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In mathematics,Mittag-Leffler summationis any of several variations of theBorel summationmethod for summing possiblydivergentformal power series, introduced byGösta Mittag-Leffler(1908)
Let
be aformal power seriesinz.
Define the transformBαy{\displaystyle \scriptstyle {\mathcal {B}}_{\alpha }y}ofy{\displaystyle \sc... | https://en.wikipedia.org/wiki/Mittag-Leffler_summation |
Incomplex analysis, thePhragmén–Lindelöf principle(ormethod), first formulated byLars Edvard Phragmén(1863–1937) andErnst Leonard Lindelöf(1870–1946) in 1908, is a technique which employs an auxiliary, parameterized function to prove the boundedness of a holomorphic functionf{\displaystyle f}(i.e,|f(z)|<M(z∈Ω){\display... | https://en.wikipedia.org/wiki/Phragm%C3%A9n%E2%80%93Lindel%C3%B6f_principle |
Inmathematics,Abelian and Tauberian theoremsaretheoremsgiving conditions for two methods of summingdivergent seriesto give the same result, named afterNiels Henrik AbelandAlfred Tauber. The original examples areAbel's theoremshowing that if a seriesconvergesto some limit then itsAbel sumis the same limit, and Tauber's ... | https://en.wikipedia.org/wiki/Abelian_and_tauberian_theorems |
Inmathematicsandnumerical analysis, the van Wijngaarden transformation is a variant on theEuler transformused to accelerate the convergence of analternating series.
One algorithm to computeEuler's transformruns as follows:
Compute a row of partial sumss0,k=∑n=0k(−1)nan{\displaystyle s_{0,k}=\sum _{n=0}^{k}(-1)^{n}a_{... | https://en.wikipedia.org/wiki/Van_Wijngaarden_transformation |
Inmathematics,complex geometryis the study ofgeometricstructures and constructions arising out of, or described by, thecomplex numbers. In particular, complex geometry is concerned with the study ofspacessuch ascomplex manifoldsandcomplex algebraic varieties, functions ofseveral complex variables, and holomorphic const... | https://en.wikipedia.org/wiki/Complex_geometry |
Inmathematics,hypercomplex analysisis the extension ofcomplex analysisto thehypercomplex numbers. The first instance is functions of aquaternion variable, where the argument is aquaternion(in this case, the sub-field of hypercomplex analysis is calledquaternionic analysis). A second instance involves functions of amot... | https://en.wikipedia.org/wiki/Hypercomplex_analysis |
Vector calculusorvector analysisis a branch of mathematics concerned with thedifferentiationandintegrationofvector fields, primarily in three-dimensionalEuclidean space,R3.{\displaystyle \mathbb {R} ^{3}.}[1]The termvector calculusis sometimes used as a synonym for the broader subject ofmultivariable calculus, which sp... | https://en.wikipedia.org/wiki/Vector_calculus |
Complex analysis, traditionally known as thetheory of functions of a complex variable, is the branch ofmathematicsthat investigatesfunctionsofcomplex numbers. It is useful in many branches of mathematics, includingnumber theoryandapplied mathematics; as well as inphysics, includinghydrodynamics,thermodynamics, andelect... | https://en.wikipedia.org/wiki/List_of_complex_analysis_topics |
Incomplex analysis, themonodromy theoremis an important result aboutanalytic continuationof acomplex-analytic functionto a larger set. The idea is that one can extend a complex-analytic function (from here on called simplyanalytic function) along curves starting in the original domain of the function and ending in the... | https://en.wikipedia.org/wiki/Monodromy_theorem |
TheRiemann–Roch theoremis an important theorem inmathematics, specifically incomplex analysisandalgebraic geometry, for the computation of the dimension of the space ofmeromorphic functionswith prescribed zeros and allowedpoles. It relates the complex analysis of a connectedcompactRiemann surfacewith the surface's pure... | https://en.wikipedia.org/wiki/Riemann%E2%80%93Roch_theorem |
Incomplex analysis,Runge's theorem(also known asRunge's approximation theorem) is named after the German mathematicianCarl Rungewho first proved it in the year 1885. It states the following:
Denoting byCthe set ofcomplex numbers, letKbe acompact subsetofCand letfbe afunctionwhich isholomorphicon an open set containing... | https://en.wikipedia.org/wiki/Runge%27s_theorem |
In themathematicalstudy ofpartial differential equations, theBateman transformis a method for solving theLaplace equationin four dimensions andwave equationin three by using aline integralof aholomorphic functionin threecomplex variables. It is named after the mathematicianHarry Bateman, who first published the result... | https://en.wikipedia.org/wiki/Bateman_transform |
Inmathematics(in particular,functional analysis),convolutionis amathematical operationon twofunctionsf{\displaystyle f}andg{\displaystyle g}that produces a third functionf∗g{\displaystyle f*g}, as theintegralof the product of the two functions after one is reflected about the y-axis and shifted. The termconvolutionref... | https://en.wikipedia.org/wiki/Convolution_kernel |
Circular convolution, also known ascyclic convolution, is a special case ofperiodic convolution, which is theconvolutionof two periodic functions that have the same period. Periodic convolution arises, for example, in the context of thediscrete-time Fourier transform(DTFT). In particular, the DTFT of the product of t... | https://en.wikipedia.org/wiki/Circular_convolution |
Inlinear algebra, acirculant matrixis asquare matrixin which all rows are composed of the same elements and each row is rotated one element to the right relative to the preceding row. It is a particular kind ofToeplitz matrix.
Innumerical analysis, circulant matrices are important because they arediagonalizedby adiscr... | https://en.wikipedia.org/wiki/Circulant_matrix |
Inmathematics, adifferential equationis anequationthat relates one or more unknownfunctionsand theirderivatives.[1]In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations... | https://en.wikipedia.org/wiki/Differential_equations |
This is alist oftransformsinmathematics.
These transforms have a continuous frequency domain: | https://en.wikipedia.org/wiki/List_of_transforms |
Inmathematics, anoperatorortransformis afunctionfrom onespace of functionsto another. Operators occur commonly inengineering,physicsand mathematics. Many areintegral operatorsanddifferential operators.
In the followingLis an operator
which takes a functiony∈F{\displaystyle y\in {\mathcal {F}}}to another functionL[y]∈... | https://en.wikipedia.org/wiki/List_of_operators |
Inmathematics, anonlocaloperatoris amappingwhich maps functions on a topological space to functions, in such a way that the value of the output function at a given point cannot be determined solely from the values of the input function in any neighbourhood of any point. An example of a nonlocal operator is theFourier t... | https://en.wikipedia.org/wiki/Nonlocal_operator |
Infunctional analysis, areproducing kernel Hilbert space(RKHS) is aHilbert spaceof functions in which point evaluation is a continuouslinear functional. Specifically, a Hilbert spaceH{\displaystyle H}of functions from a setX{\displaystyle X}(toR{\displaystyle \mathbb {R} }orC{\displaystyle \mathbb {C} }) is an RKHS if ... | https://en.wikipedia.org/wiki/Reproducing_kernel |
Incalculus,symbolic integrationis the problem of finding aformulafor theantiderivative, orindefinite integral, of a givenfunctionf(x), i.e. to find a formula for adifferentiable functionF(x) such that
The family of all functions that satisfy this property can be denoted
The termsymbolicis used to distinguish this pro... | https://en.wikipedia.org/wiki/Symbolic_integration |
Inmathematics,linearization(British English:linearisation) is finding thelinear approximationto afunctionat a given point. The linear approximation of a function is the first orderTaylor expansionaround the point of interest. In the study ofdynamical systems, linearization is a method for assessing the localstabilityof... | https://en.wikipedia.org/wiki/Linearization |
Inmathematicsandapplied mathematics,perturbation theorycomprises methods for finding anapproximate solutionto a problem, by starting from the exactsolutionof a related, simpler problem.[1][2]A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts.[3]Inregula... | https://en.wikipedia.org/wiki/Perturbation_theory |
Chapman–Enskog theoryprovides a framework in which equations ofhydrodynamicsfor a gas can be derived from theBoltzmann equation. The technique justifies the otherwise phenomenologicalconstitutive relationsappearing in hydrodynamical descriptions such as theNavier–Stokes equations. In doing so, expressions for various ... | https://en.wikipedia.org/wiki/Chapman%E2%80%93Enskog_theory#Mathematical_Formulation |
Condorcet methods
Positional voting
Cardinal voting
Quota-remainder methods
Approval-based committees
Fractional social choice
Semi-proportional representation
By ballot type
Pathological response
Strategic voting
Paradoxes ofmajority rule
Positive results
Arrow's impossibility theoremis a key result insoci... | https://en.wikipedia.org/wiki/Arrow%27s_impossibility_theorem |
SPORE, theSecurity Protocols Open Repository, is an online library ofsecurity protocolswith comments and links to papers. Each protocol is downloadable in a variety of formats, including rules for use with automatic protocol verification tools. All protocols are described usingBAN logicor the style used by Clark and Ja... | https://en.wikipedia.org/wiki/Security_Protocols_Open_Repository |
Quantum key distribution (QKD) protocolsare used inquantum key distribution. The first protocol of that kind wasBB84, introduced in 1984 byCharles H. BennettandGilles Brassard. After that, many other protocols have been defined. | https://en.wikipedia.org/wiki/Quantum_cryptographic_protocol |
Incomputational complexity theory, aninteractive proof systemis anabstract machinethat modelscomputationas the exchange of messages between two parties: aproverand averifier. The parties interact by exchanging messages in order to ascertain whether a givenstringbelongs to alanguageor not. The prover is assumed to posse... | https://en.wikipedia.org/wiki/Soundness_(interactive_proof) |
Incryptography, aring signatureis a type ofdigital signaturethat can be performed by any member of a set of users that each havekeys. Therefore, a message signed with a ring signature is endorsed by someone in a particular set of people. One of the security properties of a ring signature is that it should be computat... | https://en.wikipedia.org/wiki/Ring_signature |
TheSecure Remote Password protocol(SRP) is an augmentedpassword-authenticated key exchange(PAKE) protocol, specifically designed to work around existing patents.[1]
Like all PAKE protocols, an eavesdropper orman in the middlecannot obtain enough information to be able tobrute-force guessa password or apply adictionary... | https://en.wikipedia.org/wiki/Secure_Remote_Password_protocol |
Inprobability theory,couplingis aprooftechnique that allows one to compare two unrelated random variables (distributions)XandYby creating arandom vectorWwhosemarginal distributionscorrespond toXandYrespectively. The choice ofWis generally not unique, and the whole idea of "coupling" is about making such a choice so tha... | https://en.wikipedia.org/wiki/Coupling_(probability) |
Inprobability theory, thecentral limit theorem(CLT) states that, under appropriate conditions, thedistributionof a normalized version of the sample mean converges to astandard normal distribution. This holds even if the original variables themselves are notnormally distributed. There are several versions of the CLT, ea... | https://en.wikipedia.org/wiki/Central_limit_theorem |
Instatistics,correlationordependenceis any statistical relationship, whethercausalor not, between tworandom variablesorbivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables arelinearlyrelated.
Fami... | https://en.wikipedia.org/wiki/Correlation_and_dependence |
Inprobability theoryandstatistics, acentral momentis amomentof aprobability distributionof arandom variableabout the random variable'smean; that is, it is theexpected valueof a specified integer power of the deviation of the random variable from the mean. The various moments form one set of values by which the properti... | https://en.wikipedia.org/wiki/Central_moment |
Instatistics, alocation parameterof aprobability distributionis a scalar- or vector-valuedparameterx0{\displaystyle x_{0}}, which determines the "location" or shift of the distribution. In the literature of location parameter estimation, the probability distributions with such parameter are found to be formally defined... | https://en.wikipedia.org/wiki/Location_parameter |
Ameanis a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers.[1]There are several kinds ofmeans(or "measures ofcentral tendency") inmathematics, especially instatistics. Each attempts to summarize or typify a given group ofdata, illustrating the... | https://en.wikipedia.org/wiki/Mean |
Thesample mean(sample average) orempirical mean(empirical average), and thesample covarianceorempirical covariancearestatisticscomputed from asampleof data on one or morerandom variables.
The sample mean is theaveragevalue (ormean value) of asampleof numbers taken from a largerpopulationof numbers, where "population" ... | https://en.wikipedia.org/wiki/Sample_mean |
Beliefs depend on the available information. This idea is formalized inprobability theorybyconditioning.Conditional probabilities,conditional expectations, andconditional probability distributionsare treated on three levels:discrete probabilities,probability density functions, andmeasure theory. Conditioning leads to a... | https://en.wikipedia.org/wiki/Conditioning_(probability) |
Inprobability theory, theDoob–Dynkin lemma, named afterJoseph L. DoobandEugene Dynkin(also known as thefactorization lemma), characterizes the situation when onerandom variableis a function of another by theinclusionof theσ{\displaystyle \sigma }-algebrasgenerated by the random variables. The usual statement of the lem... | https://en.wikipedia.org/wiki/Doob%E2%80%93Dynkin_lemma |
Inprobability theory, theDoob–Dynkin lemma, named afterJoseph L. DoobandEugene Dynkin(also known as thefactorization lemma), characterizes the situation when onerandom variableis a function of another by theinclusionof theσ{\displaystyle \sigma }-algebrasgenerated by the random variables. The usual statement of the lem... | https://en.wikipedia.org/wiki/Factorization_lemma |
Inmathematics,non-commutative conditional expectationis a generalization of the notion ofconditional expectationin classicalprobability. The space of essentially bounded measurable functions on aσ{\displaystyle \sigma }-finite measure space(X,μ){\displaystyle (X,\mu )}is the canonical example of acommutative von Neuman... | https://en.wikipedia.org/wiki/Non-commutative_conditional_expectation |
Thefundamental theorem of pokeris a principle first articulated byDavid Sklansky[1]that he believes expresses the essential nature ofpokeras agameofdecision-makingin the face ofincomplete information.
Every time you play a hand differently from the way you would have played it if you could see all your opponents' card... | https://en.wikipedia.org/wiki/Fundamental_theorem_of_poker |
Inprobability theory, thelaw(orformula)of total probabilityis a fundamental rule relatingmarginal probabilitiestoconditional probabilities. It expresses the total probability of an outcome which can be realized via several distinctevents, hence the name.
The law of total probability is[1]atheoremthat states, in its di... | https://en.wikipedia.org/wiki/Law_of_total_probability |
Inprobability theory, thelaw of total covariance,[1]covariance decomposition formula, orconditional covariance formulastates that ifX,Y, andZarerandom variableson the sameprobability space, and thecovarianceofXandYis finite, then
The nomenclature in this article's title parallels the phraselaw of total variance. Some... | https://en.wikipedia.org/wiki/Law_of_total_covariance |
Inprobability theoryandmathematicalstatistics, thelaw of total cumulanceis a generalization tocumulantsof thelaw of total probability, thelaw of total expectation, and thelaw of total variance. It has applications in the analysis oftime series. It was introduced byDavid Brillinger.[1]
It is most transparent when sta... | https://en.wikipedia.org/wiki/Law_of_total_cumulance |
Aproduct distributionis aprobability distributionconstructed as the distribution of theproductofrandom variableshaving two other known distributions. Given twostatistically independentrandom variablesXandY, the distribution of the random variableZthat is formed as the productZ=XY{\displaystyle Z=XY}is aproduct distribu... | https://en.wikipedia.org/wiki/Product_distribution#expectation |
Instatistics, theHorvitz–Thompson estimator, named afterDaniel G. Horvitzand Donovan J. Thompson,[1]is a method for estimating the total[2]and mean of apseudo-populationin astratified sampleby applyinginverse probability weightingto account for the difference in the sampling distribution between the collected data and ... | https://en.wikipedia.org/wiki/Horvitz%E2%80%93Thompson_estimator |
In thisstatistics,quality assurance, andsurvey methodology,samplingis the selection of a subset or astatistical sample(termedsamplefor short) of individuals from within astatistical populationto estimate characteristics of the whole population. The subset is meant to reflect the whole population, and statisticians atte... | https://en.wikipedia.org/wiki/Sample_(statistics) |
Instatistics,stratified samplingis a method ofsamplingfrom apopulationwhich can bepartitionedintosubpopulations.
Instatistical surveys, when subpopulations within an overall population vary, it could be advantageous to sample each subpopulation (stratum) independently.
Stratificationis the process of dividing members... | https://en.wikipedia.org/wiki/Stratum_(statistics) |
Bootstrappingis a procedure for estimating the distribution of an estimator byresampling(oftenwith replacement) one's data or a model estimated from the data.[1]Bootstrapping assigns measures of accuracy (bias, variance,confidence intervals, prediction error, etc.) to sample estimates.[2][3]This technique allows estima... | https://en.wikipedia.org/wiki/Bootstrap_world |
Instatisticsand in particular inregression analysis, adesign matrix, also known asmodel matrixorregressor matrixand often denoted byX, is amatrixof values ofexplanatory variablesof a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and their specific v... | https://en.wikipedia.org/wiki/Design_matrix#Simple_linear_regression |
Linear trend estimationis astatisticaltechnique used to analyzedatapatterns.Datapatterns, or trends, occur when theinformationgathered tends to increase or decrease over time or is influenced by changes in an external factor. Linear trend estimation essentially creates a straight line on agraphofdatathat models the gen... | https://en.wikipedia.org/wiki/Linear_trend_estimation |
Segmented regression, also known aspiecewise regressionorbroken-stick regression, is a method inregression analysisin which theindependent variableis partitioned into intervals and a separate line segment is fit to each interval. Segmented regression analysis can also be performed on multivariate data by partitioning t... | https://en.wikipedia.org/wiki/Segmented_regression |
The purpose of this page is to provide supplementary materials for theordinary least squaresarticle, reducing the load of the main article with mathematics and improving its accessibility, while at the same time retaining the completeness of exposition.
Define thei{\displaystyle i}thresidualto be
Then the objectiveS{... | https://en.wikipedia.org/wiki/Proofs_involving_ordinary_least_squares |
ANewey–West estimatoris used instatisticsandeconometricsto provide an estimate of thecovariance matrixof the parameters of aregression-typemodel where the standard assumptions ofregression analysisdo not apply.[1]It was devised byWhitney K. NeweyandKenneth D. Westin 1987, although there are a number of later variants.[... | https://en.wikipedia.org/wiki/Newey%E2%80%93West_estimator |
Inprobability theory,Lorden's inequalityis a bound for themomentsof overshoot for a stopped sum ofrandom variables, first published by Gary Lorden in 1970.[1]Overshoots play a central role inrenewal theory.[2]
LetX1,X2, ... beindependent and identically distributed positive random variablesand define the sumSn=X1+X2+ ... | https://en.wikipedia.org/wiki/Lorden%27s_inequality |
Inprobability theory,Wald's martingaleis the name sometimes given to amartingaleused to study sums ofi.i.d. random variables. It is named after the mathematicianAbraham Wald, who used these ideas in a series of influential publications.[1][2][3]
Wald's martingale can be seen as discrete-time equivalent of theDoléans-D... | https://en.wikipedia.org/wiki/Wald%27s_martingale |
Inprobability theory,Spitzer's formulaorSpitzer's identitygives the joint distribution of partial sums and maximal partial sums of a collection of random variables. The result was first published byFrank Spitzerin 1956.[1]The formula is regarded as "a stepping stone in the theory of sums of independent random variables... | https://en.wikipedia.org/wiki/Spitzer%27s_formula |
ABayesian network(also known as aBayes network,Bayes net,belief network, ordecision network) is aprobabilistic graphical modelthat represents a set of variables and theirconditional dependenciesvia adirected acyclic graph(DAG).[1]While it is one of several forms ofcausal notation, causal networks are special cases of B... | https://en.wikipedia.org/wiki/Bayesian_network |
Knowledge representation(KR) aims to model information in a structured manner to formally represent it as knowledge in knowledge-based systems. Whereasknowledge representationand reasoning(KRR,KR&R, orKR²) also aims to understand, reason and interpret knowledge. KRR is widely used in the field ofartificial intelligence... | https://en.wikipedia.org/wiki/Knowledge_representation |
In the mathematicaltheory of probability, theIonescu-Tulcea theorem, sometimes called theIonesco Tulcea extension theorem, deals with the existence ofprobability measuresfor probabilistic events consisting of a countably infinite number of individual probabilistic events. In particular, the individual events may beinde... | https://en.wikipedia.org/wiki/Ionescu-Tulcea_theorem |
Inprobability theory, theBorel–Kolmogorov paradox(sometimes known asBorel's paradox) is aparadoxrelating toconditional probabilitywith respect to aneventof probability zero (also known as anull set). It is named afterÉmile BorelandAndrey Kolmogorov.
Suppose that arandom variablehas auniform distributionon aunit sphere... | https://en.wikipedia.org/wiki/Borel%E2%80%93Kolmogorov_paradox |
Inprobability theory,regular conditional probabilityis a concept that formalizes the notion of conditioning on the outcome of arandom variable. The resultingconditional probability distributionis a parametrized family of probability measures called aMarkov kernel.
Consider two random variablesX,Y:Ω→R{\displaystyle X,Y... | https://en.wikipedia.org/wiki/Regular_conditional_probability |
Instatistics, sometimes thecovariance matrixof amultivariate random variableis not known but has to beestimated.Estimation of covariance matricesthen deals with the question of how to approximate the actual covariance matrix on the basis of a sample from themultivariate distribution. Simple cases, where observations ar... | https://en.wikipedia.org/wiki/Estimation_of_covariance_matrices |
This is a list ofpublicationsinstatistics, organized by field.
Some reasons why a particular publication might be regarded as important:
Mathematical Methods of Statistics
Statistical Decision Functions
Testing Statistical Hypotheses
An Essay Towards Solving a Problem in the Doctrine of Chances
On Small Differenc... | https://en.wikipedia.org/wiki/List_of_important_publications_in_statistics#Multivariate_analysis |
Inmarketing,multivariate testingormulti-variable testingtechniques applystatistical hypothesis testingon multi-variable systems, typically consumers on websites. Techniques ofmultivariate statisticsare used.
Ininternet marketing, multivariate testing is a process by which more than one component of a website may be te... | https://en.wikipedia.org/wiki/Multivariate_testing_in_marketing |
Structural equation modeling(SEM) is a diverse set of methods used by scientists for both observational and experimental research. SEM is used mostly in the social and behavioral science fields, but it is also used in epidemiology,[2]business,[3]and other fields. A common definition of SEM is, "...a class of methodolog... | https://en.wikipedia.org/wiki/Structural_equation_modeling |
In statistics, theRV coefficient[1]is amultivariategeneralization of thesquaredPearson correlation coefficient(because the RV coefficient takes values between 0 and 1).[2]It measures the closeness of two set of points that may each be represented in amatrix.
The major approaches withinstatistical multivariate data ana... | https://en.wikipedia.org/wiki/RV_coefficient |
Bivariate analysisis one of the simplest forms ofquantitative (statistical) analysis.[1]It involves the analysis of twovariables(often denoted asX,Y), for the purpose of determining the empirical relationship between them.[1]
Bivariate analysis can be helpful in testing simplehypothesesofassociation. Bivariate analysi... | https://en.wikipedia.org/wiki/Bivariate_analysis |
Thedesign of experiments(DOE),[1]also known asexperiment designorexperimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated withexperimentsin which the design introduces c... | https://en.wikipedia.org/wiki/Design_of_experiments |
Note to admins: In case of doubt, remove this template and post a message asking for review atWT:CP.Withthis script, go tothe history with auto-selected revisions.
Note to the requestor: Make sure the page has already been reverted to a non-infringing revision or that infringing text has been removed or replaced befor... | https://en.wikipedia.org/wiki/Exploratory_data_analysis |
Soft independent modelling by class analogy(SIMCA) is astatisticalmethod forsupervised classificationof data. The method requires atraining data setconsisting of samples (or objects) with a set of attributes and their class membership. The term soft refers to the fact the classifier can identify samples as belonging to... | https://en.wikipedia.org/wiki/Soft_independent_modelling_of_class_analogies |
Univariateis a term commonly used in statistics to describe a type of data which consists of observations on only a single characteristic or attribute. A simple example of univariate data would be the salaries of workers in industry.[1]Like all the other data, univariate data can be visualized using graphs, images or o... | https://en.wikipedia.org/wiki/Univariate_analysis |
Aninterference fit, also known as apressed fitorfriction fit, is a form of fastening between twotightfittingmating parts that produces a joint which is held together byfrictionafter the parts are pushed together.[1]
Depending on the amount of interference, parts may be joined using a tap from a hammer or forced toget... | https://en.wikipedia.org/wiki/Interference_fit |
Instatistics,interval estimationis the use ofsample datatoestimateanintervalof possible values of aparameterof interest. This is in contrast topoint estimation, which gives a single value.[1]
The most prevalent forms of interval estimation areconfidence intervals(afrequentistmethod) andcredible intervals(aBayesian met... | https://en.wikipedia.org/wiki/Interval_estimation |
Probabilistic designis a discipline withinengineering design. It deals primarily with the consideration and minimization of the effects ofrandom variabilityupon the performance of anengineering systemduring the design phase. Typically, these effects studied and optimized are related to quality and reliability. It diffe... | https://en.wikipedia.org/wiki/Probabilistic_design |
Theprocess capabilityis a measurable property of aprocessto the specification, expressed as aprocess capability index(e.g., Cpkor Cpm) or as aprocess performance index(e.g., Ppkor Ppm). The output of this measurement is often illustrated by ahistogramand calculations that predict how many parts will be produced out of ... | https://en.wikipedia.org/wiki/Process_capability |
Reliability engineeringis a sub-discipline ofsystems engineeringthat emphasizes the ability of equipment to function without failure. Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, OR will operate in a defined en... | https://en.wikipedia.org/wiki/Reliability_engineering |
Aspecificationoften refers to a set of documented requirements to be satisfied by a material, design, product, or service.[1]A specification is often a type oftechnical standard.
There are different types of technical or engineering specifications (specs), and the term is used differently in different technical contex... | https://en.wikipedia.org/wiki/Specification |
Engineering toleranceis the permissible limit or limits of variation in:
Dimensions, properties, or conditions may have some variation without significantly affecting functioning of systems, machines, structures, etc. A variation beyond the tolerance (for example, a temperature that is too hot or too cold) is said to ... | https://en.wikipedia.org/wiki/Tolerance_(engineering) |
Inset theoryinmathematicsandformal logic, twosetsare said to bedisjoint setsif they have noelementin common. Equivalently, two disjoint sets are sets whoseintersectionis theempty set.[1]For example, {1, 2, 3} and {4, 5, 6} aredisjoint sets,while {1, 2, 3} and {3, 4, 5} are not disjoint. A collection of two or more sets... | https://en.wikipedia.org/wiki/Disjoint_sets |
This is aglossary of graph theory.Graph theoryis the study ofgraphs, systems of nodes orverticesconnected in pairs by lines oredges. | https://en.wikipedia.org/wiki/Glossary_of_graph_theory_terms |
Incomputer science,graph transformation, orgraph rewriting, concerns the technique of creating a newgraphout of an original graph algorithmically. It has numerous applications, ranging fromsoftware engineering(software constructionand alsosoftware verification) tolayout algorithmsand picture generation.
Graph transfor... | https://en.wikipedia.org/wiki/Graph_rewriting |
Ingraph theory, a division ofmathematics, amedian graphis anundirected graphin which every threeverticesa,b, andchave a uniquemedian: a vertexm(a,b,c) that belongs toshortest pathsbetween each pair ofa,b, andc.
The concept of median graphs has long been studied, for instance byBirkhoff & Kiss (1947)or (more explicitly... | https://en.wikipedia.org/wiki/Median_graph |
Ingraph theory, thehypercube graphQnis the graph formed from the vertices and edges of ann-dimensionalhypercube. For instance, thecube graphQ3is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube.Qnhas2nvertices,2n− 1nedges, and is aregular graphwithnedges touching each vertex.
The hypercube g... | https://en.wikipedia.org/wiki/Hypercube_graph |
Sidorenko's conjectureis a majorconjecturein the field ofextremal graph theory, posed byAlexander Sidorenkoin 1986. Roughly speaking, the conjecture states that for anybipartite graphH{\displaystyle H}andgraphG{\displaystyle G}onn{\displaystyle n}vertices with average degreepn{\displaystyle pn}, there are at leastp|E(H... | https://en.wikipedia.org/wiki/Sidorenko%27s_conjecture |
Algebraicgraph theoryis a branch ofmathematicsin whichalgebraicmethods are applied to problems aboutgraphs. This is in contrast togeometric,combinatoric, oralgorithmicapproaches. There are three main branches of algebraic graph theory, involving the use oflinear algebra, the use ofgroup theory, and the study ofgraph i... | https://en.wikipedia.org/wiki/Algebraic_graph_theory |
Ingraph theory, adistinguishing coloringordistinguishing labelingof a graph is anassignment of colorsor labels to theverticesof the graph that destroys all of the nontrivialsymmetries of the graph. The coloring does not need to be aproper coloring: adjacent vertices are allowed to be given the same color. For the color... | https://en.wikipedia.org/wiki/Distinguishing_coloring |
Ingraph theory, a mathematical discipline, afactor-critical graph(orhypomatchable graph[1][2]) is agraphwith anodd numberof vertices in which deleting one vertex in every possible way results in a graph with aperfect matching, a way of grouping the remaining vertices into adjacent pairs.
A matching of all but one vert... | https://en.wikipedia.org/wiki/Factor-critical_graph |
Incomputer science,dancing links(DLX) is a technique for adding and deleting a node from a circulardoubly linked list. It is particularly useful for efficiently implementingbacktrackingalgorithms, such asKnuth's Algorithm Xfor theexact cover problem.[1]Algorithm X is arecursive,nondeterministic,depth-first,backtracking... | https://en.wikipedia.org/wiki/Dancing_Links |
Sudoku(/suːˈdoʊkuː,-ˈdɒk-,sə-/;Japanese:数独,romanized:sūdoku,lit.'digit-single'; originally calledNumber Place)[1]is alogic-based,[2][3]combinatorial[4]number-placementpuzzle. In classic Sudoku, the objective is to fill a 9 × 9 grid with digits so that each column, each row, and each of the nine 3 × 3 subgrids that comp... | https://en.wikipedia.org/wiki/Sudokian |
Sudoku codesare non-linearforward error correctingcodes following rules ofsudokupuzzles designed for anerasure channel. Based on this model, the transmitter sends a sequence of all symbols of a solved sudoku. The receiver either receives a symbol correctly or an erasure symbol to indicate that the symbol was not receiv... | https://en.wikipedia.org/wiki/Sudoku_code |
Inprobability theoryandstatistics,varianceis theexpected valueof thesquared deviation from the meanof arandom variable. Thestandard deviation(SD) is obtained as the square root of the variance. Variance is a measure ofdispersion, meaning it is a measure of how far a set of numbers is spread out from their average value... | https://en.wikipedia.org/wiki/Variance#Properties |
Incomputational group theory, ablack box group(black-box group) is agroupGwhose elements are encoded bybit stringsof lengthN, and group operations are performed by anoracle(the "black box"). These operations include:
This class is defined to include both thepermutation groupsand thematrix groups. The upper bound on th... | https://en.wikipedia.org/wiki/Black_box_group |
Incomputability theory, aTuring reductionfrom adecision problemA{\displaystyle A}to a decision problemB{\displaystyle B}is anoracle machinethat decides problemA{\displaystyle A}given an oracle forB{\displaystyle B}(Rogers 1967, Soare 1987) in finitely many steps. It can be understood as analgorithmthat could be used to... | https://en.wikipedia.org/wiki/Turing_reduction |
In mathematics and computer science, amatroid oracleis asubroutinethrough which analgorithmmay access amatroid, an abstract combinatorial structure that can be used to describe thelinear dependenciesbetween vectors in avector spaceor thespanning treesof agraph, among other applications.
The most commonly used oracle o... | https://en.wikipedia.org/wiki/Matroid_oracle |
Inalgorithmic game theory, a branch of bothcomputer scienceandeconomics, ademand oracleis a function that, given a price-vector, returns thedemandof an agent. It is used by many algorithms related topricingand optimization inonline market. It is usually contrasted with avalue oracle, which is a function that, given a s... | https://en.wikipedia.org/wiki/Demand_oracle |
In cryptography, apadding oracle attackis an attack which uses thepaddingvalidation of a cryptographic message to decrypt the ciphertext. In cryptography, variable-length plaintext messages often have to be padded (expanded) to be compatible with the underlyingcryptographic primitive. The attack relies on having a "pad... | https://en.wikipedia.org/wiki/Padding_oracle_attack |
Theorigins ofglobal surveillancecan be traced back to the late 1940s, when theUKUSA Agreementwas jointly enacted by the United Kingdom and the United States, whose close cooperation eventually culminated in the creation of the global surveillance network, code-named "ECHELON", in 1971.[1][2]
In the aftermath of the197... | https://en.wikipedia.org/wiki/Origins_of_global_surveillance |
Global surveillancerefers to the practice ofglobalizedmass surveillanceon entire populations across national borders.[1]Although its existence was first revealed in the 1970s and led legislators to attempt to curb domestic spying by theNational Security Agency(NSA), it did not receive sustained public attention until t... | https://en.wikipedia.org/wiki/Global_surveillance_disclosures_(1970%E2%80%932013) |
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