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Since the early 2000s,Chinahas increased its presence in the TOP500 rankings ofsupercomputers, with systems like Tianhe-1A reaching the top position in 2010 and Sunway TaihuLight leading in 2016.[1]
By 2018, China had the highest number of supercomputers listed on the TOP500, reflecting its commitment to advancing com... | https://en.wikipedia.org/wiki/Supercomputing_in_China |
Several centers forsupercomputingexist acrossEurope, and distributed access to them is coordinated by European initiatives to facilitatehigh-performance computing. One such initiative, theHPC Europaproject, fits within theDistributed European Infrastructure for Supercomputing Applications(DEISA), which was formed in 20... | https://en.wikipedia.org/wiki/Supercomputing_in_Europe |
Supercomputing in Indiahas a history going back to the 1980s.[1]TheGovernment of Indiacreated an indigenous development programme as they had difficulty purchasing foreignsupercomputers.[1]As of November 2024[update], the AIRAWAT supercomputer is the fastest supercomputer in India, having been ranked 136th fastest in t... | https://en.wikipedia.org/wiki/Supercomputing_in_India |
Japanoperates a number of centers forsupercomputingwhich hold world records in speed, with theK computerbeing the world's fastest from June 2011 to June 2012,[1][2][3]andFugakuholding the lead from June 2020 until June 2022.
The K computer's performance was impressive, according to professorJack Dongarrawho maintains ... | https://en.wikipedia.org/wiki/Supercomputing_in_Japan |
TheSlurm Workload Manager, formerly known asSimple Linux Utility for Resource Management(SLURM), or simplySlurm, is afree and open-sourcejob schedulerforLinuxandUnix-likekernels, used by many of the world'ssupercomputersandcomputer clusters.
It provides three key functions:
Slurm is the workload manager on about 60% ... | https://en.wikipedia.org/wiki/Slurm_Workload_Manager |
High performance computingapplications run onmassively parallelsupercomputersconsist ofconcurrent programsdesigned usingmulti-threaded,multi-process models. The applications may consist of various constructs (threads, local processes, distributed processes, etc.) with varying degree of parallelism. Although high perfor... | https://en.wikipedia.org/wiki/Testing_high-performance_computing_applications |
Ultra Network Technologies(previously calledUltra Corporation) was a networking company. It offered high-speed network products for the scientific computing market as well as some commercial companies. It was founded in 1986 by James N. Perdue (formerly ofNASA, Ames Research Center), Drew Berding, and Wes Meador (ofCon... | https://en.wikipedia.org/wiki/Ultra_Network_Technologies |
Formal scienceis abranch of sciencestudying disciplines concerned with abstract structures described byformal systems, such aslogic,mathematics,statistics,theoretical computer science,artificial intelligence,information theory,game theory,systems theory,decision theoryandtheoretical linguistics. Whereas thenatural scie... | https://en.wikipedia.org/wiki/Formal_science |
Withintheoretical computer science, theSun–Ni law(orSun and Ni's law, also known asmemory-bounded speedup) is a memory-boundedspeedupmodel which states that as computing power increases the corresponding increase in problem size is constrained by the system’s memory capacity. In general, as a system grows in computatio... | https://en.wikipedia.org/wiki/Sun%E2%80%93Ni_law |
Network computingrefers to computers or nodes working together over anetwork.
Network computingmay also mean: | https://en.wikipedia.org/wiki/Network_computing_(disambiguation) |
TheWDR paper computerorKnow-how Computeris an educational model of a computer consisting only of a pen, a sheet of paper, and individual matches in the most simple case.[1]This allows anyone interested to learn how to program without having anelectronic computerat their disposal.
The paper computer was created in the ... | https://en.wikipedia.org/wiki/WDR_paper_computer |
ThePhillips Machine, also known as theMONIAC(Monetary National Income Analogue Computer),Phillips Hydraulic Computerand theFinancephalograph, is ananalogue computerwhich usesfluidic logicto model the workings of an economy. The name "MONIAC" is suggested by associatingmoneyandENIAC, an early electronicdigital computer.... | https://en.wikipedia.org/wiki/MONIAC |
Digital Enhanced Cordless Telecommunications(DECT) is acordless telephonystandard maintained byETSI. It originated inEurope, where it is the common standard, replacing earlier standards, such asCT1andCT2.[1]Since the DECT-2020 standard onwards, it also includesIoTcommunication.
Beyond Europe, it has been adopted byAus... | https://en.wikipedia.org/wiki/DECT |
TheGeneric Access Profile(GAP) (ETSIstandard EN 300 444[1]) describes a set of mandatory requirements to allow any conformingDECTFixed Part (base) to interoperate with any conforming DECT Portable Part (handset) to provide basic telephony services when attached to a 3.1 kHz telephone network (as defined by EN 300 176-2... | https://en.wikipedia.org/wiki/Generic_access_profile |
Apicocellis a small cellularbase stationtypically covering a small area, such as in-building (offices, shopping malls, train stations, stock exchanges, etc.), or more recently in-aircraft. In cellular networks, picocells are typically used to extend coverage to indoor areas where outdoor signals do not reach well, or t... | https://en.wikipedia.org/wiki/Picocell |
Cordless Advanced Technology—internet and quality(CAT-iq) is a technology initiative from theDigital Enhanced Cordless Telecommunications(DECT) Forum, based on ETSI TS 102 527 New Generation DECT (NG-DECT) European standard series.
NG-DECT contains backward compatible extensions to basic DECTGAP(Generic access profil... | https://en.wikipedia.org/wiki/CAT-iq |
Wi-Fi calling, also calledVoWiFi,[1]refers tomobile phonevoice calls and data that are made overIPnetworks usingWi-Fi, instead of thecell towersprovided bycellular networks.[2]Using this feature, compatible handsets are able to route regular cellular calls through a wireless LAN (Wi-Fi) network withbroadband Internet, ... | https://en.wikipedia.org/wiki/Voice_over_WLAN |
ThePersonal Handy-phone System(PHS), also known as thePersonal Communication Telephone(PCT) in Thailand, and thePersonal Access System(PAS) and commercially branded asXiaolingtong(Chinese:小灵通) inChina, was amobile networksystem operating in the 1880–1930MHzfrequency band. InJapan, it was introduced as a low-cost wirele... | https://en.wikipedia.org/wiki/Personal_Access_System |
Amateur radio, also known asham radio, is the use of theradio frequencyspectrumfor purposes ofnon-commercialexchange of messages,wirelessexperimentation, self-training, private recreation,Radiosport,contesting, andemergency communications.[1]The term"radio amateur"is used to specify"a duly authorized person interested ... | https://en.wikipedia.org/wiki/Amateur_radio |
Citizens band radio(CB radio) is aland mobile radio system, a system allowing short-distance one-to-many bidirectional voice communication among individuals, usingtwo-way radiosoperating near 27MHz(or the 11-m wavelength) in thehigh frequencyorshortwaveband. Citizens band is distinct from otherpersonal radio serviceall... | https://en.wikipedia.org/wiki/Citizens_band_radio |
TheFamily Radio Service(FRS) is an improvedwalkie-talkieradio system authorized in the United States since 1996. Thispersonal radio serviceuses channelized frequencies around 462 and 467 MHz in theultra high frequency(UHF) band. It does not suffer the interference effects found oncitizens' band(CB) at 27MHz, or the 49 ... | https://en.wikipedia.org/wiki/Family_Radio_Service |
TheGeneral Mobile Radio Service(GMRS) is aland-mobileFMUHFradioservice designed for short-range two-way voice communication and authorized under part 95 of the USFCCcode. It requires a license in theUnited States, but some GMRS compatible equipment can be used license-free inCanada. The US GMRS license is issued for a... | https://en.wikipedia.org/wiki/General_Mobile_Radio_Service |
In theUnited States, theMulti-Use Radio Service(MURS) is a licensed by rule (i.e. under part 95, subpart J, of title 47, Code of Federal Regulations[1])two-way radioservice similar to theCitizens band(CB). Established by theU.S.Federal Communications Commissionin the fall of 2000, MURS created a radio service allowing ... | https://en.wikipedia.org/wiki/Multi-Use_Radio_Service |
Intelecommunications, afemtocellis a small, low-powercellular base station, typically designed for use in a home or small business. A broader term which is more widespread in the industry issmall cell, withfemtocellas a subset. It typically connects to the service provider's network via the Internet through a wired bro... | https://en.wikipedia.org/wiki/Femtocell |
Small cellsare low-powered cellularradio access nodesthat have a ranges of around 10 meters to a few kilometers. They are base stations with low power consumption and cost. They can provide high data rates by being deployed densely to achieve high spatial spectrum efficiency.[1]
In the United States, recent FCC orders... | https://en.wikipedia.org/wiki/Small_Cells |
Amodular connectoris a type ofelectrical connectorfor cords and cables of electronic devices and appliances, such as incomputer networking, telecommunication equipment, and audio headsets.
Modular connectors were originally developed for use on specificBell Systemtelephone sets in the 1960s, and similar types found us... | https://en.wikipedia.org/wiki/8P8C |
Inradio-frequency engineering, anantenna(American English) oraerial(British English) is an electronic device that converts analternating electric currentintoradio waves(transmitting), or radio waves into an electric current (receiving).[1][2]It is the interface between radio wavespropagatingthrough space and electric c... | https://en.wikipedia.org/wiki/Antenna_(radio) |
Thebasic exchange telephone radio serviceorBETRSis a fixed radio service where amultiplexed,digital radiolink is used as the last segment of thelocal loopto providewirelesstelephone service to subscribers in remote areas. BETRS technology was developed in the mid-1980s and allows up to four subscribers to use a single ... | https://en.wikipedia.org/wiki/Basic_exchange_telephone_radio_service |
Anelectrical cableis an assembly of one or morewiresrunning side by side or bundled, which is used as anelectrical conductorto carryelectric current.
Electrical cables are used to connect two or more devices, enabling the transfer ofelectrical signals,power, or both from one device to the other. Physically, an electri... | https://en.wikipedia.org/wiki/Electrical_cable |
AnRF connector(radio frequency connector) is anelectrical connectordesigned to work atradio frequenciesin the multi-megahertz range.
RF connectors are typically used withcoaxial cablesand are designed to maintain the shielding that the coaxial design offers. Better models also minimize the change in transmission lineim... | https://en.wikipedia.org/wiki/RF_connector |
Microwave Bypass, Inc.launched the world's first fixed wireless internet access technology in 1987, a decade beforeWi-Fi. It enabled local and remote networks to connect at the then full Ethernet (802.3) data rate of 10 megabits per second, and for up to 4.3 miles.[1]
The company was founded in March 1986 by David The... | https://en.wikipedia.org/wiki/Microwave_Bypass |
Awireless Internet service provider(WISP) is anInternet service providerwith a network based onwireless networking. Technology may include commonplaceWi-Fiwireless mesh networking, or proprietary equipment designed to operate over open900 MHz,2.4 GHz, 4.9, 5, 24, and 60 GHz bands or licensed frequencies in theUHFband (... | https://en.wikipedia.org/wiki/Wireless_Internet_service_provider |
Acellular networkormobile networkis atelecommunications networkwhere the link to and from end nodes iswirelessand the network is distributed over land areas calledcells, each served by at least one fixed-locationtransceiver(such as abase station). These base stations provide the cell with the network coverage which can... | https://en.wikipedia.org/wiki/Frequency_reuse |
This article contains terminology related toCDMAInternational Roaming. To quickly find a term, click on the first letter of the term below:
#|A|B|C|D|E|F|G|H|I|J|K|L|M|N|O|P|Q|R|S|T|U|V|W|X|Y|Z
1x– See1xRTT
1xEV-DO– cdma2000 Evolution, Data Optimized
1xRTT– cdma2000 Radio Transmission Technology
2G Authentication... | https://en.wikipedia.org/wiki/List_of_CDMA_terminology |
Thenear–far problemorhearability problemis the effect of a strong signal from a near signal source in making it hard for a receiver to hear a weaker signal from a further source due toadjacent-channel interference,co-channel interference,distortion,capture effect,dynamic rangelimitation, or the like. Such a situation ... | https://en.wikipedia.org/wiki/Near%E2%80%93far_problem |
Incryptography,pseudorandom noise(PRN[1]) is asignalsimilar tonoisewhich satisfies one or more of the standard tests forstatistical randomness. Although it seems to lack any definitepattern, pseudorandom noise consists of a deterministicsequenceofpulsesthat will repeat itself after its period.[2]
Incryptographic devic... | https://en.wikipedia.org/wiki/PN_code |
Intelecommunicationsandelectronics,baud(/bɔːd/; symbol:Bd) is a commonunit of measurementofsymbol rate, which is one of the components that determine thespeed of communicationover adata channel.
It is the unit for symbol rate ormodulationrate insymbols per secondorpulses per second. It is the number of distinctsymbolc... | https://en.wikipedia.org/wiki/Baud |
GPS signalsare broadcast byGlobal Positioning Systemsatellites to enablesatellite navigation. Using these signals, receivers on or near the Earth's surface can determine their Position,Velocityand Time (PVT). The GPSsatellite constellationis operated by the2nd Space Operations Squadron(2SOPS) ofSpace Delta 8,United Sta... | https://en.wikipedia.org/wiki/GPS_signals |
Intelecommunication technology, aBarker codeorBarker sequenceis a finite sequence of digital values with the idealautocorrelationproperty. It is used as a synchronising pattern between the sender and receiver of a stream of bits.
Binary digitshave very little meaning unless the significance of the individual digits is... | https://en.wikipedia.org/wiki/Barker_code |
AGold code, also known asGold sequence, is a type of binarysequence, used intelecommunications(CDMA)[1]and satellite navigation (GPS).[2]Gold codes are named after Robert Gold.[3][4]Gold codes have bounded smallcross-correlationswithin a set, which is useful when multiple devices are broadcasting in the same frequency ... | https://en.wikipedia.org/wiki/Gold_code |
AZadoff–Chu (ZC) sequence[1]: 152is acomplex-valuedmathematicalsequencewhich, when applied to asignal, gives rise to a new signal of constantamplitude. Whencyclically shiftedversions of a Zadoff–Chu sequence are imposed upon a signal the resulting set of signals detected at the receiver areuncorrelatedwith one another.... | https://en.wikipedia.org/wiki/Zadoff%E2%80%93Chu_sequence |
Apseudorandomsequence of numbers is one that appears to bestatistically random, despite having been produced by a completelydeterministicand repeatable process.[1]Pseudorandom number generatorsare often used in computer programming, as traditional sources of randomness available to humans (such as rolling dice) rely on... | https://en.wikipedia.org/wiki/Pseudorandomness |
Intelecommunications,direct-sequence spread spectrum(DSSS) is aspread-spectrummodulationtechnique primarily used to reduce overall signalinterference. The direct-sequence modulation makes the transmitted signal wider in bandwidth than the information bandwidth.
After the despreading or removal of the direct-sequence m... | https://en.wikipedia.org/wiki/Direct-sequence_spread_spectrum |
Electromagnetic compatibility(EMC) is the ability of electrical equipment and systems to function acceptably in theirelectromagnetic environment, by limiting the unintentional generation, propagation and reception of electromagnetic energy which may cause unwanted effects such aselectromagnetic interference(EMI) or eve... | https://en.wikipedia.org/wiki/Electromagnetic_compatibility |
Electromagnetic interference(EMI), also calledradio-frequency interference(RFI) when in theradio frequencyspectrum, is a disturbance generated by an external source that affects an electrical circuit byelectromagnetic induction,electrostatic coupling, or conduction.[1]The disturbance may degrade the performance of the ... | https://en.wikipedia.org/wiki/Electromagnetic_interference |
Frequency-hopping spread spectrum(FHSS) is a method of transmitting radio signals by rapidly changing the carrier frequency among many frequencies occupying a large spectral band. The changes are controlled by a code known to bothtransmitterandreceiver. FHSS is used to avoid interference, to prevent eavesdropping, and ... | https://en.wikipedia.org/wiki/Frequency-hopping_spread_spectrum |
George Johann Carl Antheil(/ˈæntaɪl/AN-tyle; July 8, 1900 – February 12, 1959) was an Americanavant-gardecomposer, pianist, author, and inventor whose modernist musical compositions explored the sounds – musical, industrial, and mechanical – of the early 20th century. Spending much of the 1920s in Europe, Antheil retur... | https://en.wikipedia.org/wiki/George_Antheil |
Have Quick(alsoHAVEQUICK, shortHQ) is anECM-resistantfrequency-hopping systemused to protect militaryaeronautical mobile (OR)radio traffic.
Since the end ofWorld War II, U.S. and Allied military aircraft have used AM radios in theNATO harmonised 225–400 MHz UHF band(part ofNATOB band[1]) for short range air-to-air an... | https://en.wikipedia.org/wiki/HAVE_QUICK |
Hedy Lamarr(/ˈhɛdi/; bornHedwig Eva Maria Kiesler; November 9, 1914[a]– January 19, 2000) was an Austrian-born American actress and inventor. After a brief early film career inCzechoslovakia, including the controversial erotic romantic dramaEcstasy(1933), she fled from her first husband,Friedrich Mandl, and secretly m... | https://en.wikipedia.org/wiki/Hedy_Lamarr |
Open spectrum(also known asfree spectrum) is a movement to get theFederal Communications Commissionto provide moreunlicensedradio-frequencyspectrumthat is available for use by all. Proponents of the "commons model" of open spectrum advocate a future where all the spectrum is shared, and in which people useInternetproto... | https://en.wikipedia.org/wiki/Open_spectrum |
Spread-spectrum time-domain reflectometry(SSTDR) is a measurement technique to identify faults, usually in electrical wires, by observing reflected spread spectrum signals. This type oftime-domain reflectometrycan be used in various high-noise and live environments. Additionally, SSTDR systems have the additional benef... | https://en.wikipedia.org/wiki/Spread-spectrum_time-domain_reflectometry |
Time-hopping(TH) is a communications signal technique which can be used to achieveanti-jamming(AJ) orlow probability of intercept(LPI). It can also refer topulse-position modulation, which in its simplest form employs 2kdiscrete pulses (referring to the unique positions of the pulse within the transmission window) to t... | https://en.wikipedia.org/wiki/Time-hopping_spread_spectrum |
In computing,56-bit encryptionrefers to akey sizeof fifty-sixbits, or sevenbytes, forsymmetric encryption. While stronger than40-bit encryption, this still represents a relatively lowlevel of securityin the context of abrute force attack.
The US government traditionally regulated encryption for reasons of national se... | https://en.wikipedia.org/wiki/56-bit_encryption |
TheContent Scramble System(CSS) is adigital rights management(DRM) andencryptionsystem employed on many commercially producedDVD-Videodiscs. CSS utilizes aproprietary40-bitstream cipheralgorithm. The system was introduced around 1996 and was first compromised in 1999.[1]
CSS is one of several complementary systems des... | https://en.wikipedia.org/wiki/Content_Scramble_System |
Inalgebraic geometry, aderived schemeis ahomotopy-theoretic generalization of aschemein which classicalcommutative ringsare replaced with derived versions such asdifferential graded algebras, commutativesimplicial rings, orcommutative ring spectra.
From the functor of points point-of-view, a derived scheme is a sheafX... | https://en.wikipedia.org/wiki/Derived_scheme |
Pursuing Stacks(French:À la Poursuite des Champs) is an influential 1983 mathematical manuscript byAlexander Grothendieck.[1]It consists of a 12-page letter toDaniel Quillenfollowed by about 600 pages of research notes.
The topic of the work is a generalizedhomotopy theoryusinghigher category theory. The word "stacks"... | https://en.wikipedia.org/wiki/Pursuing_Stacks |
Inmathematics,derivatorsare a proposed framework[1][2]pg 190-195forhomological algebragiving a foundation for bothabelianandnon-abelianhomological algebra and various generalizations of it. They were introduced to address the deficiencies ofderived categories(such as the non-functorialityof the cone construction) and p... | https://en.wikipedia.org/wiki/Derivator |
In algebra, anoperad algebrais an "algebra" over anoperad. It is a generalization of anassociative algebraover a commutative ringR, with an operad replacingR.
Given an operadO(say, asymmetric sequencein asymmetric monoidal ∞-categoryC), analgebra over an operad, orO-algebrafor short, is, roughly, a left module overOwi... | https://en.wikipedia.org/wiki/Algebra_over_an_operad |
Inmathematics, anEn{\displaystyle {\mathcal {E}}_{n}}-algebrain asymmetric monoidalinfinity categoryCconsists of the following data:
subject to the requirements that the multiplication maps are compatible with composition, and thatμ{\displaystyle \mu }is an equivalence ifm=1{\displaystyle m=1}. An equivalent definiti... | https://en.wikipedia.org/wiki/En-ring |
Higher Topos Theoryis a treatise on the theory of∞-categorieswritten by American mathematicianJacob Lurie. In addition to introducing Lurie's new theory of∞-topoi, the book is widely considered foundational tohigher category theory.[1]Since 2018, Lurie has been transferring the contents ofHigher Topos Theory(along with... | https://en.wikipedia.org/wiki/Higher_Topos_Theory |
Inmathematics, an∞-topos(infinity-topos) is, roughly, an∞-categorysuch that its objects behave likesheavesof spaces with some choice ofGrothendieck topology; in other words, it gives an intrinsic notion of sheaves without reference to an external space. The prototypical example of an ∞-topos is the ∞-category of sheave... | https://en.wikipedia.org/wiki/%E2%88%9E-topos |
Inalgebraic geometry, a branch ofmathematics, theétale spectrumof acommutative ringor anE∞-ring, denoted by Specétor Spét, is an analog of theprime spectrumSpec of a commutative ring that is obtained by replacingZariski topologywithétale topology. The precise definition depends on one's formalism. But the idea of the d... | https://en.wikipedia.org/wiki/%C3%89tale_spectrum |
Inmathematics, thefuzzy sphereis one of the simplest and most canonical examples ofnon-commutative geometry. Ordinarily, the functions defined on asphereform a commuting algebra. A fuzzy sphere differs from an ordinary sphere because the algebra of functions on it is not commutative. It is generated byspherical harmoni... | https://en.wikipedia.org/wiki/Fuzzy_sphere |
Inmathematics, and especiallydifferential geometryandgauge theory, aconnectionon afiber bundleis a device that defines a notion ofparallel transporton the bundle; that is, a way to "connect" or identify fibers over nearby points. The most common case is that of alinear connectionon avector bundle, for which the notion ... | https://en.wikipedia.org/wiki/Koszul_connection |
Inmathematics, theMoyal product(afterJosé Enrique Moyal; also called thestar productorWeyl–Groenewold product, afterHermann WeylandHilbrand J. Groenewold) is an example of aphase-space star product. It is an associative, non-commutative product,★, on the functions onR2n{\displaystyle \mathbb {R} ^{2n}}, equipped with ... | https://en.wikipedia.org/wiki/Moyal_product |
Inmathematics,noncommutative topologyis a term used for the relationship betweentopologicalandC*-algebraicconcepts. The term has its origins in theGelfand–Naimark theorem, which implies thedualityof thecategoryoflocally compactHausdorff spacesand the category ofcommutativeC*-algebras. Noncommutative topology is related... | https://en.wikipedia.org/wiki/Noncommutative_topology |
Thephase-space formulationis a formulation ofquantum mechanicsthat places thepositionandmomentumvariables on equal footing inphase space. The two key features of the phase-space formulation are that the quantum state is described by aquasiprobability distribution(instead of awave function,state vector, ordensity matrix... | https://en.wikipedia.org/wiki/Phase_space_formulation |
In abstract algebra, aquasi-free algebrais anassociative algebrathat satisfies the lifting property similar to that of aformally smooth algebraincommutative algebra. The notion was introduced by Cuntz and Quillen for the applications tocyclic homology.[1]A quasi-free algebra generalizes afree algebra, as well as thecoo... | https://en.wikipedia.org/wiki/Quasi-free_algebra |
In mathematics,derived noncommutative algebraic geometry,[1]the derived version ofnoncommutative algebraic geometry, is the geometric study ofderived categoriesand related constructions of triangulated categories using categorical tools. Some basic examples include the bounded derived category of coherent sheaves on a ... | https://en.wikipedia.org/wiki/Derived_noncommutative_algebraic_geometry |
In mathematics, aQ-categoryoralmost quotient category[1]is acategorythat is a "milder version of a Grothendieck site."[2]A Q-category is acoreflective subcategory.[1][clarification needed]The Q stands for a quotient.
The concept of Q-categories was introduced by Alexander Rosenberg in 1988.[2]The motivation for the no... | https://en.wikipedia.org/wiki/Q-category |
Inmathematics, theSelberg trace formula, introduced bySelberg (1956), is an expression for the character of theunitary representationof aLie groupGon the spaceL2(Γ\G)ofsquare-integrable functions, whereΓis a cofinitediscrete group. The character is given by the trace of certain functions onG.
The simplest case is when... | https://en.wikipedia.org/wiki/Selberg_trace_formula |
Inmathematics, theLanglands programis a set ofconjecturesabout connections betweennumber theoryandgeometry. It was proposed byRobert Langlands(1967,1970). It seeks to relateGalois groupsinalgebraic number theorytoautomorphic formsandrepresentation theoryofalgebraic groupsoverlocal fieldsandadeles. It was described byE... | https://en.wikipedia.org/wiki/Langlands_program |
Inmathematics, theorbit method(also known as theKirillov theory,the method of coadjoint orbitsand by a few similar names) establishes a correspondence between irreducibleunitary representationsof aLie groupand itscoadjoint orbits: orbits of theaction of the groupon the dual space of itsLie algebra. The theory was intro... | https://en.wikipedia.org/wiki/Kirillov_orbit_theory |
Inmathematics, adiscrete series representationis an irreducibleunitary representationof alocally compact topological groupGthat is a subrepresentation of the leftregular representationofGon L²(G). In thePlancherel measure, such representations have positive measure. The name comes from the fact that they are exactly... | https://en.wikipedia.org/wiki/Discrete_series_representation |
Inmathematics, azonal spherical functionor often justspherical functionis a function on alocally compact groupGwith compact subgroupK(often amaximal compact subgroup) that arises as thematrix coefficientof aK-invariant vector in anirreducible representationofG. The key examples are the matrix coefficients of thespheric... | https://en.wikipedia.org/wiki/Zonal_spherical_function |
Inmathematics, specifically in therepresentation theoryofgroupsandalgebras, anirreducible representation(ρ,V){\displaystyle (\rho ,V)}orirrepof an algebraic structureA{\displaystyle A}is a nonzero representation that has no proper nontrivial subrepresentation(ρ|W,W){\displaystyle (\rho |_{W},W)}, withW⊂V{\displaystyle ... | https://en.wikipedia.org/wiki/Irreducible_representations |
Ingroup theory, a branch ofabstract algebra, acharacter tableis a two-dimensional table whose rows correspond toirreducible representations, and whose columns correspond toconjugacy classesofgroupelements. The entries consist ofcharacters, thetracesof thematricesrepresenting group elements of the column's class in the... | https://en.wikipedia.org/wiki/Character_table |
Inmathematics, more specifically ingroup theory, thecharacterof agroup representationis afunctionon thegroupthat associates to each group element thetraceof the correspondingmatrix. The character carries the essential information about the representation in a more condensed form.Georg Frobeniusinitially developedrepres... | https://en.wikipedia.org/wiki/Character_theory |
Inchemistry,molecular symmetrydescribes thesymmetrypresent inmoleculesand the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain many of a molecule'schemical properties, such as whether or not it has adipole m... | https://en.wikipedia.org/wiki/Molecular_symmetry |
This is alist ofharmonic analysistopics. See alsolist of Fourier analysis topicsandlist of Fourier-related transforms, which are more directed towards the classicalFourier seriesandFourier transformofmathematical analysis,mathematical physicsandengineering. | https://en.wikipedia.org/wiki/List_of_harmonic_analysis_topics |
This is alist ofrepresentation theorytopics, by Wikipedia page. See alsolist of harmonic analysis topics, which is more directed towards themathematical analysisaspects of representation theory.
See also:Glossary of representation theory | https://en.wikipedia.org/wiki/List_of_representation_theory_topics |
Therepresentation theoryofgroupsis a part of mathematics which examines how groups act on given structures.
Here the focus is in particular onoperations of groupsonvector spaces. Nevertheless, groups acting on other groups or onsetsare also considered. For more details, please refer to the section onpermutation repres... | https://en.wikipedia.org/wiki/Representation_theory_of_finite_groups |
Inmathematics, specifically inrepresentation theory, asemisimple representation(also called acompletely reducible representation) is alinear representationof agroupor analgebrathat is adirect sumofsimple representations(also calledirreducible representations).[1]It is an example of the general mathematical notion ofsem... | https://en.wikipedia.org/wiki/Semisimple_representation |
Achild prodigyis, technically, a child under the age of 10 who produces meaningful work in some domain at the level of an adult expert.[1][2][3]The term is also applied more broadly to describe young people who are extraordinarily talented in some field.[4]
The termwunderkind(from GermanWunderkind; literally "wonder c... | https://en.wikipedia.org/wiki/Child_prodigy |
TheDoomsday rule,Doomsday algorithmorDoomsday methodis analgorithmofdetermination of the day of the weekfor a given date. It provides aperpetual calendarbecause theGregorian calendarmoves in cycles of 400 years. The algorithm formental calculationwas devised byJohn Conwayin 1973,[1][2]drawing inspiration fromLewis Carr... | https://en.wikipedia.org/wiki/Doomsday_rule |
Thedetermination of the day of the weekfor any date may be performed with a variety ofalgorithms. In addition,perpetual calendarsrequire no calculation by the user, and are essentially lookup tables.
A typical application is to calculate theday of the weekon which someone was born or a specific event occurred.
In nume... | https://en.wikipedia.org/wiki/Calculating_the_day_of_the_week |
Hypercalculiais "a specificdevelopmentalcondition in which the ability to performmathematicalcalculations is significantly superior to general learning ability and to school attainment in maths."[1]A 2002neuroimagingstudy of a child with hypercalculia suggested greater brain volume in the righttemporal lobe. SerialSPEC... | https://en.wikipedia.org/wiki/Hypercalculia |
Theabacus systemofmental calculationis a system where users mentally visualize anabacusto carry out arithmeticalcalculations.[1]No physical abacus is used; only the answers are written down. Calculations can be made at great speed in this way. For example, in the Flash Anzan event at theAll Japan Soroban Championship... | https://en.wikipedia.org/wiki/Mental_abacus |
The titlemnemonistrefers to an individual with the ability to remember and recall unusually long lists of data, such as unfamiliar names, lists of numbers, entries in books, etc. Some mnemonists also memorize texts such as long poems, speeches, or even entire books of fiction or non-fiction. The term is derived from th... | https://en.wikipedia.org/wiki/Mnemonist |
Thesoroban(算盤, そろばん, counting tray)is anabacusdeveloped inJapan. It is derived from theancient Chinesesuanpan, imported to Japan in the 14th century.[1][nb 1]Like the suanpan, the soroban is still used today, despite the proliferation of practical and affordable pocketelectronic calculators.
The soroban is composed of... | https://en.wikipedia.org/wiki/Soroban |
Inmathematics, aDiophantine equationis anequation, typically apolynomial equationin two or moreunknownswithintegercoefficients, for which onlyintegersolutions are of interest. Alinear Diophantine equationequates the sum of two or more unknowns, with coefficients, to a constant. Anexponential Diophantine equationis one... | https://en.wikipedia.org/wiki/Diophantine_equation |
Mathematical puzzlesmake up an integral part ofrecreational mathematics. They have specific rules, but they do not usually involve competition between two or more players. Instead, to solve such apuzzle, the solver must find a solution that satisfies the given conditions. Mathematical puzzles require mathematics to sol... | https://en.wikipedia.org/wiki/Mathematical_puzzle |
Apuzzleis agame,problem, ortoythat tests a person's ingenuity orknowledge. In a puzzle, the solver is expected to put pieces together (or take them apart) in a logical way, in order to find the solution of the puzzle. There are different genres of puzzles, such ascrossword puzzles, word-search puzzles, number puzzles, ... | https://en.wikipedia.org/wiki/Puzzle |
Sideways Arithmetic From Wayside Schoolis achildren'snovelbyLouis Sacharin theWayside Schoolseries. The book contains mathematical and logic puzzles for the reader to solve, presented as whatThe New Yorkercalled "absurdist math problems."[1]The problems are interspersed with characteristically quirky stories about the ... | https://en.wikipedia.org/wiki/Sideways_Arithmetic_From_Wayside_School |
Acryptogramis a type of puzzle that consists of a short piece ofencryptedtext.[1]Generally thecipherused to encrypt the text is simple enough that the cryptogram can be solved by hand.Substitution cipherswhere each letter is replaced by a different letter, number, or symbol are frequently used. To solve the puzzle, one... | https://en.wikipedia.org/wiki/Cryptogram |
Early numeracyis a branch ofnumeracythat aims to enhance numeracy learning for younger learners, particularly those at-risk in the area ofmathematics. Usually the mathematical learning begins with simply learning the first digits, 1 through 10. This is done because it acts as an entry way to the expansion of counting. ... | https://en.wikipedia.org/wiki/Early_numeracy |
Elementary mathematics, also known asprimaryorsecondary schoolmathematics, is the study of mathematics topics that are commonly taught at the primary or secondary school levels around the world. It includes a wide range of mathematical concepts and skills, includingnumber sense,algebra,geometry,measurement, anddata ana... | https://en.wikipedia.org/wiki/Elementary_mathematics |
Inmathematics educationat theprimary schoollevel,chunking(sometimes also called thepartial quotients method) is an elementary approach for solving simpledivisionquestions by repeatedsubtraction. It is also known as thehangman methodwith the addition of a line separating the divisor, dividend, and partial quotients.[1]I... | https://en.wikipedia.org/wiki/Chunking_(division) |
Inmathematical logic, thePeano axioms(/piˈɑːnoʊ/,[1][peˈaːno]), also known as theDedekind–Peano axiomsor thePeano postulates, areaxiomsfor thenatural numberspresented by the 19th-century Italian mathematicianGiuseppe Peano. These axioms have been used nearly unchanged in a number ofmetamathematicalinvestigations, inclu... | https://en.wikipedia.org/wiki/Peano_axioms |
Inmathematics,division by zero,divisionwhere the divisor (denominator) iszero, is a unique and problematic special case. Usingfractionnotation, the general example can be written asa0{\displaystyle {\tfrac {a}{0}}}, wherea{\displaystyle a}is the dividend (numerator).
The usual definition of thequotientinelementary ari... | https://en.wikipedia.org/wiki/Division_by_zero |
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