In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of th...In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of the papers [2] and [3].展开更多
We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordi...We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.展开更多
This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations)...This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations). In reversible reactions, Haldane relationship is considered to be identical for all mechanisms considered and reversible equations can be also obtained from this rela- tionship. Some reversible reactions of the metabolism are also presented, with their equilibrium constant.展开更多
This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of th...This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose. The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C++ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of nu-merical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark’s method to verify the results.展开更多
文摘In this paper Hill's equation is discussed. A new discriminant of Hill's equation is obtained, whose convergent rate is faster than that of traditional discriminant. The results obtained generalizes ones of the papers [2] and [3].
基金the National Natural Science Foundation of China(Grant Nos.10325102,10531010)the National Basic Research Program of China(Grant No.2006CB805903)Teaching and Research Award Program for Outstanding Young Teachers,Ministry of Education of China(2001)
文摘We will introduce a type of Fredholm operators which are shown to have a certain con- tinuity in weak topologies.From this,we will prove that the fundamental matrix solutions of k-th, k≥2,order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies.Consequently,Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies.Moreover,for the scalar Hill’s equations,Sturm-Liouville eigenvalues, periodic and anti-periodic eigenvalues,and rotation numbers are all continuous in potentials with weak topologies.These results will lead to many interesting variational problems.
文摘This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations). In reversible reactions, Haldane relationship is considered to be identical for all mechanisms considered and reversible equations can be also obtained from this rela- tionship. Some reversible reactions of the metabolism are also presented, with their equilibrium constant.
文摘This paper addresses the dynamic stability problem of columns and frames subjected to axially applied periodic loads. Such a structure can become unstable under certain combinations of amplitudes and frequencies of the imposed load acting on its columns/beams. These are usually shown in the form of plots which describe regions of instability. The finite element method (FEM) is used in this work to analyse dynamic stability problems of columns. Two-noded beam elements are used for this purpose. The periodic loading is decomposed into various harmonics using Fourier series expansion. Computer codes in C++ using object oriented concepts are developed to determine the stability regions of columns subjected to periodic loading. A number of nu-merical examples are presented to illustrate the working of the program. The direct integration of the equations of motions of the discretised system is carried out using Newmark’s method to verify the results.
