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  2. Periodic sequence - Wikipedia

    en.wikipedia.org/wiki/Periodic_sequence

    A (purely) periodic sequence (with period p), or a p-periodic sequence, is a sequence a 1, a 2, a 3, ... satisfying . a n+p = a n. for all values of n. [1] [2] [3] If a sequence is regarded as a function whose domain is the set of natural numbers, then a periodic sequence is simply a special type of periodic function.

  3. Aufbau principle - Wikipedia

    en.wikipedia.org/wiki/Aufbau_principle

    For example, thallium (Z = 81) has the ground-state configuration 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 4d 10 5p 6 6s 2 4f 14 5d 10 6p 1 [4] or in condensed form, [Xe] 6s 2 4f 14 5d 10 6p 1. Other authors write the subshells outside of the noble gas core in order of increasing n , or if equal, increasing n + l , such as Tl ( Z = 81) [Xe ...

  4. Advanced oxidation process - Wikipedia

    en.wikipedia.org/wiki/Advanced_oxidation_process

    The mechanism of ·OH production (Part 1) highly depends on the sort of AOP technique that is used. For example, ozonation, UV/H 2 O 2, photocatalytic oxidation and Fenton's oxidation rely on different mechanisms of ·OH generation: UV/H 2 O 2: [6] [12] [13] H 2 O 2 + UV → 2·OH (homolytic bond cleavage of the O-O bond of H 2 O 2 leads to ...

  5. Cycles and fixed points - Wikipedia

    en.wikipedia.org/wiki/Cycles_and_fixed_points

    G has 2 fixed points, 1 2-cycle and 3 4-cycles B has 4 fixed points and 6 2-cycles GB has 2 fixed points and 2 7-cycles P * (1,2,3,4) T = (4,1,3,2) T Permutation of four elements with 1 fixed point and 1 3-cycle. In mathematics, the cycles of a permutation π of a finite set S correspond bijectively to the orbits of the subgroup generated by π ...

  6. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    Applying the f function k times to the number n = 2 k a + b will give the result 3 c a + d, where d is the result of applying the f function k times to b, and c is how many increases were encountered during that sequence. For example, for 2 5 a + 1 there are 3 increases as 1 iterates to 2, 1, 2, 1, and finally to 2 so the result is 3 3 a + 2 ...

  7. All one polynomial - Wikipedia

    en.wikipedia.org/wiki/All_one_polynomial

    Over GF(2) the AOP has many interesting properties, including: . The Hamming weight of the AOP is m + 1, the maximum possible for its degree [3]; The AOP is irreducible if and only if m + 1 is prime and 2 is a primitive root modulo m + 1 [1] (over GF(p) with prime p, it is irreducible if and only if m + 1 is prime and p is a primitive root modulo m + 1)

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  9. Adverse outcome pathway - Wikipedia

    en.wikipedia.org/wiki/Adverse_outcome_pathway

    An adverse outcome pathway (AOP) is structured representation of biological events leading to adverse effects and is considered relevant to risk assessment. [1] [2] [3] The AOP links in a linear way existing knowledge along one or more series of causally connected key events (KE) between two points — a molecular initiating event (MIE) and an adverse outcome (AO) that occur at a level of ...