Amenability

	Amenability Amenable may refer to: * Amenable group * Amenable species * Amenable number An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original number and when multiplied together give the original number. To put it algebraically, for a posi ... * Amenable set See also * Agreeableness {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Amenable Group In mathematics, an amenable group is a locally compact topological group ''G'' carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of ''G'', was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun on "''mean''". The amenability property has a large number of equivalent formulations. In the field of analysis, the definition is in terms of linear functionals. An intuitive way to understand this version is that the support of the regular representation is the whole space of irreducible representations. In discrete group theory, where ''G'' has the discrete topology, a simpler definition is used. In this setting, a group is amenable if one can say what proport ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Amenable Species Amenable species is a term used within the context of USDA's meat and poultry inspection program to signify exotic species (livestock and fowl not covered by the statutes) that might be added to the laws and thus be eligible for mandatory federal inspection, which is taxpayer-funded. An exotic species is considered an amenable species if its anatomy and biology are substantially the same as the animals currently inspected. The Poultry Products Inspection Act (P.L. 85-172, as amended; 21 U.S.C. 451 et seq.) was expanded in 2001 to cover ostrich, rhea, and emu (ratites) because USDA determined that the hazards they present to food safety are essentially the same as those posed by chickens, turkeys, ducks, etc., and the existing contamination detection and prevention systems are sufficient to control them. Buffalo have been considered for inclusion under the Federal Meat Inspection Act (21 U.S.C. 601 et seq.) because they are bovine species (like cattle). Deer and elk, on the oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Amenable Number An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original number and when multiplied together give the original number. To put it algebraically, for a positive integer ''n'', there is a multiset of ''n'' integers , for which the equalities n = \sum_^n a_i = \prod_^n a_i hold. Negative numbers are allowed in the multiset. For example, 5 is amenable since 5 = 1 + (-1) + 1 + (-1) + 5. All and only those numbers congruent to 0 or 1 (mod 4), except 4, are amenable. The first few amenable numbers are: 1, 5, 8, 9, 12, 13 ... A solution for integers of the form ''n'' = 4''k'' + 1 could be given by a set of 2''k'' (+1)s and 2''k'' (-1)s and ''n'' itself. (This generalizes the example of 5 given above.) Although not obvious from the definition, the set of amenable numbers is closed under multiplication (the product of two amenable numbers is an amenable number). All composite number A comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Amenable Set Amenable may refer to: * Amenable group * Amenable species * Amenable number An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original number and when multiplied together give the original number. To put it algebraically, for a posi ... * Amenable set See also * Agreeableness {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]