In mathematics, a graded vector space is a type of vector space that includes the extra structure of gradation, which is a decomposition of the vector space into a direct sum of vector subspaces.

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-graded vector space, often called simply a graded vector space without the prefix Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbb{N} , is a vector space V which decomposes into a direct sum of the form

where each Failed to parse (Missing texvc executable; please see math/README to configure.): V_n

Graded vector spaces are common. For example the set of all polynomials in one variable form a graded vector space, where the homogeneous elements of degree n are exactly the linear combinations of monomials of degree n.

The subspaces of a graded vector space need not be indexed by the set of natural numbers, and may be indexed by the elements of any set I. An I-graded vector space V is a vector space that can be written as a direct sum of subspaces indexed by elements i of set I:

A vector space is a mathematical structure formed by a collection of elements called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars in this context. Scalars are often taken to be real numbers, but there are also vector spaces with scalar multiplication by complex numbers, rational numbers, or generally any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called axioms, listed below. An example of a vector space is that of Euclidean vectors, which may be used to represent physical quantities such as forces: any two forces (of the same type) can be added to yield a third, and the multiplication of a force vector by a real multiplier is another force vector. In the same vein, but in a more geometric sense, vectors representing displacements in the plane or in three-dimensional space also form vector spaces.

Vector spaces are the subject of linear algebra and are well understood from this point of view, since vector spaces are characterized by their dimension, which, roughly speaking, specifies the number of independent directions in the space. A vector space may be endowed with additional structure, such as a norm or inner product. Such spaces arise naturally in mathematical analysis, mainly in the guise of infinite-dimensional function spaces whose vectors are functions. Analytical problems call for the ability to decide whether a sequence of vectors converges to a given vector. This is accomplished by considering vector spaces with additional structure, mostly spaces endowed with a suitable topology, thus allowing the consideration of proximity and continuity issues. These topological vector spaces, in particular Banach spaces and Hilbert spaces, have a richer theory.

Charles Bradford "Brad" Henry (born June 10, 1963) was the 26th Governor of the U.S. state of Oklahoma. A member of the Democratic Party, he was elected governor in 2002. Henry faced Republican US Representative Ernest Istook for re-election on November 7, 2006, and won with 66% of the vote.

Henry was the third governor and second Democrat in Oklahoma history to hold two consecutive terms, along with Democrat George Nigh and Republican Frank Keating. In 2010, Henry was ineligible to run for re-election as the Oklahoma constitution only allows two terms. His second term ended on January 10, 2011 as Oklahoma governors and other statewide elected officeholders are sworn-in on the second Monday every four years.

Henry was born in Shawnee, Oklahoma, the son of Charles Henry, a prominent judge and former state representative. After graduating from Shawnee High School, Henry attended the University of Oklahoma as a President's Leadership Scholar and earned a bachelor's degree in economics in 1985. He was a member of Delta Tau Delta Fraternity. In 1988, he was awarded his law degree from the University of Oklahoma College of Law, where he served as managing editor of the Law Review.

Pierre Michel (born 11 June 1942), is a literature professor and a scholar specializing in the French writer Octave Mirbeau.

Michel was born in Toulon, the son of the historian Henri Michel.

After defending his dissertation on the works of Octave Mirbeau at the University of Angers in 1992, Michel founded a year later, the Société Octave Mirbeau, a literary society he is currently presiding. He is also the founder and editor in chief of Cahiers Octave Mirbeau (1993).

A biographer and indefatigable authority of Mirbeau's work, Michel has published critical editions of all his work: novels, plays, articles and correspondence.

Pierre Michel was awarded the Sévigné prize in October 2003 for his edition of the first volume of Mirbeau's Correspondance générale.

3-2-1 Contact is an American science educational television show that aired on PBS from 1980 to 1988, and an adjoining children's magazine. The show, a production of the Children's Television Workshop, teaches scientific principles and their applications. Dr. Edward G. Atkins, who was responsible for much of the scientific content of the show, felt that the TV program wouldn't replace a classroom but would open the viewers to ask questions about the scientific purpose of things.

3-2-1 Contact was the brainchild of Samuel Y. Gibbon, Jr., who had been the executive producer of The Electric Company for CTW from 1971 to 1977. (Gibbon actually left CTW before Contact's production began, though he was still credited as "Senior Consultant.")

The first season of 65 programs began airing January 14, 1980 on select PBS member stations; it featured a cast of three college students who discussed science in an on-campus room known as the Workshop. The first season came to an end on April 11, 1980, but funds for more episodes were not sufficient until 1982.