Euclid's ElementsEuclid's Elements (Στοιχεῖα Stoikheîa) is a mathematical treatise consisting of 13 books attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics.
Jacobi methodIn numerical linear algebra, the Jacobi method (a.k.a. the Jacobi iteration method) is an iterative algorithm for determining the solutions of a strictly diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Audio system measurementsAudio system measurements are a means of quantifying system performance. These measurements are made for several purposes. Designers take measurements so that they can specify the performance of a piece of equipment. Maintenance engineers make them to ensure equipment is still working to specification, or to ensure that the cumulative defects of an audio path are within limits considered acceptable. Audio system measurements often accommodate psychoacoustic principles to measure the system in a way that relates to human hearing.
Audio bit depthIn digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample. In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range.
Music videoA music video, sometimes abbreviated to MV or M/V, is a video that integrates a song or an album with imagery that is produced for promotional or musical artistic purposes. Modern music videos are primarily made and used as a music marketing device intended to promote the sale of music recordings. These videos are typically shown on music television and on streaming video sites like YouTube, or more rarely shown theatrically. They can be commercially issued on home video, either as video albums or video singles.
Video codecA video codec is software or hardware that compresses and decompresses digital video. In the context of video compression, codec is a portmanteau of encoder and decoder, while a device that only compresses is typically called an encoder, and one that only decompresses is a decoder. The compressed data format usually conforms to a standard video coding format. The compression is typically lossy, meaning that the compressed video lacks some information present in the original video.
SystemA system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its boundaries, structure and purpose and is expressed in its functioning. Systems are the subjects of study of systems theory and other systems sciences. Systems have several common properties and characteristics, including structure, function(s), behavior and interconnectivity.
Sequence spaceIn functional analysis and related areas of mathematics, a sequence space is a vector space whose elements are infinite sequences of real or complex numbers. Equivalently, it is a function space whose elements are functions from the natural numbers to the field K of real or complex numbers. The set of all such functions is naturally identified with the set of all possible infinite sequences with elements in K, and can be turned into a vector space under the operations of pointwise addition of functions and pointwise scalar multiplication.
Computer-generated imageryComputer-generated imagery (CGI) is a specific-technology or application of computer graphics for creating or improving images in art, printed media, simulators, videos and video games. These images are either static (i.e. s) or dynamic (i.e. moving images). CGI both refers to 2D computer graphics and (more frequently) 3D computer graphics with the purpose of designing characters, virtual worlds, or scenes and special effects (in films, television programs, commercials, etc.).
Representable functorIn mathematics, particularly , a representable functor is a certain functor from an arbitrary into the . Such functors give representations of an abstract category in terms of known structures (i.e. sets and functions) allowing one to utilize, as much as possible, knowledge about the category of sets in other settings. From another point of view, representable functors for a category C are the functors given with C. Their theory is a vast generalisation of upper sets in posets, and of Cayley's theorem in group theory.
Finitely generated groupIn algebra, a finitely generated group is a group G that has some finite generating set S so that every element of G can be written as the combination (under the group operation) of finitely many elements of S and of inverses of such elements. By definition, every finite group is finitely generated, since S can be taken to be G itself. Every infinite finitely generated group must be countable but countable groups need not be finitely generated. The additive group of rational numbers Q is an example of a countable group that is not finitely generated.
Functor represented by a schemeIn algebraic geometry, a functor represented by a scheme X is a set-valued contravariant functor on the category of schemes such that the value of the functor at each scheme S is (up to natural bijections) the set of all morphisms . The scheme X is then said to represent the functor and that classify geometric objects over S given by F. The best known example is the Hilbert scheme of a scheme X (over some fixed base scheme), which, when it exists, represents a functor sending a scheme S to a flat family of closed subschemes of .
