Invariance of generalized wordlength patterns
نویسندگان
چکیده
The generalized wordlength pattern (GWLP) introduced by Xu and Wu (2001) for an arbitrary fractional factorial design allows one to extend the use of the minimum aberration criterion to such designs. Ai and Zhang (2004) defined the J-characteristics of a design and showed that they uniquely determine the design. While both the GWLP and the J-characteristics require indexing the levels of each factor by a cyclic group, we see that the definitions carry over with appropriate changes if instead one uses an arbitrary abelian group. This means that the original definitions rest on an arbitrary choice of group structure. We show that the GWLP of a design is independent of this choice, but that the J-characteristics are not. We briefly discuss some implications of these results.
منابع مشابه
Designs with Multiple Groups of Factors
Identities about the wordlength patterns of regular s designs and their complementary designs are established through a first-order differential equation satisfied by a structure function. The identities are then generalized to s designs with multiple groups of factors. An advantage of using the structure function and partial differential equation is that it can easily adapt to some structural ...
متن کاملFixed-point Simulation Utility for C and C++ Based Digital Signal Processing Programs
This utility software automatically converts a oating-point digital signal processing program written in C or C++ language to a xed-point program. The conversion is conducted by deening a new xed-point data class and utilizing the operator overloading characteristic of the C++ language. A generalized xed-point format which consists of the wordlength, integer wordlength, sign, overrow, and quati...
متن کاملCooperative Benefit and Cost Games under Fairness Concerns
Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...
متن کاملتبدیلات دوگانگی آبلی استاندارد در گرانش f(T)
According to the perturbation order, the equations of motion of low-energy string effective action are the generalized Einstein equations. Thus, by making use of the conformal transformation of the metric tensor, it is possible to map the low-energy string effective action into f(T) gravity, relating the dilaton field to the torsion scalar. Considering a homogeneous and isotropic universe and ...
متن کاملω-NARROWNESS AND RESOLVABILITY OF TOPOLOGICAL GENERALIZED GROUPS
Abstract. A topological group H is called ω -narrow if for every neighbourhood V of it’s identity element there exists a countable set A such that V A = H = AV. A semigroup G is called a generalized group if for any x ∈ G there exists a unique element e(x) ∈ G such that xe(x) = e(x)x = x and for every x ∈ G there exists x − 1 ∈ G such that x − 1x = xx − 1 = e(x). Also le...
متن کامل