Monopole Floer Homology
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Monopole Floer Homology
Monopole may refer to: * Magnetic monopole, or Dirac monopole, a hypothetical particle that may be loosely described as a magnet with only one pole * Monopole (mathematics), a connection over a principal bundle G with a section (the Higgs field) of the associated adjoint bundle * ''Monopole'', the first term in a multipole expansion * Monopole (wine), an appellation owned by only one winery * ''Monopole'' (album), a 2011 album by White Town * Monopole antenna, a radio antenna that replaces half of a dipole antenna with a ground plane at right-angles to the remaining half * Monopole, a tubular self-supporting telecommunications mast * ''The Monopole'', a bar in Plattsburgh, NY * Établissements Monopole, a French auto parts manufacturer, racing car builder and racing team. See also * Dipole, a particle with a north and south pole * Dyon, a particle with electric and magnetic charge * Instanton, a class of field solutions that includes monopoles * Monomial, a polynomial which ...
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Magnetic Monopole
In particle physics, a magnetic monopole is a hypothetical particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magnetic charge". Modern interest in the concept stems from high-energy physics, particle theories, notably the grand unified theory, grand unified and superstring theory, superstring theories, which predict their existence. The known elementary particles that have electric charge are electric monopoles. Magnetism in bar magnets and electromagnets is not caused by magnetic monopoles, and indeed, there is no known experimental or observational evidence that magnetic monopoles exist. A magnetic monopole is not necessarily an elementary particle, and models for magnetic monopole production can include (but are not limited to) Spin (physics), spin-0 monopoles or spin-1 massive vector mesons. The term "magnetic monopole" only refers to the nature of the particle ...
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Monopole (mathematics)
In mathematics, a monopole is a connection over a principal bundle ''G'' with a section of the associated adjoint bundle. Physical interpretation Physically, the section can be interpreted as a ''Higgs field The Higgs boson, sometimes called the Higgs particle, is an elementary particle in the Standard Model of particle physics produced by the excited state, quantum excitation of the Higgs field, one of the field (physics), fields in particl ...'', where the connection and Higgs field should satisfy the Bogomolny equations and be of finite action. See also * Nahm equations * Instanton * Magnetic monopole * Yang–Mills theory References

* * * Differential geometry Mathematical physics {{math-physics-stub ...
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Multipole Expansion
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, \R^3. Multipole expansions are useful because, similar to Taylor series, oftentimes only the first few terms are needed to provide a good approximation of the original function. The function being expanded may be real- or complex-valued and is defined either on \R^3, or less often on \R^n for some other Multipole expansions are used frequently in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region. The multipole expansion with angles is often combined with an expansion in radius. Such a combination gives an expansion describing a function throughout three-dimensional space. The multipole expansion is expressed as a sum of terms with progressively finer angular f ...
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Monopole (wine)
A () is an area controlled by a single winery (wine company) and can be as small as a named vineyard () or as large as an entire (AOC). Frequently this is mentioned on the label as it is rare for only one winery to produce all the wine from an area entitled to a certain name. Each wine is sold by only one company. The Napoleonic inheritance laws typically caused vineyards to be so finely divided among inheritors – down to even a single row of vines – that are needed to bottle commercial quantities of a wine. Whether a indicates a wine of unusual quality or not is a matter of debate. List of ''monopoles'' (in need of expansion) In Burgundy: Others *Château-Grillet AOC, of Château Grillet. * Savennières-Coulée-de-Serrant, owned by Nicolas Joly. See also *Vineyard designated wine A vineyard designated wine is a wine produced from the product of a single vineyard with that vineyard's name appearing on the wine label. Throughout the history of winemaking and viti ...
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Monopole (album)
''Monopole'' is the fifth studio album by British indie pop musical project White Town Jyoti Prakash Mishra (born 30 July 1966), better known by his stage name White Town, is a British-Indian singer, musician, and record producer, producer. He is best known for his 1997 hit song "Your Woman". Early life Jyoti Prakash Mishra was ..., released in 2011 through Bzangy Records. Track listing References {{Authority control 2011 albums White Town albums Alternative rock albums by British artists Electronica albums by British artists ...
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Monopole Antenna
A monopole antenna is a class of radio antenna consisting of a straight rod-shaped conductor, often mounted perpendicularly over some type of conductive surface, called a ground plane. The current from the transmitter is applied, or for receiving antennas the output signal voltage to the receiver is taken, between the monopole and the ground plane. One side of the feedline to the transmitter or receiver is connected to the lower end of the monopole element, and the other side is connected to the ground plane, which may be the Earth. This contrasts with a dipole antenna which consists of two identical rod conductors, with the current from the transmitter applied between the two halves of the antenna. The monopole antenna is related mathematically to the dipole. The vertical monopole is an omnidirectional antenna with a low gain of 2 - 5  dBi, and radiates most of its power in horizontal directions or low elevation angles. Common types of monopole antenna are the w ...
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Radio Masts And Towers
Radio masts and towers are typically tall structures designed to support antenna (radio), antennas for telecommunications and broadcasting, including television. There are two main types: guyed and self-supporting structures. They are among the tallest human-made structures. Masts are often named after the broadcasting organizations that originally built them or currently use them. A mast radiator or radiating tower is one in which the metal mast or tower itself is energized and functions as the transmitting antenna. Terminology The terms "mast" and "tower" are often used interchangeably. However, in structural engineering terms, a tower is a self-supporting or cantilevered structure, while a Guyed mast, mast is held up by stays or guy-wires. ; A ''mast'': is a guyed mast, a thin structure without the shear strength to stand unsupported, that uses attached guy lines for stability. They may be mounted on the ground or on top of buildings. Typical ''masts'' are of steel latt ...
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Plattsburgh, NY
Plattsburgh is a city in and the county seat of Clinton County, New York, United States, situated on the north-western shore of Lake Champlain. The population was 19,841 at the 2020 census. The population of the surrounding (and separately incorporated) Town of Plattsburgh was 11,886 as of the 2020 census, making the combined population of Plattsburgh to be 31,727. Plattsburgh lies just to the northeast of Adirondack Park, immediately outside of the park boundaries. It is the second largest community in the North Country region (after Watertown), and serves as the main commercial hub for the sparsely populated northern Adirondack Mountains. The land around Plattsburgh was previously inhabited by the Iroquois, Western Abenaki, Mohican, and Mohawk people. Samuel de Champlain was the first ever recorded European that sailed into Champlain Valley and later claimed the region as a part of New France in 1609. Plattsburgh was the site of the Amphibious warfare, amphibious Battl ...
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Monopole (company)
Établissements Monopole was a French manufacturing company that produced parts for automobile engines. The company also built and raced a series of small displacement endurance racing cars. After a series of mergers and acquisitions the Monopole name was retired in Europe, but survives in Africa in the name of a former licensee. History "Établissements SIM SA" was a company based in Morges, Switzerland that operated a foundry and machine shops. In 1920 they used American investment capital to start another company called Établissements Monopole in Poissy on the outskirts of Paris, France. The new company specialised in producing pistons, piston-rings, valves, and other parts for automobile engines, and was managed by a Mr. Guerne. The company's name is abbreviated Ets. Monopole, but "Monopole-Poissy" was used in the company's own literature. In 1937–38, majority ownership of Monopole was acquired by André Hémard, son of Guy-Aristide Hémard of the Hémard distilling conce ...
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Dipole
In physics, a dipole () is an electromagnetic phenomenon which occurs in two ways: * An electric dipole moment, electric dipole deals with the separation of the positive and negative electric charges found in any electromagnetic system. A simple example of this system is a pair of charges of equal magnitude but opposite sign separated by some typically small distance. (A permanent electric dipole is called an electret.) * A magnetic dipole is the closed circulation of an electric current system. A simple example is a single loop of wire with constant current through it. A bar magnet is an example of a magnet with a permanent magnetic dipole moment. Dipoles, whether electric or magnetic, can be characterized by their dipole moment, a vector quantity. For the simple electric dipole, the electric dipole moment points from the negative charge towards the positive charge, and has a magnitude equal to the strength of each charge times the separation between the charges. (To be precis ...
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Dyon
In physics, a dyon is a hypothetical particle in 4-dimensional theories with both electric and magnetic charges. A dyon with a zero electric charge is usually referred to as a magnetic monopole. Many grand unified theories predict the existence of both magnetic monopoles and dyons. Dyons were first proposed by Julian Schwinger in 1969 as a phenomenological alternative to quarks. He extended the Dirac quantization condition to the dyon and used the model to predict the existence of a particle with the properties of the J/ψ meson prior to its discovery in 1974. The allowed charges of dyons are restricted by the Dirac quantization condition. This states in particular that their magnetic charge must be integral, and that their electric charges must all be equal modulo 1. The Witten effect, demonstrated by Edward Witten in his 1979 paper, states that the electric charges of dyons must all be equal, modulo one, to the product of their magnetic charge and the theta angle of the th ...
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Instanton
An instanton (or pseudoparticle) is a notion appearing in theoretical and mathematical physics. An instanton is a classical solution to equations of motion with a finite, non-zero action, either in quantum mechanics or in quantum field theory. More precisely, it is a solution to the equations of motion of the classical field theory on a Euclidean spacetime. In such quantum theories, solutions to the equations of motion may be thought of as critical points of the action. The critical points of the action may be local maxima of the action, local minima, or saddle points. Instantons are important in quantum field theory because: * they appear in the path integral as the leading quantum corrections to the classical behavior of a system, and * they can be used to study the tunneling behavior in various systems such as a Yang–Mills theory. Relevant to dynamics, families of instantons permit that instantons, i.e. different critical points of the equation of motion, be rela ...
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