If <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$F$$</EquationSource> </InlineEquation> is a full factorial design and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$D$$</EquationSource> </InlineEquation> is a fraction of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$F$$</EquationSource> </InlineEquation>, then for a given monomial ordering, the algebraic method gives a saturated polynomial basis for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$$D$$</EquationSource> </InlineEquation> which can be used for regression. Consider now an algebraic basis for the complementary fraction of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$$D$$</EquationSource> </InlineEquation> in <InlineEquation ID="IEq6"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation></equationsource></inlineequation>

Identities and bounds for the reliability of coherent systems are analysed and computed using the techniques of commutative algebra. The techniques are applied to the analysis of some of the most relevant k-out-of-n class systems. The efficiency of the algebraic approach in obtaining exact...

This paper presents a new procedure to construct families of spatial approximation-prediction functions which depend on several parameters. The method is based on partitions of the unity. In order to find optimal functions in these families we introduce a Vietoris simplicial set associated to an...

Classical dimensional analysis in its original form starts by expressing the units for derived quantities, such as force, in terms of power products of basic units etc. This suggests the use of toric ideal theory from algebraic geometry. Within this the Graver basis provides a unique primitive...