in this work, we investigate the transfer of some homological properties from a ring $r$ to its amalgamated duplication along some ideal $i$ of $r$ $rbowtie i$, and then generate new and original families of rings with these properties.

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

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...

Abstmet-This paper introduces a frequency-weighted frequency-weighted balanced reduction method controller reduction scheme which offcrs good closed-loop (Enns, 1984a, b) and the idea of representing a stability under use of the reduced order controller. By combining the use of a stable fractional representation of the controller as a stable coprime factorization (Liu controller with a frequenc...

We present new methods for comoutiw the ereatest common . " " right divisor of polynomial matrices. These methods imolve the recently shldied generalized Sylvester and eeneralized Bezoutian resultant matrices,~hich require no polynomial o&ations. They can provide a row proper -test common right divisor, test for coprimeness and calculate dual d&cal indices. The generalized resultant matrices ar...

Wavelets, filter banks and multiresolution signal analysis, have been used independently in the fields of applied mathematics, computer vision and signal processing. It is interesting to note that they performed similar functions in different fields. It is recently, that they converged to form a single theory. In the paper, it is shown that the fundamental idea was the same in all the fields i....