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  2. Word problem (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Word_problem_(mathematics)

    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 .

  3. Model-based clustering - Wikipedia

    en.wikipedia.org/wiki/Model-based_clustering

    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 ...

  4. Tree of primitive Pythagorean triples - Wikipedia

    en.wikipedia.org/wiki/Tree_of_primitive...

    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 ...

  5. Existential theory of the reals - Wikipedia

    en.wikipedia.org/wiki/Existential_theory_of_the...

    [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 ...

  6. Happy ending problem - Wikipedia

    en.wikipedia.org/wiki/Happy_ending_problem

    In mathematics, the "happy ending problem" (so named by Paul Erdős because it led to the marriage of George Szekeres and Esther Klein [1]) is the following statement: Theorem — any set of five points in the plane in general position [ 2 ] has a subset of four points that form the vertices of a convex quadrilateral .

  7. List of FASB pronouncements - Wikipedia

    en.wikipedia.org/wiki/List_of_FASB_pronouncements

    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 ...

  8. American Mathematics Competitions - Wikipedia

    en.wikipedia.org/wiki/American_Mathematics...

    The American Mathematics Competitions (AMCs) are the first of a series of competitions in secondary school mathematics sponsored by the Mathematical Association of America (MAA) that determine the United States of America's team for the International Mathematical Olympiad (IMO). The selection process takes place over the course of roughly five ...

  9. Mapping class group of a surface - Wikipedia

    en.wikipedia.org/wiki/Mapping_class_group_of_a...

    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.