many-dimensional
81Hilbert space — For the Hilbert space filling curve, see Hilbert curve. Hilbert spaces can be used to study the harmonics of vibrating strings. The mathematical concept of a Hilbert space, named after David Hilbert, generalizes the notion of Euclidean space. It… …
82Physical Sciences — ▪ 2009 Introduction Scientists discovered a new family of superconducting materials and obtained unique images of individual hydrogen atoms and of a multiple exoplanet system. Europe completed the Large Hadron Collider, and China and India took… …
83nature, philosophy of — Introduction the discipline that investigates substantive issues regarding the actual features of nature as a reality. The discussion here is divided into two parts: the philosophy of physics and the philosophy of biology. In this… …
84Cartesian coordinate system — Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2, 3) in green, (−3, 1) in red, (−1.5, −2.5) in blue, and the origin (0, 0) in purple. A Cartesian coordinate system specifies each point… …
85Dual space — In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors… …
86Representation theory — This article is about the theory of representations of algebraic structures by linear transformations and matrices. For the more general notion of representations throughout mathematics, see representation (mathematics). Representation theory is… …
87Earth Sciences — ▪ 2009 Introduction Geology and Geochemistry The theme of the 33rd International Geological Congress, which was held in Norway in August 2008, was “Earth System Science: Foundation for Sustainable Development.” It was attended by nearly… …
88Mathematics and Physical Sciences — ▪ 2003 Introduction Mathematics Mathematics in 2002 was marked by two discoveries in number theory. The first may have practical implications; the second satisfied a 150 year old curiosity. Computer scientist Manindra Agrawal of the… …
89Nobel Prizes — ▪ 2009 Introduction Prize for Peace The 2008 Nobel Prize for Peace was awarded to Martti Ahtisaari, former president (1994–2000) of Finland, for his work over more than 30 years in settling international disputes, many involving ethnic,… …
90arts, East Asian — Introduction music and visual and performing arts of China, Korea, and Japan. The literatures of these countries are covered in the articles Chinese literature, Korean literature, and Japanese literature. Some studies of East Asia… …
