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The Möbius function () is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832. [ i ] [ ii ] [ 2 ] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula .
Rifampicin, also known as rifampin, is an ansamycin antibiotic used to treat several types of bacterial infections, including tuberculosis (TB), Mycobacterium avium complex, leprosy, and Legionnaires' disease. [3]
Rifampin rapidly kills fast-dividing bacilli strains as well as "persisters" cells, which remain biologically inactive for long periods of time that allow them to evade antibiotic activity. [7] In addition, rifabutin and rifapentine have both been used against tuberculosis acquired in HIV-positive patients.
In non-resistant TB, rifampin binds the beta subunit of RNA polymerase and disrupts transcription elongation. Mutation in the rpoB gene changes the sequence of amino acids and eventual conformation, or arrangement, of the beta subunit. In this case, rifampin can no longer bind or prevent transcription, and the bacterium is resistant. [19] [20]
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For example, if one starts with Euler's totient function φ, and repeatedly applies the transformation process, one obtains: φ the totient function; φ ∗ 1 = I, where I(n) = n is the identity function; I ∗ 1 = σ 1 = σ, the divisor function; If the starting function is the Möbius function itself, the list of functions is: μ, the Möbius ...
Isoniazid/rifampicin, also known as isoniazid/rifampin, is a medication used to treat tuberculosis. [1] It is a fixed dose combination of isoniazid and rifampicin (rifampin). [1] It is used together with other antituberculosis medication. [1] It is taken by mouth. [1] It is on the World Health Organization's List of Essential Medicines. [2]
Scientists at the Italian drug company Achifar discovered rifabutin in 1975. (Eventually Archifar became part of Farmitalia Carlo Erba, a unit of the conglomerate Montedison which was subsequently bought by Pharmacia) This company's Adria Laboratories subsidiary filed for Food and Drug Administration (FDA) approval of rifabutin under the brand name Mycobutin in the early 1990s and the drug ...