Let D be a fixed connected component of reductive algebraic group over an algebraically closed field. We use variant the Springer representation to define and study partition into finitely many Strata, one which is open set regular elements. show that Strata are indexed by defined purely in terms Weyl its automorphism D.

We introduce the following simpler variant of Tur\'an problem: Given integers $n>k>r\geq 2$ and $m\geq 1$, what is smallest integer $t$ for which there exists an $r$-uniform hypergraph with $n$ vertices, edges $m$ connected components such that any $k$-subset vertex set contains at least one edge? prove some general estimates this quantity its limit, normalized by $\binom{n}{r}$, as $n\rightarr...

The notion of graph covers is a discretization covering spaces introduced and deeply studied in topology. In discrete mathematics theoretical computer science, they have attained lot attention from both the structural complexity perspectives. Nonetheless, disconnected graphs were usually omitted considerations with explanation that it sufficient to understand coverings connected components targ...

It is shown that a commutative reduced ring R is a Baer ring if and only if it is a CS-ring; if and only if every dense subset of Spec (R) containing Max (R) is an extremally disconnected space; if and only if every non-zero ideal of R is essential in a principal ideal generated by an idempotent.

In this chapter, two cellular manufacturing systems, namely connected cells and disconnected cells, have been studied, and their performance was compared with respect to average flowtime and work-inprocess inventory under make-to-order demand strategy. The study was performed in a medical device manufacturing company considering their a) existing system b) variations from the existing system by...

Bayes Nets simplify probabilistic models, making it easy to work with these models. Unfortunately, sometimes people devise models that are too complicated to allow calculation of exact probabilities, so they instead use approximate inference, such as Markov Chain Monte Carlo (MCMC). However, MCMC can fail if the Bayes Net has zero-probability states that “disconnect” the state space. In this pa...