This paper generalizes the method of Ng6 and Winkler （2010, 2011） for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation （AODE） to the case of a higher orde...This paper generalizes the method of Ng6 and Winkler （2010, 2011） for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation （AODE） to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.展开更多
By integrating photoinduced electron transfer（PET） into the design of functional bioluminogenic probes,Urano and his coworkers recently developed a new rational design strategy, BioLeT. It is expected that this BioL...By integrating photoinduced electron transfer（PET） into the design of functional bioluminogenic probes,Urano and his coworkers recently developed a new rational design strategy, BioLeT. It is expected that this BioLeT strategy will enable us to design and develop new bioluminescence probes for detecting various biomolecules with no catalytic or reactive activity.展开更多
We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its...We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.展开更多
基金supported by the Austrian Science Foundation(FWF) via the Doctoral Program "Computational Mathematics" under Grant No.W1214Project DK11,the Project DIFFOP under Grant No.P20336-N18+2 种基金the SKLSDE Open Fund SKLSDE-2011KF-02the National Natural Science Foundation of China under Grant No.61173032the Natural Science Foundation of Beijing under Grant No.1102026,and the China Scholarship Council
文摘This paper generalizes the method of Ng6 and Winkler （2010, 2011） for finding rational general solutions of a first order non-autonomous algebraic ordinary differential equation （AODE） to the case of a higher order AODE, provided a proper parametrization of its solution hypersurface. The authors reduce the problem of finding the rational general solution of a higher order AODE to finding the rational general solution of an associated system. The rational general solutions of the original AODE and its associated system are in computable 1-1 correspondence. The authors give necessary and sufficient conditions for the associated system to have a rational solution based on proper reparametrization of invariant algebraic space curves. The authors also relate invariant space curves to first integrals and characterize rationally solvable systems by rational first integrals.
基金Financial support from the National Program on Key Basic Research Project(No.2013CB734000)the Program of New Century Excellent Talents in University(No.NCET-11-0306)+1 种基金the Shandong Natural Science Foundation(No.JQ201019)the Fundamental Research Funds of Shandong University(No.2014JC008)
文摘By integrating photoinduced electron transfer（PET） into the design of functional bioluminogenic probes,Urano and his coworkers recently developed a new rational design strategy, BioLeT. It is expected that this BioLeT strategy will enable us to design and develop new bioluminescence probes for detecting various biomolecules with no catalytic or reactive activity.
基金partially supported by a MINECO-FEDER(Grant No.MTM2016-77278-P)a MINECO(Grant No.MTM2013-40998-P)+1 种基金an AGAUR(Grant No.2014SGR-568)partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
