an r-module m is called epi-retractable if every submodule of mr is a homomorphic image of m. it is shown that if r is a right perfect ring, then every projective slightly compressible module mr is epi-retractable. if r is a noetherian ring, then every epi-retractable right r-module has direct sum of uniform submodules. if endomorphism ring of a module mr is von-neumann regular, then m is semi-...

The catenary degree of an element s of a cancellative commutative monoid S is a nonnegative integer measuring the distance between the irreducible factorizations of s. The catenary degree of the monoid S, defined as the supremum over all catenary degrees occurring in S, has been heavily studied as an invariant of nonunique factorization. In this paper, we investigate the set C(S) of catenary de...

In the design process of a 2x25kV power supply, the location and sizing of autotransformers and the choice of the catenary type are usually two aspects very closely interrelated. As a result, the number of autotransformers can normally be reduced or augmented if the catenary is upgraded or downgraded respectively. In this paper, coupling equations between these two aspects are described in deta...

We construct an algorithmwhich computes the catenary and tame degree of a numerical semigroup. As an example we explicitly calculate the catenary and tame degree of numerical semigroups generated by arithmetical sequences in terms of their first element, the number of elements in the sequence and the difference between two consecutive elements of the sequence.

The pantograph current collector-catenary contact has been recognized as an established cause of permanent electromagnetic perturbation in a railway environment. In this paper the problems due to pantograph-catenary crawling are addressed. Introducing a suitable model for the radiating contacts, results in agreement with classical fields theory and with experimental measurements may be deduced....

This work presents a fully three-dimensional methodology for the computational analysis of the interaction between catenary and pantographs. The finite element method is used to support the modeling of the catenary while a multibody dynamics methodology is applied to support the pantograph modeling. The contact between the two subsystems is described using a penalty contact formulation. An high...

The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

Davies Gilbert's work on the catenary is notable on two counts. First, it influenced Thomas Telford in formulating his final design for the Menai Strait suspension bridge (1826); and second, it established for the first time the form of the 'catenary of equal strength'. The classical catenary is a uniform flexible chain or cable hanging freely under gravity between supports. The 'catenary of eq...