In mathematics, the mean value theorem (or Lagrange theorem) states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.
The École polytechnique fédérale de Lausanne (EPFL; English: Swiss Federal Institute of Technology in Lausanne; Eidgenössische Technische Hochschule Lausanne) is a public research university in Lausanne, Switzerland. Established in 1853, EPFL has placed itself as a university specializing in engineering and natural sciences. EPFL is part of the ETH Domain, which is directly dependent on the Federal Department of Economic Affairs, Education and Research.
Xenon is a chemical element with the symbol Xe and atomic number 54. It is a dense, colorless, odorless noble gas found in Earth's atmosphere in trace amounts. Although generally unreactive, it can undergo a few chemical reactions such as the formation of xenon hexafluoroplatinate, the first noble gas compound to be synthesized. Xenon is used in flash lamps and arc lamps, and as a general anesthetic. The first excimer laser design used a xenon dimer molecule (Xe2) as the lasing medium, and the earliest laser designs used xenon flash lamps as pumps.
In mathematical analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.
In chemistry, perxenates are salts of the yellow xenon-containing anion XeO64-. This anion has octahedral molecular geometry, as determined by Raman spectroscopy, having O–Xe–O bond angles varying between 87° and 93°. The Xe–O bond length was determined by X-ray crystallography to be 1.875 Å. Perxenates are synthesized by the disproportionation of xenon trioxide when dissolved in strong alkali: 2 XeO3 ( ()) + 4 OH− ( ()) → Xe ( ()) + XeO64- ( ()) + O2 ( ()) + 2 H2O ( ()) When Ba(OH)2 is used as the alkali, barium perxenate can be crystallized from the resulting solution.