Finitary relationIn mathematics, a finitary relation over sets X1, ..., Xn is a subset of the Cartesian product X1 × ⋯ × Xn; that is, it is a set of n-tuples (x1, ..., xn) consisting of elements xi in Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true. The non-negative integer n giving the number of "places" in the relation is called the arity, adicity or degree of the relation.
Bilingual dictionaryA bilingual dictionary or translation dictionary is a specialized dictionary used to translate words or phrases from one language to another. Bilingual dictionaries can be unidirectional, meaning that they list the meanings of words of one language in another, or can be bidirectional, allowing translation to and from both languages. Bidirectional bilingual dictionaries usually consist of two sections, each listing words and phrases of one language alphabetically along with their translation.
Language deathIn linguistics, language death occurs when a language loses its last native speaker. By extension, language extinction is when the language is no longer known, including by second-language speakers, when it becomes known as an extinct language. A related term is linguicide, the death of a language from natural or political causes, and, rarely, glottophagy, the absorption or replacement of a minor language by a major language.
Specialized dictionaryA specialized dictionary is a dictionary that covers a relatively restricted set of phenomena. The definitive book on the subject (Cowie 2009) includes chapters on some of the dictionaries included below: synonyms pronunciations names (place names and personal names) phrases and idioms dialect terms slang quotations etymologies rhymes lyrics Dictionaries of idioms and slang are common in most cultures.
Webster's DictionaryWebster's Dictionary is any of the English language dictionaries edited in the early 19th century by Noah Webster (1758–1843), an American lexicographer, as well as numerous related or unrelated dictionaries that have adopted the Webster's name in his honor. "Webster's" has since become a genericized trademark in the United States for English dictionaries, and is widely used in dictionary titles. Merriam-Webster is the corporate heir to Noah Webster's original works, which are in the public domain.
Group actionIn mathematics, a group action on a space is a group homomorphism of a given group into the group of transformations of the space. Similarly, a group action on a mathematical structure is a group homomorphism of a group into the automorphism group of the structure. It is said that the group acts on the space or structure. If a group acts on a structure, it will usually also act on objects built from that structure. For example, the group of Euclidean isometries acts on Euclidean space and also on the figures drawn in it.
Computer clusterA computer cluster is a set of computers that work together so that they can be viewed as a single system. Unlike grid computers, computer clusters have each node set to perform the same task, controlled and scheduled by software. The components of a cluster are usually connected to each other through fast local area networks, with each node (computer used as a server) running its own instance of an operating system. In most circumstances, all of the nodes use the same hardware and the same operating system, although in some setups (e.
Syntactic ambiguitySyntactic ambiguity, also called structural ambiguity, amphiboly or amphibology, is a situation where a sentence may be interpreted in more than one way due to ambiguous sentence structure. Syntactic ambiguity does not come from the range of meanings of single words, but from the relationship between the words and clauses of a sentence, and the sentence structure hidden behind the word order. In other words, a sentence is syntactically ambiguous when a reader or listener can reasonably interpret one sentence as having multiple possible structures.
AnalysisAnalysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though analysis as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (analysis, "a breaking-up" or "an untying;" from ana- "up, throughout" and lysis "a loosening"). From it also comes the word's plural, analyses.
Homogeneous relationIn mathematics, a homogeneous relation (also called endorelation) on a set X is a binary relation between X and itself, i.e. it is a subset of the Cartesian product X × X. This is commonly phrased as "a relation on X" or "a (binary) relation over X". An example of a homogeneous relation is the relation of kinship, where the relation is between people. Common types of endorelations include orders, graphs, and equivalences. Specialized studies of order theory and graph theory have developed understanding of endorelations.
Network theoryIn mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components. Network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience.
Reductive groupIn mathematics, a reductive group is a type of linear algebraic group over a field. One definition is that a connected linear algebraic group G over a perfect field is reductive if it has a representation that has a finite kernel and is a direct sum of irreducible representations. Reductive groups include some of the most important groups in mathematics, such as the general linear group GL(n) of invertible matrices, the special orthogonal group SO(n), and the symplectic group Sp(2n).
