Conformal and Contact Kinetic Dynamics and Their Geometrization

We propose a conformal generalization of the reversible Vlasov equation of kinetic plasma dynamics, called conformal kinetic theory. In order to arrive at this formalism, we start with the conformal Hamiltonian dynamics of particles and lift it to the dynamical formulation of the associated kinetic theory. The resulting theory represents a simple example of a geometric pathway from dissipative particle motion to dissipative kinetic motion. We also derive the kinetic equations of a continuum of particles governed by the contact Hamiltonian dynamics, which may be interpreted in the context of relativistic mechanics. Once again we start with the contact Hamiltonian dynamics and lift it to a kinetic theory, called contact kinetic dynamics. Finally, we project the contact kinetic theory to conformal kinetic theory so that they form a geometric hierarchy.Comment: Minor revision

Mıxed Fuzzy Soft Topologıcal Spaces

Bu tezde, herhangi bir fuzzy soft kümesi üzerinde tanımlanan fuzzy soft topolojiye göre tümleyen tanımı verilmis ve bu tanımla birlikte bu küme üzerinde sabitlestirilmis fuzzy soft topolojik uzay tanımlanmıstır. Daha sonra, bu uzayın sayılabilirligi ile ilgili teoremler verilip ispatlanmıstır.In this thesis, the definition complement is given according to fuzzy soft topology defined over a fuzzy soft set and together with this definition mixed fuzzy soft topological space is defined. Then, related theorems of this space are given and proven