enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Scheme (mathematics) - Wikipedia

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

    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).

  3. Function field of an algebraic variety - Wikipedia

    en.wikipedia.org/wiki/Function_field_of_an...

    In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V.In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.

  4. Function approximation - Wikipedia

    en.wikipedia.org/wiki/Function_approximation

    Several progressively more accurate approximations of the step function. An asymmetrical Gaussian function fit to a noisy curve using regression.. In general, a function approximation problem asks us to select a function among a well-defined class [citation needed] [clarification needed] that closely matches ("approximates") a target function [citation needed] in a task-specific way.

  5. Geometric function theory - Wikipedia

    en.wikipedia.org/wiki/Geometric_function_theory

    Analytic continuation of natural logarithm (imaginary part) Analytic continuation is a technique to extend the domain of a given analytic function.Analytic continuation often succeeds in defining further values of a function, for example in a new region where an infinite series representation in terms of which it is initially defined becomes divergent.

  6. Functional analysis - Wikipedia

    en.wikipedia.org/wiki/Functional_analysis

    Geometry of Banach spaces contains many topics. One is combinatorial approach connected with Jean Bourgain; another is a characterization of Banach spaces in which various forms of the law of large numbers hold. Noncommutative geometry. Developed by Alain Connes, partly building on earlier notions, such as George Mackey's approach to ergodic ...

  7. Limit (mathematics) - Wikipedia

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

    On the other hand, if X is the domain of a function f(x) and if the limit as n approaches infinity of f(x n) is L for every arbitrary sequence of points {x n} in X − x 0 which converges to x 0, then the limit of the function f(x) as x approaches x 0 is equal to L. [10] One such sequence would be {x 0 + 1/n}.

  8. Algebraic torus - Wikipedia

    en.wikipedia.org/wiki/Algebraic_torus

    The notion of invariant given above generalizes naturally to tori over arbitrary base schemes, with functions taking values in more general rings. While the order of the extension group is a general invariant, the other two invariants above do not seem to have interesting analogues outside the realm of fraction fields of one-dimensional domains ...

  9. Hilbert's axioms - Wikipedia

    en.wikipedia.org/wiki/Hilbert's_axioms

    Removing five axioms mentioning "plane" in an essential way, namely I.4–8, and modifying III.4 and IV.1 to omit mention of planes, yields an axiomatization of Euclidean plane geometry. Hilbert's axioms, unlike Tarski's axioms, do not constitute a first-order theory because the axioms V.1–2 cannot be expressed in first-order logic.