The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic ma...The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.展开更多
In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular famil...In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.展开更多
We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yi...We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yimen, and Luquan, were selected and their attenuations of P and S waves were measured by using the extended coda-normalization method. The six stations were classified into three regions according to their location, that is, Baoshan area, Yongsheng-Lijiang-Heqing (YLH) area and Luquan-Yimen (LY) area. The values of QS-1 and QP-1 are expressed as QS-1=0.00867 f-0.86, QP-1=0.01155 f-0.93, QS-1=0.01824 f-0.92, QP-1=0.02288 f-0.92, and QS-1=0.01647 f-0.91, QP-1=0.02826 f-0.97 in Baoshan, YLH, LY areas respectively. The attenuation of YLH, LY are closer to each other, however, Baoshan area is apparently lower. Comparing attenuation in the three areas with other areas of the world using the same method, it is suggested that the attenuations of P and S waves in YLH and LY areas are close to Kanto of Japan, but much higher than southeast of South Korea. The QS-1 and QP-1 in Baoshan area are slightly higher than southeastern South Korea. Furthermore, the results indicate that our QS-1 in Yunnan area is close to others by analyzing the coda attenuation.展开更多
The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s...The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.展开更多
This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's ...This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.展开更多
This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic an...This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic analysis is based on the representation of initial encryption algorithm as a system of multivariate quadratic equations, which define relations between a secret key and a cipher text. Extended linearization method is evaluated as a method for solving the nonlinear sys- tem of equations.展开更多
We discuss the basic concept of compartmental modelling in pharmacokinetics and demonstrate that all the solutions admitted by multi-compartment models of classical pharmacokinetics are expressed as linear combination...We discuss the basic concept of compartmental modelling in pharmacokinetics and demonstrate that all the solutions admitted by multi-compartment models of classical pharmacokinetics are expressed as linear combinations of exponential functions of time.This lends itself to data analysis that depends on fitting exponential functions to finite size sets.A mathematical method developed a long time ago to deal with this type of problem is called Prony’s method.We discuss the usefulness of this method in pharmacokinetic modeling and apply it to a particular data set obtained for the drug mibefradil.In spite of the method’s power in dealing with well-behaved data sets,we indicate the existence of severe limitations since real concentration curves coming from pharmacokinetic data are seldom purely exponential.展开更多
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
基金Project supported by the National Natural Science Foundation of China(Nos.11202136,11372195,11502147,and 11602146)
文摘The dynamic stability of axially moving viscoelastic Rayleigh beams is pre- sented. The governing equation and simple support boundary condition are derived with the extended Hamilton＇s principle. The viscoelastic material of the beams is described as the Kelvin constitutive relationship involving the total time derivative. The axial tension is considered to vary longitudinally. The natural frequencies and solvability condition are obtained in the multi-scale process. It is of interest to investigate the summation parametric resonance and principal parametric resonance by using the Routh-Hurwitz criterion to obtain the stability condition. Numerical examples show the effects of viscos- ity coefficients, mean speed, beam stiffness, and rotary inertia factor on the summation parametric resonance and principle parametric resonance. The differential quadrature method （DQM） is used to validate the value of the stability boundary in the principle parametric resonance for the first two modes.
基金The first author is partially supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research as part of the Collaboratory on Mathematics for Mesoscopic Modeling of Materials under Award Number DE-SC-0009249, and the Key Program of National Natural Science Foundation of China with Grant No. 91430215. The second author is supported by State Key Laboratory of Scientific and Engineering Computing （LSEC）, National Center for Mathematics and Interdisciplinary Sciences of Chinese Academy of Sciences （NCMIS）, and National Natural Science Foundation of China with Grant No. 11471026 he is thankful to the Center for Computational Mathematics and Applications, the Pennsylvania State University, where he worked on this manuscript as a visiting scholar. The authors are grateful to Professor Jinchao Xu, Dr. Yuanming Xiao and Dr. Maximilian Metti for their valuable suggestions and discussions, to Professor Haijun Wu for his valuable help on preparing the numerical example, and to the anonymous referee for the valuable comments and suggestion which lead to improvements of the paper.
文摘In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.
基金The specialized fund for pre-study of national key basic study (2002CCD01700)national key project of science and technology from China Ministry of Science and Technology during the 10th Five-year Plan (2004BA601B01-04-03)
文摘We analyzed digital seismogram data of 5668 earthquakes that occurred in Yunnan region between July of 1999 and December of 2003. Among the 22 seismic stations, six ones, namely Baoshan, Yongsheng, Lijiang, Heqing, Yimen, and Luquan, were selected and their attenuations of P and S waves were measured by using the extended coda-normalization method. The six stations were classified into three regions according to their location, that is, Baoshan area, Yongsheng-Lijiang-Heqing (YLH) area and Luquan-Yimen (LY) area. The values of QS-1 and QP-1 are expressed as QS-1=0.00867 f-0.86, QP-1=0.01155 f-0.93, QS-1=0.01824 f-0.92, QP-1=0.02288 f-0.92, and QS-1=0.01647 f-0.91, QP-1=0.02826 f-0.97 in Baoshan, YLH, LY areas respectively. The attenuation of YLH, LY are closer to each other, however, Baoshan area is apparently lower. Comparing attenuation in the three areas with other areas of the world using the same method, it is suggested that the attenuations of P and S waves in YLH and LY areas are close to Kanto of Japan, but much higher than southeast of South Korea. The QS-1 and QP-1 in Baoshan area are slightly higher than southeastern South Korea. Furthermore, the results indicate that our QS-1 in Yunnan area is close to others by analyzing the coda attenuation.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61571355,61801349,and 61601355)
文摘The scattering characteristics of the periodic surface of infinite and finite media are investigated in detail.The Fourier expression of the scattering field of the periodic surface is obtained in terms of Huygens’ s principle and Floquet’s theorem.Using the extended boundary condition method(EBCM) and T-matrix method, the scattering amplitude factor is solved,and the correctness of the algorithm is verified by use of the law of conservation of energy.The scattering cross section of the periodic surface in the infinitely long region is derived by improving the scattering cross section of the finite period surface.Furthermore, the effects of the incident wave parameters and the geometric structure parameters on the scattering of the periodic surface are analyzed and discussed.By reasonable approximation, the scattering calculation methods of infinite and finite long surfaces are unified.Besides, numerical results show that the dielectric constant of the periodic dielectric surface has a significant effect on the scattering rate and transmittance.The period and amplitude of the surface determine the number of scattering intensity peaks, and, together with the incident angle, influence the scattering intensity distribution.
文摘This paper presents a new approach for solving a class of infinite horizon nonlinear optimal control problems (OCPs).In this approach,a nonlinear two-point boundary value problem (TPBVP),derived from Pontryagin's maximum principle,is transformed into a sequence of linear time-invariant TPBVPs.Solving the latter problems in a recursive manner provides the optimal control law and the optimal trajectory in the form of uniformly convergent series.Hence,to obtain the optimal solution,only the techniques for solving linear ordinary differential equations are employed.An efficient algorithm is also presented,which has low computational complexity and a fast convergence rate.Just a few iterations are required to find an accurate enough suboptimal trajectory-control pair for the nonlinear OCP.The results not only demonstrate the efficiency,simplicity,and high accuracy of the suggested approach,but also indicate its effectiveness in practical use.
文摘This paper observes approaches to algebraic analysis of GOST 28147-89 encryption algorithm (also known as simply GOST), which is the basis of most secure information systems in Russia. The general idea of algebraic analysis is based on the representation of initial encryption algorithm as a system of multivariate quadratic equations, which define relations between a secret key and a cipher text. Extended linearization method is evaluated as a method for solving the nonlinear sys- tem of equations.
文摘We discuss the basic concept of compartmental modelling in pharmacokinetics and demonstrate that all the solutions admitted by multi-compartment models of classical pharmacokinetics are expressed as linear combinations of exponential functions of time.This lends itself to data analysis that depends on fitting exponential functions to finite size sets.A mathematical method developed a long time ago to deal with this type of problem is called Prony’s method.We discuss the usefulness of this method in pharmacokinetic modeling and apply it to a particular data set obtained for the drug mibefradil.In spite of the method’s power in dealing with well-behaved data sets,we indicate the existence of severe limitations since real concentration curves coming from pharmacokinetic data are seldom purely exponential.
