Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of...Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.展开更多
This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L syst...This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L systems. We have also defined a classification of GL systems and proved a sufficient and necessary condition for the equivalence of two subclasses of GL systems: two GPDOL (a class of deterministic GL systems) systems L[ m1, m2, ??? mj] and L[ n1, n2, ??? nk] are e-quivalent, iff k = j and there exists a common divisor g of all mi and a common divisor h of all nj such that (?) i: mi/g = nj/h.展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 19971035).
文摘Systems of quasilinear first order PDE are studied in the framework of contact manifold. All of the local stable geometric solutions of such systems are classified by using versal deformation and the classification of stable map germs of type ∑1 in singularity theory.
基金This work was partially supported by Pre-973 Project 2001 CCA03000, the National Natural ScienceFoundation of China (Grant No. 69733020) Brain and Mind Foundation of the Chinese Academy of Sciences, Innovation Foundation of AMSS, IOM and ICT.
文摘This paper proposes the concept of generalized L systems, GL systems for short, which can describe asynchronized concurrent phenomena. We have proved that the GL systems are proper extensions of the traditional L systems. We have also defined a classification of GL systems and proved a sufficient and necessary condition for the equivalence of two subclasses of GL systems: two GPDOL (a class of deterministic GL systems) systems L[ m1, m2, ??? mj] and L[ n1, n2, ??? nk] are e-quivalent, iff k = j and there exists a common divisor g of all mi and a common divisor h of all nj such that (?) i: mi/g = nj/h.
