Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Mathematical beautyMathematical beauty is the aesthetic pleasure derived from the abstractness, purity, simplicity, depth or orderliness of mathematics. Mathematicians may express this pleasure by describing mathematics (or, at least, some aspect of mathematics) as beautiful or describe mathematics as an art form, (a position taken by G. H. Hardy) or, at a minimum, as a creative activity. Comparisons are made with music and poetry. Mathematicians describe an especially pleasing method of proof as elegant.
Rubik's CubeThe Rubik's Cube is a 3-D combination puzzle originally invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik. Originally called the Magic Cube, the puzzle was licensed by Rubik to be sold by Pentangle Puzzles in the UK in 1978, and then by Ideal Toy Corp in 1980 via businessman Tibor Laczi and Seven Towns founder Tom Kremer. The cube was released internationally in 1980 and became one of the most recognized icons in popular culture. It won the 1980 German Game of the Year special award for Best Puzzle.
Content managementContent management (CM) is a set of processes and technologies that supports the collection, managing, and publishing of information in any form or medium. When stored and accessed via computers, this information may be more specifically referred to as digital content, or simply as content. Digital content may take the form of text (such as electronic documents), images, multimedia files (such as audio or video files), or any other file type that follows a content lifecycle requiring management.
Intersection theoryIn mathematics, intersection theory is one of the main branches of algebraic geometry, where it gives information about the intersection of two subvarieties of a given variety. The theory for varieties is older, with roots in Bézout's theorem on curves and elimination theory. On the other hand, the topological theory more quickly reached a definitive form. There is yet an ongoing development of intersection theory. Currently the main focus is on: virtual fundamental cycles, quantum intersection rings, Gromov-Witten theory and the extension of intersection theory from schemes to stacks.
Enterprise content managementEnterprise content management (ECM) extends the concept of content management by adding a timeline for each content item and, possibly, enforcing processes for its creation, approval, and distribution. Systems using ECM generally provide a secure repository for managed items, analog or digital. They also include one (or more) methods for importing content to bring manage new items, and several presentation methods to make items available for use. Although ECM content may be protected by digital rights management (DRM), it is not required.
Web contentWeb content is the text, visual or audio content that is made available online and user encountered as part of the online usage and experience on websites. It may include text, , sounds and audio, online videos, among other items placed within web pages. In the book Information Architecture for the World Wide Web, Lou Rosenfeld and Peter Morville wrote, "We define content broadly as 'the stuff in your website.
Linear system of divisorsIn algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family. These arose first in the form of a linear system of algebraic curves in the projective plane. It assumed a more general form, through gradual generalisation, so that one could speak of linear equivalence of divisors D on a general scheme or even a ringed space (X, OX).
Klein bottleIn mathematics, the Klein bottle (ˈklaɪn) is an example of a non-orientable surface; that is, informally, a one-sided surface which, if traveled upon, could be followed back to the point of origin while flipping the traveler upside down. More formally, the Klein bottle is a two-dimensional manifold on which one cannot define a normal vector at each point that varies continuously over the whole manifold. Other related non-orientable surfaces include the Möbius strip and the real projective plane.
Whitney embedding theoremIn mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney: The strong Whitney embedding theorem states that any smooth real m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in the real 2m-space, \R^{2m}, if m > 0. This is the best linear bound on the smallest-dimensional Euclidean space that all m-dimensional manifolds embed in, as the real projective spaces of dimension m cannot be embedded into real (2m − 1)-space if m is a power of two (as can be seen from a characteristic class argument, also due to Whitney).
