This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

nowadays, right to environment, during constitutions, court decisions and administrative procedures, in internal public law have been identified and secured. the recognition of this right in public law is dependent on normative evolutions. with the promotion of the tight to environment in constitutional norms, we can speak about the real impact of the constitutionalization in contemporary publi...

this essay studies theory of lex mercatoria which is based on the assumption of existence of a third legal system along with the national and international legal systems regulating international commercial relations. for this purpose, the essay discusses the backgrounds of creation and emergence of the theory, its narrow and broad meaning, elements of which and the extent that it has been recog...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...

The nonlocal nonlinear buckling of a double layer graphene sheet (DLGS) covered by zinc oxide (ZnO) piezoelectric layers is investigated in this study. The surrounding circumstances of the system are considered as a Pasternak foundation including spring constants and a shear layer. Graphene sheets are subjected to longitudinal magnetic field and biaxial forces. On the other hand, the ZnO piezoe...