Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Electrical efficiencyThe efficiency of a system in electronics and electrical engineering is defined as useful power output divided by the total electrical power consumed (a fractional expression), typically denoted by the Greek small letter eta (η – ήτα). If energy output and input are expressed in the same units, efficiency is a dimensionless number. Where it is not customary or convenient to represent input and output energy in the same units, efficiency-like quantities have units associated with them.
Two-dimensional electron gasA two-dimensional electron gas (2DEG) is a scientific model in solid-state physics. It is an electron gas that is free to move in two dimensions, but tightly confined in the third. This tight confinement leads to quantized energy levels for motion in the third direction, which can then be ignored for most problems. Thus the electrons appear to be a 2D sheet embedded in a 3D world. The analogous construct of holes is called a two-dimensional hole gas (2DHG), and such systems have many useful and interesting properties.
Economic efficiencyIn microeconomics, economic efficiency, depending on the context, is usually one of the following two related concepts: Allocative or Pareto efficiency: any changes made to assist one person would harm another. Productive efficiency: no additional output of one good can be obtained without decreasing the output of another good, and production proceeds at the lowest possible average total cost. These definitions are not equivalent: a market or other economic system may be allocatively but not productively efficient, or productively but not allocatively efficient.
Hydrogen chlorideThe compound hydrogen chloride has the chemical formula and as such is a hydrogen halide. At room temperature, it is a colourless gas, which forms white fumes of hydrochloric acid upon contact with atmospheric water vapor. Hydrogen chloride gas and hydrochloric acid are important in technology and industry. Hydrochloric acid, the aqueous solution of hydrogen chloride, is also commonly given the formula HCl. Hydrogen chloride is a diatomic molecule, consisting of a hydrogen atom H and a chlorine atom Cl connected by a polar covalent bond.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
Fuel efficiencyFuel efficiency is a form of thermal efficiency, meaning the ratio of effort to result of a process that converts chemical potential energy contained in a carrier (fuel) into kinetic energy or work. Overall fuel efficiency may vary per device, which in turn may vary per application, and this spectrum of variance is often illustrated as a continuous . Non-transportation applications, such as industry, benefit from increased fuel efficiency, especially fossil fuel power plants or industries dealing with combustion, such as ammonia production during the Haber process.
Seasonal energy efficiency ratioIn the United States, the efficiency of air conditioners is often rated by the seasonal energy efficiency ratio (SEER) which is defined by the Air Conditioning, Heating, and Refrigeration Institute, a trade association, in its 2008 standard AHRI 210/240, Performance Rating of Unitary Air-Conditioning and Air-Source Heat Pump Equipment. A similar standard is the European seasonal energy efficiency ratio (ESEER). The SEER rating of a unit is the cooling output during a typical cooling-season divided by the total electric energy input during the same period.
Light-emitting diodeA light-emitting diode (LED) is a semiconductor device that emits light when current flows through it. Electrons in the semiconductor recombine with electron holes, releasing energy in the form of photons. The color of the light (corresponding to the energy of the photons) is determined by the energy required for electrons to cross the band gap of the semiconductor. White light is obtained by using multiple semiconductors or a layer of light-emitting phosphor on the semiconductor device.
InterhalogenIn chemistry, an interhalogen compound is a molecule which contains two or more different halogen atoms (fluorine, chlorine, bromine, iodine, or astatine) and no atoms of elements from any other group. Most interhalogen compounds known are binary (composed of only two distinct elements). Their formulae are generally , where n = 1, 3, 5 or 7, and X is the less electronegative of the two halogens. The value of n in interhalogens is always odd, because of the odd valence of halogens.
