Non-analytic smooth functionIn mathematics, smooth functions (also called infinitely differentiable functions) and analytic functions are two very important types of functions. One can easily prove that any analytic function of a real argument is smooth. The converse is not true, as demonstrated with the counterexample below. One of the most important applications of smooth functions with compact support is the construction of so-called mollifiers, which are important in theories of generalized functions, such as Laurent Schwartz's theory of distributions.
Flexible AC transmission systemA flexible alternating current transmission system (FACTS) is a system composed of static equipment used for the alternating current (AC) transmission of electrical energy. It is meant to enhance controllability and increase power transfer capability of the network. It is generally a power electronics-based system. FACTS is defined by the Institute of Electrical and Electronics Engineers (IEEE) as "a power electronic based system and other static equipment that provide control of one or more AC transmission system parameters to enhance controllability and increase power transfer capability".
High-voltage direct currentA high-voltage direct current (HVDC) electric power transmission system (also called a power superhighway or an electrical superhighway) uses direct current (DC) for electric power transmission, in contrast with the more common alternating current (AC) transmission systems. Most HVDC links use voltages between 100 kV and 800 kV. However, a 1,100 kV link in China was completed in 2019 over a distance of with a power capacity of 12 GW. With this dimension, intercontinental connections become possible which could help to deal with the fluctuations of wind power and photovoltaics.
Analytic functionIn mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about converges to the function in some neighborhood for every in its domain.
Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Bump functionIn mathematics, a bump function (also called a test function) is a function on a Euclidean space which is both smooth (in the sense of having continuous derivatives of all orders) and compactly supported. The set of all bump functions with domain forms a vector space, denoted or The dual space of this space endowed with a suitable topology is the space of distributions. The function given by is an example of a bump function in one dimension.
V-2 rocketThe V-2 (Vergeltungswaffe 2), with the technical name Aggregat 4 (A-4), was the world's first long-range guided ballistic missile. The missile, powered by a liquid-propellant rocket engine, was developed during the Second World War in Nazi Germany as a "vengeance weapon" and assigned to attack Allied cities as retaliation for the Allied bombings of German cities. The V-2 rocket also became the first artificial object to travel into space by crossing the Kármán line (edge of space) with the vertical launch of MW 18014 on 20 June 1944.
Operation PaperclipOperation Paperclip was a secret United States intelligence program in which more than 1,600 German scientists, engineers, and technicians were taken from the former Nazi Germany to the U.S. for government employment after the end of World War II in Europe, between 1945 and 1959. Conducted by the Joint Intelligence Objectives Agency (JIOA), it was largely carried out by special agents of the U.S. Army's Counterintelligence Corps (CIC). Many of these personnel were former members and some were former leaders of the Nazi Party.
Distribution (mathematics)Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distributions make it possible to differentiate functions whose derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used in the theory of partial differential equations, where it may be easier to establish the existence of distributional solutions (weak solutions) than classical solutions, or where appropriate classical solutions may not exist.
Power supplyA power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a result, power supplies are sometimes referred to as electric power converters. Some power supplies are separate standalone pieces of equipment, while others are built into the load appliances that they power. Examples of the latter include power supplies found in desktop computers and consumer electronics devices.
