The purpose of this paper is to give the definition of projective 3-space PG(3,q) over Galois field GF(q), q = pm for some prime number p and some integer m.
Also, the definition of the plane in PG(3,q) is given and state the principle of duality.
Moreover some theorems in PG(3,q) are proved.
The article describes a certain computation method of -arcs to construct the number of distinct -arcs in for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons
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The aim of this paper is to construct cyclic subgroups of the projective general linear group over from the companion matrix, and then form caps of various degrees in . Geometric properties of these caps as secant distributions and index distributions are given and determined if they are complete. Also, partitioned of into disjoint lines is discussed.
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The purpose of this paper is to find an arc of degree five in 31 ,29),(2, =qqPG , with stabilizer group of type dihedral group of degree five 5 D and arcs of degree six and ten with stabilizer groups of type alternating group of degree five 5 A , then study the effect of 5 D and 5A on the points of projective plane. Also, find a pentastigm which has collinear diagonal points.
The basis of this paper is to study the concept of almost projective semimodules as a generalization of projective semimodules. Some of its characteristics have been discussed, as well as some results have been generalized from projective semimodules.
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Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.
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In this paper mildly-regular topological space was introduced via the concept of mildly g-open sets. Many properties of mildly - regular space are investigated and the interactions between mildly-regular space and certain types of topological spaces are considered. Also the concept of strong mildly-regular space was introduced and a main theorem on this space was proved.
The aim of this paper is to introduces and study the concept of CSO-compact space via the notation of simply-open sets as well as to investigate their relationship to some well known classes of topological spaces and give some of his properties.