this paper extends the notion of ditopology to the case where openness and closedness are given in terms of {em a priori} unrelated drading functions. the resulting notion of graded ditopology is considered both in the setting of lattices and in that textures, the relation between the two approaches being discussed in detail. interrelations between graded ditopologies and ditopologies on textur...

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...

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...