A frame or framework is a structural system or a skeleton that supports other components of the object. It is used in this basic sense in art, construction, and mechanical engineering, and the expression 'frame' for eyeglasses.
The word also has many extended, metaphorical meanings in various fields:
The Frames is also the name of an Irish rock band, fronted by Glen Hansard.
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A frame or framework is a structural system or a skeleton that supports other components of the object. Category theoretically, a G-graded algebra A is an object in the category of G-graded vector spaces together with a morphism of the degree of the identity of G. one complete game of snooker; a match usually comprises at least three frames. Examples of G-graded algebras include:. in psychology, Framing (psychology). (If we don't require that the ring has an identity element, we can extend the definition from monoids to semigroups. in law, to frame someone is to make it look as if they committed a crime when they in fact did not commit said crime, as in the title of the movie Who Framed Roger Rabbit; see frameup. A graded algebra is then the same thing as a N-graded algebra, where N is the monoid of natural numbers.
See frame (dance). such that. the connection between lead and follow in partner dancing. A G-graded algebra A is an algebra with a direct sum decomposition. each player's turn in bowling games. We can generalize the definition of a graded algebra to an arbitrary monoid G as an index set. also in mathematics, a frame can refer to a complete Heyting algebra. One example is the close relationship between homogeneous polynomials and projective varieties.
Also projective frame. Graded algebras are much used in commutative algebra and algebraic geometry, homological algebra and algebraic topology. See vierbein for an orthonormal frame. Examples of graded algebras are common in mathematics:. in mathematics, a frame is an abstract concept on a manifold, generalising frame of reference to a basis for the tangent bundle varying from point to point. Since rings may be regarded as Z-algebras, a graded ring is defined to be a graded Z-algebra. a frame of reference in physics. An ideal, or other set in A, is homogeneous if for every element a it contains, the homogeneous parts of a are also contained in it.
a narrative frame in literature, film, or storytelling. Elements of An are known as homogeneous elements of degree n. a frame tale in literature. such that. Semantic frames in cognitive science, linguistics, or communication theory. A graded algebra A is an algebra that has a direct sum decomposition. the frame problem in artificial intelligence, a data structure for representing a stereotyped situation. .
in video compression different frames –- called I-frames, P-frames, B-frames, and D-frames –- are used for motion compensation. The group ring of a group is naturally graded by that group; similarly, monoid rings are graded by the corresponding monoid. a complete image, or the set of all picture elements representing it, in video display. The cohomology ring H• in any cohomology theory is also graded, being the direct sum of the Hn. one of the film frames or video frames composing a film or video
an A-frame, often used as a caning -, whipping - or flogging frame, used for securing the victim of physical punishment (either standing with his hands tied where the side bars meet above him, or to bend over the shorter cross-bar). The tensor algebra T•V of a vector space V. frames are often called after a shape they resemble, e.g. The homogeneous elements of degree n are exactly the homogeneous polynomials of degree n. in mechanical engineering, a bicycle frame, for instance. Polynomial rings. a beehive frame.
a space frame in construction. in art, a picture frame is a solid border around a picture or painting.