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Insociolinguistics, asociolectis aform of language(non-standard dialect, restrictedregister) or a set oflexical itemsused by a socioeconomic class, profession, age group, or other social group.[1][2]
Sociolects involve both passive acquisition of particular communicative practices through association with a local comm... | https://en.wikipedia.org/wiki/Sociolect |
TheParsley massacre(Spanish:el corte"the cutting";[5]Creole:kout kouto-a"the stabbing"[6]) (French:Massacre du Persil;Spanish:Masacre del Perejil;Haitian Creole:Masak nan Pèsil) was a mass killing ofHaitiansliving in illegal settlements[7]and occupied land in theDominican Republic's northwestern frontier and in certain... | https://en.wikipedia.org/wiki/Parsley_massacre |
Atongue twisteris a phrase that is designed to be difficult toarticulateproperly, and can be used as a type of spoken (or sung)word game. Additionally, they can be used as exercises to improve pronunciation and fluency. Some tongue twisters produce results that are humorous (or humorously vulgar) when they are misprono... | https://en.wikipedia.org/wiki/Tongue-twister |
U and non-U English usage, where "U" stands forupper classand "non-U" represents the aspiringmiddleandlower classes, was part of the terminology of popular discourse of social dialects (sociolects) inBritainin the 1950s.[1]The different vocabularies can often appear quite counter-intuitive: the middle classes prefer "f... | https://en.wikipedia.org/wiki/U_and_non-U_English |
Insystems engineering, thesystem usability scale(SUS) is a simple, ten-item attitudeLikert scalegiving a global view of subjective assessments ofusability. It was developed by John Brooke[1]atDigital Equipment Corporationin theUKin 1986 as a tool to be used inusability engineeringofelectronic officesystems.
The usabil... | https://en.wikipedia.org/wiki/System_usability_scale |
Usabilitycan be described as the capacity of a system to provide a condition for its users to perform the tasks safely, effectively, and efficiently while enjoying the experience.[1]Insoftware engineering, usability is the degree to which a software can be used by specified consumers to achieve quantified objectives wi... | https://en.wikipedia.org/wiki/Usability |
Acontinued fractionis amathematical expressionthat can be written as afractionwith adenominatorthat is a sum that contains another simple or continued fraction. Depending on whether thisiterationterminates with a simple fraction or not, the continued fraction isfiniteorinfinite.
Different fields ofmathematicshave diff... | https://en.wikipedia.org/wiki/Continued_fraction |
Inmathematics,convergence testsare methods of testing for theconvergence,conditional convergence,absolute convergence,interval of convergenceor divergence of aninfinite series∑n=1∞an{\displaystyle \sum _{n=1}^{\infty }a_{n}}.
If the limit of the summand is undefined or nonzero, that islimn→∞an≠0{\displaystyle \lim _{n... | https://en.wikipedia.org/wiki/Convergence_tests |
Inmathematics, aseriesis thesumof the terms of aninfinite sequenceof numbers. More precisely, an infinite sequence(a1,a2,a3,…){\displaystyle (a_{1},a_{2},a_{3},\ldots )}defines aseriesSthat is denoted
Thenthpartial sumSnis the sum of the firstnterms of the sequence; that is,
A series isconvergent(orconverges) if and ... | https://en.wikipedia.org/wiki/Convergent_series |
Les séries divergentes sont en général quelque chose de bien fatal et c’est une honte qu’on ose y fonder aucune démonstration.
("Divergent series are in general something fatal, and it is a disgrace to base any proof on them." Often translated as "Divergent series are an invention of the devil …")
Inmathematics, adive... | https://en.wikipedia.org/wiki/Divergent_series |
Inmathematics, aninfinite expressionis anexpressionin which someoperatorstake an infinite number ofarguments, or in which the nesting of the operators continues to an infinite depth.[1]A generic concept for infinite expression can lead to ill-defined or self-inconsistent constructions (much like aset of all sets), but ... | https://en.wikipedia.org/wiki/Infinite_expression_(mathematics) |
Inmathematics, for asequenceof complex numbersa1,a2,a3, ... theinfinite product
is defined to be thelimitof thepartial productsa1a2...anasnincreases without bound. The product is said toconvergewhen the limit exists and is not zero. Otherwise the product is said todiverge. A limit of zero is treated specially in orde... | https://en.wikipedia.org/wiki/Infinite_product |
Thislist of mathematical seriescontains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums.
SeeFaulhaber's formula.
The first few values are:
Seezeta constants.
The first few values are:
Finite sums:
Infinite sums, valid for|z|<1{\displaystyle |z|<1}(seepolyl... | https://en.wikipedia.org/wiki/List_of_mathematical_series |
Inmathematics, asequence transformationis anoperatoracting on a given space ofsequences(asequence space). Sequence transformations includelinear mappingssuch asdiscrete convolutionwith another sequence andresummationof a sequence and nonlinear mappings, more generally. They are commonly used forseries acceleration, tha... | https://en.wikipedia.org/wiki/Sequence_transformation |
Inmathematics, aseries expansionis a technique that expresses afunctionas an infinite sum, orseries, of simpler functions. It is a method for calculating afunctionthat cannot be expressed by just elementary operators (addition, subtraction, multiplication and division).[1]
The resulting so-calledseriesoften can be lim... | https://en.wikipedia.org/wiki/Series_expansion |
Inmathematics, aZorn ringis analternative ringin which for every non-nilpotentxthere exists an elementysuch thatxyis a non-zeroidempotent(Kaplansky 1968, pages 19, 25).Kaplansky (1951)named them afterMax August Zorn, who studied a similar condition in (Zorn 1941).
Forassociative rings, the definition of Zorn ring can ... | https://en.wikipedia.org/wiki/Zorn_ring |
Inmathematics, aMalcev algebra(orMaltsev algebraorMoufang–Liealgebra) over afieldis anonassociative algebrathat is antisymmetric, so that
and satisfies theMalcev identity
They were first defined byAnatoly Maltsev(1955).
Malcev algebras play a role in the theory ofMoufang loopsthat generalizes the role ofLie algebras... | https://en.wikipedia.org/wiki/Maltsev_algebra |
Inmathematics, aMalcev algebra(orMaltsev algebraorMoufang–Liealgebra) over afieldis anonassociative algebrathat is antisymmetric, so that
and satisfies theMalcev identity
They were first defined byAnatoly Maltsev(1955).
Malcev algebras play a role in the theory ofMoufang loopsthat generalizes the role ofLie algebras... | https://en.wikipedia.org/wiki/Malcev_algebra |
Inmathematicsandabstract algebra, aBol loopis analgebraic structuregeneralizing the notion ofgroup. Bol loops are named for the Dutch mathematicianGerrit Bolwho introduced them in (Bol 1937).
Aloop,L, is said to be aleft Bol loopif it satisfies theidentity
whileLis said to be aright Bol loopif it satisfies
These id... | https://en.wikipedia.org/wiki/Bol_loop |
Agyrovector spaceis amathematicalconcept proposed by Abraham A. Ungar for studyinghyperbolic geometryin analogy to the wayvector spacesare used inEuclidean geometry.[1]Ungar introduced the concept of gyrovectors that have addition based on gyrogroups instead of vectors which have addition based ongroups. Ungar devel... | https://en.wikipedia.org/wiki/Gyrogroup |
Ingeometry, aMoufang plane, named forRuth Moufang, is a type ofprojective plane, more specifically a special type oftranslation plane. A translation plane is a projective plane that has atranslation line, that is, a line with the property that the group of automorphisms that fixes every point of the lineactstransitivel... | https://en.wikipedia.org/wiki/Moufang_plane |
In mathematics,Moufang polygonsare a generalization byJacques Titsof theMoufang planesstudied byRuth Moufang, and are irreduciblebuildingsof rank two that admit the action ofroot groups.
In a book on the topic, Tits and Richard Weiss[1]classify them all. An earlier theorem, proved independently by Tits and Weiss,[2][3]... | https://en.wikipedia.org/wiki/Moufang_polygon |
Square root algorithmscompute the non-negativesquare rootS{\displaystyle {\sqrt {S}}}of a positivereal numberS{\displaystyle S}.
Since all square roots ofnatural numbers, other than ofperfect squares, areirrational,[1]square roots can usually only be computed to some finite precision: thesealgorithmstypically construct... | https://en.wikipedia.org/wiki/Methods_of_computing_square_roots |
This is alist ofpolynomialtopics, by Wikipedia page. See alsotrigonometric polynomial,list of algebraic geometry topics.
Polynomial mapping | https://en.wikipedia.org/wiki/List_of_polynomial_topics |
Inmathematics, asquare rootof a numberxis a numberysuch thaty2=x{\displaystyle y^{2}=x}; in other words, a numberywhosesquare(the result of multiplying the number by itself, ory⋅y{\displaystyle y\cdot y}) isx.[1]For example, 4 and −4 are square roots of 16 because42=(−4)2=16{\displaystyle 4^{2}=(-4)^{2}=16}.
Everynonn... | https://en.wikipedia.org/wiki/Square_root |
Inmathematics, thecomposition operator∘{\displaystyle \circ }takes twofunctions,f{\displaystyle f}andg{\displaystyle g}, and returns a new functionh(x):=(g∘f)(x)=g(f(x)){\displaystyle h(x):=(g\circ f)(x)=g(f(x))}. Thus, the functiongisappliedafter applyingftox.(g∘f){\displaystyle (g\circ f)}is pronounced "the compositi... | https://en.wikipedia.org/wiki/Function_composition |
TheAbel equation, named afterNiels Henrik Abel, is a type offunctional equationof the form
or
The forms are equivalent whenαisinvertible.horαcontrol theiterationoff.
The second equation can be written
Takingx=α−1(y), the equation can be written
For a known functionf(x), a problem is to solve the functional equatio... | https://en.wikipedia.org/wiki/Abel_equation |
Schröder's equation,[1][2][3]named afterErnst Schröder, is afunctional equationwith oneindependent variable: given the functionh, find the functionΨsuch that
∀xΨ(h(x))=sΨ(x).{\displaystyle \forall x\;\;\;\Psi {\big (}h(x){\big )}=s\Psi (x).}
Schröder's equation is an eigenvalue equation for thecomposition operatorCh... | https://en.wikipedia.org/wiki/Schr%C3%B6der%27s_equation |
Inmathematics,superfunctionis a nonstandard name for aniterated functionfor complexified continuous iteration index. Roughly, for somefunctionfand for some variablex, the superfunction could be defined by the expression
Then,S(z;x) can be interpreted as the superfunction of the functionf(x).
Such a definition is vali... | https://en.wikipedia.org/wiki/Superfunction |
Fractional calculusis a branch ofmathematical analysisthat studies the several different possibilities of definingreal numberpowers orcomplex numberpowers of thedifferentiationoperatorD{\displaystyle D}Df(x)=ddxf(x),{\displaystyle Df(x)={\frac {d}{dx}}f(x)\,,}
and of theintegrationoperatorJ{\displaystyle J}[Note 1]Jf(... | https://en.wikipedia.org/wiki/Fractional_calculus |
Inmathematics, ahalf-exponential functionis afunctional square rootof anexponential function. That is, afunctionf{\displaystyle f}such thatf{\displaystyle f}composedwith itself results in an exponential function:[1][2]f(f(x))=abx,{\displaystyle f{\bigl (}f(x){\bigr )}=ab^{x},}for some constantsa{\displaystyle a}andb{\d... | https://en.wikipedia.org/wiki/Half-exponential_function |
Inmathematics,exponentiation, denotedbn, is anoperationinvolving two numbers: thebase,b, and theexponentorpower,n.[1]Whennis a positiveinteger, exponentiation corresponds to repeatedmultiplicationof the base: that is,bnis theproductof multiplyingnbases:[1]bn=b×b×⋯×b×b⏟ntimes.{\displaystyle b^{n}=\underbrace {b\times b\... | https://en.wikipedia.org/wiki/Exponentiation |
In mathematics, asum of radicalsis defined as a finitelinear combinationofnth roots:
wheren,ri{\displaystyle n,r_{i}}arenatural numbersandki,xi{\displaystyle k_{i},x_{i}}arereal numbers.
A particular special case arising incomputational complexity theoryis thesquare-root sum problem, asking whether it is possible to ... | https://en.wikipedia.org/wiki/Sum_of_radicals |
In mathematics, thegeometric meanis ameanoraveragewhich indicates acentral tendencyof a finite collection ofpositive real numbersby using the product of their values (as opposed to thearithmetic meanwhich uses their sum). The geometric mean ofn{\displaystyle n}numbers is thenth rootof theirproduct, i.e., for a colle... | https://en.wikipedia.org/wiki/Geometric_mean |
Thetwelfth root of twoor212{\displaystyle {\sqrt[{12}]{2}}}(orequivalently21/12{\displaystyle 2^{1/12}}) is analgebraicirrational number, approximately equal to 1.0594631. It is most important in Westernmusic theory, where it represents thefrequencyratio(musical interval) of asemitone(Playⓘ) intwelve-tone equal tempera... | https://en.wikipedia.org/wiki/Twelfth_root_of_two |
In mathematics, annth-orderArgand system(named afterFrenchmathematicianJean-Robert Argand) is acoordinate systemconstructed around thenthroots of unity. From theorigin,naxes extend such that the angle between each axis and the axes immediately before and after it is 360/ndegrees. For example, thenumber lineis the 2nd-o... | https://en.wikipedia.org/wiki/Argand_system |
Inalgebraic number theory, acyclotomic fieldis anumber fieldobtained byadjoiningacomplexroot of unitytoQ{\displaystyle \mathbb {Q} }, thefieldofrational numbers.[1]
Cyclotomic fields played a crucial role in the development of modernalgebraand number theory because of their relation withFermat's Last Theorem. It was i... | https://en.wikipedia.org/wiki/Cyclotomic_field |
Inmathematicsandgroup theory, the termmultiplicative grouprefers to one of the following concepts:
Thegroup scheme ofn-throots of unityis by definition the kernel of then-power map on the multiplicative group GL(1), considered as agroup scheme. That is, for any integern> 1 we can consider the morphism on the multiplic... | https://en.wikipedia.org/wiki/Group_scheme_of_roots_of_unity |
Innumber theory,Ramanujan's sum, usually denotedcq(n), is a function of two positive integer variablesqandndefined by the formula
where (a,q) = 1 means thataonly takes on valuescoprimetoq.
Srinivasa Ramanujanmentioned the sums in a 1918 paper.[1]In addition to the expansions discussed in this article, Ramanujan's sum... | https://en.wikipedia.org/wiki/Ramanujan%27s_sum |
Innumber theory, theTeichmüller characterω{\displaystyle \omega }(at a primep{\displaystyle p}) is acharacterof(Z/qZ)×{\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{\times }}, whereq=p{\displaystyle q=p}ifp{\displaystyle p}is odd andq=4{\displaystyle q=4}ifp=2{\displaystyle p=2}, taking values in the roots of unity of th... | https://en.wikipedia.org/wiki/Teichm%C3%BCller_character |
Inmathematics, theLucas sequencesUn(P,Q){\displaystyle U_{n}(P,Q)}andVn(P,Q){\displaystyle V_{n}(P,Q)}are certainconstant-recursiveinteger sequencesthat satisfy therecurrence relation
whereP{\displaystyle P}andQ{\displaystyle Q}are fixedintegers. Any sequence satisfying this recurrence relation can be represented as a... | https://en.wikipedia.org/wiki/Lucas_sequence |
Pell's equation, also called thePell–Fermat equation, is anyDiophantine equationof the formx2−ny2=1,{\displaystyle x^{2}-ny^{2}=1,}wherenis a given positivenonsquareinteger, and integer solutions are sought forxandy. InCartesian coordinates, the equation is represented by ahyperbola; solutions occur wherever the curve ... | https://en.wikipedia.org/wiki/Pell%27s_equation |
Adiabatic quantum computation(AQC) is a form ofquantum computingwhich relies on theadiabatic theoremto perform calculations[1]and is closely related toquantum annealing.[2][3][4][5]
First, a (potentially complicated)Hamiltonianis found whose ground state describes the solution to the problem of interest. Next, a syste... | https://en.wikipedia.org/wiki/Adiabatic_quantum_computation |
Incomputational complexity theory,bounded-error quantum polynomial time(BQP) is the class ofdecision problemssolvable by aquantum computerinpolynomial time, with an error probability of at most 1/3 for all instances.[1]It is the quantum analogue to thecomplexity classBPP.
A decision problem is a member ofBQPif there e... | https://en.wikipedia.org/wiki/BQP |
Acellular automaton(pl.cellular automata, abbrev.CA) is a discretemodel of computationstudied inautomata theory. Cellular automata are also calledcellular spaces,tessellation automata,homogeneous structures,cellular structures,tessellation structures, anditerative arrays.[2]Cellular automata have found application in v... | https://en.wikipedia.org/wiki/Cellular_automaton |
Cloud-basedquantum computingis the invocation of quantumemulators,simulatorsor processors through the cloud. Increasingly, cloud services are being looked on as the method for providing access to quantum processing. Quantum computers achieve their massive computing power by initiatingquantum physicsinto processing powe... | https://en.wikipedia.org/wiki/Cloud-based_quantum_computing |
Inquantum mechanics,counterfactual definiteness(CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume theexistenceof objects, and properties of objects, even when they have not beenmeasured).[1][2]The term "counterfactual... | https://en.wikipedia.org/wiki/Counterfactual_definiteness |
Counterfactual quantum computationis a method of inferring the result of a computation without actually running aquantum computerotherwise capable of actively performing that computation.
PhysicistsGraeme MitchisonandRichard Jozsaintroduced the notion of counterfactual computing[1]as an application of quantum computin... | https://en.wikipedia.org/wiki/Counterfactual_quantum_computation |
Landauer's principleis aphysical principlepertaining to a lowertheoreticallimit ofenergy consumptionofcomputation. It holds that an irreversible change ininformationstored in a computer, such as merging two computational paths, dissipates a minimum amount of heat to its surroundings.[1]It is hypothesized that energy co... | https://en.wikipedia.org/wiki/Landauer%27s_principle |
Inlogic, alogical connective(also called alogical operator,sentential connective, orsentential operator) is alogical constant. Connectives can be used to connect logical formulas. For instance in thesyntaxofpropositional logic, thebinaryconnective∨{\displaystyle \lor }can be used to join the twoatomic formulasP{\displa... | https://en.wikipedia.org/wiki/Logical_connective |
Theone-way quantum computer, also known asmeasurement-based quantum computer(MBQC), is a method ofquantum computingthat first prepares anentangledresource state, usually acluster stateorgraph state, then performs singlequbitmeasurements on it. It is "one-way" because the resource state is destroyed by the measurements... | https://en.wikipedia.org/wiki/One-way_quantum_computer |
Inquantum computing, aquantum algorithmis analgorithmthat runs on a realistic model ofquantum computation, the most commonly used model being thequantum circuitmodel of computation.[1][2]A classical (or non-quantum) algorithm is a finite sequence of instructions, or a step-by-step procedure for solving a problem, where... | https://en.wikipedia.org/wiki/Quantum_algorithm |
Aquantum cellular automaton(QCA) is an abstract model ofquantum computation, devised in analogy to conventional models ofcellular automataintroduced byJohn von Neumann. The same name may also refer toquantum dot cellular automata, which are a proposed physical implementation of "classical" cellular automata by exploiti... | https://en.wikipedia.org/wiki/Quantum_cellular_automaton |
Inquantum information theory, aquantum channelis a communication channel that can transmitquantum information, as well as classical information. An example of quantum information is the general dynamics of aqubit. An example of classical information is a text document transmitted over theInternet.
Terminologically, ... | https://en.wikipedia.org/wiki/Quantum_channel |
In themathematical study of logicand thephysicalanalysis ofquantum foundations,quantum logicis a set of rules for manipulation ofpropositionsinspired by the structure ofquantum theory. The formal system takes as its starting point an observation ofGarrett BirkhoffandJohn von Neumann, that the structure of experiment... | https://en.wikipedia.org/wiki/Quantum_logic |
Inquantum computing,quantum memoryis thequantum-mechanicalversion of ordinarycomputer memory. Whereas ordinary memory stores information asbinarystates (represented by "1"s and "0"s), quantum memory stores aquantum statefor later retrieval. These states hold useful computational information known asqubits. Unlike the c... | https://en.wikipedia.org/wiki/Quantum_memory |
Quantum networksform an important element ofquantum computingandquantum communicationsystems. Quantum networks facilitate the transmission of information in the form of quantum bits, also calledqubits, between physically separated quantum processors. A quantum processor is a machine able to performquantum circuitson a ... | https://en.wikipedia.org/wiki/Quantum_network |
Inquantum mechanics, frequent measurements cause thequantum Zeno effect, a reduction in transitions away from the systems initial state, slowing a systemstime evolution.[1]: 5
Sometimes this effect is interpreted as "a system cannot change while you are watching it".[2]One can "freeze" the evolution of the system by m... | https://en.wikipedia.org/wiki/Quantum_Zeno_effect |
Reversible computingis anymodel of computationwhere every step of theprocessistime-reversible. This means that, given the output of a computation, it's possible to perfectly reconstruct the input. In systems thatprogressdeterministicallyfrom one state to another, a key requirement for reversibility is aone-to-onecorres... | https://en.wikipedia.org/wiki/Reversible_computing |
Inquantum mechanics, theSchrödinger equationdescribes how a system changes with time. It does this by relating changes in the state of the system to the energy in the system (given by an operator called theHamiltonian). Therefore, once the Hamiltonian is known, the time dynamics are in principle known. All that remains... | https://en.wikipedia.org/wiki/Unitary_transformation_(quantum_mechanics) |
Exponential growthoccurs when a quantity grows as anexponential functionof time. The quantity grows at a ratedirectly proportionalto its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now.
In more technical language, its instantaneousrate of change(that i... | https://en.wikipedia.org/wiki/Exponential_growth |
Radioactive decay(also known asnuclear decay,radioactivity,radioactive disintegration, ornuclear disintegration) is the process by which an unstableatomic nucleusloses energy byradiation. A material containing unstable nuclei is consideredradioactive. Three of the most common types of decay arealpha,beta, andgamma deca... | https://en.wikipedia.org/wiki/Radioactive_decay |
Inmathematics, specifically inelementary arithmeticandelementary algebra, given an equation between twofractionsorrational expressions, one cancross-multiplyto simplify the equation or determine the value of a variable.
The method is also occasionally known as the "cross your heart" method because lines resembling a h... | https://en.wikipedia.org/wiki/Cross_multiplication |
Inmathematics, amultipleis theproductof any quantity and aninteger.[1]In other words, for the quantitiesaandb, it can be said thatbis a multiple ofaifb=nafor some integern, which is called themultiplier. Ifais notzero, this is equivalent to saying thatb/a{\displaystyle b/a}is an integer.
Whenaandbare both integers, an... | https://en.wikipedia.org/wiki/Multiple_(mathematics) |
FRACTRANis aTuring-completeesoteric programming languageinvented by the mathematicianJohn Conway. A FRACTRAN program is anordered listof positivefractionstogether with an initial positive integer inputn. The program is run by updating the integernas follows:
Conway 1987gives the following FRACTRAN program, called PRIM... | https://en.wikipedia.org/wiki/FRACTRAN |
Acircleis ashapeconsisting of allpointsin aplanethat are at a given distance from a given point, thecentre. The distance between any point of the circle and the centre is called theradius. The length of a line segment connecting two points on the circle and passing through the centre is called thediameter. A circle bou... | https://en.wikipedia.org/wiki/Circle |
Inmathematics, anellipseis aplane curvesurrounding twofocal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes acircle, which is the special type of ellipse in which the two focal points are the same. The elongation of an ellipse is measured by ... | https://en.wikipedia.org/wiki/Ellipse |
Inmathematics, aparabolais aplane curvewhich ismirror-symmetricaland is approximately U-shaped. It fits several superficially differentmathematicaldescriptions, which can all be proved to define exactly the same curves.
One description of a parabola involves apoint(thefocus) and aline(thedirectrix). The focus does not... | https://en.wikipedia.org/wiki/Parabola |
Ingeometry, adegenerate conicis aconic(a second-degreeplane curve, defined by apolynomial equationof degree two) that fails to be anirreducible curve. This means that the defining equation is factorable over thecomplex numbers(or more generally over analgebraically closed field) as the product of two linear polynomials... | https://en.wikipedia.org/wiki/Degenerate_conic |
Inmathematics, theharmonic meanis a kind ofaverage, one of thePythagorean means.
It is the most appropriate average forratiosandratessuch as speeds,[1][2]and is normally only used for positive arguments.[3]
The harmonic mean is thereciprocalof thearithmetic meanof the reciprocals of the numbers, that is, thegeneraliz... | https://en.wikipedia.org/wiki/Harmonic_mean |
Inprobability theoryandstatistics, there are several relationships amongprobability distributions. These relations can be categorized in the following groups:
Multiplying the variable by any positive real constant yields ascalingof the original distribution.
Some are self-replicating, meaning that the scaling yields t... | https://en.wikipedia.org/wiki/Relationships_among_probability_distributions#Reciprocal_of_a_random_variable |
Incombinatorialmathematics, alarge setofpositive integers
is one such that theinfinite sumof the reciprocals
diverges. Asmall setis any subset of the positive integers that is not large; that is, one whose sum of reciprocals converges.
Large sets appear in theMüntz–Szász theoremand in theErdős conjecture on arithme... | https://en.wikipedia.org/wiki/Large_set_(combinatorics) |
Inmathematics,statisticsand elsewhere,sums of squaresoccur in a number of contexts: | https://en.wikipedia.org/wiki/Sum_of_squares_(disambiguation) |
Inmathematicsandstatistics,sums of powersoccur in a number of contexts: | https://en.wikipedia.org/wiki/Sums_of_powers |
The17-animal inheritance puzzleis amathematical puzzleinvolving unequal butfair allocationofindivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.) which must be divided in some stated proportion among a number of beneficiaries. It is a common ex... | https://en.wikipedia.org/wiki/17-animal_inheritance_puzzle |
Inmathematics, amultipleis theproductof any quantity and aninteger.[1]In other words, for the quantitiesaandb, it can be said thatbis a multiple ofaifb=nafor some integern, which is called themultiplier. Ifais notzero, this is equivalent to saying thatb/a{\displaystyle b/a}is an integer.
Whenaandbare both integers, an... | https://en.wikipedia.org/wiki/Submultiple |
Inmathematics, asuperparticular ratio, also called asuperparticular numberorepimoric ratio, is theratioof two consecutiveinteger numbers.
More particularly, the ratio takes the form:
Thus:
A superparticular number is when a great number contains a lesser number, to which it is compared, and at the same time one part... | https://en.wikipedia.org/wiki/Superparticular_ratio |
Incomplex analysis, theargument principle(orCauchy's argument principle) is a theorem relating the difference between the number ofzeros and polesof ameromorphic functionto acontour integralof the function'slogarithmic derivative.
Iffis a meromorphic function inside and on some closed contourC, andfhas no zeros or pol... | https://en.wikipedia.org/wiki/Argument_principle |
Control theoryis a field ofcontrol engineeringandapplied mathematicsthat deals with thecontrolofdynamical systemsin engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing anydelay,overshoot, ... | https://en.wikipedia.org/wiki/Control_theory#Stability |
Filter designis the process of designing asignal processing filterthat satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to an acceptable degree.
The filter design process can be described as an optimization problem... | https://en.wikipedia.org/wiki/Filter_design |
Insignal processing, afilteris a device or process that removes some unwanted components or features from asignal. Filtering is a class ofsignal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing somefrequenciesor frequency... | https://en.wikipedia.org/wiki/Filter_(signal_processing) |
Incomplex analysis, a branch of mathematics, theGauss–Lucas theoremgives ageometricrelation between therootsof apolynomialPand the roots of itsderivativeP'. The set of roots of a real or complex polynomial is a set ofpointsin thecomplex plane. The theorem states that the roots ofP'all lie within theconvex hullof the ro... | https://en.wikipedia.org/wiki/Gauss%E2%80%93Lucas_theorem |
Inmathematicsand in particular the field ofcomplex analysis,Hurwitz's theoremis a theorem associating thezeroesof asequenceofholomorphic,compactlocally uniformly convergentfunctions with that of their corresponding limit. The theorem is named afterAdolf Hurwitz.
Let {fk} be a sequence of holomorphic functions on a con... | https://en.wikipedia.org/wiki/Hurwitz%27s_theorem_(complex_analysis) |
Inmathematics,Marden's theorem, named afterMorris Mardenbut proved about 100 years earlier by Jörg Siebeck, gives a geometric relationship between the zeroes of a third-degreepolynomialwithcomplexcoefficients and the zeroes of itsderivative. See alsogeometrical properties of polynomial roots.
A cubic polynomial has th... | https://en.wikipedia.org/wiki/Marden%27s_theorem |
Incontrol theoryandstability theory, theNyquist stability criterionorStrecker–Nyquist stability criterion, independently discovered by the German electrical engineerFelix Strecker[de]atSiemensin 1930[1][2][3]and the Swedish-American electrical engineerHarry NyquistatBell Telephone Laboratoriesin 1932,[4]is a graphical ... | https://en.wikipedia.org/wiki/Nyquist_stability_criterion |
Inmathematics,signal processingandcontrol theory, apole–zero plotis a graphical representation of arationaltransfer functionin thecomplex planewhich helps to convey certain properties of the system such as:
A pole-zero plot shows the location in the complex plane of thepoles and zerosof thetransfer functionof adynamic... | https://en.wikipedia.org/wiki/Pole%E2%80%93zero_plot |
Inmathematics, more specificallycomplex analysis, theresidueis acomplex numberproportional to thecontour integralof ameromorphic functionalong a path enclosing one of itssingularities. (More generally, residues can be calculated for any functionf:C∖{ak}k→C{\displaystyle f\colon \mathbb {C} \setminus \{a_{k}\}_{k}\right... | https://en.wikipedia.org/wiki/Residue_(complex_analysis) |
Rouché's theorem, named afterEugène Rouché, states that for any twocomplex-valuedfunctionsfandgholomorphicinside some regionK{\displaystyle K}with closed contour∂K{\displaystyle \partial K}, if|g(z)| < |f(z)|on∂K{\displaystyle \partial K}, thenfandf+ghave the same number of zeros insideK{\displaystyle K}, where each ze... | https://en.wikipedia.org/wiki/Rouch%C3%A9%27s_theorem |
Inmathematics,Sendov's conjecture, sometimes also calledIlieff's conjecture, concerns the relationship between the locations ofrootsandcritical pointsof apolynomial functionof acomplex variable. It is named afterBlagovest Sendov.
Theconjecturestates that for a polynomial
with all rootsr1, ...,rninside theclosed unit... | https://en.wikipedia.org/wiki/Sendov%27s_conjecture |
Inengineering,applied mathematics, andphysics, theBuckinghamπtheoremis a keytheoremindimensional analysis. It is a formalisation ofRayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain numbernphysical variables, then the original eq... | https://en.wikipedia.org/wiki/Buckingham_%CF%80_theorem |
Dimensionless numbers(orcharacteristic numbers) have an important role in analyzing the behavior offluidsand their flow as well as in othertransport phenomena.[1]They include theReynoldsand theMach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such asdensity,visc... | https://en.wikipedia.org/wiki/Dimensionless_numbers_in_fluid_mechanics |
AFermi problem(orFermi question,Fermi quiz), also known as anorder-of-magnitude problem, is anestimationproblem inphysicsorengineeringeducation, designed to teachdimensional analysisorapproximationof extreme scientific calculations. Fermi problems are usuallyback-of-the-envelope calculations. Fermi problems typically i... | https://en.wikipedia.org/wiki/Fermi_estimate |
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/Numerical-value_equation |
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/Rayleigh%27s_method_of_dimensional_analysis |
Similitudeis a concept applicable to the testing ofengineeringmodels. A model is said to havesimilitudewith the real application if the two sharegeometricsimilarity,kinematicsimilarity anddynamicsimilarity.Similarityandsimilitudeare interchangeable in this context.
The termdynamic similitudeis often used as a catch-all... | https://en.wikipedia.org/wiki/Similitude |
Asystem of units of measurement, also known as asystem of unitsorsystem of measurement, is a collection ofunits of measurementand rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science andcommerce. Instances in use include theInterna... | https://en.wikipedia.org/wiki/System_of_measurement |
TheDadda multiplieris a hardwarebinary multiplierdesign invented by computer scientistLuigi Daddain 1965.[1]It uses a selection offull and half addersto sum the partial products in stages (theDadda treeorDadda reduction) until two numbers are left. The design is similar to theWallace multiplier, but the different reduc... | https://en.wikipedia.org/wiki/Dadda_multiplier |
Adivision algorithmis analgorithmwhich, given twointegersNandD(respectively the numerator and the denominator), computes theirquotientand/orremainder, the result ofEuclidean division. Some are applied by hand, while others are employed by digital circuit designs and software.
Division algorithms fall into two main cat... | https://en.wikipedia.org/wiki/Division_algorithm |
Inmathematicsandcomputer science,Horner's method(orHorner's scheme) is an algorithm forpolynomial evaluation. Although named afterWilliam George Horner, this method is much older, as it has been attributed toJoseph-Louis Lagrangeby Horner himself, and can be traced back many hundreds of years to Chinese and Persian mat... | https://en.wikipedia.org/wiki/Horner_scheme |
Becausematrix multiplicationis such a central operation in manynumerical algorithms, much work has been invested in makingmatrix multiplication algorithmsefficient. Applications of matrix multiplication in computational problems are found in many fields includingscientific computingandpattern recognitionand in seemingl... | https://en.wikipedia.org/wiki/Matrix_multiplication_algorithm |
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