Error functionIn mathematics, the error function (also called the Gauss error function), often denoted by erf, is a complex function of a complex variable defined as: Some authors define without the factor of . This nonelementary integral is a sigmoid function that occurs often in probability, statistics, and partial differential equations. In many of these applications, the function argument is a real number. If the function argument is real, then the function value is also real.
Gamma functionIn mathematics, the gamma function (represented by Γ, the capital letter gamma from the Greek alphabet) is one commonly used extension of the factorial function to complex numbers. The gamma function is defined for all complex numbers except the non-positive integers. For every positive integer n, Derived by Daniel Bernoulli, for complex numbers with a positive real part, the gamma function is defined via a convergent improper integral: The gamma function then is defined as the analytic continuation of this integral function to a meromorphic function that is holomorphic in the whole complex plane except zero and the negative integers, where the function has simple poles.
Function (mathematics)In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
Transcendental functionIn mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Formally, an analytic function f (z) of one real or complex variable z is transcendental if it is algebraically independent of that variable.
Thermal radiationThermal radiation is electromagnetic radiation generated by the thermal motion of particles in matter. Thermal radiation is generated when heat from the movement of charges in the material (electrons and protons in common forms of matter) is converted to electromagnetic radiation. All matter with a temperature greater than absolute zero emits thermal radiation. At room temperature, most of the emission is in the infrared (IR) spectrum. Particle motion results in charge-acceleration or dipole oscillation which produces electromagnetic radiation.
Beta functionIn mathematics, the beta function, also called the Euler integral of the first kind, is a special function that is closely related to the gamma function and to binomial coefficients. It is defined by the integral for complex number inputs such that . The beta function was studied by Leonhard Euler and Adrien-Marie Legendre and was given its name by Jacques Binet; its symbol Β is a Greek capital beta. The beta function is symmetric, meaning that for all inputs and .
Electromagnetic radiationIn physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields.
Laser ablationLaser ablation or photoablation (also called laser blasting) is the process of removing material from a solid (or occasionally liquid) surface by irradiating it with a laser beam. At low laser flux, the material is heated by the absorbed laser energy and evaporates or sublimates. At high laser flux, the material is typically converted to a plasma. Usually, laser ablation refers to removing material with a pulsed laser, but it is possible to ablate material with a continuous wave laser beam if the laser intensity is high enough.
Dielectric gasA dielectric gas, or insulating gas, is a dielectric material in gaseous state. Its main purpose is to prevent or rapidly quench electric discharges. Dielectric gases are used as electrical insulators in high voltage applications, e.g. transformers, circuit breakers (namely sulfur hexafluoride circuit breakers), switchgear (namely high voltage switchgear), radar waveguides, etc.
FluorineFluorine is a chemical element with the symbol F and atomic number 9. It is the lightest halogen and exists at standard conditions as a highly toxic, pale yellow diatomic gas. As the most electronegative reactive element, it is extremely reactive, as it reacts with all other elements except for the light inert gases. Among the elements, fluorine ranks 24th in universal abundance and 13th in terrestrial abundance.
IonizationIonization (or ionisation) is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation.
SulfurSulfur (also spelled sulphur in British English) is a chemical element with the symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula S8. Elemental sulfur is a bright yellow, crystalline solid at room temperature. Sulfur is the tenth most abundant element by mass in the universe and the fifth most on Earth. Though sometimes found in pure, native form, sulfur on Earth usually occurs as sulfide and sulfate minerals.
Vacuum interrupterIn electrical engineering, a vacuum interrupter is a switch which uses electrical contacts in a vacuum. It is the core component of medium-voltage circuit-breakers, generator circuit-breakers, and high-voltage circuit-breakers. Separation of the electrical contacts results in a metal vapour arc, which is quickly extinguished. Vacuum interrupters are widely used in utility power transmission systems, power generation unit, and power-distribution systems for railways, arc furnace applications, and industrial plants.
Excimer laserAn excimer laser, sometimes more correctly called an exciplex laser, is a form of ultraviolet laser which is commonly used in the production of microelectronic devices, semiconductor based integrated circuits or "chips", eye surgery, and micromachining. Since 1960s excimer lasers are widely used in high-resolution photolithography machines, one of the critical technologies required for microelectronic chip manufacturing. The term excimer is short for 'excited dimer', while exciplex is short for 'excited complex'.
Monotonic functionIn mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus, a function defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease.
ChalcogenThe chalcogens (ore forming) (ˈkælkədʒənz ) are the chemical elements in group 16 of the periodic table. This group is also known as the oxygen family. Group 16 consists of the elements oxygen (O), sulfur (S), selenium (Se), tellurium (Te), and the radioactive elements polonium (Po) and livermorium (Lv). Often, oxygen is treated separately from the other chalcogens, sometimes even excluded from the scope of the term "chalcogen" altogether, due to its very different chemical behavior from sulfur, selenium, tellurium, and polonium.
Circuit breakerA circuit breaker is an electrical safety device designed to protect an electrical circuit from damage caused by overcurrent. Its basic function is to interrupt current flow to protect equipment and to prevent the risk of fire. Unlike a fuse, which operates once and then must be replaced, a circuit breaker can be reset (either manually or automatically) to resume normal operation. Circuit breakers are made in varying sizes, from small devices that protect low-current circuits or individual household appliances, to large switchgear designed to protect high voltage circuits feeding an entire city.
ThermographyInfrared thermography (IRT), thermal video and/or thermal imaging, is a process where a thermal camera captures and creates an image of an object by using infrared radiation emitted from the object in a process, which are examples of infrared imaging science. Thermographic cameras usually detect radiation in the long-infrared range of the electromagnetic spectrum (roughly 9,000–14,000 nanometers or 9–14 μm) and produce images of that radiation, called thermograms.
Industrial gasIndustrial gases are the gaseous materials that are manufactured for use in industry. The principal gases provided are nitrogen, oxygen, carbon dioxide, argon, hydrogen, helium and acetylene, although many other gases and mixtures are also available in gas cylinders. The industry producing these gases is also known as industrial gas, which is seen as also encompassing the supply of equipment and technology to produce and use the gases. Their production is a part of the wider chemical Industry (where industrial gases are often seen as "specialty chemicals").
