Order isomorphismIn the mathematical field of order theory, an order isomorphism is a special kind of monotone function that constitutes a suitable notion of isomorphism for partially ordered sets (posets). Whenever two posets are order isomorphic, they can be considered to be "essentially the same" in the sense that either of the orders can be obtained from the other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections.
Order topologyIn mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order topology on X is generated by the subbase of "open rays" for all a, b in X. Provided X has at least two elements, this is equivalent to saying that the open intervals together with the above rays form a base for the order topology.
Real numberIn mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature. Here, continuous means that pairs of values can have arbitrarily small differences. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives.
Free-electron laserA free-electron laser (FEL) is a (fourth generation) light source producing extremely brilliant and short pulses of radiation. An FEL functions and behaves in many ways like a laser, but instead of using stimulated emission from atomic or molecular excitations, it employs relativistic electrons as a gain medium. Radiation is generated by a bunch of electrons passing through a magnetic structure (called undulator or wiggler).
Order theoryOrder theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing statements such as "this is less than that" or "this precedes that". This article introduces the field and provides basic definitions. A list of order-theoretic terms can be found in the order theory glossary. Orders are everywhere in mathematics and related fields like computer science. The first order often discussed in primary school is the standard order on the natural numbers e.
Space elevatorA space elevator, also referred to as a space bridge, star ladder, and orbital lift, is a proposed type of planet-to-space transportation system, often depicted in science fiction. The main component would be a cable (also called a tether) anchored to the surface and extending into space. An Earth-based space elevator cannot be constructed with a tall tower supported from below due to the immense weight—instead, it would consist of a cable with one end attached to the surface near the equator and the other end attached to a counterweight in space beyond geostationary orbit (35,786 km altitude).
Photonic crystalA photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic lattices (crystal structure) of semiconductors affect their conductivity of electrons. Photonic crystals occur in nature in the form of structural coloration and animal reflectors, and, as artificially produced, promise to be useful in a range of applications.
ScatteringScattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by localized non-uniformities (including particles and radiation) in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection.
Non-rocket spacelaunchNon-rocket spacelaunch refers to theoretical concepts for launch into space where much of the speed and altitude needed to achieve orbit is provided by a propulsion technique that is not subject to the limits of the rocket equation. Although all space launches to date have been rockets, a number of alternatives to rockets have been proposed. In some systems, such as a combination launch system, skyhook, rocket sled launch, rockoon, or air launch, a portion of the total delta-v may be provided, either directly or indirectly, by using rocket propulsion.
Speckle (interference)Speckle, speckle pattern, or speckle noise is a granular degrading the as a consequence of interference among wavefronts in coherent imaging systems, such as radar, synthetic aperture radar (SAR), medical ultrasound and optical coherence tomography. Speckle is not external noise; rather, it is an inherent fluctuation in diffuse reflections, because the scatterers are not identical for each cell, and the coherent illumination wave is highly sensitive to small variations in phase changes.
