Connection (principal bundle)In mathematics, and especially differential geometry and gauge theory, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P over a smooth manifold M is a particular type of connection which is compatible with the action of the group G. A principal connection can be viewed as a special case of the notion of an Ehresmann connection, and is sometimes called a principal Ehresmann connection.
Quality assuranceQuality assurance (QA) is the term used in both manufacturing and service industries to describe the systematic efforts taken to assure that the product(s) delivered to customer(s) meet with the contractual and other agreed upon performance, design, reliability, and maintainability expectations of that customer. The core purpose of Quality Assurance is to prevent mistakes and defects in the development and production of both manufactured products, such as automobiles and shoes, and delivered services, such as automotive repair and athletic shoe design.
Quality of serviceQuality of service (QoS) is the description or measurement of the overall performance of a service, such as a telephony or computer network, or a cloud computing service, particularly the performance seen by the users of the network. To quantitatively measure quality of service, several related aspects of the network service are often considered, such as packet loss, bit rate, throughput, transmission delay, availability, jitter, etc.
Connection formIn mathematics, and specifically differential geometry, a connection form is a manner of organizing the data of a connection using the language of moving frames and differential forms. Historically, connection forms were introduced by Élie Cartan in the first half of the 20th century as part of, and one of the principal motivations for, his method of moving frames. The connection form generally depends on a choice of a coordinate frame, and so is not a tensorial object.
Network on a chipA network on a chip or network-on-chip (NoC ˌɛnˌoʊˈsiː or nɒk ) is a network-based communications subsystem on an integrated circuit ("microchip"), most typically between modules in a system on a chip (SoC). The modules on the IC are typically semiconductor IP cores schematizing various functions of the computer system, and are designed to be modular in the sense of network science. The network on chip is a router-based packet switching network between SoC modules.
Connection (mathematics)In geometry, the notion of a connection makes precise the idea of transporting local geometric objects, such as tangent vectors or tensors in the tangent space, along a curve or family of curves in a parallel and consistent manner. There are various kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most elementary type of connection, gives a means for parallel transport of tangent vectors on a manifold from one point to another along a curve.
Connection (vector bundle)In mathematics, and especially differential geometry and gauge theory, a connection on a fiber bundle is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of a linear connection on a vector bundle, for which the notion of parallel transport must be linear. A linear connection is equivalently specified by a covariant derivative, an operator that differentiates sections of the bundle along tangent directions in the base manifold, in such a way that parallel sections have derivative zero.
Connection-oriented communicationIn telecommunications and computer networking, connection-oriented communication is a communication protocol where a communication session or a semi-permanent connection is established before any useful data can be transferred. The established connection ensures that data is delivered in the correct order to the upper communication layer. The alternative is called connectionless communication, such as the datagram mode communication used by Internet Protocol (IP) and User Datagram Protocol, where data may be delivered out of order, since different network packets are routed independently and may be delivered over different paths.
System on a chipA system on a chip or system-on-chip (SoC ,ˈɛsoʊsiː; pl. SoCs ,ˈɛsoʊsiːz) is an integrated circuit that integrates most or all components of a computer or other electronic system. These components almost always include on-chip central processing unit (CPU), memory interfaces, input/output devices, input/output interfaces, and secondary storage interfaces, often alongside other components such as radio modems and a graphics processing unit (GPU) – all on a single substrate or microchip.
Levi-Civita connectionIn Riemannian or pseudo-Riemannian geometry (in particular the Lorentzian geometry of general relativity), the Levi-Civita connection is the unique affine connection on the tangent bundle of a manifold (i.e. affine connection) that preserves the (pseudo-)Riemannian metric and is torsion-free. The fundamental theorem of Riemannian geometry states that there is a unique connection which satisfies these properties. In the theory of Riemannian and pseudo-Riemannian manifolds the term covariant derivative is often used for the Levi-Civita connection.
