we consider the class $mathfrak m$ of $bf r$--modules where $bf r$ is an associative ring. let $a$ be a module over a group ring $bf r$$g$, $g$ be a group and let $mathfrak l(g)$ be the set of all proper subgroups of $g$. we suppose that if $h in mathfrak l(g)$ then $a/c_{a}(h)$ belongs to $mathfrak m$. we investigate an $bf r$$g$--module $a$ such that $g not = g'$, $c_{g}(a) = 1$. we stud...

The identi®ability problem is addressed for n-compartment linear mammillary and catenary models, for the common case of input and output in the ®rst compartment and prior information about one or more model rate constants. We ®rst de®ne the concept of independent constraints and show that n-compartment linear mammillary or catenary models are uniquely identi®able under nÿ 1 independent constrai...

This study develops an integrated data-driven and model-driven approach (template matching) that clusters the urban railroad point clouds into three classes of rail track, contact cable, and catenary cable. The employed dataset covers 630 m of the Dutch urban railroad corridors in which there are four rail tracks, two contact cables, and two catenary cables. The dataset includes only geometrica...

This work addresses the problem of identifiability, that is, the question of whether parameters can be recovered from data, for linear compartment models. Using standard differential algebra techniques, the question of whether a given model is generically locally identifiable is equivalent to asking whether the Jacobian matrix of a certain coefficient map, arising from input-output equations, i...

The high-speed rail system provides a fast, reliable and comfortable means to transport large number of travelers over long distances. The existence of bird nests in overhead catenary system (OCS) can hazard to the safety of the high-speed rails, which will potentially result in long time delays and expensive damages. A vision-based intelligent inspection system capable of automatic detection o...

In this paper‎, ‎we introduce the notion of $(m,n)$-‎algebr‎aically compact modules as an analogue of algebraically‎ ‎compact modules and then we show that $(m,n)$-algebraically‎ ‎compactness‎ ‎and $(m,n)$-pure injectivity for modules coincide‎. ‎Moreover‎, ‎further characterizations of a‎ ‎$(m,n)$-pure injective module over a commutative ring are given‎.

 The class of ads modules with the SIP (briefly‎, ‎$SA$-modules) is studied‎. ‎Various conditions for a module to be $SA$-module are given‎. ‎It is proved that for a quasi-continuous module $M$‎, ‎$M$ is a UC-module if and only if $M$ is an $SA$-module‎. ‎Also‎, ‎it is proved that the direct sum of two $SA$-modules as $R$-modules is an $SA$-module when $R$ is the sum of the annihilators of thes...

In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

The problem of the catenary can be used as an illustrating example for the methods of modern applied mathematics. Starting oo from a practical problem, modelling consists in transforming this into a mathematical problem, using physical principles and empirical laws. The mathematical question is then imbedded into an appropriate theory and solved. The solutions have to be analyzed with respect t...