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Projection Geometry
Projection, projections or projective may refer to: Physics * Projection (physics), the action/process of light, heat, or sound reflecting from a surface to another in a different direction * The display of images by a projector Optics, graphics, and cartography * Map projection, reducing the surface of a three-dimensional planet to a flat map * Graphical projection, the production of a two-dimensional image of a three-dimensional object Chemistry * Fischer projection, a two-dimensional representation of a three-dimensional organic molecule * Haworth projection, a way of writing a structural formula to represent the cyclic structure of monosaccharides * Natta projection, a way to depict molecules with complete stereochemistry in two dimensions in a skeletal formula * Newman projection, a visual representation of a chemical bond from front to back Mathematics * Projection (mathematics), any of several different types of geometrical mappings ** Projection (linear alg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (physics)
The vector projection of a vector on (or onto) a nonzero vector , sometimes denoted \operatorname_\mathbf \mathbf (also known as the vector component or vector resolution of in the direction of ), is the orthogonal projection of onto a straight line parallel to . It is a vector parallel to , defined as: \mathbf_1 = a_1\mathbf where a_1 is a scalar, called the scalar projection of onto , and is the unit vector in the direction of . In turn, the scalar projection is defined as: a_1 = \left\, \mathbf\right\, \cos\theta = \mathbf\cdot\mathbf where the operator ⋅ denotes a dot product, ‖a‖ is the length of , and ''θ'' is the angle between and . Which finally gives: \mathbf_1 = \left(\mathbf \cdot \mathbf\right) \mathbf = \frac \frac = \frac = \frac ~ . The scalar projection is equal to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of . The vector component or vector resolute of perpendi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Object
In category theory, the notion of a projective object generalizes the notion of a projective module. Projective objects in abelian categories are used in homological algebra. The dual notion of a projective object is that of an injective object. Definition An object P in a category \mathcal is ''projective'' if for any epimorphism e:E\twoheadrightarrow X and morphism f:P\to X, there is a morphism \overline:P\to E such that e\circ \overline=f, i.e. the following diagram commutes: That is, every morphism P\to X factors through every epimorphism E\twoheadrightarrow X. If ''C'' is locally small, i.e., in particular \operatorname_C(P, X) is a set for any object ''X'' in ''C'', this definition is equivalent to the condition that the hom functor (also known as corepresentable functor) : \operatorname(P,-)\colon\mathcal\to\mathbf preserves epimorphisms. Projective objects in abelian categories If the category ''C'' is an abelian category such as, for example, the category of abeli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Projection
Power projection (or force projection or strength projection), in international relations, is the capacity of a state to deploy and sustain forces outside its territory. The ability of a state to project its power into an area may serve as an effective diplomatic lever, influencing the decision-making process and acting as a potential deterrent on other states' behavior.Pravda (Правда(17 Mar 2022) Zelenskyy explained the essence of the new military alliance U24 from Zelenskyy's night address verbatim: "I addressed the United States and all responsible states with a proposition to create a new U24 union: a new union that will ensure that each aggressor receives a coordinated world response quickly, effectively, and immediately - not in weeks, months, years, but for the first 24 hours after the attack." "We can no longer trust existing institutions. We cannot expect bureaucrats in international organisations to change fast enough, so we must look for new guara ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projections (journal)
''Projections: The Journal for Movies and Mind'' is an interdisciplinary peer-reviewed academic journal that explores the way in which the mind experiences, understands, and interprets the audio-semantic and narrative structures of cinema and other visual media. It is published by Berghahn Books in association with The Society for Cognitive Studies of the Moving Image and it is edited by Ted Nannicelli. The journal was the recipient of the 2008 AAP/PSP Prose Award for Best New Journal in Social Sciences and Humanities. Editors The following people have been editors of the journal: * 2009-2018: Stephen Prince * 2018-present: Ted Nannicelli Indexing and abstracting ''Projections'' is indexed and abstracted in: *British Humanities Index *GEOBASE GEOBASE is a database, multidisciplinary in scope, which indexes bibliographic information and abstracts for the Geographical, Earth, and Ecological sciences, published by Engineering Information, a subsidiary of Elsevier. The br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (alchemy)
Projection was the ultimate goal of Western alchemy. Once the philosopher's stone or powder of projection had been created, the process of projection would be used to transmute a lesser substance into a higher form; often lead into gold. Typically, the process is described as casting a small portion of the Stone into a molten base metal. Claims and demonstrations The seventeenth century saw an increase in tales of physical transmutation and projection. These are variously explained as examples of charlatanism, fiction, pseudo-scientific error, or missed metaphor. The following is a typical account of the projection process described by Jan Baptista van Helmont in his ''De Natura Vitae Eternae''. Other reports include: * Elias Ashmole's '' Theatrum Chemicum Britannicum'' lists an account of Edward Kelley making projections from lesser metals into both gold and silver. Kelley's success is also recorded by John Dee. * Alexander Seton was reported to have projected a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projections (film)
''Projections'' ( hr, Projekcije) is a 2013 Croatian drama film directed by Zrinko Ogresta. Cast * Jasna Bilušić as Barbara * Polona Juh as Natasa * Vladimir Jurc as Professor Blau * Ksenija Marinković as Alemka * Jelena Miholjević as Simona * Bojan Navojec as Bojan * Ksenija Pajić Ksenija Pajić (born 30 June 1961) is a Croatia , image_flag = Flag of Croatia.svg , image_coat = Coat of arms of Croatia.svg , anthem = " Lijepa naša domovino"("Our Beautiful Homeland") , image_map ... as Irena References External links Projekcijeat hrfilm.hr * 2013 drama films 2013 films Croatian drama films Films set in Zagreb {{Croatia-film-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projections (John Handy Album)
''Projections'' is an album by saxophonist John Handy's Concert Ensemble featuring tracks recorded in 1968 and originally released on the Columbia label. accessed November 10, 2015 Reception awarded the album 4 stars and its review by Scott Yanow states, "The music (much more concise in general than on the previous two Columbias) contains plenty of surprises and is difficult to categorize (somewhere between the avant-garde and hard bop), although it does not reach the same heights as ''New View''".Track listing ''All compositions by John Handy'' # "Three in One" - 4:00 # "Projections" - 3:15 # "A Song of Uranus" - 9:03 # "Senôra Nancye" - 6:30 # "D ...[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projections (The Blues Project Album)
''Projections'' is the second album by American blues rock band The Blues Project. Produced by Tom Wilson and released by Verve/Folkways in November 1966, the album was their first studio release and examined a more rock-based sound. Jim Marshall was credited as the photographer of the album cover. Soon after the release of this album, Al Kooper left the band in the spring of 1967 to form Blood, Sweat & Tears. Recording Keyboardist and vocalist Al Kooper was the most prominent member of the band, having recently played on Bob Dylan's seminal album ''Highway 61 Revisited''. However, ''Projections'' was very much a group effort, developing the band's unique style that drew upon blues, jazz, folk, soul, and psychedelic influences. According to Danny Kalb, the record company was not interested in the band's artistic merit and "just wanted to make a few bucks". The band was disappointed by this lack of creative input and did not see the album cover or hear the mix until the record ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Presupposition
In the branch of linguistics known as pragmatics, a presupposition (or PSP) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. Examples of presuppositions include: * ''Jane no longer writes fiction.'' ** Presupposition: Jane once wrote fiction. * ''Have you stopped eating meat?'' ** Presupposition: you had once eaten meat. * ''Have you talked to Hans?'' ** Presupposition: Hans exists. A presupposition must be mutually known or assumed by the speaker and addressee for the utterance to be considered appropriate in context. It will generally remain a necessary assumption whether the utterance is placed in the form of an assertion, denial, or question, and can be associated with a specific lexical item or grammatical feature (presupposition trigger) in the utterance. Crucially, negation of an expression does not change its presuppositions: ''I want to do it again'' and ''I don't want to do it again'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection Principle
In linguistics, the projection principle is a stipulation proposed by Noam Chomsky as part of the phrase structure component of generative-transformational grammar. The projection principle is used in the derivation of phrases under the auspices of the principles and parameters theory. Details Under the projection principle, the properties of lexical items must be preserved while generating the phrase structure of a sentence. The principle, as formulated by Chomsky in ''Knowledge of Language: Its Nature, Origin and Use'' (1986), states that "lexical structure must be represented categorically at every syntactic level" (Chomsky 1986: 84). Chomsky further defined the projection principle as "representations at each level of syntax(MF, D, S) are projected from the lexicon in that they observe the subcategorisation properties of lexical items." This refers to the fact that every individual piece of a syntactic structure is part of a particular category (i.e. “John” is a member of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (linguistics)
In linguistics, X-bar theory is a model of phrase-structure grammar and a theory of syntactic category formation that was first proposed by Noam Chomsky in 1970Chomsky, Noam (1970). Remarks on Nominalization. In: R. Jacobs and P. Rosenbaum (eds.) ''Reading in English Transformational Grammar'', 184–221. Waltham: Ginn. and further developed by Ray Jackendoff (1974, 1977a, 1977bJackendoff, Ray (1977b) Constraints on Phrase Structure Rules, in P. W. Culicover, T. Wasow & A. Akmajian (eds.), ''Formal Syntax'', Academic Press, New York, pp. 249–83.), along the lines of the theory of generative grammar put forth in the 1950s by Chomsky. It attempts to capture the structure of phrasal categories with a single uniform structure called the X-bar schema, basing itself on the assumption that any phrase in natural language is an XP (X phrase) that is headed by a given syntactic category X. It played a significant role in resolving issues that phrase structure rules had, representative of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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