In this paper we construct a natural category ~r of locally and topologically ringed spaces which contains both the category of locally noetherian formal schemes and the category of rigid analytic varieties as full subcategories. This category has applications in algebraic geometry and rigid analytic geometry. The idea of the definition of the category ~r is the following. From a formal point o...

In this paper, crashworthiness characteristics of conical steel tubes stiffened by annular rings and rigid polyurethane foam are investigated. For this purpose, wide circumferential rings are created from the outer surface of the conical tube at some determined areas along tube length. In fact, this method divides a long conical tube into several tubes of shorter length. When this structure is ...

Let R be a ring, σ an automorphism of R and δ a σ-derivation of R. We recall that a ring R is said to be a δ-ring if aδ(a) ∈ P (R) implies a ∈ P (R), where P (R) denotes the prime radical of R. It is known that, if R is a Noetherian ring, σ an automorphism of R such that aσ(a) ∈ P (R) implies a ∈ P (R) and δ a σ-derivation of R such that R is a δ-ring with σ(δ(a)) = δ(σ(a)), for all a ∈ R, then...

Beam theory was used to evaluate the stiffness of a simulated orthodontic model as affected by the type of bracket, interbracket distance, type of ligature tie, and size of segment. For a given deflection, the model generated greater force (increased stiffness) as the beam constant (N) increased. N increased as interbracket distance increased. Metal ties were as rigid or more rigid than o-rings...

In this paper, we consider a depth inequality of Auslander which holds for finitely generated Tor-rigid modules over commutative Noetherian local rings. We raise the question whether such can be extended $n$-Tor-rigid modules, and obtain an affirmative answer $2$-Tor-rigid that are generically free. Furthermore, in appendix, use Dao's eta function determine new classes hypersurfaces quotient un...

let r and s be reduced rings with identities whose idempotents are central, and let m be an(r, s)-bimodule such that annr (m)=0. in this paper, we determine first the structure of automorphisms ofthe triangular ring, =sr mt0, and then, for all automorphisms α ,β of t we determine the structureof (α,β)-derivations of t.