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The aim of this thesis is to study invariants of Diophantine forms and equations. These invariants are the transformations that do not change the original equations and forms. This thesis has a different view to the concept of invariants from Hlibertian view. Based on this new definition, by having one of the solutions of the equation, new solutions can be found with invariant method. The number of these solutions can be finite or infinite. In case of infinite solutions this method is more important. The focus of this thesis is on forms and linear invariants. The most important result in this text is about two main theorems that can classify the invariants of all completely decomposable... 

Stress tensors and their rates are fundamental quantities in modeling the behavior of materials in the field of nonlinear continuum mechanics. One of the most remarkable applications of stress rates is their presence in the rate type constitutive equations of materials.
Co-rotational rates are corresponding to the rates which are measured by an observer who is in a reference rotating coordinate system. In general, under some specific conditions for the spin of a co-rotational rate, the rate of an Eulerian tensor would be objective. In this thesis, the objective co-rotational rates of Eulerian stress tensors for isotropic elastic materials under large deformations are obtained for the...