Duality (optimization)In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.
ProsoponProsopon (UKˈprɒsəpɒn, USprəˈsoʊ-; from πρόσωπον prósōpon; plural: πρόσωπα prósōpa) is a theological term used in Christian theology as designation for the concept of a divine person. The term has a particular significance in Christian Triadology (study of the Trinity), and also in Christology. In English language, the form prosopon is used mainly in scholarly works, related to theology, philosophy or history of religion, while it is also commonly translated as person, both in scholarly or non-scholarly writings.
NestorianismNestorianism is a term used in Christian theology and Church history to refer to several mutually related but doctrinally distinct sets of teachings. The first meaning of the term is related to the original teachings of Christian theologian Nestorius ( () 450 AD), who promoted specific doctrines in the fields of Christology and Mariology. The second meaning of the term is much wider, and relates to a set of later theological teachings, that were traditionally labeled as Nestorian, but differ from the teachings of Nestorius in origin, scope and terminology.
Amorphous metalAn amorphous metal (also known as metallic glass, glassy metal, or shiny metal) is a solid metallic material, usually an alloy, with disordered atomic-scale structure. Most metals are crystalline in their solid state, which means they have a highly ordered arrangement of atoms. Amorphous metals are non-crystalline, and have a glass-like structure. But unlike common glasses, such as window glass, which are typically electrical insulators, amorphous metals have good electrical conductivity and can show metallic luster.
Hypostasis (philosophy and religion)Hypostasis (plural: hypostases), from the Greek ὑπόστασις (hypóstasis), is the underlying state or underlying substance and is the fundamental reality that supports all else. In Neoplatonism the hypostasis of the soul, the intellect (nous) and "the one" was addressed by Plotinus. In Christian theology, the Holy Trinity consists of three hypostases: Hypostasis of the Father, Hypostasis of the Son, and Hypostasis of the Holy Spirit. Pseudo-Aristotle used hypostasis in the sense of material substance.
Knapsack problemThe knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible. It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Travelling salesman problemThe travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP.
Curse of dimensionalityThe curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional settings such as the three-dimensional physical space of everyday experience. The expression was coined by Richard E. Bellman when considering problems in dynamic programming. Dimensionally cursed phenomena occur in domains such as numerical analysis, sampling, combinatorics, machine learning, data mining and databases.
Cost curveIn economics, a cost curve is a graph of the costs of production as a function of total quantity produced. In a free market economy, productively efficient firms optimize their production process by minimizing cost consistent with each possible level of production, and the result is a cost curve. Profit-maximizing firms use cost curves to decide output quantities. There are various types of cost curves, all related to each other, including total and average cost curves; marginal ("for each additional unit") cost curves, which are equal to the differential of the total cost curves; and variable cost curves.
