1. I n t r o d u c t i o n Graded normal logics ( G N L s ) are the extensions of modal normal logics to a language with graded modalities. The interpretation in usual Kripke models of a formula <>hA (n < w), whose main operator is a graded possibility, is there are more than n accessible worlds where A is true. When graded modalities were introduced (in [7], independently rediscovering a forme...

For any finitely generated abelian group Q, we reduce the problem of classification of Q-graded simple Lie algebras over an algebraically closed field of “good” characteristic to the problem of classification of gradings on simple Lie algebras. In particular, we obtain the full classification of finite-dimensional Q-graded simple Lie algebras over any algebraically closed field of characteristi...

Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

This research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. Heat conduction equation in cylindrical coordinate system is solved. Thermal conductivity coefficient is graded along the radial direction. By considering a symmetric distribution of temperature, loading and boundary conditions, strain-displacement and stress-strain relations can b...

Much attention is focused on the relationship between rough sets and many-valued modal logic to deal with approximate reasoning. This paper discusses graded puts forward G(S5). Secondly, by employing operators that correspond operations in G(S5), we introduce concept of upper lower truth degrees a logical formula. Then, propose conditional degrees. Several basic interesting properties are addre...