Dihedral groupIn mathematics, a dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. Dihedral groups are among the simplest examples of finite groups, and they play an important role in group theory, geometry, and chemistry. The notation for the dihedral group differs in geometry and abstract algebra. In geometry, D_n or Dih_n refers to the symmetries of the n-gon, a group of order 2n. In abstract algebra, D_2n refers to this same dihedral group.
Σ-algebraIn mathematical analysis and in probability theory, a σ-algebra (also σ-field) on a set X is a nonempty collection Σ of subsets of X closed under complement, countable unions, and countable intersections. The ordered pair is called a measurable space. The σ-algebras are a subset of the set algebras; elements of the latter only need to be closed under the union or intersection of finitely many subsets, which is a weaker condition.
Abelian groupIn mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.
São Miguel IslandSão Miguel Island (ˈsɐ̃w miˈɣɛl; Portuguese for "Saint Michael"), nicknamed "The Green Island" (Ilha Verde), is the largest and most populous island in the Portuguese archipelago of the Azores. The island covers and has around 140,000 inhabitants, with 45,000 people residing in Ponta Delgada, the archipelago's largest city. In 1427, São Miguel became the second of the islands discovered by Gonçalo Velho Cabral to be settled by colonists from continental Portugal.
AlgebraAlgebra () is the study of variables and the rules for manipulating these variables in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields.
Miguel CovarrubiasMiguel Covarrubias, also known as José Miguel Covarrubias Duclaud (22 November 1904 — 4 February 1957) was a Mexican painter, caricaturist, illustrator, ethnologist and art historian. Along with his American colleague Matthew W. Stirling, he was the co-discoverer of the Olmec civilization. José Miguel Covarrubias Duclaud was born 22 November 1904 in Mexico City. After graduating from the Escuela Nacional Preparatoria at the age of 14, he started producing caricatures and illustrations for texts and training materials published by the Mexican Ministry of Public Education.
Blue noteIn jazz and blues, a blue note is a note that—for expressive purposes—is sung or played at a slightly different pitch from standard. Typically the alteration is between a quartertone and a semitone, but this varies depending on the musical context. Like the blues in general, the blue notes can mean many things. One quality that they all have in common, however, is that they are lower than one would expect, classically speaking. But this flatness may take several forms. On the one hand, it may be a microtonal affair of a quarter-tone or so.
Federal Reserve NoteFederal Reserve Notes, also United States banknotes, are the currently issued banknotes of the United States dollar. The United States Bureau of Engraving and Printing produces the notes under the authority of the Federal Reserve Act of 1913 and issues them to the Federal Reserve Banks at the discretion of the Board of Governors of the Federal Reserve System. The Reserve Banks then circulate the notes to their member banks, at which point they become liabilities of the Reserve Banks and obligations of the United States.
Miguel A. CatalánMiguel Antonio Catalán y Sañudo (1894–1957) was a Spanish spectroscopist. Miguel Antonio Catalán y Sañudo was born in Zaragoza, he obtained his degree in chemistry from the University of Zaragoza and received his doctorate in Madrid in 1917 for his thesis about spectrochemistry. In 1920, he began work as a researcher at Imperial College London. Examining the spectrum of the arc of manganese, he determined that the optical spectra of complex atoms consisted of groups of lines –which he called "multipletes"- between which existed certain characteristic regularities.
Associative algebraIn mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over the field K.
