All articles starting with P
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Projective duality
Projective duality is a symmetry of projective geometry in which the roles of points and lines can be exchanged, so the dual of any true theorem is also true.
Projective geometry
Projective geometry is the branch of mathematics studying properties of figures that survive projection, keeping incidence and the cross-ratio while discarding distance, angle, and parallelism; it underlies perspective and computer vision.
Projective hierarchy
The projective hierarchy is a classification of sets of real numbers, built from the analytic sets by complementation and projection, introduced by Lusin and Sierpiński in 1925.
Projective Hilbert space
The projective Hilbert space is the space of quantum pure states, formed from a Hilbert space by identifying vectors that differ by a nonzero complex factor.
Projective line
The projective line is the one-dimensional projective space over a field K, formed by adding a single point at infinity to the ordinary affine line.
Projective measurement (quantum mechanics)
A projective measurement, also called a von Neumann measurement, is a quantum-mechanical measurement whose outcomes are the eigenvalues of the measured observable, to which the state is projected.
Projective module
A projective module, also called a finitely generated projective module in the finite case, is a module over a ring that behaves like a free module, characterized by the lifting property for homomorphisms.
Projective plane
A projective plane is a geometric structure of points and lines in which every pair of lines meets, achieved by adding points at infinity to parallel lines.
Projective representation
A projective representation of a group assigns operators to group elements that multiply only up to a scalar factor, classified by the second group cohomology H²(G, U(1)).
Projective resolution
A projective resolution of a module is an exact sequence of projective modules ending in it, the standard tool for computing derived functors such as Ext and Tor.
Projective space
Projective space, written KP^n, is the set of lines through the origin of a vector space, adding points at infinity so any two lines meet in one point.
Projective test
Projective test: ambiguous-stimulus personality assessment (Rorschach Inkblot Test, Thematic Apperception Test, sentence completion, drawings) based on the projective hypothesis; controversial psychometrics, worldwide clinical use, multimethod complementary role.
Projective variety
A projective variety is a subset of projective space cut out by homogeneous polynomials, one of the two basic objects of classical algebraic geometry alongside affine varieties.
Projective verse
Projective verse is a theory of open-form poetry set out by Charles Olson in his 1950 essay of that name, founding statement of the Black Mountain poets.
Projector
A projector, also called an image projector, is an optical instrument that casts an enlarged image from film, a transparency, or a display chip onto a screen.
Projector augmented-wave method
The projector augmented-wave (PAW) method is an electronic structure method for density functional theory, introduced by P. E. Blöchl in 1994, that combines pseudopotential efficiency with all-electron accuracy.
ProjectWise
ProjectWise is a project collaboration and engineering information management software product from Bentley Systems, launched in 1999 and used by 46 U.S. State Departments of Transportation.
Projek: High Council
Projek: High Council, 2023 Malaysian Astro drama series by Anwari Ashraf and Zulaikha Zakaria; 10 episodes on bullying and the High Council student hierarchy at fictional boarding school KUDRAT; spawned Kahar film and Kudrat 1968 prequel.
Projekt Melody
Projekt Melody (メロディー) is an American 3D anime-styled VTuber and adult streamer who debuted on Chaturbate in February 2020 as the first virtual adult-content streamer, joined VShojo in November 2020, and returned to independence in July 2025.
Projekt Revolution
Projekt Revolution was an annual touring music festival organized and headlined by Linkin Park from 2002 to 2011. It featured 49 different acts, bringing rock and hip-hop music together.
Projota
Projota (José Tiago Sabino Pereira, born 1986) is a Brazilian rapper from São Paulo whose 2016 hit Ela só quer paz brought rap into the mainstream.
Prokaryote
Prokaryote: a single-celled organism lacking a nucleus and membrane-bound organelles, covering the domains Bacteria and Archaea. Cells are 0.1–5.0 μm, DNA sits in a nucleoid, and the group is polyphyletic.
Prokhorov's theorem
Prokhorov's theorem is a result in probability theory stating that a family of probability measures on a Polish space is tight if and only if every sequence has a weakly convergent subsequence.
Prokhorovka
Prokhorovka (Прохоровка) names an early Sarmatian kurgan cemetery near an Orenburg village in the Southern Urals, eponym of the Prokhorovka culture (4th–2nd centuries BC), excavated by Rudenko in 1916 and Yablonsky in 2003–2005; also a Ukrainian Dnipro village and a Belgorod Oblast settlement.
Prokofiev (Mercurian crater)
Prokofiev, a 112-km crater near Mercury's north pole named for composer Sergey Prokofiev, hosts the largest radar-bright polar deposit, interpreted as surface water ice with a 26 m thickness upper limit.
Prokop the Great
Prokop the Great (Prokop Veliký, Prokop Holý, c. 1380–1434) was a Bohemian Hussite priest who led the Taborite armies after Žižka, won at Ústí, Tachov, and Domažlice, led the glorious rides, and fell at Lipany in 1434.
Prokop the Lesser
Prokop the Lesser (Prokop Malý), also called Prokupek, was a Hussite commander who headed the radical Orphans field army from 1428 and died at the Battle of Lipany in 1434.
Prokopios (Ecumenical Patriarch of Constantinople)
Prokopios I (Greek Προκόπιος), family name Pelekasis, was Ecumenical Patriarch of Constantinople from 1785 to 1789, deposed by Sultan Selim III and exiled to Mount Athos until 1797.
Prokopy Lyapunov
Prokopy Lyapunov (Прокопий Ляпунов) was a Ryazan voevoda and duma nobleman who organized and led the First Volunteer Army of 1611 until Cossacks killed him that July.
Prokopyevsk
Prokopyevsk (Прокопьевск), a coal-mining city in Kemerovo Oblast, Russia, on the Aba River; third city of the oblast, city since 1931, coking-coal center of Kuzbass, Order of the Red Banner of Labour 1981.