Glossary of chess

This page explains commonly used terms in chess in alphabetical order. Some of these have their own pages, like fork and pin. For a list of unorthodox chess pieces, see Fairy chess piece; for a list of terms specific to chess problems, see Glossary of chess problems; for a list of chess-related games, see Chess variants.

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    [adjective: prophylactic] Prophylactic techniques include the blockade, overprotection, and the mysterious rook move.

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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Glossary_of_chess

    Rank (differential topology)

    In mathematics, the rank of a differentiable map f : M → N between differentiable manifolds at a point p ∈ M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map

    from the tangent space at p to the tangent space at f(p). As a linear map between vector spaces it has a well-defined rank, which is just the dimension of the image in Tf(p)N:

    Constant rank maps

    A differentiable map f : M → N is said to have constant rank if the rank of f is the same for all p in M. Constant rank maps have a number of nice properties and are an important concept in differential topology.

    Three special cases of constant rank maps occur. A constant rank map f : M → N is

  • an immersion if rank f = dim M (i.e. the derivative is everywhere injective),
  • a submersion if rank f = dim N (i.e. the derivative is everywhere surjective),
  • a local diffeomorphism if rank f = dim M = dim N (i.e. the derivative is everywhere bijective).

    • The map f itself need not be injective, surjective, or bijective for these conditions to hold, only the behavior of the derivative is important. For example, there are injective maps which are not immersions and immersions which are not injections. However, if f : M → N is a smooth map of constant rank then

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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Rank_(differential_topology)

    Rank of a partition

    In mathematics, particularly in the fields of number theory and combinatorics, the rank of a partition of a positive integer is a certain integer associated with the partition. In fact at least two different definitions of rank appear in the literature. The first definition, with which most of this article is concerned, is that the rank of a partition is the number obtained by subtracting the number of parts in the partition from the largest part in the partition. The concept was introduced by Freeman Dyson in a paper published in the journal Eureka. It was presented in the context of a study of certain congruence properties of the partition function discovered by the Indian mathematical genius Srinivasa Ramanujan. A different concept, sharing the same name, is used in combinatorics, where the rank is taken to be the size of the Durfee square of the partition.

    Definition

    By a partition of a positive integer n we mean a finite multiset λ = { λk, λk − 1, . . . , λ1 } of positive integers satisfying the following two conditions:

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    This page contains text from Wikipedia, the Free Encyclopedia - https://wn.com/Rank_of_a_partition

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    Raunchy

    by: Raunchy

    It always turns me on to see
    The way you look at me
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    Deadly severed spiteful tongue
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    Run like crazy, run to the sea
    Sea is what you see in me
    Track to the city filth that lies below
    When I'm with you the streets are fields where flowers grow
    You look pretty in every stitch you're in, I'm a little boy
    I'm in love with you in ways they'll never try
    Set sails for the future head on into the night
    Set sails for the future head on into the night
    A rose dressed in thorns
    Yet your touch is just a feeble plot
    A rose dressed in thorns
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    Yet your touch is just a feeble plot
    Kick up a fire and watch them explode
    Track to the city filth that lies below
    When I'm with you the streets are fields where flowers grow
    You look pretty in every stitch you're in, I'm a little boy
    I'm in love with you in ways they'll never try
    Set sails for the future head on into the night




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