منابع مشابه
Hilbert Bases for Orthogonal Arrays
In this paper, we relate the problem of generating all 2-level orthogonal arrays of given dimension and force, i.e. elements in OA(n, m), where n is the number of factors and m the force, to the solution of an Integer Programming problem involving rational convex cones. We do not restrict the number of points in the array, i.e. we admit any number of replications. This problem can be theoretica...
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Let X be a set of vectors in R m. X is said to be a Hilbert base if every vector in R m which can be written both as a linear combination of members of X with nonnegative coeecients and as a linear combination with integer coeecients can also be written as a linear combination with nonnegative integer coeecients. Denote by H the collection of the graphs whose family of cuts is a Hilbert base. I...
متن کاملOperator-valued bases on Hilbert spaces
In this paper we develop a natural generalization of Schauder basis theory, we term operator-valued basis or simply ov-basis theory, using operator-algebraic methods. We prove several results for ov-basis concerning duality, orthogonality, biorthogonality and minimality. We prove that the operators of a dual ov-basis are continuous. We also dene the concepts of Bessel, Hilbert ov-basis and obta...
متن کاملOrthogonal Arrays
Definition Orthogonal arrays (OAs) are objects that are most often generated via algebraic arguments. They have a number of applications in applied mathematics, and have often been studied by algebraic mathematicians as objects of interest in their own right. Our treatment will reflect their use as representations of statistical experimental designs. An OA is generally presented as a two-dimens...
متن کاملOrthogonal Arrays
(say) is called symmetric, otherwise, the array is said to be asymmetric. Several methods of construction of symmetric as well as asymmetric OAs are available in the literature. Some important methods will be discussed here. One of the principal applications of the OAs is in the selection of level combinations for fractional factorial experiments. An OA of strength t is equivalent to an orthogo...
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ژورنال
عنوان ژورنال: Journal of Statistical Theory and Practice
سال: 2007
ISSN: 1559-8608,1559-8616
DOI: 10.1080/15598608.2007.10411842