The research group at the Department of Mathematical Sciences of Loughborough University is young and what I hope is that the successful completion of this project will boost the status of the group and weave Loughborough into the fabric of UK

Algebraic Geometry."

Several researchers (see Booth, 1988; Greeno, 1991; Kieran, 1992; Lins, 1990) suggest that many of the fundamental difficulties experienced by beginning algebra students are due to their failure to identify equivalent forms of an

algebraic expression.

Therefore, the cryptographic community turns to address much concern on Boolean functions resisting fast

algebraic attack, besides their

algebraic immunity.

We say that a connected linear

algebraic k-group G is k-split, or split over k, if its unipotent radical [R.sup.u] (G) is defined and split over k, and the reductive quotient group G/[R.sup.u] (G) is defined and split over k.

Vasantha Kandasamy and Florentin Smarandache [2-57], since 2003, and it was called Neutrosophic

Algebraic Structures.

In algebra real life problems are constructed into unknown equations forms and then laws are followed for solving

algebraic equations.

As singular points of an

algebraic curve are the solutions of a polynomial system, most of algorithms in [10-15] solve the polynomial system either by Grobner basis method described in [16] or by resultant computation.

* In Section 2, we give a few definitions, mostly illustrating the link between context-free grammars, solutions of positive

algebraic systems and N-algebraic functions.

With the fundamentals of these, the paper focuses on the research of topology choice and repairing control based on density weighted

algebraic connectivity; when the vertex and links are not always constant, they can change with time.

Radford (2001) said that teachers of mathematics "need to deepen [their] own understanding of the nature of

algebraic thinking and the way it relates to generalisation".

2 MATHEMATICAL ASPECT OF SOLVING

ALGEBRAIC EQUATIONS