A student, supported by his classmates, throws a piece of chalk at the teacher who is writing on the blackboard. The teacher rapidly turns back and promptly catches him in the act. The student blushes and suddenly realizes how bad it was what he did. What happened to the guy? Why did he decide to throw the piece of chalk? And why, after a few seconds, he would have liked that what he did had ne...

Saul: "And it came to pass, when the evil spirit from God was upon Saul, that David took an harp* and played with his hand; so Saul was refreshed and was well, and the evil spirit departed from him." Music was a treatment for meflt3 diseases in ancient Egypt and Greec. The present interest in therapy dates from 1947. Sir SteUa Wilson, then Music Director of ^ Arts Council, pointed out tP, altho...

The quality of teachers prepared for basic education in Africa and other continents of the world is a consequence of the knowledge of content acquired and the pedagogy. Effective teaching practice supervision could determine the level of teacher trainees’ performance in the art of teaching. The study investigated the differences in performance of teacher trainees who embarked on continuous Teac...

(3) a. [to John leave] (building the embedded IP) b. [John1 [to John1 leave] (moving John to the Spec IP) c. [wants[John1 [to John1 leave]] (building the matrix VP) d. [John1 [wants[John1 [to John1 leave]]] (moving John to the Spec VP) e. [John1 [John1 wants[John1 [to John1 leave]]]] (building TP and moving John to its Spec) f. [John1 [John1 wants[John1 [to John1 leave]]]] (deleting all copies ...

let  $r$ be a commutative noetherian ring and $i$ be an ideal of $r$. we say that $i$ satisfies the persistence property if  $mathrm{ass}_r(r/i^k)subseteq mathrm{ass}_r(r/i^{k+1})$ for all positive integers $kgeq 1$, which $mathrm{ass}_r(r/i)$ denotes the set of associated prime ideals of $i$. in this paper, we introduce a class of square-free monomial ideals in the polynomial ring  $r=k[x_1,ld...

the colorful paths and rainbow paths have been considered by severalauthors.a colorful directed path in a digraph $g$ is a directed path with $chi(g)$ vertices whose colors are different. a $v$-colorful directed path is such a directed path, starting from $v$. we prove that for a given $3$-regular triangle-free digraph $g$ determining whether there is a proper $chi(g)$-coloring of $g$such that ...

It is known (see e.g. [2], [4], [5], [6]) that continuous variations in the entries of a complex square matrix induce its eigenvalues. If such variation arises from one real parameter α∈[0,1], then eigenvalues follow paths plane as α shifts 0 to 1. The intent here study nature these eigenpaths, including their behavior under small perturbations variations, well resulting eigenpairings matrices ...