We consider the problem of finding all the permutations corresponding to a given Young tableau. We introduce a recursive algorithm, deleting the elements from the tableau in reverse order which were inserted by the Schensted algorithm.

This paper deals with some classes of morphisms in a category which we call networks of morphisms. These networks are linked with full reflective subcategories. The notion of saturated subcategory is introduced and studied. Each reflective subcategory is shown to be saturated.

Let $X$ be Banach space and let $T, \bar T=T+\delta T$ be bounded linear operators on $X$. Suppose that $T$ has the Drazin inverse $T^D$ and $\text{Ind} (T)=n$. In this paper, we show that if $\|\delta T\|$ is sufficiently small and $\text{Ran} (\bar T^n) \cap \text{Ker} (({T^D})^n) = \{0\}$, then $\bar T$ is Drazin invertible with $\text{Ind} (\bar T)\le n$. In this case, the expression of $\bar T^D$ is given and the upper bounds of $\|\bar T^D\|$ and $$\dfrac{\|\bar T^D-T^D\|}{\|T^D\|}$$ are established. If $\dim X<\infty$, replacing $\text{Ran} (\bar T^n) \cap \text{Ker} (({T^D})^n) = \{0\}$ by $\text{rank} (\bar T^n) = \text{rank} (T^n)$, we obtain the same perturbation results of the Drazin invertible matrix $T$ as in the case of $\dim X=\infty$.

In an article published in 1979, Kainen and Bernhart [1] laid the groundwork for further study of book embeddings of graphs. They define an $n$-book as a line $L$ in 3-space, called the spine, and $n$ half-planes, called pages, with $L$ as their common boundary. An $n$-book embedding of a graph $G$ is an embedding of $G$ in an $n$-book so that the vertices of $G$ lie on the spine and each edge of $G$ lies within a single page so that no two edges cross. The book thickness $bt(G)$ or page number $pg(G)$ of a graph $G$ is the smallest $n$ so that $G$ has an $n$-book embedding. Finding the book thickness of an arbitrary graph is a difficult problem. Even with a pre-specified vertex ordering, the problem has been shown to be NP-complete [6]. In this paper we will introduce book embeddings with particular focus on results for graphs with small book thickness.

Newton's Method, the recursive algorithm for computing the roots of an equation, is one of the most efficient and best known numerical techniques. The basics of the method are taught in any first-year calculus course. However, in most cases the two most important questions are often left unanswered. These questions are, "Where do I start?" and "When do I stop?" We give criteria for determining when a given value is a good starting value and how many iterations it will take to ensure that we have reached an approximate solution to within any predetermined accuracy.

The use of dynamic geometry software in constructing loci with various conditions placed on the distances from two fixed points is described, where either (1) the sum of the squares, (2) the difference of the squares, (3) the ratio, or (4) the product of the two distances is constant. The equation of each locus analytically is also derived. In the first three cases, the loci are circles or lines. In the fourth case, the locus is a spiric section described by a quartic equation.