We prove the canonical models introduced in [D] do not exist for some graded normal logics with symmetric models, namely KB ~ KBD ~ KBT ~ so that we define a new kind of canonical models, the general ones, and show they exist and work well in every case.

We define a graded twisted-coassociative coproduct on the tensor algebra TW of any Zn-graded vector space W . If W is the desuspension space ↓V of a graded vector space V , the coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1to-1 with sequences πs, s ≥ 1, of s-linear maps on V (resp. Zn-graded Loday structures on V , sequences tha...

We study the graded derivation-based noncommutative diierential geometry of the Z 2-graded algebra M (njm) of complex (n + m) (n + m)-matrices with the \usual block matrix grading" (for n 6 = m). Beside the (innnite-dimensional) algebra of graded forms the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated...

The hyperfield came into being due to a mathematical necessity that appeared during the study of valuation theory fields by M. Krasner, who also defined hyperring, which is related in same way as ring field. and hyperfields, well rings hyperrings, border on each other, it natural problems open questions arise their boundary areas. This paper presents such occasions, more specifically, introduce...

this paper deals with the determination of displacement function and thermal stresses of a finite length isotropic functionally graded hollow cylinder subjected to uniform temperature field. the solution of the governing thermoelastic equation is obtained, as suggested by spencer et al. for anisotropic laminates.  numerical calculations are also carried out for fgm (functionally graded material...

Let $G$ be a group with identity $e$. $R$ commutative $G$-graded ring non-zero identity, $S\subseteq h(R)$ multiplicatively closed subset of and $M$ graded $R$-module. In this article, we introduce study the concept $S$-1-absorbing prime submodules. A submodule $N$ $(N:_{R}M)\cap S=\emptyset$ is said to prime, if there exists an $s_{g}\in S$ such that whenever $a_{h}b_{h'}m_{k}\in N$, then eith...

In this paper we discuss the question of integrating differential graded Lie algebras (DGLA) to groups (DGLG). We first recall classical problem integration in context, and recollect known results. Then, define category study its properties. show how associate a algebra every group vice versa. For DGLA ? DGLG direction, main “tools” are Hopf Harish-Chandra pairs (HCP)—we HCPs explain those rela...