Brown dwarfBrown dwarfs (also called failed stars) are substellar objects that are not massive enough to sustain nuclear fusion of ordinary hydrogen (1H) into helium in their cores, unlike a main-sequence star. Instead, they have a mass between the most massive gas giant planets and the least massive stars, approximately 13 to 80 times that of Jupiter (). However, they can fuse deuterium (2H) and the most massive ones (> ) can fuse lithium (7Li).
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Integral equationIn mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
MetallicityIn astronomy, metallicity is the abundance of elements present in an object that are heavier than hydrogen and helium. Most of the normal currently detectable (i.e. non-dark) matter in the universe is either hydrogen or helium, and astronomers use the word "metals" as a convenient short term for "all elements except hydrogen and helium". This word-use is distinct from the conventional chemical or physical definition of a metal as an electrically conducting solid.
Red dwarfA red dwarf is the smallest and coolest kind of star on the main sequence. Red dwarfs are by far the most common type of star in the Milky Way, at least in the neighborhood of the Sun. However, as a result of their low luminosity, individual red dwarfs cannot be easily observed. From Earth, not one star that fits the stricter definitions of a red dwarf is visible to the naked eye. Proxima Centauri, the nearest star to the Sun, is a red dwarf, as are fifty of the sixty nearest stars.
Stochastic differential equationA stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs have many applications throughout pure mathematics and are used to model various behaviours of stochastic models such as stock prices, random growth models or physical systems that are subjected to thermal fluctuations. SDEs have a random differential that is in the most basic case random white noise calculated as the derivative of a Brownian motion or more generally a semimartingale.
G-type main-sequence starA G-type main-sequence star (spectral type: G-V), also often, and imprecisely called a yellow dwarf, or G star, is a main-sequence star (luminosity class V) of spectral type G. Such a star has about 0.9 to 1.1 solar masses and an effective temperature between about 5,300 and 6,000 K. Like other main-sequence stars, a G-type main-sequence star converts the element hydrogen to helium in its core by means of nuclear fusion, but can also fuse helium when hydrogen runs out.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
