Adjoint representationIn mathematics, the adjoint representation (or adjoint action) of a Lie group G is a way of representing the elements of the group as linear transformations of the group's Lie algebra, considered as a vector space. For example, if G is , the Lie group of real n-by-n invertible matrices, then the adjoint representation is the group homomorphism that sends an invertible n-by-n matrix to an endomorphism of the vector space of all linear transformations of defined by: . For any Lie group, this natural representation is obtained by linearizing (i.
Triple productIn geometry and algebra, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.
Average bitrateIn telecommunications, average bitrate (ABR) refers to the average amount of data transferred per unit of time, usually measured per second, commonly for digital music or video. An MP3 file, for example, that has an average bit rate of 128 kbit/s transfers, on average, 128,000 bits every second. It can have higher bitrate and lower bitrate parts, and the average bitrate for a certain timeframe is obtained by dividing the number of bits used during the timeframe by the number of seconds in the timeframe.
Kronecker productIn mathematics, the Kronecker product, sometimes denoted by ⊗, is an operation on two matrices of arbitrary size resulting in a block matrix. It is a specialization of the tensor product (which is denoted by the same symbol) from vectors to matrices and gives the matrix of the tensor product linear map with respect to a standard choice of basis. The Kronecker product is to be distinguished from the usual matrix multiplication, which is an entirely different operation. The Kronecker product is also sometimes called matrix direct product.
Abessive caseIn linguistics, abessive (abbreviated or ), caritive and privative (abbreviated ) is the grammatical case expressing the lack or absence of the marked noun. In English, the corresponding function is expressed by the preposition without or by the suffix -less. The name abessive is derived from abesse "to be away/absent", and is especially used in reference to Uralic languages. The name caritive is derived from carere "to lack", and is especially used in reference to Caucasian languages.
Accusative caseThe accusative case (abbreviated ) of a noun is the grammatical case used to receive the direct object of a transitive verb. In the English language, the only words that occur in the accusative case are pronouns: "me", "him", "her", "us", "whom", and "them". For example, the pronoun she, as the subject of a clause, is in the nominative case ("She wrote a book"); but if the pronoun is instead the object of the verb, it is in the accusative case and she becomes her ("Fred greeted her"). For compound direct objects, it would be, e.
Process architectureProcess architecture is the structural design of general process systems. It applies to fields such as computers (software, hardware, networks, etc.), business processes (enterprise architecture, policy and procedures, logistics, project management, etc.), and any other process system of varying degrees of complexity. Processes are defined as having inputs, outputs and the energy required to transform inputs to outputs. Use of energy during transformation also implies a passage of time: a process takes real time to perform its associated action.
Derivation (differential algebra)In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: More generally, if M is an A-bimodule, a K-linear map D : A → M that satisfies the Leibniz law is also called a derivation. The collection of all K-derivations of A to itself is denoted by DerK(A). The collection of K-derivations of A into an A-module M is denoted by DerK(A, M).
