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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]
The role of the deoxyriboside form of 8-oxoguanine, 8-oxo-2'-deoxyguanosine (abbreviated 8-oxo-dG or 8-OHdG) in cancer and aging also applies to 8-oxoguanine. Oxoguanine glycosylase is employed in the removal of 8-oxoguanine from DNA by the process of base excision repair.
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.
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.
Sodium sulfide (or hydrogen sulfide and base). Illustrated by the selective reduction of dinitrophenol to the nitroaminophenol. [11] Tin(II) chloride [12] Titanium(III) chloride; Samarium [13] Hydroiodic acid [14] Metal hydrides are typically not used to reduce aryl nitro compounds to anilines because they tend to produce azo compounds. (See below)
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The reduced form of the system is: = + = +, with vector of reduced form errors that each depends on all structural errors, where the matrix A must be nonsingular for the reduced form to exist and be unique. Again, each endogenous variable depends on potentially each exogenous variable.
Acid–base extraction is a subclass of liquid–liquid extractions and involves the separation of chemical species from other acidic or basic compounds. [1] It is typically performed during the work-up step following a chemical synthesis to purify crude compounds [2] and results in the product being largely free of acidic or basic impurities.