The concepts of free modules, projective modules, injective modules and the likeform an important area in module theory. The notion of free fuzzy modules was introducedby Muganda as an extension of free modules in the fuzzy context. Zahedi and Ameriintroduced the concept of projective and injective L-modules. In this paper we give analternate definition for projective L-modules. We prove that e...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...

We review some recent work on fiber-optic sensors for the high-speed railway environment. In particular, we show convenient fiber-optic solutions for rail and wheel monitoring, perimeter security and catenary protection in changeover sections. OCIS codes: (060.2370) Fiber optic sensors; (060.3735) Fiber Bragg gratings

Flow fields around reformed earth embankment windbreak walls (REEWWs) with five different porosities under crosswind were studied using the improved delayed detached eddy simulation (IDDES) based on SST ?-? turbulence model by computational fluid dynamics (CFD) in this paper. Based simulated flow field results, finite element method (FEM) was adopted to analyze wind-induced displacement of cate...

This is the second paper in a series presenting case studies in modern large-scale constrained optimization [9]. In this paper, we consider the shape of a hanging chain, which, in equilibrium, minimizes the potential energy of the chain. In addition to the tutorial aspects of this paper, we also emphasize the importance of certain modeling issues such as convex vs. nonconvex formulations of giv...

A. Problems involving chains of irreducible factorizations in atomic integral domains and monoids have been the focus of much recent literature. If S is a commutative cancellative atomic monoid, then the catenary degree of S (denoted c(S )) and the tame degree of S (denoted t(S )) are combinatorial invariants of S which describe the behavior of chains of factorizations. In this note, we ...

Air gap impulse discharge characteristics of railway tunnel-catenary at high-altitude are great significance to the electrical insulation design. The existing altitude correction methods for non-uniform air gaps not applicable tunnel-catenary. To investigate tunnel-catenary, a typical structural model was built in an artificial climate chamber. Different altitudes were simulated by adjusting at...