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  2. Inversion (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Inversion_(discrete...

    An inversion may be denoted by the pair of places (2, 4) or the pair of elements (5, 2). The inversions of this permutation using element-based notation are: (3, 1), (3, 2), (5, 1), (5, 2), and (5,4). In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order.

  3. Inversive geometry - Wikipedia

    en.wikipedia.org/wiki/Inversive_geometry

    This is called circle inversion or plane inversion. The inversion taking any point P (other than O ) to its image P ' also takes P ' back to P , so the result of applying the same inversion twice is the identity transformation which makes it a self-inversion (i.e. an involution).

  4. Octahedral symmetry - Wikipedia

    en.wikipedia.org/wiki/Octahedral_symmetry

    The four hexagonal cycles have the inversion (the black knot on top) in common. The hexagons are symmetric, so e.g. 3 and 4 are in the same cycle. A regular octahedron has 24 rotational (or orientation-preserving) symmetries, and 48 symmetries altogether. These include transformations that combine a reflection and a rotation.

  5. Reciprocal polynomial - Wikipedia

    en.wikipedia.org/wiki/Reciprocal_polynomial

    Reciprocal polynomials have several connections with their original polynomials, including: deg p = deg p ∗ if is not 0.; p(x) = x n p ∗ (x −1). [2]α is a root of a polynomial p if and only if α −1 is a root of p ∗.

  6. Inverse function rule - Wikipedia

    en.wikipedia.org/wiki/Inverse_function_rule

    Integrating this relationship gives = ′ (()) +.This is only useful if the integral exists. In particular we need ′ to be non-zero across the range of integration. It follows that a function that has a continuous derivative has an inverse in a neighbourhood of every point where the derivative is non-zero.

  7. Why Am I Snacking So Much? (& How to Stop) - AOL

    www.aol.com/why-am-snacking-much-stop-125800077.html

    If you’re feeling hunger cues (e.g., a rumbling stomach), go ahead and grab that snack, guilt-free! But if you’re reaching for a snack because of another trigger, consider a snack-free way to ...

  8. 6. Worms and other parasitic infections. With heavy worm burdens or certain parasitic infections, dogs can vomit. You may see worms in the vomit, but an absence of worms doesn’t mean parasites ...

  9. Improper rotation - Wikipedia

    en.wikipedia.org/wiki/Improper_rotation

    The direct subgroup of S 2n is C n, order n, index 2, being the rotoreflection generator applied twice. For odd n, S 2n contains an inversion, denoted C i or S 2. S 2n is the direct product: S 2n = C n × S 2, if n is odd. For any n, if odd p is a divisor of n, then S 2n/p is a subgroup of S 2n, index p. For example S 4 is a subgroup of S 12 ...

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