The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason t...The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason to its scientific reason. Its essential ideas stem from the people-centered theory, the view of happiness in the material- purposed theory, the communist life style, the material hegemonist principle, and the rational action principles of economic technology. In the 21st century, in order to deal with the dangerous situation of human beings’ exist- ence from the root, the philosophy of the limitation theory must be established, which has the eco-reason as the value support, integrates all the original wisdom of human beings and reflects human’s spiritual needs of the age as well as the direction of human future development. The whole percept of this new philosophy is that “all things have souls”; its basic law of existence is “the ceaseless life circle”; its survival goal is the view of happiness in the harmony of material and spirit; its social action guidance and principle are (environment, society, humanity) the environment ecologism and the integral-and-mutual action principle (of human beings &society, individual &society, and present age & posterity).展开更多
In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We ...In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.展开更多
In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit...In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit cycles can be located by our theorems. Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or 'nth order compatible with each other' or 'nth order contained in each other'.展开更多
Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler c...Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.展开更多
In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is hon...In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is honest and thus unique. We then further show that this honest Feller minimum process is not only positive recurrent but also strongly ergodic. The generating function of the important stationary distribution is explicitly expressed. For the interest of comparison and completeness, the results of the Markov branching processes with killing and instantaneous resurrection are also briefly stated. A new result regarding strong ergodicity of this difficult case is presented. The birth and death process with killing and resurrection together with another example is also analyzed.展开更多
A predator-prey system is investigated for the global stability and existences of limit cycleand at least two limit cycles by using qualitative analysis and the idea of Poincare'-BendixsonTheoy.
文摘The philosophical root of all human beings’ existence crisis in the contemporary times is the philosophy of the unlimited theory. The inner spiritual supporting force is the construction from its theoretical reason to its scientific reason. Its essential ideas stem from the people-centered theory, the view of happiness in the material- purposed theory, the communist life style, the material hegemonist principle, and the rational action principles of economic technology. In the 21st century, in order to deal with the dangerous situation of human beings’ exist- ence from the root, the philosophy of the limitation theory must be established, which has the eco-reason as the value support, integrates all the original wisdom of human beings and reflects human’s spiritual needs of the age as well as the direction of human future development. The whole percept of this new philosophy is that “all things have souls”; its basic law of existence is “the ceaseless life circle”; its survival goal is the view of happiness in the harmony of material and spirit; its social action guidance and principle are (environment, society, humanity) the environment ecologism and the integral-and-mutual action principle (of human beings &society, individual &society, and present age & posterity).
文摘In this paper, we discuss the limit cycles of the systemdx/dt=y·[1+(A(x)]oy/dt=(-x+δy+α_1x^2+α_2xy+α_5x^2y)[1+B(x)] (1)where A(x)=sum form i=1 to n(a_ix~), B(x)=sum form j=1 to m(β_jx^j) and 1+B(x)>0. We prove that (1) possesses at most one limit cycle and give out the necessary and sufficient conditions of existence and uniqueness of limit cycles.
文摘In this paper, we have proved several theorems which guarantee that the Lienard equation has at least one or n limit cycles without using the traditional assumption G Thus some results in [3-5] are extended. The limit cycles can be located by our theorems. Theorems 3 and 4 give sufficient conditions for the existence of n limit cycles having no need of the conditions that the function F(x) is odd or 'nth order compatible with each other' or 'nth order contained in each other'.
文摘Liénard’s equation is a kind of important ordinary differential equations frequently appearing in engineering and technology, and hence receives great attention of many mathematicians. In 1949, H. J. Eckweiler conjectured that the equation +μsin+x=0 has infinite number of limit cycles. Then H. S. Hochstadt and B. Stephan, R. N. D’Heedene and others proved that this equation has at least n limit cycles in the interval |x|<(n+1)π for specified parameter μ. In 1980, Professor Zhang Zhifen proved that this equation has exact n limit cycles in the interval |x|<(n+1)π for any nonzero parameter μ, and thus pushed the related work forward greatly. In this paper, we shall prove that the Liénard’s equation has exact n limit cycles in a finite interval under a class of very general condition.
基金Xiangtan University New Staff Research Start-up Grant (Grant No. 08QDZ27)
文摘In this paper, we consider Markov branching processes with killing and resurrection. We first show that the Markov branching process with killing and stable resurrection is just the Feller minimum process which is honest and thus unique. We then further show that this honest Feller minimum process is not only positive recurrent but also strongly ergodic. The generating function of the important stationary distribution is explicitly expressed. For the interest of comparison and completeness, the results of the Markov branching processes with killing and instantaneous resurrection are also briefly stated. A new result regarding strong ergodicity of this difficult case is presented. The birth and death process with killing and resurrection together with another example is also analyzed.
文摘A predator-prey system is investigated for the global stability and existences of limit cycleand at least two limit cycles by using qualitative analysis and the idea of Poincare'-BendixsonTheoy.
