let $r$ be a commutative ring. in this paper we assert some properties of finitely generated comultiplication modules and fitting ideals of them.

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.

We have developed a hybrid system to predict the secondary structures (alpha-helix, beta-sheet and coil) of proteins and achieved 66.4% accuracy, with correlation coefficients of C(coil) = 0.429, C alpha = 0.470 and C beta = 0.387. This system contains three subsystems ("experts"): a neural network module, a statistical module and a memory-based reasoning module. First, the three experts indepe...

Thickening of tree stems is the result of secondary growth, accomplished by the meristematic activity of the vascular cambium. Secondary growth of the stem entails developmental cascades resulting in the formation of secondary phloem outwards and secondary xylem (i.e., wood) inwards of the stem. Signaling and transcriptional reprogramming by the phytohormone ethylene modifies cambial growth and...

let r be a ring,  be an endomorphism of r and mr be a -rigid module. amodule mr is called quasi-baer if the right annihilator of a principal submodule of r isgenerated by an idempotent. it is shown that an r-module mr is a quasi-baer module if andonly if m[[x]] is a quasi-baer module over the skew power series ring r[[x; ]].

Secondary homotopy groups supplement the structure of classical homotopy groups. They yield a track functor on the track category of pointed spaces compatible with fiber sequences, suspensions and loop spaces. They also yield algebraic models of (n − 1)-connected (n + 1)-types for n ≥ 0. Introduction The computation of homotopy groups of spheres in low degrees in [Tod62] uses heavily secondary ...