Rings of SaturnThe rings of Saturn are the most extensive ring system of any planet in the Solar System. They consist of countless small particles, ranging in size from micrometers to meters, that orbit around Saturn. The ring particles are made almost entirely of water ice, with a trace component of rocky material. There is still no consensus as to their mechanism of formation. Although theoretical models indicated that the rings were likely to have formed early in the Solar System's history, newer data from Cassini suggested they formed relatively late.
Finite ringIn mathematics, more specifically abstract algebra, a finite ring is a ring that has a finite number of elements. Every finite field is an example of a finite ring, and the additive part of every finite ring is an example of an abelian finite group, but the concept of finite rings in their own right has a more recent history. Although rings have more structure than groups, the theory of finite rings is simpler than that of finite groups.
Ring (mathematics)In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ring is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series.
Bounded set (topological vector space)In functional analysis and related areas of mathematics, a set in a topological vector space is called bounded or von Neumann bounded, if every neighborhood of the zero vector can be inflated to include the set. A set that is not bounded is called unbounded. Bounded sets are a natural way to define locally convex polar topologies on the vector spaces in a dual pair, as the polar set of a bounded set is an absolutely convex and absorbing set. The concept was first introduced by John von Neumann and Andrey Kolmogorov in 1935.
General linear groupIn mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns (and also the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position.
Finite groupIn abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century.
Finite geometryA finite geometry is any geometric system that has only a finite number of points. The familiar Euclidean geometry is not finite, because a Euclidean line contains infinitely many points. A geometry based on the graphics displayed on a computer screen, where the pixels are considered to be the points, would be a finite geometry. While there are many systems that could be called finite geometries, attention is mostly paid to the finite projective and affine spaces because of their regularity and simplicity.
Category of ringsIn mathematics, the category of rings, denoted by Ring, is the whose objects are rings (with identity) and whose morphisms are ring homomorphisms (that preserve the identity). Like many categories in mathematics, the category of rings is , meaning that the class of all rings is proper. The category Ring is a meaning that the objects are sets with additional structure (addition and multiplication) and the morphisms are functions that preserve this structure.
Rings of JupiterThe planet Jupiter has a system of faint planetary rings. The Jovian rings were the third ring system to be discovered in the Solar System, after those of Saturn and Uranus. The main ring was discovered in 1979 by the Voyager 1 space probe and the system was more thoroughly investigated in the 1990s by the Galileo orbiter. The main ring has also been observed by the Hubble Space Telescope and from Earth for several years. Ground-based observation of the rings requires the largest available telescopes.
NK Lokomotiva ZagrebNogometni klub Lokomotiva Zagreb (Lokomotiva Zagreb Football Club), commonly known as Lokomotiva Zagreb or simply Lokomotiva, is a Croatian professional football club based in Zagreb. It competes in the Croatian First Football League, the country's top division. Founded in 1914, the club's only period of success came in the late 1940s and early 1950s before spending most of the following five decades in lower-level leagues. Between 2007 and 2009 they won three consecutive promotions to rise from the fourth level to the first in the Croatian football league system.
Product of ringsIn mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the . Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings.
Martha Reeves (anchorite)Martha Reeves (born 1941) is a vowed Anglican solitary (or anchorite), with Rowan Williams, the former Archbishop of Canterbury, as bishop-protector. A graduate of the Madeira School (Class of 1959), she is also a Stanford-educated professor of theology who has written numerous articles and books under the name "Maggie Ross" as well as translated a number of Carthusian Novice Conferences. Reeves, at one time Desmond Tutu's spiritual director, was Bell Distinguished Professor in Anglican and Ecumenical Studies appointed to the Department of Philosophy and Religion, Kendall College of Arts and Sciences, The University of Tulsa.
