In this paper, four aspects of particular characteristics of Applied Mathematics different from those of Pure Mathematics are summarized by comparison. These aspects concern the origin of problems, method of problem s...In this paper, four aspects of particular characteristics of Applied Mathematics different from those of Pure Mathematics are summarized by comparison. These aspects concern the origin of problems, method of problem solving, confirmation of results, and development of new methods.展开更多
In this paper we give the results of the qualitative investigation of Bruslator’s differential equation: Lefever, Nicolis and Prigogine have pointed out that the Eq. (1) describes the simplest and the most fundamenta...In this paper we give the results of the qualitative investigation of Bruslator’s differential equation: Lefever, Nicolis and Prigogine have pointed out that the Eq. (1) describes the simplest and the most fundamental mathematical model of oscillations in biochemistry. They have proved that the Eq. (1) possesses the stable limit cycle under the展开更多
In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global gen...In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global general solutions of normal polynomial systems, and obtain their representation theorem. Finally, we give some applications of the theorem.展开更多
Ⅰ. PROBLEM AND RESULTS In physics, in order to describe a motion mathematically one needs a space-time reference system ∑(x, y z; t). From the mathematical point of view, any two reference systems are equivalent, on...Ⅰ. PROBLEM AND RESULTS In physics, in order to describe a motion mathematically one needs a space-time reference system ∑(x, y z; t). From the mathematical point of view, any two reference systems are equivalent, one only needs a transformation between the coordinates of the two systems.展开更多
Ⅰ. PROBLEM AND RESULTS In our previous paper general description of DEPS is given, and as an example concrete results of the system of the Bautin type are given in (2)However, the number of parameters of the Bautin t...Ⅰ. PROBLEM AND RESULTS In our previous paper general description of DEPS is given, and as an example concrete results of the system of the Bautin type are given in (2)However, the number of parameters of the Bautin type is reduced by one using a special rotation, although it is inconvenient for general purposes.展开更多
A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be appl...A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.展开更多
In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet tr...In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.展开更多
文摘In this paper, four aspects of particular characteristics of Applied Mathematics different from those of Pure Mathematics are summarized by comparison. These aspects concern the origin of problems, method of problem solving, confirmation of results, and development of new methods.
文摘In this paper we give the results of the qualitative investigation of Bruslator’s differential equation: Lefever, Nicolis and Prigogine have pointed out that the Eq. (1) describes the simplest and the most fundamental mathematical model of oscillations in biochemistry. They have proved that the Eq. (1) possesses the stable limit cycle under the
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, using the Strong Rooted Theorem of complex polynomial systems we prove the existence of global general solutions of a class of complex polynomial systems, discuss the qualitative structure of global general solutions of normal polynomial systems, and obtain their representation theorem. Finally, we give some applications of the theorem.
文摘Ⅰ. PROBLEM AND RESULTS In physics, in order to describe a motion mathematically one needs a space-time reference system ∑(x, y z; t). From the mathematical point of view, any two reference systems are equivalent, one only needs a transformation between the coordinates of the two systems.
文摘Ⅰ. PROBLEM AND RESULTS In our previous paper general description of DEPS is given, and as an example concrete results of the system of the Bautin type are given in (2)However, the number of parameters of the Bautin type is reduced by one using a special rotation, although it is inconvenient for general purposes.
基金This work is supported by the National Science Fund of Peop1e's Republic of China
文摘A thorough investigation of the systemd^2y(x):dx^2+p(x)y(x)=0with periodic impulse coefficientsp(x)={1,0≤x<x_0(2π>0> -η, x_0≤x<2π(η>p(x)=p(x+2π),-∞<x<∞is given, and the method can be applied to one with other periodic impulse coefficients.
基金This project is supported by the National Natural Science Foundation of China
文摘In this paper, the topological of integral surfaces near certain of Lyapunov type singularpoints and certain type of nodes of ordinary differential equations in complex domain are studied.We introduce Briot-Bouquet transformation, in order to study the topological structure of integralsurfaces near higher order singular points. At last we give an estimate of the makimum numberof isolated limit integral surfaces passing through certain type of higher order singular points.
