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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 .
In August 2020, the U.S. Food and Drug Administration (FDA) became aware of nitrosamine impurities in certain samples of rifampin. [61] The FDA and manufacturers are investigating the origin of these impurities in rifampin, and the agency is developing testing methods for regulators and industry to detect the 1-methyl-4-nitrosopiperazine (MNP ...
The rifamycin group includes the classic rifamycin drugs as well as the rifamycin derivatives rifampicin (or rifampin), rifabutin, rifapentine, rifalazil and rifaximin. Rifamycin, sold under the trade name Aemcolo, is approved in the United States for treatment of travelers' diarrhea in some circumstances. [1] [2] [3]
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In a bacterium without the proper mutation(s) in rpoB rifampicin binds to a site near the fork in the β subunit and prevents the polymerase from transcribing more than two or three base pairs of any RNA sequence and stopping production of proteins within the cell.
Rifapentine in pregnant women has not been studied, but animal reproduction studies have resulted in fetal harm and were teratogenic. If rifapentine or rifampin are used in late pregnancy, coagulation should be monitored due to a possible increased risk of maternal postpartum hemorrhage and infant bleeding. [2]
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 ...
The following was moved here from the "Moebius arithmetical function" article: In number theory is very important another sum, defined by: M(n) = ∑ μ(n) . This function is closely linked with the positions of zeroes of Euler - Riemann ζ- function. The connection between M(n) and Riemann conjecture was known to Thomas Joannes Stieltjes.