Cauchy sequenceIn mathematics, a Cauchy sequence, named after Augustin-Louis Cauchy, is a sequence whose elements become arbitrarily close to each other as the sequence progresses. More precisely, given any small positive distance, all but a finite number of elements of the sequence are less than that given distance from each other. It is not sufficient for each term to become arbitrarily close to the term. For instance, in the sequence of square roots of natural numbers: the consecutive terms become arbitrarily close to each other – their differences tend to zero as the index n grows.
Kerr metricThe Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which makes exact solutions very difficult to find. The Kerr metric is a generalization to a rotating body of the Schwarzschild metric, discovered by Karl Schwarzschild in 1915, which described the geometry of spacetime around an uncharged, spherically symmetric, and non-rotating body.
Philosophy of space and timePhilosophy of space and time is the branch of philosophy concerned with the issues surrounding the ontology and epistemology of space and time. While such ideas have been central to philosophy from its inception, the philosophy of space and time was both an inspiration for and a central aspect of early analytic philosophy. The subject focuses on a number of basic issues, including whether time and space exist independently of the mind, whether they exist independently of one another, what accounts for time's apparently unidirectional flow, whether times other than the present moment exist, and questions about the nature of identity (particularly the nature of identity over time).
Power densityPower density is the amount of power (time rate of energy transfer) per unit volume. In energy transformers including batteries, fuel cells, motors, power supply units etc., power density refers to a volume, where it is often called volume power density, expressed as W/m3. In reciprocating internal combustion engines, power density (power per swept volume or brake horsepower per cubic centimeter) is an important metric, based on the internal capacity of the engine, not its external size.
Geometric distributionIn probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set ; The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set . Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other.
Apple Lossless Audio CodecThe Apple Lossless Audio Codec (ALAC), also known as Apple Lossless, or Apple Lossless Encoder (ALE), is an audio coding format, and its reference audio codec implementation, developed by Apple Inc. for lossless data compression of digital music. After initially keeping it proprietary from its inception in 2004, in late 2011 Apple made the codec available open source and royalty-free. Traditionally, Apple has referred to the codec as Apple Lossless, though more recently it has begun to use the abbreviated term ALAC when referring to the codec.
Convergence of random variablesIn probability theory, there exist several different notions of convergence of random variables. The convergence of sequences of random variables to some limit random variable is an important concept in probability theory, and its applications to statistics and stochastic processes. The same concepts are known in more general mathematics as stochastic convergence and they formalize the idea that a sequence of essentially random or unpredictable events can sometimes be expected to settle down into a behavior that is essentially unchanging when items far enough into the sequence are studied.
Limit (mathematics)In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to and direct limit in . In formulas, a limit of a function is usually written as (although a few authors use "Lt" instead of "lim") and is read as "the limit of f of x as x approaches c equals L".
Lossless compressionLossless compression is a class of data compression that allows the original data to be perfectly reconstructed from the compressed data with no loss of information. Lossless compression is possible because most real-world data exhibits statistical redundancy. By contrast, lossy compression permits reconstruction only of an approximation of the original data, though usually with greatly improved compression rates (and therefore reduced media sizes).
Surface waveIn physics, a surface wave is a mechanical wave that propagates along the interface between differing media. A common example is gravity waves along the surface of liquids, such as ocean waves. Gravity waves can also occur within liquids, at the interface between two fluids with different densities. Elastic surface waves can travel along the surface of solids, such as Rayleigh or Love waves. Electromagnetic waves can also propagate as "surface waves" in that they can be guided along with a refractive index gradient or along an interface between two media having different dielectric constants.
