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  2. While several different routes to the 1,3,2,4-dithiadiphosphetane 2,4-disulfides exist the most commonly used is the electrophilic aromatic substitution reaction of an arene with P 4 S 10. An alternative reaction is the reaction of a thiol with P 4 S 10 to form a substance like the Davy reagent. The Davy reagent is identical to Lawesson's ...

  3. List of space groups - Wikipedia

    en.wikipedia.org/wiki/List_of_space_groups

    The possible screw axes are: 2 1, 3 1, 3 2, 4 1, 4 2, 4 3, 6 1, 6 2, 6 3, 6 4, and 6 5. Wherever there is both a rotation or screw axis n and a mirror or glide plane m along the same crystallographic direction, they are represented as a fraction or n/m.

  4. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For any integer n, n ≡ 1 (mod 2) if and only if 3n + 14 (mod 6). Equivalently, ⁠ n − 1 / 3 ⁠ ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 124 loop (the inverse of the 421 loop of the unaltered function f defined in the Statement of the problem section of ...

  5. 1 + 2 + 3 + 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = ⁠ 1 / 6 ⁠, B 4 = ⁠− + 1 / 30 ⁠, and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]

  6. Non-celiac gluten sensitivity - Wikipedia

    en.wikipedia.org/wiki/Non-celiac_gluten_sensitivity

    Reported symptoms of NCGS are similar to those of celiac disease, [30] [31] with most patients reporting both gastrointestinal and non-gastrointestinal symptoms. [29] [32] In the "classical" presentation of NCGS, gastrointestinal symptoms are similar to those of irritable bowel syndrome, and are also not distinguishable from those of wheat allergy, but there is a different interval between ...

  7. 1 − 2 + 3 − 4 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88...

    The idea becomes clearer by considering the general series 1 − 2x + 3x 24x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.

  8. List of 4X video games - Wikipedia

    en.wikipedia.org/wiki/List_of_4X_video_games

    Endless Space 2 [3] Amplitude Studios: Sci-fi (Space) WIN, OSX: Endless Space 2 is a turn-based strategy, science fiction 4X game. It is the sequel to the Endless Space. 2017: Oriental Empires [3] Iceberg Interactive: Historical: WIN: Turn-based. 2017: Stars in Shadow [58] Ashdar Games: Sci-fi (Space) WIN: Turn-based strategy in the vein of ...

  9. Trichlorobenzene - Wikipedia

    en.wikipedia.org/wiki/Trichlorobenzene

    Trichlorobenzene (TCB) may refer to any of three isomeric chlorinated derivatives of benzene with the molecular formula C 6 H 3 Cl 3. They differ by the positions of the chlorine atoms around the ring: 1,2,3-Trichlorobenzene; 1,2,4-Trichlorobenzene; 1,3,5-Trichlorobenzene