We investigate the gravitational instability (GI) of dust-ring structures and formation planetesimals by their collapse. The normalized dispersion relation a self-gravitating ring structure includes two parameters that are related to its width line mass (the per unit length). survey these calculate growth rate wavenumber. Additionally, we planetesimal GI is formed secular protoplanetary disk. a...

The cylindrical shell is a widely used structure in engineering practice, and its main form of failure instability due to buckling. As classical problem the field mechanics, stability shells has been studied extensively. However, large difference between theoretically predicted results critical buckling load experimental for subjected uniform axial pressure contributed continuous development th...

in this paper, we introduce the new notion of n-f-clean rings as a generalization of f-clean rings. next, we investigate some properties of such rings. we prove that mn(r) is n-f-clean for any n-f-clean ring r. we also, get a condition under which the denitions of n-cleanness and n-f-cleanness are equivalent.

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

for a fixed positive integer , we say a ring with identity is n-generalized right principally quasi-baer, if for any principal right ideal of , the right annihilator of is generated by an idempotent. this class of rings includes the right principally quasi-baer rings and hence all prime rings. a certain n-generalized principally quasi-baer subring of the matrix ring are studied, and connections...