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  2. Hodge theory - Wikipedia

    en.wikipedia.org/wiki/Hodge_theory

    In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.

  3. Generalization - Wikipedia

    en.wikipedia.org/wiki/Generalization

    A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. [1] Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model ).

  4. Inductive reasoning - Wikipedia

    en.wikipedia.org/wiki/Inductive_reasoning

    Inductive reasoning is any of various methods of reasoning in which broad generalizations or principles are derived from a body of observations. [1] [2] This article is concerned with the inductive reasoning other than deductive reasoning (such as mathematical induction), where the conclusion of a deductive argument is certain, given the premises are correct; in contrast, the truth of the ...

  5. Representation theory - Wikipedia

    en.wikipedia.org/wiki/Representation_theory

    Automorphic forms are a generalization of modular forms to more general analytic functions, perhaps of several complex variables, with similar transformation properties. [44] The generalization involves replacing the modular group PSL 2 (R) and a chosen congruence subgroup by a semisimple Lie group G and a discrete subgroup Γ.

  6. Group representation - Wikipedia

    en.wikipedia.org/wiki/Group_representation

    The general theory for Lie groups deals with semidirect products of the two types, by means of general results called Mackey theory, which is a generalization of Wigner's classification methods. Representation theory also depends heavily on the type of vector space on which the group acts. One distinguishes between finite-dimensional ...

  7. Logical reasoning - Wikipedia

    en.wikipedia.org/wiki/Logical_reasoning

    [60] [73] An intimately connected factor is that the sample is random and representative. This means that it includes a fair and balanced selection of individuals with different key characteristics. For example, when making a generalization about human beings, the sample should include members of different races, genders, and age groups.

  8. Trump's economic team may get easy Senate rides. That ... - AOL

    www.aol.com/finance/trumps-economic-team-may...

    Some of President-elect Donald Trump's cabinet picks are facing hurdle after hurdle on the road to confirmation but not those on his economic team (at least so far).

  9. Straw man - Wikipedia

    en.wikipedia.org/wiki/Straw_man

    Aikin and Casey expanded on this model in 2010, introducing a third form. Referring to the "representative form" as the classic straw man, and the "selection form" as the weak man, the third form is called the hollow man. A hollow man argument is one that is a complete fabrication, where both the viewpoint and the opponent expressing it do not ...