Quaternion groupIn group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset of the quaternions under multiplication. It is given by the group presentation where e is the identity element and commutes with the other elements of the group. Another presentation of Q8 is The quaternion group Q8 has the same order as the dihedral group D4, but a different structure, as shown by their Cayley and cycle graphs: In the diagrams for D4, the group elements are marked with their action on a letter F in the defining representation R2.
Symmetry (physics)In physics, a symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation. A family of particular transformations may be continuous (such as rotation of a circle) or discrete (e.g., reflection of a bilaterally symmetric figure, or rotation of a regular polygon). Continuous and discrete transformations give rise to corresponding types of symmetries.
Fundamental groupIn the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the loops contained in the space. It records information about the basic shape, or holes, of the topological space. The fundamental group is the first and simplest homotopy group. The fundamental group is a homotopy invariant—topological spaces that are homotopy equivalent (or the stronger case of homeomorphic) have isomorphic fundamental groups.
Spherical coordinate systemIn mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin; its polar angle measured from a fixed polar axis or zenith direction; and the azimuthal angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the fixed axis, measured from another fixed reference direction on that plane.
Isomorphism theoremsIn mathematics, specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship between quotients, homomorphisms, and subobjects. Versions of the theorems exist for groups, rings, vector spaces, modules, Lie algebras, and various other algebraic structures. In universal algebra, the isomorphism theorems can be generalized to the context of algebras and congruences.
Permutation groupIn mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). The group of all permutations of a set M is the symmetric group of M, often written as Sym(M). The term permutation group thus means a subgroup of the symmetric group. If M = {1, 2, ..., n} then Sym(M) is usually denoted by Sn, and may be called the symmetric group on n letters.
Docosahexaenoic acidDocosahexaenoic acid (DHA) is an omega-3 fatty acid that is a primary structural component of the human brain, cerebral cortex, skin, and retina. In physiological literature, it is given the name 22:6(n-3). It can be synthesized from alpha-linolenic acid or obtained directly from maternal milk (breast milk), fatty fish, fish oil, or algae oil. DHA's structure is a carboxylic acid (-oic acid) with a 22-carbon chain (docosa- derives from the Ancient Greek for 22) and six (hexa-) cis double bonds (-en-); with the first double bond located at the third carbon from the omega end.
Circular symmetryIn geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself. Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the special orthogonal group SO(2), and unitary group U(1). Reflective circular symmetry is isomorphic with the orthogonal group O(2). A 2-dimensional object with circular symmetry would consist of concentric circles and annular domains.
AdvertisingAdvertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers. It is typically used to promote a specific good or service, but there are wide range of uses, the most common being the commercial advertisement. Commercial advertisements often seek to generate increased consumption of their products or services through "branding", which associates a product name or image with certain qualities in the minds of consumers.
Ad hocAd hoc is a Latin phrase meaning literally 'for this'. In English, it typically signifies a solution for a specific purpose, problem, or task rather than a generalized solution adaptable to collateral instances. (Compare with a priori.) Common examples are ad hoc committees and commissions created at the national or international level for a specific task. In other fields, the term could refer to, for example, a military unit created under special circumstances (see task force), a handcrafted network protocol (e.
Omega-3 fatty acidOmega−3 fatty acids, also called Omega−3 oils, ω−3 fatty acids or n−3 fatty acids, are polyunsaturated fatty acids (PUFAs) characterized by the presence of a double bond, three atoms away from the terminal methyl group in their chemical structure. They are widely distributed in nature, being important constituents of animal lipid metabolism, and they play an important role in the human diet and in human physiology. The three types of omega−3 fatty acids involved in human physiology are α-linolenic acid (ALA), eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA).
Wireless ad hoc networkA wireless ad hoc network (WANET) or mobile ad hoc network (MANET) is a decentralized type of wireless network. The network is ad hoc because it does not rely on a pre-existing infrastructure, such as routers or wireless access points. Instead, each node participates in routing by forwarding data for other nodes. The determination of which nodes forward data is made dynamically on the basis of network connectivity and the routing algorithm in use.
