Dimension and Disconnection

dedekind modules and dimension of modules

در این پایان نامه، در ابتدا برای مدول ها روی دامنه های پروفر شرایط معادل به دست آورده ایم و خواصی از ددکیند مدول ها روی دامنه های پروفر مشخص کرده ایم. در ادامه برای ددکیند مدول های با تولید متناهی روی حلقه های به طور صحیح بسته شرایط معادل به دست آورده ایم و ددکیند مدول های ضربی را مشخص کرده ایم. گزاره هایی در مورد بعد ددکیند مدول ها بیان کرده ایم. در پایان، قضایای lying over و going down را برا...

Disconnection and Responsibility

Szeged Dimension and $PI_v$ Dimension of Composite Graphs

Let $G$ be a simple connected graph. In this paper, Szeged dimension and PI$_v$ dimension of graph $G$ are introduced. It is proved that if $G$ is a graph of Szeged dimension $1$ then line graph of $G$ is 2-connected. The dimensions of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components is computed. Also explicit formulas of Sze...

Network disconnection problems

Network disconnection problems are defined from a network attacker's point of view. In a centralized network where flows are supplied from a source node to the other nodes, called demand nodes, a network attacker aims to block the supply to demand nodes by destroying edges. As destroying edges incurs expenses, an attacker considers the following three different strategies. The first problem, de...

The starburst - AGN disconnection

Optical studies of starbursts, AGN and their connections usually leave out galaxies whose emission lines are too weak to warrant reliable measurement and classification. Yet, weak line galaxies abound, and deserve a closer look. We show that these galaxies are either massive, metal rich star-forming systems, or, more often, LINERs. From our detailed stellar population analysis, we find that the...