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.

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; ]].

Department of Engineering, University of Cambridge Trumpington Street, Cambridge CB2 1PZ, U.K. Abstract The optimal shape of cover plates for circular, symmetric retractable roof structures based on a grid of multi-angulated rods connected by revolute joints is considered. It is assumed that these cover plates are co-planar, and hence they are not allowed to overlap in any configuration; they a...

The secondary male sex characteristics of Hoplolaimus galeatus consisted of caudal alae, two independently retractable spicules and a gubernaculum with two bilobed titillae. The spicules were dimorphic, with the outer one possessing a velum. When both spicules were completely extruded, the only open orifice on the ventral surface of the posterior region was formed by the close association of th...

In this paper we describe a novel wearable interaction device that is based on the principle of a badge reel often found in corporate environments. Our prototype device is composed of hardware components from an ordinary off-the-shelf game pad. Preliminary results of a user study show that the device allows for a more accurate and intuitive interaction than an ordinary game pad when performing ...

For a fixed graph H, let Ret(H) denote the problem of deciding whether a given input graph is retractable to H. We classify the complexity of Ret(H) when H is a graph (with loops allowed) where each connected component has at most one cycle, i.e., a pseudoforest. In particular, this result extends the known complexity classifications of Ret(H) for reflexive and irreflexive cycles to general cyc...

We present a new Monte Carlo scheme for the efficient simulation of multipolymer systems. The method permits chains to be inserted into the system using a biased growth technique. The growth proceeds via the use of a retractable feeler, which probes possible pathways ahead of the growing chain. By recoiling from traps and excessively dense regions, the growth process yields high success rates f...

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

Positrons are accumulated within a Penning trap designed to make more precise measurements of the positron and electron magnetic moments. The retractable radioactive source used is weak enough to require no license for handling radioactive material, and the radiation dosage 1 m from the source gives an exposure several times smaller than the average radiation dose on the earth's surface. The 10...