We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.

Tilting theory in cluster categories of hereditary algebras has been developed in [BMRRT] and [BMR]. These results are generalized to cluster categories of hereditary abelian categories. Furthermore, for any tilting object T in a hereditary abelian category H, we verify that the tilting functor HomH(T,−) induces a triangle equivalence from the cluster category C(H) to the cluster category C(A),...

This thesis is concerned with higher cluster tilting objects in generalized higher cluster categories and tropical friezes associated with Dynkin diagrams. The generalized cluster category arising from a suitable 3-Calabi-Yau differential graded algebra was introduced by C. Amiot. It is Hom-finite, 2-Calabi-Yau and admits a canonical cluster-tilting object. In this thesis, we extend these resul...

The development of the tilting train can contribute to solve the economic burden and enhance the transportation means of areas that did not share the benefits of the high speed railway. But the dynamic behavior caused by the interaction between the train and the track as well as the environmental vibrations along the railway should be evaluated to secure the safety of the train and riding comfo...

The software package SPuDS has previously been shown to accurately predict crystal structures of AMX(3) and A(1 - x)A'(x)MX(3) perovskites that have undergone octahedral tilting distortions. This paper describes the extension of this technique and its accuracy for A(2)MM'X(6) ordered double perovskites with the aristotype Fm\overline 3m cubic structure, as well as those that have undergone octa...