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The definition of a KZ-reduced basis was given by Aleksandr Korkin and Yegor Ivanovich Zolotarev in 1877, a strengthened version of Hermite reduction. The first algorithm for constructing a KZ-reduced basis was given in 1983 by Kannan. [2] The block Korkine-Zolotarev (BKZ) algorithm was introduced in 1987. [3]
An early successful application of the LLL algorithm was its use by Andrew Odlyzko and Herman te Riele in disproving Mertens conjecture. [5]The LLL algorithm has found numerous other applications in MIMO detection algorithms [6] and cryptanalysis of public-key encryption schemes: knapsack cryptosystems, RSA with particular settings, NTRUEncrypt, and so forth.
8-Oxoguanine (8-hydroxyguanine, 8-oxo-Gua, or OH 8 Gua) is one of the most common DNA lesions resulting from reactive oxygen species [2] modifying guanine, and can result in a mismatched pairing with adenine resulting in G to T and C to A substitutions in the genome. [3] In humans, it is primarily repaired by DNA glycosylase OGG1.
Hydrosilanes can reduce 1,1-disubstituted double bonds that form stable tertiary carbocations upon protonation. Trisubstituted double bonds may be reduced selectively in the presence of 1,2-disubstituted or monosubstituted alkenes. [15] Aromatic compounds may be reduced with TFA and triethylsilane.
FAD can be reduced to FADH 2 through the addition of 2 H + and 2 e −. FADH 2 can also be oxidized by the loss of 1 H + and 1 e − to form FADH. The FAD form can be recreated through the further loss of 1 H + and 1 e −. FAD formation can also occur through the reduction and dehydration of flavin-N(5)-oxide. [8]
The reduction of nitroaromatics is conducted on an industrial scale. [1] Many methods exist, such as: Catalytic hydrogenation using: Raney nickel [2] or palladium-on-carbon, [3] [4] [5] platinum(IV) oxide, or Urushibara nickel. [6] Iron in acidic media. [7] [8] [9] Sodium hydrosulfite [10] Sodium sulfide (or hydrogen sulfide and base ...
It is sometimes called a normal form of f by G. In general this form is not uniquely defined because there are, in general, several elements of G that can be used for reducing f; this non-uniqueness is the starting point of Gröbner basis theory. The definition of the reduction shows immediately that, if h is a normal form of f by G, one has
[8] Since isotopy classes are disjoint, the number of reduced Latin squares gives an upper bound on the number of isotopy classes. Also, the total number of Latin squares is n!(n − 1)! times the number of reduced squares. [9] One can normalize a Cayley table of a quasigroup in the same manner as a reduced Latin square.