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  2. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    That is, xlim sup X n if and only if there exists a subsequence (X n k) of (X n) such that xX n k for all k. lim inf X n consists of elements of X which belong to X n for all except finitely many n (i.e., for cofinitely many n). That is, xlim inf X n if and only if there exists some m > 0 such that xX n for all n > m.

  3. Orthogonal polynomials - Wikipedia

    en.wikipedia.org/wiki/Orthogonal_polynomials

    In other words, the sequence is obtained from the sequence of monomials 1, x, x 2, … by the Gram–Schmidt process with respect to this inner product. Usually the sequence is required to be orthonormal , namely, P n , P n = 1 , {\displaystyle \langle P_{n},P_{n}\rangle =1,} however, other normalisations are sometimes used.

  4. Bell-shaped function - Wikipedia

    en.wikipedia.org/wiki/Bell-shaped_function

    The Gaussian function is the archetypal example of a bell shaped function. A bell-shaped function or simply 'bell curve' is a mathematical function having a characteristic "bell"-shaped curve. These functions are typically continuous or smooth, asymptotically approach zero for large negative/positive x, and have a single, unimodal maximum at ...

  5. (G,X)-manifold - Wikipedia

    en.wikipedia.org/wiki/(G,X)-manifold

    In geometry, if X is a manifold with an action of a topological group G by analytical diffeomorphisms, the notion of a (G, X)-structure on a topological space is a way to formalise it being locally isomorphic to X with its G-invariant structure; spaces with a (G, X)-structure are always manifolds and are called (G, X)-manifolds.

  6. Moser's worm problem - Wikipedia

    en.wikipedia.org/wiki/Moser's_worm_problem

    Moser's worm problem (also known as mother worm's blanket problem) is an unsolved problem in geometry formulated by the Austrian-Canadian mathematician Leo Moser in 1966. The problem asks for the region of smallest area that can accommodate every plane curve of length 1.

  7. Gan Kim Yong - Wikipedia

    en.wikipedia.org/wiki/Gan_Kim_Yong

    During the 2020 general election, Gan led the four-member PAP team contesting in Chua Chu Kang GRC and won about 59% of the vote. During the COVID-19 pandemic in Singapore , Gan and Lawrence Wong were appointed co-chairs of a multi-ministerial committee set up by the government on 22 January 2020 to manage the situation. [ 7 ]

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