Total orderIn mathematics, a total order or linear order is a partial order in which any two elements are comparable. That is, a total order is a binary relation on some set , which satisfies the following for all and in : (reflexive). If and then (transitive). If and then (antisymmetric). or (strongly connected, formerly called total). Reflexivity (1.) already follows from connectedness (4.), but is required explicitly by many authors nevertheless, to indicate the kinship to partial orders.
Accelerating expansion of the universeObservations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered during 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which both used distant type Ia supernovae to measure the acceleration.
Linear approximationIn mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.
Complete partial orderIn mathematics, the phrase complete partial order is variously used to refer to at least three similar, but distinct, classes of partially ordered sets, characterized by particular completeness properties. Complete partial orders play a central role in theoretical computer science: in denotational semantics and domain theory. A complete partial order, abbreviated cpo, can refer to any of the following concepts depending on context. A partially ordered set is a directed-complete partial order (dcpo) if each of its directed subsets has a supremum.
Negative energyNegative energy is a concept used in physics to explain the nature of certain fields, including the gravitational field and various quantum field effects. Gravitational energy Gravitational energy, or gravitational potential energy, is the potential energy a massive object has because it is within a gravitational field. In classical mechanics, two or more masses always have a gravitational potential. Conservation of energy requires that this gravitational field energy is always negative, so that it is zero when the objects are infinitely far apart.
Island arcIsland arcs are long chains of active volcanoes with intense seismic activity found along convergent tectonic plate boundaries. Most island arcs originate on oceanic crust and have resulted from the descent of the lithosphere into the mantle along the subduction zone. They are the principal way by which continental growth is achieved. Island arcs can either be active or inactive based on their seismicity and presence of volcanoes. Active arcs are ridges of recent volcanoes with an associated deep seismic zone.
Moment problemIn mathematics, a moment problem arises as the result of trying to invert the mapping that takes a measure μ to the sequence of moments More generally, one may consider for an arbitrary sequence of functions Mn. In the classical setting, μ is a measure on the real line, and M is the sequence { xn : n = 0, 1, 2, ... }. In this form the question appears in probability theory, asking whether there is a probability measure having specified mean, variance and so on, and whether it is unique.
Greatest element and least elementIn mathematics, especially in order theory, the greatest element of a subset of a partially ordered set (poset) is an element of that is greater than every other element of . The term least element is defined dually, that is, it is an element of that is smaller than every other element of Let be a preordered set and let An element is said to be if and if it also satisfies: for all By switching the side of the relation that is on in the above definition, the definition of a least element of is obtained.
Volcanic arcA volcanic arc (also known as a magmatic arc) is a belt of volcanoes formed above a subducting oceanic tectonic plate, with the belt arranged in an arc shape as seen from above. Volcanic arcs typically parallel an oceanic trench, with the arc located further from the subducting plate than the trench. The oceanic plate is saturated with water, mostly in the form of hydrous minerals such as micas, amphiboles, and serpentines. As the oceanic plate is subducted, it is subjected to increasing pressure and temperature with increasing depth.
