Complex torusIn mathematics, a complex torus is a particular kind of complex manifold M whose underlying smooth manifold is a torus in the usual sense (i.e. the cartesian product of some number N circles). Here N must be the even number 2n, where n is the complex dimension of M. All such complex structures can be obtained as follows: take a lattice Λ in a vector space V isomorphic to Cn considered as real vector space; then the quotient group is a compact complex manifold. All complex tori, up to isomorphism, are obtained in this way.
Real structureIn mathematics, a real structure on a complex vector space is a way to decompose the complex vector space in the direct sum of two real vector spaces. The prototype of such a structure is the field of complex numbers itself, considered as a complex vector space over itself and with the conjugation map , with , giving the "canonical" real structure on , that is . The conjugation map is antilinear: and . A real structure on a complex vector space V is an antilinear involution .
Solid of revolutionIn geometry, a solid of revolution is a solid figure obtained by rotating a plane figure around some straight line (the axis of revolution), which may not intersect the generatrix (except at its boundary). The surface created by this revolution and which bounds the solid is the surface of revolution. Assuming that the curve does not cross the axis, the solid's volume is equal to the length of the circle described by the figure's centroid multiplied by the figure's area (Pappus's second centroid theorem).
Hot swappingHot swapping is the replacement or addition of components to a computer system without stopping, shutting down, or rebooting the system; hot plugging describes the addition of components only. Components which have such functionality are said to be hot-swappable or hot-pluggable; likewise, components which do not are cold-swappable or cold-pluggable. Most desktop computer hardware, such as CPUs and memory, are only cold-pluggable.
Mineral-insulated copper-clad cableMineral-insulated copper-clad cable is a variety of electrical cable made from copper conductors inside a copper sheath, insulated by inorganic magnesium oxide powder. The name is often abbreviated to MICC or MI cable, and colloquially known as pyro (because the original manufacturer and vendor for this product in the UK was a company called Pyrotenax). A similar product sheathed with metals other than copper is called mineral insulated metal sheathed (MIMS) cable.
CoachbuilderA coachbuilder or body-maker is someone who manufactures bodies for passenger-carrying vehicles. Coachwork is the body of an automobile, bus, horse-drawn carriage, or railway carriage. The word "coach" was derived from the Hungarian town of Kocs. A vehicle body constructed by a coachbuilder may be called a "coachbuilt body" (British English) or "custom body" (American English). Prior to the popularization of unibody construction in the 1960s, there were many independent coachbuilders who built bodies on chassis provided by a manufacturer, often for luxury or sports cars.
Doubling the cubeDoubling the cube, also known as the Delian problem, is an ancient geometric problem. Given the edge of a cube, the problem requires the construction of the edge of a second cube whose volume is double that of the first. As with the related problems of squaring the circle and trisecting the angle, doubling the cube is now known to be impossible to construct by using only a compass and straightedge, but even in ancient times solutions were known that employed other tools.
Cube (algebra)In arithmetic and algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example 23 = 8 or (x + 1)3. The cube is also the number multiplied by its square: n3 = n × n2 = n × n × n. The cube function is the function x ↦ x3 (often denoted y = x3) that maps a number to its cube. It is an odd function, as (−n)3 = −(n3).
