Absolute magnitude is a measure of the luminosity of a celestial object, on an inverse logarithmic astronomical magnitude scale. An object's absolute magnitude is defined to be equal to the apparent magnitude that the object would have if it were viewed from a distance of exactly 10 parsecs, without extinction of its light due to absorption by interstellar matter and cosmic dust. By hypothetically placing all objects at a standard reference distance from the observer, their luminosities can be directly compared among each other on a magnitude scale.
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel.
In mathematics, convolution is a mathematical operation on two functions that produces a third function that expresses how the shape of one is modified by the other. The term convolution refers to both the result function and to the process of computing it. It is defined as the integral of the product of the two functions after one is reversed and shifted. The integral is evaluated for all values of shift, producing the convolution function.
In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body when decelerating from its current speed to a state of rest. Formally, a kinetic energy is any term in a system's Lagrangian which includes a derivative with respect to time.
In mathematics, the mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints. It is one of the most important results in real analysis. This theorem is used to prove statements about a function on an interval starting from local hypotheses about derivatives at points of the interval.
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Relative density, or specific gravity, is the ratio of the density of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ; for gases, the reference is air at room temperature. The term "relative density" is often preferred in scientific usage.
A Fourier series is a sum that represents a periodic function as a sum of sine and cosine waves. The frequency of each wave in the sum, or harmonic, is an integer multiple of the periodic function's fundamental frequency. Each harmonic's phase and amplitude can be determined using harmonic analysis. A Fourier series may potentially contain an infinite number of harmonics. Summing part of but not all the harmonics in a function's Fourier series produces an approximation to that function. For example, using the first few harmonics of the Fourier series for a square wave yields an approximation of a square wave.
In fluid dynamics, Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluid's potential energy. The principle is named after Daniel Bernoulli who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form. The principle is only applicable for isentropic flows: when the effects of irreversible processes and non-adiabatic processes are small and can be neglected.
In differential geometry, a Riemannian manifold or Riemannian space(M, g), so called after the German mathematician Bernhard Riemann, is a real, smooth manifold M equipped with a positive-definite inner product gp on the tangent space TpM at each point p.
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, it is often represented as the product of force and displacement. A force is said to do positive work if it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.
Some Buddhist terms and concepts lack direct translations into English that cover the breadth of the original term. Below are given a number of important Buddhist terms, short definitions, and the languages in which they appear. In this list, an attempt has been made to organize terms by their original form and give translations and synonyms in other languages along with the definition.
In the mathematical field of differential geometry, a metric tensor allows defining distances and angles near each point of a surface, in the same way as inner product allows defining distances and angles in Euclidean spaces. More precisely, a metric tensor at a point of a manifold is a bilinear form defined on the tangent space at this point.
Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities used in Lagrangian mechanics with (generalized) momenta. Both theories provide interpretations of classical mechanics and describe the same physical phenomena.
A mongoose is a small terrestrial carnivorous mammal belonging to the family Herpestidae. This family is currently split into two subfamilies, the Herpestinae and the Mungotinae. The Herpestinae comprises 23 living species that are native to southern Europe, Africa and Asia, whereas the Mungotinae comprises 11 species native to Africa. The Herpestidae originated about 21.8 ± 3.6 million years ago in the Early Miocene and genetically diverged into two main genetic lineages between 19.1 and 18.5 ± 3.5 million years ago.
Bushmeat is meat from wildlife species that are hunted for human consumption, most often referring to the meat of game in Africa. Bushmeat represents a primary source of animal protein and a cash-earning commodity for inhabitants of humid tropical forest regions in Africa, Latin America and Asia. Bushmeat is an important food resource for poor people, particularly in rural areas.
In orbital mechanics, mean motion is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. The concept applies equally well to a small body revolving about a large, massive primary body or to two relatively same-sized bodies revolving about a common center of mass. While nominally a mean, and theoretically so in the case of two-body motion, in practice the mean motion is not typically an average over time for the orbits of real bodies, which only approximate the two-body assumption. It is rather the instantaneous value which satisfies the above conditions as calculated from the current gravitational and geometric circumstances of the body's constantly-changing, perturbed orbit.
