared radiative transfer equation of water target,a twinchannel difference model(DM) was proposed to improve the calibration precision by conquering the limitation that the atmospheric condition when image is acquiring cannot be truly obtained in the traditional radiometric simulation calibration method.The analysis of surface,atmosphere and top-of-atmosphere(TOA) radiative energy decomposition demonstrated that the apparent TOA radiance of the uncalibrated channel is the differential combination of two reference channels.The DM avoids impacts from atmospheric temperature and density.The only impact is from water vapor(WV) content.Based on the fitting error analysis of 742 mid-latitude atmospheric profiles(column WV content:0-5×10 3 atm cm) selected from TIGR database,the DM is insensitive to WV content.The maximum error is less than 0.2 K when the view zenith angels(VZAs) of reference channels and uncalibrated channel are less than 30.The error becomes 0.3 K when VZAs range from 30 to 40 and 0.6 K when VZAs are in 40-50.Because the uncertainty increases when VZAs are larger than 50,the best range of VZAs is 30-50.The vicarious calibration results at Lake Qinghai field indicated that the calibration precision of the DM cross-calibration by using MODIS bands 31 and 32 as reference channels to calibrate IRS band 08 is similar to that of vicarious calibration.Therefore,the DM is a reliable alternative tool for sensor on-orbit calibration and validation with high precision and frequency.展开更多
Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation wh...Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions(kink/antikink solitons, singular,periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.展开更多
文摘Aim To study a class of boundary value problem of hyperbolic partial functional differential equations with continuous deviating arguments. Methods An averaging technique was used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Results and Conclusion The known results of oscillation of solutions for a class of boundary value problem of hyperbolic partial functional differential equations with discrete deviating arguments are generalized, and the oscillatory criteria of solutions for such equation with two kinds of boundary value conditions are obtained.
基金supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province
文摘A new approach is presented by means of a new general ansitz and some relations among Jacobian elliptic functions, which enables one to construct more new exact solutions of nonlinear differential-difference equations. As an example, we apply this new method to Hybrid lattice, diseretized mKdV lattice, and modified Volterra lattice. As a result, many exact solutions expressible in rational formal hyperbolic and elliptic functions are conveniently obtained with the help of Maple.
基金sponsored by the National Natural Science Foundation of China(No.41074080)the National Science and Technology Major Project(No.2011ZX05019-008)+1 种基金the Science Foundation of China University of Petroleum-Beijing(No.KYJJ2012-05-11)the PetroChina Innovation Foundation(No.2012D-5006-0301)
文摘Several parameters are needed to describe the converted-wave （C-wave） moveout in processing multi-component seismic data, because of asymmetric raypaths and anisotropy. As the number of parameters increases, the converted wave data processing and analysis becomes more complex. This paper develops a new moveout equation with two parameters for C-waves in vertical transverse isotropy （VTI） media. The two parameters are the C-wave stacking velocity （Vc2） and the squared velocity ratio （7v,i） between the horizontal P-wave velocity and C-wave stacking velocity. The new equation has fewer parameters, but retains the same applicability as previous ones. The applicability of the new equation and the accuracy of the parameter estimation are checked using model and real data. The form of the new equation is the same as that for layered isotropic media. The new equation can simplify the procedure for C-wave processing and parameter estimation in VTI media, and can be applied to real C-wave processing and interpretation. Accurate Vc2 and Yvti can be deduced from C-wave data alone using the double-scanning method, and the velocity ratio model is suitable for event matching between P- and C-wave data.
基金The research is SUpported by the NatlOllal Science Foundation of China(No.10371096)
文摘Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid.
基金supported by the National Natural Science Foundation of China (Grant No. 40971227)the International Corporation Program of Science and Technology Ministry of China (Grant No. 2010DFA21880)
文摘Based on the conduction and transformation of the thermal infrared radiative transfer equation of water target,a twinchannel difference model(DM) was proposed to improve the calibration precision by conquering the limitation that the atmospheric condition when image is acquiring cannot be truly obtained in the traditional radiometric simulation calibration method.The analysis of surface,atmosphere and top-of-atmosphere(TOA) radiative energy decomposition demonstrated that the apparent TOA radiance of the uncalibrated channel is the differential combination of two reference channels.The DM avoids impacts from atmospheric temperature and density.The only impact is from water vapor(WV) content.Based on the fitting error analysis of 742 mid-latitude atmospheric profiles(column WV content:0-5×10 3 atm cm) selected from TIGR database,the DM is insensitive to WV content.The maximum error is less than 0.2 K when the view zenith angels(VZAs) of reference channels and uncalibrated channel are less than 30.The error becomes 0.3 K when VZAs range from 30 to 40 and 0.6 K when VZAs are in 40-50.Because the uncertainty increases when VZAs are larger than 50,the best range of VZAs is 30-50.The vicarious calibration results at Lake Qinghai field indicated that the calibration precision of the DM cross-calibration by using MODIS bands 31 and 32 as reference channels to calibrate IRS band 08 is similar to that of vicarious calibration.Therefore,the DM is a reliable alternative tool for sensor on-orbit calibration and validation with high precision and frequency.
文摘Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions(kink/antikink solitons, singular,periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
