Logarithmic derivativeIn mathematics, specifically in calculus and complex analysis, the logarithmic derivative of a function f is defined by the formula where is the derivative of f. Intuitively, this is the infinitesimal relative change in f; that is, the infinitesimal absolute change in f, namely scaled by the current value of f. When f is a function f(x) of a real variable x, and takes real, strictly positive values, this is equal to the derivative of ln(f), or the natural logarithm of f.
ThiopheneThiophene is a heterocyclic compound with the formula C4H4S. Consisting of a planar five-membered ring, it is aromatic as indicated by its extensive substitution reactions. It is a colorless liquid with a benzene-like odor. In most of its reactions, it resembles benzene. Compounds analogous to thiophene include furan (C4H4O), selenophene (C4H4Se) and pyrrole (C4H4NH), which each vary by the heteroatom in the ring. Thiophene was discovered as a contaminant in benzene.
Wirtinger derivativesIn complex analysis of one and several complex variables, Wirtinger derivatives (sometimes also called Wirtinger operators), named after Wilhelm Wirtinger who introduced them in 1927 in the course of his studies on the theory of functions of several complex variables, are partial differential operators of the first order which behave in a very similar manner to the ordinary derivatives with respect to one real variable, when applied to holomorphic functions, antiholomorphic functions or simply differentiabl
IndoleIndole is an aromatic, heterocyclic, organic compound with the formula . It has a bicyclic structure, consisting of a six-membered benzene ring fused to a five-membered pyrrole ring. Indole is widely distributed in the natural environment and can be produced by a variety of bacteria. As an intercellular signal molecule, indole regulates various aspects of bacterial physiology, including spore formation, plasmid stability, resistance to drugs, biofilm formation, and virulence.
Mycobacterium tuberculosisMycobacterium tuberculosis (M. tb), also known as Koch's bacillus, is a species of pathogenic bacteria in the family Mycobacteriaceae and the causative agent of tuberculosis. First discovered in 1882 by Robert Koch, M. tuberculosis has an unusual, waxy coating on its cell surface primarily due to the presence of mycolic acid. This coating makes the cells impervious to Gram staining, and as a result, M. tuberculosis can appear weakly Gram-positive. Acid-fast stains such as Ziehl–Neelsen, or fluorescent stains such as auramine are used instead to identify M.
