Scientific Research Publishing

Read  full  paper  at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=53575#.VMnXsSzQrzE Author(s)     Julio Romero , Scott H. Murray Affiliation(s) Faculty of Education, Science, Technology and Mathematics, University of Canberra, Canberra, Australia . ABSTRACT This paper describes the construction and enumeration of mixed orthogonal arrays (MOA) to produce optimal experimental designs. A MOA is a multiset whose rows are the different combinations of factor levels, discrete values of the variable under study, having very well defined features such as symmetry and strength three (all main interactions are taken in consideration). The applied methodology blends the fields of combinatorics and group theory by applying the ideas of orbits, stabilizers and isomorphisms to array generation and enumeration. Integer linear programming was used in order to exploit the symmetry property of the arrays under study. The backtrack search ...

Read full paper at: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=51184#.VFsmlmfHRK0 Author(s)   Rahman Khatibi Affiliation(s) Consultant Mathematical Modeller, Swindon, UK . ABSTRACT New operators are presented to introduce “arithmetic calculus”, where 1) the operators are just obvious mathematical facts, and 2) arithmetic calculus refers to summing and subtracting operations without solving equations. The sole aim of this paper is to make a case for arithmetic calculus, which is lurking in conventional mathematics and science but has no identity of its own. The underlying thinking is: 1) to shift the focus from the whole sequence to any of its single elements; and 2) to factorise each el...