we show that every semi-artinian module which is contained in a direct sum of finitely presented modules in $si[m]$, is weakly co-semisimple if and only if it is regular in $si[m]$. as a consequence, we observe that every semi-artinian ring is regular in the sense of von neumann if and only if its simple modules are $fp$-injective.

in this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. in particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over noetherian rings are proved. moreover, w...

We continue to study nitary abstract elementary classes, de ned in [7]. We introduce a concept of weak κ -categoricity and an f-primary model in a א0 -stable simple nitary AEC with the extension property, and gain the following theorem: Let (K,4K) be a simple nitary AEC, weakly categorical in some uncountable κ . Then (K,4K) is weakly categorical in each λ ≥ min{κ,i(2א0 )+} . We have that if th...

We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that RR is close to AA. Thus, when the algorithm is used to solve the semi-normal equations RRx = A b, we obtain a weakly stable method for the solution of a nonsingular Toeplitz or Hankel linear systemAx = b. The algorithm also applies to the solution of the full-rank Toeplitz ...

a method for solving a class of weakly singular volterra integral equations is given by using the fractional differential transform method. the approximate solution of these equa­tions is calculated in the form of a finite series with easily computable terms. while in some examples this series solution increased up to the exact closed solution, in some other examples, we can see the accuracy an...

n this paper, we prove some common fixed point theorems for multivalued mappings and we present some new generalization contractive conditions under the condition of weak compatibility. our results extends chang-chen’s results  as well as ´ciri´c results. an example is given to support the usability of our results.

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .