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v = v 1 ∧ v 2 and both w ≤ ~ v 1 and w ≤ ~ v 2 hold. This defines a preorder ≤ ~ on W ( X ), so an equivalence relation can be defined by w ~ v when w ≤ ~ v and v ≤ ~ w . One may then show that the partially ordered quotient set W ( X )/~ is the free bounded lattice FX .
Model-based clustering [1] based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not ...
This can be seen by applying in turn each of the unimodular inverse matrices A −1, B −1, and C −1 to an arbitrary primitive Pythagorean triple (d, e, f), noting that by the above reasoning primitivity and the Pythagorean property are retained, and noting that for any triple larger than (3, 4, 5) exactly one of the inverse transition ...
This article is an incomplete list of Financial Accounting Standards Board (FASB) pronouncements, which consist of Statements of Financial Accounting Standards ("SFAS" or simply "FAS"), Statements of Financial Accounting Concepts, Interpretations, Technical Bulletins, and Staff Positions, which together presented rules and guidelines for preparing, presenting, and reporting financial ...
[9] [6] The method of cylindrical algebraic decomposition, by George E. Collins (1975), improved the time dependence to doubly exponential, [9] [10] of the form () where is the number of bits needed to represent the coefficients in the sentence whose value is to be determined, is the number of polynomials in the sentence, is their total degree ...
The class of in the mapping class group does not depend on the choice of made above, and the resulting element is called the Dehn twist about . If c {\displaystyle c} is not null-homotopic this mapping class is nontrivial, and more generally the Dehn twists defined by two non-homotopic curves are distinct elements in the mapping class group.
In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x = 0 and x 2 = 0 define the same algebraic variety but different schemes) and allowing "varieties" defined over any commutative ring (for example, Fermat curves are defined over the integers).
The National Library of Medicine Technical Bulletin is a public domain information newsletter of the Office of Engagement and Training, United States National Library of Medicine (NLM). [ 1 ] [ 2 ] The newsletter contains current news and information for NLM products and services, listings for NLM events, [ 3 ] and update notes for NLM ...