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**Paracompact uniform honeycombs**- In geometry, uniform honeycombs in hyperbolic space are tessellations of convex uniform polyhedron cells. In 3-dimensional hyperbolic space there are 23 Coxeter group families of paracompact uniform honeycombs, generated as Wythoff constructions, and represented by ring permutations of the Coxeter diagrams for each family. These families can produce uniform honeycombs with infinite or unbounded facets or vertex figure, including ideal vertices at infinity, similar to the hyperbolic uniform ti...
**Point group**- In geometry, a point group is a group of geometric symmetries (isometries) that keep at least one point fixed. Point groups can exist in a Euclidean space with any dimension, and every point group in dimension d is a subgroup of the orthogonal group O(d). Point groups can be realized as sets of orthogonal matrices M that transform point x into point y:where the origin is the fixed point. Point-group elements can either be rotations (determinant of M = 1) or else reflections, or improper rotat...
**Properties of metals, metalloids and nonmetals**- The chemical elements can be broadly divided into metals, metalloids and nonmetals according to their shared physical and chemical properties. All metals have a shiny appearance (at least when freshly polished); are good conductors of heat and electricity; form alloys with other metals; and have at least one basic oxide. Metalloids are metallic-looking brittle solids that are either semiconductors or exist in semiconducting forms, and have amphoteric or weakly acidic oxides. Typical nonmetals...
**Portugal national football team 2000–19 results**- This page is a list of all the matches that Portugal national football team has played between 2000 and 2019.
**PFC CSKA Sofia in European football**- This article lists the results of CSKA Sofia in the UEFA Champions League, European Cup, UEFA Cup and the UEFA Cup Winners' Cup since they first entered European competition in season 1956-57.Including 2013-14 season.Including 2012-13 season.First legCDNA Sofia v Dinamo BucureștiSecond legDinamo București v CDNA Sofiawon 10–4 on aggregateRed Star Belgrade v CDNA SofiaCDNA Sofia v Red Star Belgradelost 3–4 on aggregateCDNA Sofia v VasasVasas v CDNA Sofialost 3–7 on aggregate.Atléti...
**Portal:Video games**- A video game is an electronic game that involves interaction with a user interface to generate visual feedback on a video device. The word video in video game traditionally referred to a raster display on a device. However, with the popular use of the term "video game", it now implies any type of display device. The electronic systems used to play video games are known as platforms; examples of these are video game consoles, personal computers, and mobile devices. Specialized video games such...
**Particle filter**- Particle filters or Sequential Monte Carlo (SMC) methods are a set of genetic-type particle Monte Carlo methodologies to solve the filtering problem. The term "particle filters" was first coined in 1996 by Del Moral in reference to mean field interacting particle methods used in fluid mechanics since the beginning of the 1960s. The terminology "sequential Monte Carlo" was proposed by Liu and Chen in 1998.From the statistical and probabilistic point of view, particle filters can be interpreted...
**Pronunciation of asteroid names**- This page alphabetically lists the first thousand asteroids to be numbered, which are mostly in the asteroid belt.See also pronunciation of Jupiter trojans' names.
**Philippines national football team results**- This article details the international fixtures and results of the Philippines national football team. All scores prior to 2000 list the Philippines' goal tally first.
**Portugal national football team 1980–99 results**- This page is a list of all the matches that Portugal national football team has played between 1980 and 1999.
**Perturbation theory (quantum mechanics)**- In quantum mechanics, perturbation theory is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy l...
**Portuguese local election, 2013**- The Portuguese local election of 2013 took place on 29 September. The election consisted of three separate elections in the 308 Portuguese municipalities, the election for the Municipal Chambers, whose winner is elected mayor, another election for the Municipal Assembly, as well an election for the lower-level Parish Assembly, whose winner is elected parish president. This last will be held separately in the more than 3,000 parishes around the country. There was a reduction in the number of P...
**Point groups in four dimensions**- In geometry, a point group in four dimensions is an isometry group in four dimensions that leaves the origin fixed, or correspondingly, an isometry group of a 3-sphere.There are four basic isometries of 4-dimensional point symmetry: reflection symmetry, rotational symmetry, rotoreflection, and double rotation.For cross-referencing, also given here are quaternion based notations by Patrick du Val (1964) and John Conway (2003). Conway's notation allows the order of the group to be computed as a...
**Poker probability (Omaha)**- Omaha Hold'em, like many similar poker variants, is probabilistic. Thus, the probability of many events can be determined by direct calculation. The probabilities are shown here for many commonly occurring events in the game of Omaha hold 'em as well as probabilities and odds for specific situations. In most cases, the probabilities and odds are approximations due to rounding.When calculating probabilities for a card game such as Omaha, there are two basic approaches.Often, the key to determi...
**Philippines at the 2015 Southeast Asian Games**- The Philippines will be competing at the 28th Southeast Asian Games which took place in Singapore from 5 to 16 June 2015. The Philippines contingent was composed of 472 athletes and 136 sporting officials who will be headlining in 35 out of the 36 sports.Singapore National Olympic Committee trimmed the number of "Traditional" sports and prioritized sports that are staged in the Olympics to increase the level of competition among nations in key sports. 24 of the 36 sports played in this editio...
**Probability derivations for making rank-based hands in Omaha hold 'em**- The probability derivations for starting hands making four of a kind, a full house, three of a kind, two pair, one pair and no pair in Omaha hold 'em are separate for each of the starting hand rank types.The derivations require identifying the individual cases that yield each possible hand and are sometimes rather detailed, so it is useful to use a notation to indicate the shape of the board for each case. The rank type of the hand is shown using upper case letters to indicate ranks. The rank...
**Principalization (algebra)**- In the mathematical field of algebraic number theory, the concept of principalization refers to a situation when, given an extension of algebraic number fields, some ideal (or more generally fractional ideal) of the ring of integers of the smaller field isn't principal but its extension to the ring of integers of the larger field is. Its study has origins in the work of Ernst Kummer on ideal numbers from the 1840s, who in particular proved that for every algebraic number field there exists an...
**Philippines**- Coordinates: 13°N 122°E / 13°N 122°E / 13; 122Pinoy (colloquial masculine)Pinay (colloquial feminine)The Philippines (/ˈfɪlᵻpiːnz/; Filipino: Pilipinas [ˌpɪlɪˈpinɐs]), officially the Republic of the Philippines (Filipino: Republika ng Pilipinas), is a sovereign island country in Southeast Asia situated in the western Pacific Ocean. It consists of about 7,641 islands that are categorized broadly under three main geographical divisions from north to south: Luzon, Visayas, and Mindanao. The c...
**Pre-2016 statewide opinion polling for the United States presidential election, 2016**- This article is a collection of statewide polls for the United States presidential election, 2016. The polls listed here, by state are from 2013 to December 31, 2015 and provide early data on opinion polling between a possible Republican candidate against a possible Democratic candidate.Note: Some states did not conduct polling before December 31, 20153 electoral votes(Republican in 2008) 59%–38%(Republican in 2012) 55%–41%11 electoral votes(Republican in 2008) 53%–45%(Republican in 2012) 53%...
**PAOK FC in European football**- PAOK F.C. history and statistics in the UEFA competitions.: Match forfeited due to crowd invasion. Paris Saint-Germain were awarded a 3–0 win.: The first leg finished 2–1 to Maccabi Tel-Aviv but was awarded 3–0 against PAOK for fielding a suspended player.: Metalist Kharkiv were removed from the Champions League following their win over PAOK, after UEFA found them guilty of match fixing in the Ukrainian league in contravention of UEFA regulations. As a result, PAOK were reinstated in the Cham...
**Plancherel theorem for spherical functions**- In mathematics, the Plancherel theorem for spherical functions is an important result in the representation theory of semisimple Lie groups, due in its final form to Harish-Chandra. It is a natural generalisation in non-commutative harmonic analysis of the Plancherel formula and Fourier inversion formula in the representation theory of the group of real numbers in classical harmonic analysis and has a similarly close interconnection with the theory of differential equations. It is the special...
**Port Adelaide–Norwood SANFL rivalry**- The Port Adelaide–Norwood rivalry is Australian rules football's oldest and one of its most intense rivalries. It is contested between the Port Adelaide Football Club and the Norwood Football Club. Together Port Adelaide (36) and Norwood (30) have won 66 South Australian National Football League (SANFL) premierships since the founding of the competition in 1878. As the SANFL competition has been suspended due to war, only 132 seasons have been played, therefore together Port Adelaide and Norw...
**Polish złoty**- The złoty (pronounced [ˈzwɔtɨ] ( listen); sign: zł; code: PLN), which literally means "golden", is the currency of Poland. The modern złoty is subdivided into 100 groszy (singular: grosz; alternative plural form: grosze). The recognized English form of the word is zloty, plural zloty or zlotys. The currency sign, zł, is composed of the Polish lower-case letters z and ł (Unicode: U+007A z LATIN SMALL LETTER Z & U+0142 ł LATIN SMALL LETTER L WITH STROKE).As a result of inflation in the...
**Poisson point process**- In probability, statistics and related fields, a Poisson point process or Poisson process (also called a Poisson random measure, Poisson random point field or Poisson point field) is a type of random mathematical object that consists of points randomly located on a mathematical space. The process has convenient mathematical properties, which has led to it being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as...
**Provinces of the Philippines**- Independent cityIndependent municipalityComponent citySitioPurokIsland groupsJudicial regionsLegislative districtsThe provinces of the Philippines (Filipino: Mga Lalawigan ng Pilipinas) are the primary political and administrative divisions of the Philippines. There are 81 provinces at present, further subdivided into component cities and municipalities. The National Capital Region, as well as independent cities, are independent of any provincial government. Each province is governed by an el...
**Paraguay at the FIFA World Cup**- The FIFA World Cup is an international association football competition contested by the men's national teams of the members of Fédération Internationale de Football Association (FIFA), the sport's global governing body. The championship has been awarded every four years since the first tournament in 1930, except in 1942 and 1946, due to World War II.The tournament consists of two parts, the qualification phase and the final phase (officially called the World Cup Finals). The qualification ph...
**Passengers of the RMS Titanic**- The passengers of the RMS Titanic were among the estimated 2,344 people who sailed on the maiden voyage of the second of the White Star Line's Olympic class ocean liners, from Southampton, England to New York City in the US state of New York. Partway through the voyage, the ship struck an iceberg and sank in the early morning of 15 April 1912, resulting in the deaths of over 1,500 people, including approximately 815 of the passengers.The Titanic's passengers were divided into three separate c...
**Plate theory**- In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draws on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. The typical thickness to width ratio of a plate structure is less than 0.1. A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem. The aim of plate theory...
**Pershing missile bibliography**- This Pershing missile bibliography is a list of works related to the Pershing 1 and Pershing 1a Field Artillery Missile Systems and the Pershing II Weapon System.Leonard Cheshire created the World Memorial Fund for Disaster Relief in 1990. The charity obtained Pershing and SS-20 scrap material and created memorabilia for fund raising.
**Portugal national football team 1960–79 results**- This page is a list of all the matches that Portugal national football team has played between 1960 and 1979.
**Pierra Menta**- The Pierra Menta has been an annual competition of ski mountaineering at Arêches-Beaufort in the region of Beaufort, Savoie south-eastern France since 1986. The Pierra Menta is one of the three best known races of the Alps (les grandes trois de ski de montagne) besides the Patrouille des Glaciers and the Trofeo Mezzalama.Pierra Menta is a stage of La Grande Course that includes the most important ski mountaineering competitions of the season.The athletes have to travel a cumulative altitude d...
**President of the United Nations Security Council**- The President of the United Nations Security Council is the presiding officer of that body. The president is the head of the delegation from the Security Council member state that holds the rotating presidency. For September 2016, the post is held by the delegation of New Zealand.Article 30 of the United Nations Charter states that the Security Council is empowered to establish rules of procedure, "including the method of selecting its President". The Security Council has established the foll...
**Presidential Unit Citation (United States)**- The Presidential Unit Citation (PUC), originally called the Distinguished Unit Citation, is awarded to units of the United States Armed Forces, and those of allied countries, for extraordinary heroism in action against an armed enemy on or after 7 December 1941 (the date of the Attack on Pearl Harbor and the start of American involvement in World War II). The unit must display such gallantry, determination, and esprit de corps in accomplishing its mission under extremely difficult and hazardo...
**Penns Valley Area School District**- Jefrey Wall, Business ManagerSherri Connell Ast Super, Salary $116,144 (2013)Brian K. Griffith, Compliance OfficerDustin Dalton, PVAJSHS salary $101,626 (2013)$26,115,852 (2016-17) $23.7 million (2013-14)$13,330 (2008)$13,516.41 (2010)The Penns Valley Area School District is a small rural, public school district serving the south-eastern portions of Centre County, Pennsylvania. It encompasses the boroughs of Centre Hall and Millheim, Pennsylvania, as well as the townships of Potter, Gregg, Pe...
**Pritzker Military Presents**- Pritzker Military Presents is an original programming series produced by the Pritzker Military Museum & Library. It airs on PBS channel WYCC weekly and there are currently over 400 episodes. Weekly topics cover various parts of military history.Pritzker Military Presents is a series of recordings of events in which guests come to the Pritzker Military Museum and Library in downtown Chicago and discuss topics related to military history. The episodes take a variety of formats such as:NOTE:...
**Path integral formulation**- The path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique trajectory for a system with a sum, or functional integral, over an infinity of possible trajectories to compute a quantum amplitude.The basic idea of the path integral formulation can be traced back to Norbert Wiener, who introduced the Wiener integral for solving problems in diffusion and Bro...
**P-group generation algorithm**- In mathematics, specifically group theory, finite groups of prime power order p n {\displaystyle p^{n}} , for a fixed prime number p {\displaystyle p} and varying integer exponents n ≥ 0 {\displaystyle n\geq 0} , are briefly called finite p-groups.The p-group generation algorithm by M. F. Newman and E. A. O'Brien is a recursive process for constructing the descendant tree of an assigned finite p-group which is taken as the root of the tree.For a finite p-group...
**Propositional calculus**- Propositional calculus (also called propositional logic, sentential calculus, sentential logic, or sometimes zeroth-order logic) is the branch of mathematical logic concerned with the study of propositions (whether they are true or false) that are formed by other propositions with the use of logical connectives, and how their value depends on the truth value of their components. Logical connectives are found in natural languages. In English for example, some examples are "and" (conjunction), ...
**Painted turtle**- C. p. belliiC. p. dorsalisC. p. marginataC. p. pictaThe painted turtle (Chrysemys picta) is the most widespread native turtle of North America. It lives in slow-moving fresh waters, from southern Canada to Louisiana and northern Mexico, and from the Atlantic to the Pacific. The turtle is the only species of the genus Chrysemys, which is part of the pond turtle family Emydidae. Fossils show that the painted turtle existed 15 million years ago. Four ...
**Polylogarithm**- In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or rational functions. In quantum statistics, the polylogarithm function appears as the closed form of integrals of the Fermi–Dirac distribution and the Bose–Einstein distribution, and is also known as the Fermi–Dirac integral or the...
**Phonological history of English**- The phonological history of English describes the changing phonology of the English language over time, starting from its roots in proto-Germanic to diverse changes in different dialects of modern English.NOTE: In the following description, abbreviations are used as follows:This section summarizes the changes occurring within distinct time periods, covering the last 2,000 years or so. Within each subsection, changes are in approximate chronological order.The time periods for some of the early...
**Pétanque World Championships**- Pétanque World Championships are international pétanque competitions organized by the International Federation of Petanque and Provencal game; F.I.P.J.P. (Federation Internationale de Pétanque et Jeux Provençaux).The FIPJP Men's Triples World Championships were first held in 1959 in Spa, Belgium. Additional championship categories were subsequently added for young people (jeunes), women, and for precision shooting (tir de precision). In 2015, a Singles World Championship was added.Currently -...
**Plug-in electric vehicle**- A plug-in electric vehicle (PEV) is any motor vehicle that can be recharged from an external source of electricity, such as wall sockets, and the electricity stored in the rechargeable battery packs drives or contributes to drive the wheels. PEV is a subset of electric vehicles that includes all-electric or battery electric vehicles (BEVs), plug-in hybrid vehicles (PHEVs), and electric vehicle conversions of hybrid electric vehicles and conventional internal combustion engine vehicles. In Chi...
**Polyharmonic spline**- Polyharmonic splines are used for function approximation and data interpolation. They are very useful for interpolating and fitting scattered data in many dimensions. A special case is the thin plate spline.A polyharmonic spline is a linear combination of polyharmonic radial basis functions (RBFs) denoted by ϕ {\displaystyle \phi } plus a polynomial term:whereThe polynomial with the coefficients v {\displaystyle \mathbf {v} } improves fitting accuracy for polyharmonic s...
**Proofs of trigonometric identities**- Proofs of trigonometric identities are used to show relations between trigonometric functions. This article will list trigonometric identities and prove them.Referring to the diagram at the right, the six trigonometric functions of θ are:The following identities are trivial algebraic consequences of these definitions and the division identity.They rely on multiplying or dividing the numerator and denominator of fractions by a variable. Ie,OrTwo angles whose sum is π/2 radians (90 degrees) are...
**Panama Papers**- The Panama Papers are 11.5 million leaked documents that detail financial and attorney–client information for more than 214,488 offshore entities. The leaked documents were created by Panamanian law firm and corporate service provider Mossack Fonseca; some date back to the 1970s.The leaked documents illustrate how wealthy individuals and public officials are able to keep personal financial information private. While offshore business entities are often not illegal, reporters found that some o...
**Prussian Union of churches**- The Prussian Union of Churches (known under multiple other names) was a major church body which emerged in the 1817 from a series of decrees by Frederick William III of Prussia that united the Lutheran Church and the Reformed Church in Prussia.It became the biggest independent religious organisation in the German Empire and later Weimar Germany, with about 18 million parishioners. The church underwent two schisms (one permanent since the 1830s, one temporary 1934–1948), due to changes in gove...
**PIAA Football Teams, Conferences and Leagues**- As of the 2014-2015 and the 2015-2016 school years, there will be 583 high school football teams competing in the Pennsylvania Interscholastic Athletic Association's (PIAA) 12 Districts. Each district is divided into numerous leagues and conferences, with four class rankings of A, AA, AAA and AAAA. As of the beginning of the 2014-15 school year the PIAA will have 144 A class, 145 AA class, 146 AAA class and 148 AAAA class ranked schools competing throughout the football season. Every 2 years ...
**Paravector**- The name paravector is used for the sum of a scalar and a vector in any Clifford algebra (Clifford algebra is also known as geometric algebra in the physics community.)This name was given by J. G. Maks, Doctoral Dissertation, Technische Universiteit Delft (Netherlands), 1989.The complete algebra of paravectors along with corresponding higher grade generalizations, all in the context of the Euclidean space of three dimensions, is an alternative approach to the spacetime algebra (STA) introduce...
**Pacific Coast Championships**- The Pacific Coast Championships was an annual men's tennis tournament. It was the second-oldest ongoing tennis tournament in the United States and ran from 1889 until 2013. Its final edition, known by its sponsored name SAP Open, was an ATP World Tour 250 series event on the Association of Tennis Professionals tour and played indoors on a hard surface at the SAP Center at San Jose.The tournament began in 1889 as the Pacific Coast Championships at the Old Del Monte Lodge in Monterey, Californi...

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