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Inmathematics, aroot of unityis anycomplex numberthat yields 1 whenraisedto some positiveintegerpowern. Roots of unity are used in many branches of mathematics, and are especially important innumber theory, the theory ofgroup characters, and thediscrete Fourier transform. It is occasionally called ade Moivre numberafte... | https://en.wikipedia.org/wiki/Root_of_unity |
Inmathematics, aquadratic equationis a polynomial equation of the seconddegree. The general form is
wherea≠ 0.
The quadratic equation on a numberx{\displaystyle x}can be solved using the well-knownquadratic formula, which can be derived bycompleting the square. That formula always gives the roots of the quadratic equ... | https://en.wikipedia.org/wiki/Solving_quadratic_equations_with_continued_fractions |
Thesquare-root sum problem(SRS) is a computationaldecision problemfrom the field ofnumerical analysis, with applications tocomputational geometry.
SRS is defined as follows:[1]
Given positive integersa1,…,ak{\displaystyle a_{1},\ldots ,a_{k}}and an integert, decide whether∑i=1kai≤t{\displaystyle \sum _{i=1}^{k}{\sqrt... | https://en.wikipedia.org/wiki/Square-root_sum_problem |
ThePenrose method(orsquare-root method) is a method devised in 1946 by ProfessorLionel Penrose[1]for allocating the voting weights of delegations (possibly a single representative) in decision-making bodies proportional to thesquare rootof the population represented by this delegation. This is justified by the fact tha... | https://en.wikipedia.org/wiki/Square_root_principle |
Inquantum computingand specifically thequantum circuitmodel of computation, aquantum logic gate(or simplyquantum gate) is a basic quantum circuit operating on a small number ofqubits. Quantum logic gates are the building blocks of quantum circuits, like classicallogic gatesare for conventional digital circuits.
Unlike... | https://en.wikipedia.org/wiki/Quantum_gate#Square_root_of_NOT_gate_(√NOT) |
Inmodular arithmeticcomputation,Montgomery modular multiplication, more commonly referred to asMontgomery multiplication, is a method for performing fast modular multiplication. It was introduced in 1985 by the American mathematicianPeter L. Montgomery.[1][2]
Montgomery modular multiplication relies on a special repr... | https://en.wikipedia.org/wiki/Montgomery_reduction |
Kochanski multiplication[1]is analgorithmthat allowsmodular arithmetic(multiplication or operations based on it, such asexponentiation) to be performed efficiently when the modulus is large (typically several hundred bits). This has particular application innumber theoryand incryptography: for example, in theRSAcryptos... | https://en.wikipedia.org/wiki/Kochanski_multiplication |
Inmodular arithmetic,Barrett reductionis analgorithmdesigned to optimize the calculation ofamodn{\displaystyle a\,{\bmod {\,}}n\,}[1]without needing a fastdivision algorithm. It replaces divisions with multiplications, and can be used whenn{\displaystyle n}is constant anda<n2{\displaystyle a<n^{2}}. It was introduced i... | https://en.wikipedia.org/wiki/Barrett_reduction |
Aquantityis subject toexponential decayif it decreases at a rateproportionalto its current value. Symbolically, this process can be expressed by the followingdifferential equation, whereNis the quantity andλ(lambda) is a positive rate called theexponential decay constant,disintegration constant,[1]rate constant,[2]ort... | https://en.wikipedia.org/wiki/Exponential_decay |
Afraction(fromLatin:fractus, "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, three-quarters. Acommon,vulgar,[n 1]orsimplefraction (examples:1/2an... | https://en.wikipedia.org/wiki/Fraction |
Inmathematics, ahyperbolais a type ofsmoothcurve lying in a plane, defined by its geometric properties or byequationsfor which it is the solution set. A hyperbola has two pieces, calledconnected componentsor branches, that are mirror images of each other and resemble two infinitebows. The hyperbola is one of the three ... | https://en.wikipedia.org/wiki/Hyperbola |
Inprobability theoryandstatistics, aninverse distributionis the distribution of thereciprocalof a random variable. Inverse distributions arise in particular in theBayesiancontext ofprior distributionsandposterior distributionsforscale parameters. In thealgebra of random variables, inverse distributions are special case... | https://en.wikipedia.org/wiki/Inverse_distribution |
Inmathematicsand especiallynumber theory, thesum of reciprocals(orsum of inverses) generally is computed for thereciprocalsof some or all of thepositiveintegers(counting numbers)—that is, it is generally the sum ofunit fractions. If infinitely many numbers have their reciprocals summed, generally the terms are given i... | https://en.wikipedia.org/wiki/List_of_sums_of_reciprocals |
Arepeating decimalorrecurring decimalis adecimal representationof a number whosedigitsare eventuallyperiodic(that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to betermina... | https://en.wikipedia.org/wiki/Repeating_decimal |
Inmathematics,6-sphere coordinatesare acoordinate systemfor three-dimensional space obtained byinvertingthe 3DCartesian coordinatesacross theunit 2-spherex2+y2+z2=1{\displaystyle x^{2}+y^{2}+z^{2}=1}. They are so named because thelociwhere one coordinate is constant formspherestangent to theoriginfrom one of six sides... | https://en.wikipedia.org/wiki/6-sphere_coordinates |
Aunit fractionis a positivefractionwith one as itsnumerator, 1/n. It is themultiplicative inverse(reciprocal) of thedenominatorof the fraction, which must be a positivenatural number. Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc. When an object is divided into equal parts, each part is a unit fraction of the whole.
Multi... | https://en.wikipedia.org/wiki/Unit_fraction |
Incomplex analysis(a branch of mathematics), apoleis a certain type ofsingularityof acomplex-valued functionof acomplexvariable. It is the simplest type of non-removable singularityof such a function (seeessential singularity). Technically, a pointz0is a pole of a functionfif it is azeroof the function1/fand1/fisholomo... | https://en.wikipedia.org/wiki/Zeros_and_poles |
Inengineeringandscience,dimensional analysisis the analysis of the relationships between differentphysical quantitiesby identifying theirbase quantities(such aslength,mass,time, andelectric current) andunits of measurement(such as metres and grams) and tracking these dimensions as calculations or comparisons are perfor... | https://en.wikipedia.org/wiki/Dimensional_analysis |
Amultiplication algorithmis analgorithm(or method) tomultiplytwo numbers. Depending on the size of the numbers, different algorithms are more efficient than others. Numerous algorithms are known and there has been much research into the topic.
The oldest and simplest method, known sinceantiquityaslong multiplicationor... | https://en.wikipedia.org/wiki/Multiplication_algorithm |
TheKaratsuba algorithmis a fastmultiplication algorithmforintegers. It was discovered byAnatoly Karatsubain 1960 and published in 1962.[1][2][3]It is adivide-and-conquer algorithmthat reduces the multiplication of twon-digit numbers to three multiplications ofn/2-digit numbers and, by repeating this reduction, to at m... | https://en.wikipedia.org/wiki/Karatsuba_algorithm |
Toom–Cook, sometimes known asToom-3, named afterAndrei Toom, who introduced the new algorithm with its low complexity, andStephen Cook, who cleaned the description of it, is amultiplication algorithmfor large integers.
Given two large integers,aandb, Toom–Cook splits upaandbintoksmaller parts each of lengthl, and perf... | https://en.wikipedia.org/wiki/Toom%E2%80%93Cook_multiplication |
TheSchönhage–Strassen algorithmis an asymptotically fastmultiplication algorithmfor largeintegers, published byArnold SchönhageandVolker Strassenin 1971.[1]It works by recursively applyingfast Fourier transform(FFT) overthe integers modulo2n+1{\displaystyle 2^{n}+1}. The run-timebit complexityto multiply twon-digit num... | https://en.wikipedia.org/wiki/Sch%C3%B6nhage%E2%80%93Strassen_algorithm |
Inmathematics, amultiplication table(sometimes, less formally, atimes table) is amathematical tableused to define amultiplicationoperationfor an algebraic system.
Thedecimalmultiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithm... | https://en.wikipedia.org/wiki/Multiplication_table |
Abinary multiplieris anelectronic circuitused indigital electronics, such as acomputer, tomultiplytwobinary numbers.
A variety ofcomputer arithmetictechniques can be used to implement a digital multiplier. Most techniques involve computing the set ofpartial products,which are then summed together usingbinary adders. T... | https://en.wikipedia.org/wiki/Binary_multiplier |
Booth's multiplication algorithmis amultiplication algorithmthat multiplies two signedbinarynumbers intwo's complement notation. Thealgorithmwas invented byAndrew Donald Boothin 1950 while doing research oncrystallographyatBirkbeck CollegeinBloomsbury,London.[1]Booth's algorithm is of interest in the study ofcomputer a... | https://en.wikipedia.org/wiki/Booth%27s_multiplication_algorithm |
Incomputing,floating-point arithmetic(FP) isarithmeticon subsets ofreal numbersformed by asignificand(asignedsequence of a fixed number of digits in somebase) multiplied by aninteger powerof that base.
Numbers of this form are calledfloating-point numbers.[1]: 3[2]: 10
For example, the number 2469/200 is a floating-po... | https://en.wikipedia.org/wiki/Floating-point_arithmetic |
Incomputing, especiallydigital signal processing, themultiply–accumulate(MAC) ormultiply–add(MAD) operation is a common step that computes the product of two numbers and adds that product to anaccumulator. The hardware unit that performs the operation is known as amultiplier–accumulator(MAC unit); the operation itself... | https://en.wikipedia.org/wiki/Multiply%E2%80%93accumulate_operation |
Incomputing, especiallydigital signal processing, themultiply–accumulate(MAC) ormultiply–add(MAD) operation is a common step that computes the product of two numbers and adds that product to anaccumulator. The hardware unit that performs the operation is known as amultiplier–accumulator(MAC unit); the operation itself... | https://en.wikipedia.org/wiki/Fused_multiply%E2%80%93add |
AWallace multiplieris ahardwareimplementation of abinary multiplier, a digital circuit that multiplies two integers. It uses a selection of full and halfadders(theWallace treeorWallace reduction) to sum partial products in stages until two numbers are left. Wallace multipliers reduce as much as possible on each layer, ... | https://en.wikipedia.org/wiki/Wallace_tree |
Inmathematics, thefactorialof a non-negativeintegern{\displaystyle n},denotedbyn!{\displaystyle n!},is theproductof all positive integers less than or equalton{\displaystyle n}.The factorialofn{\displaystyle n}also equals the product ofn{\displaystyle n}with the next smaller factorial:n!=n×(n−1)×(n−2)×(n−3)×⋯×3×2×1=n×(... | https://en.wikipedia.org/wiki/Factorial |
Genaille–Lucas rulers(also known asGenaille's rods) are anarithmetictool invented byHenri Genaille, a French railway engineer, in 1891. The device is a variant ofNapier's bones. By representing thecarrygraphically, the user can read off the results of simplemultiplicationproblems directly, with no intermediatemental ... | https://en.wikipedia.org/wiki/Genaille%E2%80%93Lucas_rulers |
Lunar arithmetic, formerly calleddismal arithmetic,[1][2]is a version ofarithmeticin which the addition and multiplicationoperationson digits are defined as themax and minoperations. Thus, in lunar arithmetic,
The lunar arithmetic operations on nonnegative multidigit numbers are performed as in usual arithmetic as ill... | https://en.wikipedia.org/wiki/Lunar_arithmetic |
Napier's bonesis a manually operated calculating device created byJohn NapierofMerchiston,Scotlandfor thecalculationof products andquotientsof numbers. The method was based onlattice multiplication, and also calledrabdology, a word invented by Napier. Napier published his version in1617.[1]It was printed inEdinburghand... | https://en.wikipedia.org/wiki/Napier%27s_bones |
Inmathematics,ancient Egyptian multiplication(also known asEgyptian multiplication,Ethiopian multiplication,Russian multiplication, orpeasant multiplication), one of twomultiplicationmethods used by scribes, is a systematic method for multiplying two numbers that does not require themultiplication table, only the abili... | https://en.wikipedia.org/wiki/Peasant_multiplication |
Inmathematics, aproductis the result ofmultiplication, or anexpressionthat identifiesobjects(numbers orvariables) to be multiplied, calledfactors. For example, 21 is the product of 3 and 7 (the result of multiplication), andx⋅(2+x){\displaystyle x\cdot (2+x)}is the product ofx{\displaystyle x}and(2+x){\displaystyle (2+... | https://en.wikipedia.org/wiki/Product_(mathematics) |
Aslide ruleis a hand-operatedmechanical calculatorconsisting ofslidablerulersfor conducting mathematical operations such asmultiplication,division,exponents,roots,logarithms, andtrigonometry. It is one of the simplestanalog computers.[1][2]
Slide rules exist in a diverse range of styles and generally appear in a linea... | https://en.wikipedia.org/wiki/Slide_rule |
Incryptography,GMRis adigital signaturealgorithmnamed after its inventorsShafi Goldwasser,Silvio MicaliandRon Rivest.
As withRSAthe security of the system is related to the difficulty offactoring very large numbers. But, in contrast to RSA, GMR is secure againstadaptivechosen-message attacks, which is the currently ac... | https://en.wikipedia.org/wiki/GMR_(cryptography) |
49°15′24″N122°59′57″W / 49.256613°N 122.9990452°W /49.256613; -122.9990452
D-Wave Quantum Inc.is aquantum computingcompany with locations inPalo Alto, CaliforniaandBurnaby, British Columbia. D-Wave claims to be the world's first company to sell computers that exploit quantum effects in their operation.[2]D-Wave's e... | https://en.wikipedia.org/wiki/D-Wave_Systems |
Electronic quantum holography(also known as quantumholographic data storage) is aninformation storagetechnology which can encode and read outdataat unprecedented density storing as much as 35bitsperelectron.[1]
In 2009,Stanford University's Department of Physics set a new world record for the smallest writing using as... | https://en.wikipedia.org/wiki/Electronic_quantum_holography |
Thisglossary of quantum computingis a list of definitions of terms and concepts used inquantum computing, its sub-disciplines, and related fields. | https://en.wikipedia.org/wiki/Glossary_of_quantum_computing |
TheIntelligence Advanced Research Projects Activity(IARPA) is an organization, within theOffice of the Director of National Intelligence(ODNI), that is responsible for leading research to overcome difficult challenges facing theUnited States Intelligence Community.[1]IARPA characterizes its mission as follows: "To envi... | https://en.wikipedia.org/wiki/IARPA |
India's quantum computeris the proposed and plannedquantum computerto be developed by 2026. A quantum computer is a computer based on quantum phenomena and governed by the principles ofquantum mechanicsinphysics. In the present time, India has a small scale quantum computer of 7qubitsdeveloped atTata Institute of Funda... | https://en.wikipedia.org/wiki/India%27s_quantum_computer |
IonQis aquantum computinghardware and software company headquartered inCollege Park, Maryland. The company develops general-purposetrapped ion quantum computersand accompanying software to generate, optimize, and executequantum circuits.
IonQ was co-founded byChristopher Monroeand Jungsang Kim, professors atDuke Unive... | https://en.wikipedia.org/wiki/IonQ |
IQMmay refer to: | https://en.wikipedia.org/wiki/IQM |
This is alist of emerging technologies, which arein-development technical innovationsthat have significant potential in their applications. The criteria for this list is that the technology must:
Listing here is not a prediction that the technology will become widely adopted, only a recognition of significantpotential... | https://en.wikipedia.org/wiki/List_of_emerging_technologies |
This list containsquantum processors, also known as quantum processing units (QPUs). Some devices listed below have only been announced at press conferences so far, with no actual demonstrations or scientific publications characterizing the performance.
Quantum processors are difficult to compare due to the differenta... | https://en.wikipedia.org/wiki/List_of_quantum_processors |
Magic state distillationis a method for creating more accuratequantum statesfrom multiple noisy ones, which is important[1]for buildingfault tolerantquantum computers. It has also been linked[2]toquantum contextuality, a concept thought to contribute to quantum computers' power.[3]
The technique was first proposed byE... | https://en.wikipedia.org/wiki/Magic_state_distillation |
Metacomputingis allcomputingand computing-oriented activity which involves computingknowledge(science and technology) utilized for theresearch, development and application of different types of computing. It may also deal with numerous types of computing applications, such as: industry, business, management and human... | https://en.wikipedia.org/wiki/Metacomputing |
Natural computing,[1][2]also callednatural computation, is a terminology introduced to encompass three classes of methods: 1) those that take inspiration from nature for the development of novel problem-solving techniques; 2) those that are based on the use of computers to synthesize natural phenomena; and 3) those tha... | https://en.wikipedia.org/wiki/Natural_computing |
Optical computingorphotonic computinguseslight wavesproduced bylasersor incoherent sources fordata processing, data storage ordata communicationforcomputing. For decades,photonshave shown promise to enable a higherbandwidththan theelectronsused in conventional computers (seeoptical fibers).
Most research projects focu... | https://en.wikipedia.org/wiki/Optical_computing |
Aquantum busis a device which can be used to store or transfer information between independentqubitsin aquantum computer, or combine two qubits into asuperposition. It is thequantumanalog of aclassical bus.
There are several physical systems that can be used to realize a quantum bus, includingtrapped ions,photons, and... | https://en.wikipedia.org/wiki/Quantum_bus |
Quantum cognitionuses the mathematical formalism of quantum probability theory to model psychology phenomena when classicalprobability theoryfails.[1]The field focuses on modeling phenomena incognitive sciencethat have resisted traditional techniques or where traditional models seem to have reached a barrier (e.g., hum... | https://en.wikipedia.org/wiki/Quantum_cognition |
Withinquantum technology, aquantum sensorutilizes properties of quantum mechanics, such asquantum entanglement,quantum interference, andquantum statesqueezing, which have optimized precision and beat current limits insensor technology.[1]The field of quantum sensing deals with the design and engineering of quantum sour... | https://en.wikipedia.org/wiki/Quantum_sensor |
Quantum volumeis a metric that measures the capabilities and error rates of aquantum computer. It expresses the maximum size of squarequantum circuitsthat can be implemented successfully by the computer. The form of the circuits is independent from the quantum computer architecture, but compiler can transform and optim... | https://en.wikipedia.org/wiki/Quantum_volume |
Quantum weirdnessencompasses the aspects ofquantum mechanicsthat challenge and defy human physical intuition.[1]
Human physical intuition is based on macroscopic physical phenomena as are experienced in everyday life, which can mostly be adequately described by theNewtonian mechanicsofclassical physics.[2]Early 20th-c... | https://en.wikipedia.org/wiki/Quantum_weirdness |
Rigetti Computing, Inc.is aBerkeley, California-based developer of Superconducting quantumintegrated circuitsused forquantum computers. Rigetti also develops a cloud platform called Forest that enables programmers to write quantum algorithms.[2]
Rigetti Computing was founded in 2013 byChad Rigetti, a physicist with a... | https://en.wikipedia.org/wiki/Rigetti_Computing |
Asupercomputeris a type ofcomputerwith a high level of performance as compared to a general-purpose computer. The performance of a supercomputer is commonly measured infloating-pointoperations per second (FLOPS) instead ofmillion instructions per second(MIPS). Since 2022, supercomputers have existed which can perform o... | https://en.wikipedia.org/wiki/Supercomputer |
Theoretical computer scienceis a subfield ofcomputer scienceandmathematicsthat focuses on theabstractand mathematical foundations ofcomputation.
It is difficult to circumscribe the theoretical areas precisely. TheACM'sSpecial Interest Group on Algorithms and Computation Theory(SIGACT) provides the following descriptio... | https://en.wikipedia.org/wiki/Theoretical_computer_science |
Unconventional computing(also known asalternative computingornonstandard computation) iscomputingby any of a wide range of new or unusual methods.
The termunconventional computationwas coined byCristian S. CaludeandJohn Castiand used at the First International Conference on Unconventional Models of Computation[1]in 19... | https://en.wikipedia.org/wiki/Unconventional_computing |
Valleytronics(fromvalleyandelectronics) is an experimental area insemiconductorsthat exploits localextrema("valleys") in theelectronic band structure. Certainsemiconductorshave multiple "valleys" in the electronic band structure of the firstBrillouin zone, and are known as multivalley semiconductors.[1][2]Valleytronics... | https://en.wikipedia.org/wiki/Valleytronics |
TheGSM Interworking Profile, usually abbreviated to GIP and sometimes to IWP, is a profile forDECTthat allows a DECT base station to form part of a GSM network, given suitable handsets. While proposed and tested, notably inSwitzerlandin 1995, the system has never been commercially deployed. Infrastructure issues make i... | https://en.wikipedia.org/wiki/GSM_Interworking_Profile |
IP-DECTis a technology used for on-site wireless communications. It uses theDECTair interfacefor reliable wireless voice and data communication between handsets and base stations and the well establishedVoIPtechnology for the corded voice communication between base stations and server functions.
The advantage is the c... | https://en.wikipedia.org/wiki/IP-DECT |
CT2is a cordless telephony standard that was used in the early 1990s to provide short-range proto-mobile phone service in some countries in Europe and in Hong Kong. It is considered the precursor to the more successfulDECTsystem. CT2 was also referred to by its marketing name,Telepoint.
CT2 is a digitalFDMAsystem that... | https://en.wikipedia.org/wiki/CT2 |
Net3was aWi-Fi-like system developed, manufactured and commercialised byOlivettiin the early 1990s. It could wirelessly connect PCs to anEthernetfixedLANat a speed of up to 512 kbit/s, over a very wide area. It was a micro-cellular system, in which each base station had an effective range of about 100m indoors, 300m ou... | https://en.wikipedia.org/wiki/Net3 |
corDECTis awireless local loopstandard developed inIndiabyIIT Madrasand Midas Communications atChennai, under leadership of ProfAshok Jhunjhunwala, based on theDECTdigitalcordless phonestandard.[1]
The technology is aFixed WirelessOption, which has extremely low capital costs and is ideal for small start ups to scale,... | https://en.wikipedia.org/wiki/CorDECT |
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/Wideband_Digital_Enhanced_Cordless_Telecommunications |
Unlicensed Personal Communications ServicesorUPCS bandis the 1920–1930MHzfrequency bandallocated by the United StatesFederal Communications Commission(FCC) for short rangePersonal Communications Services(PCS) applications in theUnited States, such as theDigital Enhanced Cordless Telecommunications(DECT) wireless protoc... | https://en.wikipedia.org/wiki/Unlicensed_Personal_Communications_Services |
Amicrocellis a cell in amobile phone networkserved by a low powercellularbase station(tower), covering a limited area such as a mall, a hotel, or a transportation hub. A microcell is usually larger than apicocell, though the distinction is not always clear. A microcell uses power control to limit the radius of its cove... | https://en.wikipedia.org/wiki/Microcell |
Wireless local loop(WLL) is the use of a wireless communications link as the "last mile/ first mile" connection for deliveringplain old telephone service(POTS) orInternet access(marketed under the term "broadband") to telecommunications customers.
Various types of WLL systems and technologies exist.
Other terms for t... | https://en.wikipedia.org/wiki/Wireless_local_loop |
CDMA spectral efficiencyrefers to thesystem spectral efficiencyin bit/s/Hz/site orErlang/MHz/site that can be achieved in a certainCDMAbased wireless communication system. CDMA techniques (also known asspread spectrum) are characterized by a very lowlink spectral efficiencyin (bit/s)/Hz as compared to non-spread spectr... | https://en.wikipedia.org/wiki/CDMA_spectral_efficiency |
Interim Standard 95(IS-95) was the first digital cellular technology that usedcode-division multiple access(CDMA). It was developed byQualcommand later adopted as a standard by theTelecommunications Industry Associationin TIA/EIA/IS-95 release published in 1995. The proprietary name for IS-95 iscdmaOne.
It is a2Gmobil... | https://en.wikipedia.org/wiki/CdmaOne |
Indigital communications, achipis a pulse of adirect-sequence spread spectrum(DSSS) code, such as a pseudo-random noise (PN) code sequence used in direct-sequencecode-division multiple access(CDMA)channel accesstechniques.
In a binary direct-sequence system, each chip is typically a rectangular pulse of +1 or −1 ampli... | https://en.wikipedia.org/wiki/Orthogonal_variable_spreading_factor |
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/Pseudorandom_noise |
Quadrature-division multiple access(QDMA) is a radio protocol.[1]The term combines two standard terms intelecommunications,CDMAandQPSK.
QDMA is used forlocal area networks, usually wireless short-range such asWiMax. CDMA and QDMA are especially suitable for modern communications, for example, the transmission of short... | https://en.wikipedia.org/wiki/Quadrature-division_multiple_access |
Inwireless communicationsystems, therise over thermal(ROT) indicates the ratio between the total interference received on abase stationand thethermal noise.[1]
The ROT is a measurement of congestion of acellular telephone network. The acceptable level of ROT is often used to define the capacity of systems using CDMA ... | https://en.wikipedia.org/wiki/Rise_over_thermal |
Intelecommunications, especiallyradio communication,spread spectrumare techniques by which asignal(e.g., an electrical, electromagnetic, or acoustic) generated with a particularbandwidthis deliberately spread in thefrequency domainover a widerfrequency band. Spread-spectrum techniques are used for the establishment of ... | https://en.wikipedia.org/wiki/Spread_spectrum |
Incomputational complexity theory, acomputational hardness assumptionis the hypothesis that a particular problem cannot be solved efficiently (whereefficientlytypically means "inpolynomial time"). It is not known how toprove(unconditional) hardness for essentially any useful problem. Instead,computer scientistsrely onr... | https://en.wikipedia.org/wiki/Computational_hardness_assumption |
40-bit encryptionrefers to a (now broken)key sizeof forty bits, or fivebytes, forsymmetric encryption; this represents a relatively lowlevel of security. A forty bit length corresponds to a total of 240possible keys. Although this is a large number in human terms (about atrillion), it is possible to break this degree o... | https://en.wikipedia.org/wiki/40-bit_encryption |
Derived algebraic geometryis a branch of mathematics that generalizesalgebraic geometryto a situation wherecommutative rings, which provide local charts, are replaced by eitherdifferential graded algebras(overQ{\displaystyle \mathbb {Q} }),simplicial commutative ringsorE∞{\displaystyle E_{\infty }}-ring spectrafromalge... | https://en.wikipedia.org/wiki/Derived_algebraic_geometry |
Noncommutative geometry(NCG) is a branch ofmathematicsconcerned with a geometric approach tononcommutative algebras, and with the construction ofspacesthat are locally presented by noncommutative algebras of functions, possibly in some generalized sense. A noncommutative algebra is anassociative algebrain which the mul... | https://en.wikipedia.org/wiki/Noncommutative_geometry |
Ring homomorphisms
Algebraic structures
Related structures
Algebraic number theory
Noncommutative algebraic geometry
Free algebra
Clifford algebra
Noncommutative algebraic geometryis a branch ofmathematics, and more specifically a direction innoncommutative geometry, that studies the geometric properties of form... | https://en.wikipedia.org/wiki/Noncommutative_algebraic_geometry |
Inmathematics,noncommutative harmonic analysisis the field in which results fromFourier analysisare extended totopological groupsthat are notcommutative.[1]Sincelocally compact abelian groupshave a well-understood theory,Pontryagin duality, which includes the basic structures ofFourier seriesandFourier transforms, the ... | https://en.wikipedia.org/wiki/Noncommutative_harmonic_analysis |
In themathematicalfield ofrepresentation theory,group representationsdescribe abstractgroupsin terms ofbijectivelinear transformationsof avector spaceto itself (i.e. vector spaceautomorphisms); in particular, they can be used to represent group elements asinvertible matricesso that the group operation can be represente... | https://en.wikipedia.org/wiki/Representation_theory_(group_theory) |
Mental calculation(also known asmentalcomputation[1]) consists ofarithmeticalcalculationsmade by themind, within thebrain, with no help from any supplies (such as pencil and paper) or devices such as acalculator. People may use mental calculation when computing tools are not available, when it is faster than other mean... | https://en.wikipedia.org/wiki/Mental_calculation |
Theparallel operator‖{\displaystyle \|}(pronounced "parallel",[1]following theparallel lines notation from geometry;[2][3]also known asreduced sum,parallel sumorparallel addition) is abinary operationwhich is used as a shorthand inelectrical engineering,[4][5][6][nb 1]but is also used inkinetics,fluid mechanicsandfinan... | https://en.wikipedia.org/wiki/Parallel_addition_(mathematics) |
Verbal arithmetic, also known asalphametics,cryptarithmetic,cryptarithmorword addition, is a type ofmathematical gameconsisting of a mathematicalequationamong unknownnumbers, whosedigitsare represented bylettersof the alphabet. The goal is to identify the value of each letter. The name can be extended to puzzles that... | https://en.wikipedia.org/wiki/Verbal_arithmetic |
Theabsolute differenceof tworeal numbersx{\displaystyle x}andy{\displaystyle y}is given by|x−y|{\displaystyle |x-y|}, theabsolute valueof theirdifference. It describes the distance on thereal linebetween the points corresponding tox{\displaystyle x}andy{\displaystyle y}, and is a special case of theLpdistancefor all1≤p... | https://en.wikipedia.org/wiki/Absolute_difference |
Elementary arithmeticis a branch ofmathematicsinvolvingaddition,subtraction,multiplication, anddivision. Due to its low level ofabstraction, broad range of application, and position as the foundation of all mathematics, elementary arithmetic is generally the first branch of mathematics taught in schools.[1][2]
Innumer... | https://en.wikipedia.org/wiki/Elementary_arithmetic |
Inmathematicsandcomputing, themethod of complementsis a technique to encode a symmetric range of positive and negativeintegersin a way that they can use the samealgorithm(ormechanism) foradditionthroughout the whole range. For a given number ofplaceshalf of the possible representations of numbers encode the positive nu... | https://en.wikipedia.org/wiki/Method_of_complements |
Inmathematics, anegative numberis theoppositeof a positivereal number.[1]Equivalently, a negative number is a real number that isless thanzero. Negative numbers are often used to represent themagnitudeof a loss or deficiency. Adebtthat is owed may be thought of as a negative asset. If a quantity, such as the charge on ... | https://en.wikipedia.org/wiki/Negative_number |
Theplus sign(+) and theminus sign(−) aremathematical symbolsused to denotepositiveandnegativefunctions, respectively. In addition, the symbol+represents the operation ofaddition, which results in asum, while the symbol−representssubtraction, resulting in adifference.[1]Their use has been extended to many other meanings... | https://en.wikipedia.org/wiki/Plus_and_minus_signs |
In mathematics,monusis an operator on certaincommutativemonoidsthat are notgroups. A commutative monoid on which a monus operator is defined is called acommutative monoid with monus, orCMM. The monus operator may be denoted with the−symbol because thenatural numbersare a CMM undersubtraction; it is also denoted with th... | https://en.wikipedia.org/wiki/Monus |
Thematerial conditional(also known asmaterial implication) is abinary operationcommonly used inlogic. When the conditional symbol→{\displaystyle \to }isinterpretedas material implication, a formulaP→Q{\displaystyle P\to Q}is true unlessP{\displaystyle P}is true andQ{\displaystyle Q}is false.
Material implication is us... | https://en.wikipedia.org/wiki/Material_conditional |
Theparadoxes of material implicationare a group oftrue formulaeinvolvingmaterial conditionalswhose translations into natural language are intuitively false when the conditional is translated as "if ... then ...". A material conditional formulaP→Q{\displaystyle P\rightarrow Q}is true unlessP{\displaystyle P}is true andQ... | https://en.wikipedia.org/wiki/Paradoxes_of_material_implication |
Theformal fallacyofaffirming a disjunctalso known as thefallacy of the alternative disjunctor afalse exclusionary disjunctoccurs when adeductiveargument takes the followinglogical form:[1]
Or inlogical operators:
Where⊢{\displaystyle {}\vdash {}}denotes alogical assertion.
The fallacy lies in concluding that onedisj... | https://en.wikipedia.org/wiki/Affirming_a_disjunct |
InBoolean logic,logical NOR,[1]non-disjunction, orjoint denial[1]is a truth-functional operator which produces a result that is the negation oflogical or. That is, a sentence of the form (pNORq) is true precisely when neitherpnorqis true—i.e. when bothpandqarefalse. It is logically equivalent to¬(p∨q){\displaystyle \ne... | https://en.wikipedia.org/wiki/Ampheck |
Incomputer science, thecontrolled NOT gate(alsoC-NOTorCNOT),controlled-Xgate,controlled-bit-flip gate,Feynman gateorcontrolled Pauli-Xis aquantum logic gatethat is an essential component in the construction of agate-basedquantum computer. It can be used toentangleand disentangleBell states. Any quantum circuit can be s... | https://en.wikipedia.org/wiki/Controlled_NOT_gate |
Inclassical logic,disjunctive syllogism[1][2](historically known asmodus tollendo ponens(MTP),[3]Latinfor "mode that affirms by denying")[4]is avalidargument formwhich is asyllogismhaving adisjunctive statementfor one of itspremises.[5][6]
An example inEnglish:
Inpropositional logic,disjunctive syllogism(also known a... | https://en.wikipedia.org/wiki/Disjunctive_syllogism |
Inlogic,disjunction(also known aslogical disjunction,logical or,logical addition, orinclusive disjunction) is alogical connectivetypically notated as∨{\displaystyle \lor }and read aloud as "or". For instance, theEnglishlanguage sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formu... | https://en.wikipedia.org/wiki/Inclusive_or |
Inmathematics, aninvolution,involutory function, orself-inverse function[1]is afunctionfthat is its owninverse,
for allxin thedomainoff.[2]Equivalently, applyingftwice produces the original value.
Any involution is abijection.
Theidentity mapis a trivial example of an involution. Examples of nontrivial involutions i... | https://en.wikipedia.org/wiki/Involution_(mathematics) |
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