The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine ...The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.展开更多
A close study of Heisenberg uncertainty principles reveals many significant facts,and all four major physical quantities,energy,time,momentum and length,have both lower and upper limits.Now,many questions come up.What...A close study of Heisenberg uncertainty principles reveals many significant facts,and all four major physical quantities,energy,time,momentum and length,have both lower and upper limits.Now,many questions come up.What are these limits?Some answers may lead to the understanding of the development of our universe.What is the shortest limit of time?At the beginning of big bang,there exists a tre-mendously short time,the Planck time.This may be just the shortest time limit in our universe.The longest time limit might be the lifetime of our universe.The longest length might be the final diameter of our expanding universe.All these lead to a finite universe.Two more coupling formulae are formed for the other two pairs of physical quantities,mass and speed,thermal energy and temperature.These four physical quantities must also have limits.We already knew that speed has upper limit and temperature has lower limit.By these two formulae,Planck and Einstein equations are derived directly.Since most other physical quantities are somewhat related to these major physical quantities,it seems that there exists a principle of limitation of physical quantities.A quantitative sketch of big bang is described.It also shows that our universe will contract back to another big bang.The principle of limitation opens up some fields of investigation.It may bring nature back to the harmony and determined world described by classical physics.展开更多
This paper presents an analysis of a paper entitled"Principle of limitation of physical quantities and cyclic universe"and proposes different results for some formulae from that report.In addition,this paper...This paper presents an analysis of a paper entitled"Principle of limitation of physical quantities and cyclic universe"and proposes different results for some formulae from that report.In addition,this paper shows that the principle of limits coupling may lead to an approximation of current theories(i.e.,quantum theory and relativistic theory),which have interesting correlations with the Plank formula and the special theory of relativity.展开更多
基金Supported by Science Fund of the Education Departmentof Guangxi province( 2 0 0 3) and the NationalNatural Science Foundation of China( 1 0 361 0 0 3)
文摘The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.
文摘A close study of Heisenberg uncertainty principles reveals many significant facts,and all four major physical quantities,energy,time,momentum and length,have both lower and upper limits.Now,many questions come up.What are these limits?Some answers may lead to the understanding of the development of our universe.What is the shortest limit of time?At the beginning of big bang,there exists a tre-mendously short time,the Planck time.This may be just the shortest time limit in our universe.The longest time limit might be the lifetime of our universe.The longest length might be the final diameter of our expanding universe.All these lead to a finite universe.Two more coupling formulae are formed for the other two pairs of physical quantities,mass and speed,thermal energy and temperature.These four physical quantities must also have limits.We already knew that speed has upper limit and temperature has lower limit.By these two formulae,Planck and Einstein equations are derived directly.Since most other physical quantities are somewhat related to these major physical quantities,it seems that there exists a principle of limitation of physical quantities.A quantitative sketch of big bang is described.It also shows that our universe will contract back to another big bang.The principle of limitation opens up some fields of investigation.It may bring nature back to the harmony and determined world described by classical physics.
文摘This paper presents an analysis of a paper entitled"Principle of limitation of physical quantities and cyclic universe"and proposes different results for some formulae from that report.In addition,this paper shows that the principle of limits coupling may lead to an approximation of current theories(i.e.,quantum theory and relativistic theory),which have interesting correlations with the Plank formula and the special theory of relativity.
