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  2. Order type - Wikipedia

    en.wikipedia.org/wiki/Order_type

    In mathematics, especially in set theory, two ordered sets X and Y are said to have the same order type if they are order isomorphic, that is, if there exists a bijection (each element pairs with exactly one in the other set) : such that both f and its inverse are monotonic (preserving orders of elements).

  3. Order (group theory) - Wikipedia

    en.wikipedia.org/wiki/Order_(group_theory)

    An example of the latter is a(x) = x+1, b(x) = x−1 with ab(x) = x. If ab = ba , we can at least say that ord( ab ) divides lcm (ord( a ), ord( b )). As a consequence, one can prove that in a finite abelian group, if m denotes the maximum of all the orders of the group's elements, then every element's order divides m .

  4. Moore–Penrose inverse - Wikipedia

    en.wikipedia.org/wiki/Moore–Penrose_inverse

    The Python package NumPy provides a pseudoinverse calculation through its functions matrix.I and linalg.pinv; its pinv uses the SVD-based algorithm. SciPy adds a function scipy.linalg.pinv that uses a least-squares solver. The MASS package for R provides a calculation of the Moore–Penrose inverse through the ginv function. [24]

  5. Lenstra elliptic-curve factorization - Wikipedia

    en.wikipedia.org/wiki/Lenstra_elliptic-curve...

    The slope of the tangent line at some point A=(x, y) is s = (3x 2 + 5)/(2y) (mod n). Using s we can compute 2A. If the value of s is of the form a/b where b > 1 and gcd(a,b) = 1, we have to find the modular inverse of b. If it does not exist, gcd(n,b) is a non-trivial factor of n. First we compute 2P.

  6. Exclusive or - Wikipedia

    en.wikipedia.org/wiki/Exclusive_or

    Exclusive or with one specified input, as a function of the other input, is an involution or self-inverse function; applying it twice leaves the variable input unchanged. A ⊕ B {\\displaystyle ~A\\oplus B~}

  7. Tom Cruise honored with distinguished public service award ...

    www.aol.com/tom-cruise-honored-distinguished...

    Tom Cruise is choosing to accept a major honor from the U.S. Navy.. The "Top Gun" star, 62, on Tuesday received the Navy's Distinguished Public Service Award, the highest honor that Navy Secretary ...

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  9. American Airlines suspends flights to Haiti indefinitely - AOL

    www.aol.com/american-airlines-suspends-flights...

    American Airlines is no longer resuming its daily service out of Miami into Port-au-Prince's Toussaint Louverture International Airport.