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  2. Duality (mathematics) - Wikipedia

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

    For instance, linear algebra duality corresponds in this way to bilinear maps from pairs of vector spaces to scalars, the duality between distributions and the associated test functions corresponds to the pairing in which one integrates a distribution against a test function, and Poincaré duality corresponds similarly to intersection number ...

  3. Duality (optimization) - Wikipedia

    en.wikipedia.org/wiki/Duality_(optimization)

    The duality gap is zero if and only if strong duality holds. Otherwise the gap is strictly positive and weak duality holds. [5] In computational optimization, another "duality gap" is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem.

  4. List of dualities - Wikipedia

    en.wikipedia.org/wiki/List_of_dualities

    In mathematics, a duality, generally speaking, translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one fashion, often (but not always) by means of an involution operation: if the dual of A is B, then the dual of B is A.

  5. Dual linear program - Wikipedia

    en.wikipedia.org/wiki/Dual_linear_program

    The max-flow min-cut theorem is a special case of the strong duality theorem: flow-maximization is the primal LP, and cut-minimization is the dual LP. See Max-flow min-cut theorem#Linear program formulation. Other graph-related theorems can be proved using the strong duality theorem, in particular, Konig's theorem. [9]

  6. Boolean algebra - Wikipedia

    en.wikipedia.org/wiki/Boolean_algebra

    In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false , usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.

  7. Zeros and poles - Wikipedia

    en.wikipedia.org/wiki/Zeros_and_poles

    A function f is meromorphic in an open set U if for every point z of U there is a neighborhood of z in which at least one of f and 1/f is holomorphic. If f is meromorphic in U, then a zero of f is a pole of 1/f, and a pole of f is a zero of 1/f. This induces a duality between zeros and poles, that is

  8. Conjunction/disjunction duality - Wikipedia

    en.wikipedia.org/.../Conjunction/disjunction_duality

    In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, [1] [2] [3] also called the duality principle. [ 4 ] [ 5 ] [ 6 ] It is the most widely known example of duality in logic. [ 1 ]

  9. Symbolab - Wikipedia

    en.wikipedia.org/wiki/Symbolab

    Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

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