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...

an r-module m is called strongly noncosingular if it has no nonzero rad-small (cosingular) homomorphic image in the sense of harada. it is proven that (1) an r-module m is strongly noncosingular if and only if m is coatomic and noncosingular; (2) a right perfect ring r is artinian hereditary serial if and only if the class of injective modules coincides with the class of (strongly) noncosingula...

In modern road surveys, hanging power cables are among the most commonly-found geometric features. These cables are catenary curves that are conventionally modelled with three parameters in 2D Cartesian space. With the advent and popularity of the mobile mapping system (MMS), the 3D point clouds of hanging power cables can be captured within a short period of time. These point clouds, similarly...

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Recently, the coupled dynamical simulation of pantograph and catenary in high speed trains has found much interest. The equations of motion form a partial diierential-algebraic equation (PDAE) that combines a partial diierential equation (PDE) for the catenary and a diierential-algebraic equation (DAE) for the pantograph. In the present paper we discuss the relation of this PDAE model to curren...

In this paper a user-friendly environment for the representation of the dynamic results on the pantograph-catenary interactions is presented. This environment consists of an interactive interface for the representation of graphics and another for the representation of video. By means of the first interface for the representation of graphics, the user can interact with the different graphic repr...

This paper presents a method for modeling and analysis of cablestayed bridges under the action of moving vehicles. Accurate and efficient finite elements are used for modeling the bridge structure. A beam element is adopted for modeling the girder and the pylons. Whereas, a two-node catenary cable element derived using exact analytical expressions for the elastic catenary, is adopted for modeli...

Thus far, the main cables have been referred to as catenary cables. For a cable to assume the shape of a catenary, the load on the cable must be uniformly distributed. Under the spaced suspender loading, the shape is closer to a parabola. The difference between the two is very slight. Since the equation for a parabola is easier to work with, most engineers use the parabola equation in the desig...