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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 18 "Pythagorean means," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 5 " the " } {HYPERLNK 45 "arithmetic" 5 "Definition/arithmetic" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "geometric" 5 "Definition/geometric" "" }{TEXT -1 6 ", and " } {HYPERLNK 45 "harmonic means" 5 "Definition/harmonicmean" "" }{TEXT -1 11 ". 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 18 "Pythagorean triple" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 19 "Pythagorean numbers" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 42 " any set of three integers satisfying the " } {HYPERLNK 45 "Diophantine equation" 5 "Definition/Diophantineequation" "" }{TEXT -1 1 " " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 7 "^(2 )+ " } {TEXT 22 1 "y" } {TEXT -1 5 "^2 = " } {TEXT 22 1 "z" } {TEXT -1 4 "^2. " } } {PARA 0 "> " 0 "" {TEXT -1 56 "As proved by Euclid and Diophantus, these have the form " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 3 " = " } {TEXT 22 1 "a" } {TEXT -1 7 "^(2 )- " } {TEXT 22 1 "b" } {TEXT -1 4 "^2, " } {TEXT 22 1 "y" } {TEXT -1 4 " = 2" } {TEXT 22 2 "ab" } {TEXT -1 2 ", " } {TEXT 22 1 "z" } {TEXT -1 3 " = " } {TEXT 22 1 "a" } {TEXT -1 7 "^(2 )+e " } {TEXT 22 1 "b" } {TEXT -1 4 "^2, " } } {PARA 0 "> " 0 "" {TEXT -1 17 "for any integral " } {TEXT 22 1 "a" } {TEXT -1 5 " and " } {TEXT 22 1 "b" } {TEXT -1 2 ". " } {HYPERLNK 45 "Fermat's last theorem" 5 "Definition/Fermatslasttheorem" "" }{TEXT -1 68 " asserts that there are no analogous triples for higher powers, and " } {HYPERLNK 45 "Waring's problem" 5 "Definition/Waringsproblem" "" }{TEXT -1 30 " seeks to generalize further. " } } } ineequation" "" }{TEXT -1 1 " " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 7 "^(2 )+ " } {TEXT 22 1 "y" } {TEXT -1 5 "^2 = " } {TEXT 22 1 "z" } {TEXT -1 4 "^2. 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" } } {PARA 0 "> " 0 "" {TEXT -1 4 "The " } {TEXT 22 2 "q-" } {TEXT -1 34 "binomial coefficient tends to the " } {HYPERLNK 45 "binomial coefficient" 5 "Definition/binomialcoefficient" "" }{TEXT -1 4 " as " } {TEXT 22 2 "q h" } {TEXT -1 77 "increases to unity, and satisfies [n m] = [(n-1) m] + q^(n-m)*[(n-1) (m-1)]. " } } {PARA 0 "> " 0 "" {TEXT -1 26 "For non-negative integers " } {TEXT 22 1 "n" } {TEXT -1 5 " and " } {TEXT 22 1 "m" } {TEXT -1 6 ", the " } {TEXT 22 2 "q-" } {TEXT -1 40 "binomial coefficient is a polynomial in " } {TEXT 22 1 "q" } {TEXT -1 6 ". For " } {TEXT 22 3 "q=1" } {TEXT -1 49 ", the polynomial equals the binomial coefficient." } } {PARA 0 "> " 0 "" {TEXT -1 24 "This is an example of a " } {TEXT 22 11 "q-expansion" } {TEXT -1 4 " or " } {TEXT 22 9 "q-series." } {TEXT -1 10 " See also " } {HYPERLNK 45 "triple-product identity of Jacobi" 5 "Definition/triple-productidentityofJacobi" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "Rogers-Ramanujan identities" 5 "Definition/Rogers-Ramanujanidentities" "" }{TEXT -1 2 ". " } } } -1 4 "The " } {TEXT 22 2 "q-" } {TEXT -1 34 "binomial coefficient tends to the " } {HYPERLNK 45 "binomial coefficient" 5 "Definition/binomialcoefficient" "" }{TEXT -1 4 " as " } {TEXT 22 2 "q hdefinition,Qr_algorithmmQR algorithm definitiondefinition,QralgorithmmQR algorithm definitiondefinition,Qseriesq-series definitiondefinition,Quadranglequadrangle definitiondefinition,Quadrantzquadrant definitiondefinition,Quadrateequadrate definitiondefinition,Quadratfreiquadratfrei definitiondefinition,QuadraticSHquadratic form definitionPquadratic definitionquadratic equation definitiondefinition,QuadraticCongruence"*quadratic congruence definitionMathdictionary,roottestTroot test definitionMathdictionary,rose`rose definitionMathdictionary,rot"rot definition*Mathdictionary,rotating_frame_of_reference)(rotating frame of reference definition'Mathdictionary,rotatingframeofreference)(rotating frame of reference definitionMathdictionary,rotation(0curl definition?rotation 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angle definitionmathdictionary,ReEntrant&re-entrant definition mathdictionary,Re_Entering_Angle@re-entering angle definitionmathdictionary,Re_Entrant&re-entrant definition mathdictionary,Re_entering_angle@re-entering angle definitionmathdictionary,Re_entrant&re-entrant definitionmathdictionary,ReachablePointsreachable set definitionmathdictionary,ReachableSetreachable set definitionmathdictionary,Reachable_Pointsreachable set definitiondefinition,Quasigroupquasi-group definitiondefinition,Quasilinearqquasi-linear definitiondefinition,Quasilinearequation#Tquasi-linear equation definitiondefinition,Quasimetrictquasi-metric definitiondefinition,Quasinewtonmethod!ېquasi-Newton method definitiondefinition,Quasiorderingquasi-ordering definitiondefinition,Quasiquotationwquasi-quotation definitiondefinition,Quasitautologyquasi-tautology definitiondefinition,Quaternaryquaternary definitionDefinition,radius_of_curvature!Kradius of curvature definitionDefinition,radius_of_gyration hradius of 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definitionQbinomial,MathDictionary'Qbinomial,Mathdictionary'Qbinomial,definition'Qbinomial,dictionary'Qbinomial,mathdictionary'Qed,DefinitionQed,DictionaryQed,MathDictionaryQed,MathdictionaryQed,definitionQed,dictionaryQed,mathdictionaryQef,Definition3Qef,Dictionary3Qef,MathDictionary3Qef,Mathdictionary3Qef,definition3Qef,dictionary3Qef,mathdictionary3P{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "quadratic," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 1 " " } {TEXT 39 4 "1a. " } {TEXT -1 22 "of the second degree. " } } {PARA 0 "> " 0 "" {TEXT 39 3 "b. " } {TEXT -1 181 " (of an expression, function, or equation) containing one or more terms in which the variable is raised to the second power, but no variables are raised to a higher positive power. " } {TEXT 39 2 "2." } {TEXT -1 2 " (" } {TEXT 22 14 "as substantive" } {TEXT -1 4 ") a " } {HYPERLNK 45 "quadratic equation" 5 "Definition/quadraticequation" "" }{TEXT -1 2 ". " } } } 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triple definitionծPythagorean numbers definitiondefinition,pythagoreantriple hdPythagorean triple definition definition,q-iR definitionZ definition^Q definitiondefinition,q-binomial'q-binomial definitiondefinition,q-expansion-q-expansion definitiondefinition,q-seriesq-series definitiondefinition,q_binomial'q-binomial definitiondefinition,q_expansion-q-expansion definitiondefinition,q_seriesq-series definitiondictionary,qexpansion-q-expansion definitiondictionary,qr_algorithmmQR algorithm definitiondictionary,qralgorithmmQR algorithm definitiondictionary,qseriesq-series definitiondictionary,quadranglequadrangle definitiondictionary,quadrantzquadrant definitiondictionary,quadrateequadrate definitiondictionary,quadratfreiquadratfrei definitiondictionary,quadraticSHquadratic form definitionPquadratic definitionquadratic equation definitiondictionary,quadratic_congruence"*quadratic congruence definition Definition,Quadratic_Convergence#Gquadratic convergence definitionDefinition,Quadratic_Equation quadratic equation definitionDefinition,Quadratic_FormHquadratic form definition Definition,Quadratic_Programming#iquadratic programming definition Definition,Quadratic_Reciprocity#mhquadratic reciprocity definitionDefinition,Quadratic_ResidueOQquadratic residue definitionDefinition,Quadratic_congruence"*quadratic congruence definition Definition,Quadratic_convergence#Gquadratic convergence definitiondictionary,Qr_algorithmmQR algorithm definitiondictionary,QralgorithmmQR algorithm definitiondictionary,Qseriesq-series definitiondictionary,Quadranglequadrangle definitiondictionary,Quadrantzquadrant definitiondictionary,Quadrateequadrate definitiondictionary,Quadratfreiquadratfrei definitiondictionary,QuadraticSHquadratic form definitionPquadratic definitionquadratic equation definitiondictionary,QuadraticCongruence"*quadratic congruence definitionMathdictionary,qef3QEF definitionMathdictionary,qexpansion-q-expansion definitionMathdictionary,qr_algorithmmQR algorithm definitionMathdictionary,qralgorithmmQR algorithm definitionMathdictionary,qseriesq-series definitionMathdictionary,quadranglequadrangle definitionMathdictionary,quadrantzquadrant definitionMathdictionary,quadrateequadrate definitionMathdictionary,quadratfreiquadratfrei definitionMathdictionary,quadraticSHquadratic form definitionPquadratic definitionquadratic equation definition Dictionary,Quadratic_Convergence#Gquadratic convergence definitionDictionary,Quadratic_Equation quadratic equation definitionDictionary,Quadratic_FormHquadratic form definition Dictionary,Quadratic_Programming#iquadratic programming definition Dictionary,Quadratic_Reciprocity#mhquadratic reciprocity definitionDictionary,Quadratic_ResidueOQquadratic residue definitionDictionary,Quadratic_congruence"*quadratic congruence definition Dictionary,Quadratic_convergence#Gquadratic convergence definition^ {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 2 "Q," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 12 " the set of " } {HYPERLNK 45 "rational numbers" 5 "Definition/rationalnumber" "" }{TEXT -1 10 ". Compare " } {HYPERLNK 45 "N" 5 "Definition/N" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "R" 5 "Definition/R" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "Z" 5 "Definition/Z" "" }{TEXT -1 1 "." } } } outerautomorphismaoutercaratheodorymeasurGouterjordanmeasurNouterlebesguemeasur outermeasurNoutletmLoutliNoutput/{ |,E.Mb#q+ outputmodelE outputset  outputvariabl +boutsidS(852DUar%x/ҝB j(Voutstand *NvUoutward7 (EPV[Zdvdoval 1rotherwis('!#B$(f-ABBDJ5Kt[[5]t,x:gΚ-[yy</our;8"outlf -.G !)*Z,I./05:>y?AADbE|FJLN ZZ\^:be[o#qrrLss~%wdRB8n'outcomWOm*$D)*C-Ye|\Ƒ_I;outdegreouter7 .y:BGa_uNAN2K\b{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "Rademacher functions," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 26 " the family of functions {" } {TEXT 22 4 "f[n]" } {TEXT -1 119 "} defined on the unit interval by the formula f[n](x) = (-1)^(i+1) if (i-1)/2^n <= x < i/2^n for each positive integer " } {TEXT 22 2 "n." } {TEXT -1 16 " Alternatively, " } {TEXT 22 4 "f[n]" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 42 ") can be defined to be the sign of sin(2^(" } {TEXT 22 1 "n" } {TEXT -1 3 ")pi" } {TEXT 22 1 "x" } {TEXT -1 30 "), for a non-negative integer " } {TEXT 22 2 "n." } {TEXT -1 59 " (Named after the German-born analyst and number theorist, " } {TEXT 22 22 "Hans Adolph Rademacher" } {TEXT -1 75 " (1892-1969), who was persecuted by the Nazis and took refuge in the USA.) 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 18 "quadratic equation" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 9 "quadratic" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 25 " an equation of the form " } } {PARA 0 "> " 0 "" {TEXT 22 2 "ax" } {TEXT -1 5 "^2 + " } {TEXT 22 2 "bx" } {TEXT -1 3 " + " } {TEXT 22 1 "c" } {TEXT -1 53 " = 0, of which the roots are in general given by the " } {TEXT 22 17 "quadratic formula" } {TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 2 "=-" } {TEXT 22 1 "b" } {TEXT -1 10 " +/- sqrt(" } {TEXT 22 1 "b" } {TEXT -1 8 "^(2 )- 4" } {TEXT 22 2 "ac" } {TEXT -1 4 ")/(2" } {TEXT 22 1 "a" } {TEXT -1 11 ") in which " } {TEXT 22 1 "b" } {TEXT -1 8 "^(2) - 4" } {TEXT 22 2 "ac" } {TEXT -1 8 " is the " } {HYPERLNK 45 "discriminant" 5 "Definition/discriminant" "" }{TEXT 22 1 "." } {TEXT -1 10 " See also " } {HYPERLNK 45 "solution by 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HPQuadratic,MathDictionary HPQuadratic,Mathdictionary HPQuadratic,definition HPQuadratic,dictionary HPQuadratic,mathdictionary HPQuadraticCongruence,Definition*QuadraticCongruence,Dictionary*"QuadraticCongruence,MathDictionary*"QuadraticCongruence,Mathdictionary*QuadraticCongruence,definition*QuadraticCongruence,dictionary*"QuadraticCongruence,mathdictionary*QuadraticConvergence,DefinitionGpvalupvq +px GpypyramidB: pythagora/,-pythagorastheorem++ pythagorean;.hd.ojծpythagoreanmean ,;ojpythagoreannumber +hdծpythagoreantriplhd qbinomial'qedqef3qexpans-qpHsqrm qralgorithmmqser quadrangl\d Gquadrant z{ puregeometr +: purelyatomicrpurelydiscontinuou<purelyimaginar"&puremathematic<pureset1  purestrategFpuresurd`purport.5DEN_purposW+!H!4Rdt\uwk1[o -0\xpursu #pursuithput;91~J d5G=.putat /putt ]puzzlNpv +WMathdictionary,Quadrilateralqquadrilateral definitionMathdictionary,Quadrinomialquadrinomial definition"Mathdictionary,QualitativeIdentity"[qualitative identity 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Quadratic_programming,Dictionaryiiߡalsolinearsubjectpossibrealcontinuoumaximizatminimizatinvolvbranchmathdictionardictionardefinitionqindexprogramquadraticquadraticprogramdefinit}Qunitmultipldenotsymbolmathdictionardictionardefinitiontindexteradefinitnotherconventagrenobutreferrmaysecondknownalsofirstthirdcaserespectivesubmodulidealrespectholdanalogouintersectabcontainwithkernelimagisomorphicthetakerstatmodulringgroupsuchimposstructuralgebraicparticularsetsexisttheyconcernresultsetmathdictionardictionardefinitioniindextheoremisomorphismisomorphismtheoremdefinitquadratic_form,MathdictionaryHquadratic_form,definitionHquadratic_form,dictionaryHquadratic_form,mathdictionaryH quadratic_programming,Definitioni quadratic_programming,Dictionaryi$quadratic_programming,MathDictionaryi$quadratic_programming,Mathdictionaryi quadratic_programming,definitioni quadratic_programming,dictionaryi$quadratic_programming,mathdictionaryi quadratic_reciprocity,Definitionmh 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{TEXT -1 3 " a " } {HYPERLNK 45 "complete quadrangle" 5 "Definition/completequadrangle" "" }{TEXT -1 91 ", consisting of a total of six lines and all their points of intersection, including three " } {HYPERLNK 45 "diagonal points" 5 "Definition/diagonalpoint" "" }{TEXT -1 1 "." } } } " } {TEXT 39 3 "1. " } {TEXT -1 178 "a plane figure consisting of four points each joined by at least two lines to two other points. The line segments between the vertices may intersect (so that the figure is not a " } {HYPERLNK 45 "polygon" 5 "Definition/polygon" "" }{TEXT -1 19 "). A quadrangle is " } {TEXT 22 6 "convex" } {TEXT -1 31 " if both diagonals lie inside, " } {HYPERLNK 45 "re-entrant" 5 "Definition/re-entrant" "" }{TEXT -1 25 " if one lies outside and " } {TEXT 22 7 "crossed" } {TEXT -1 30 " if both lie outside. Compare " } {HYPERLNK 45 "quadrilateral" 5 "Definition/quadrilateral" "" }{TEXT -1 11 ". See also " } {HYPERLNK 45 "dual" 5 "Definition/dual" "" }{TEXT -1 2 ". " } } {PARA ϝdefinition,Quaternion݃quaternion definitiondefinition,Quatrefoil0quatrefoil definitiondefinition,Queueuqueue definitiondefinition,QueueingTheoryGqueueing theory definitiondefinition,Queueing_TheoryGqueueing theory definitiondefinition,Queueing_theoryGqueueing theory definitiondefinition,QueueingtheoryGqueueing theory definitiondefinition,Quinaryhquinary definitiondefinition,Quindecagonquindecagon definitiondefinition,Quintic*quintic definitiondictionary,Radius_of_torsionradius of torsion definitiondictionary,Radius_vector/radius vector definitiondictionary,Radiusofconvergence#/radius of convergence definitiondictionary,Radiusofcurvature!Kradius of curvature definitiondictionary,Radiusofgyration hradius of gyration definition"dictionary,Radiusofnormalcurvature(~radius of normal curvature definitiondictionary,Radiusoftorsionradius of torsion definitiondictionary,Radiusvector/radius vector definitiondefinition,quotientring4*factor ring definitionquotient ring definitiondefinition,quotientrule-quotient rule definitiondefinition,quotientspace6a^quotient space definitionfactor space definitiondefinition,quotienttopologyquotient topology definition definition,r7iR definitionreal number definitionyr definitiondefinition,r-module5eR-module definitiondefinition,r_module5eR-module definitiondefinition,raabe_testRaabe's test definitiondefinition,raabes_testRaabe's test definitiondefinition,raabestestRaabe's test definitionDefinition,Repeated_integrationD5repeated integration definitionF@multiple integration definitionDefinition,Repeated_root6pUmultiple root definitionbrepeated root definitionDefinition,Repeated_series,repeated series definitionDefinition,Repeatedintegral>?multiple integral definition`repeated integral definitionDefinition,RepeatedintegrationD5repeated integration definitionF@multiple integration definitionDefinition,Repeatedroot6pUmultiple root definitionbrepeated root definitionDefinition,Repeatedseries,repeated series definitionDefinition,RepeatingDecimal>!recurring decimal definitionrepeating decimal definitionQuadratic_Congruence,Dictionary*#Quadratic_Congruence,MathDictionary*#Quadratic_Congruence,Mathdictionary*Quadratic_Congruence,definition*Quadratic_Congruence,dictionary*#Quadratic_Congruence,mathdictionary* Quadratic_Convergence,DefinitionG Quadratic_Convergence,DictionaryG$Quadratic_Convergence,MathDictionaryG$Quadratic_Convergence,MathdictionaryG Quadratic_Convergence,definitionG Quadratic_Convergence,dictionaryG"quadraticcongruence,mathdictionary*quadraticconvergence,DefinitionGquadraticconvergence,DictionaryG#quadraticconvergence,MathDictionaryG#quadraticconvergence,MathdictionaryGquadraticconvergence,definitionGquadraticconvergence,dictionaryG#quadraticconvergence,mathdictionaryGquadraticequation,Definitionquadraticequation,Dictionary quadraticequation,MathDictionary quadraticequation,Mathdictionaryquadraticequation,definitionquadraticequation,dictionaryPlengthplacnumbsamesequencfinitelementalladvancmathdictionardictionardefinitioncindexpermutatcycliccyclicpermutatdefinitPOpisuminfinittendabssincconvergexamplspecialnextmagnitudlessalwayaddingaftererrorcasevaluabsolutzeromonotonicaldecreastermverifonlyneedestablishresultleibnizsalternatingseriestestleibnizleibnizalternatingseriestestmathdictionardictionardefinitionaindextestserialternatalternatingseriestestdefinitintegratdanieldaniellintegratdefinit*{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "quadratic congruence," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "congruence" 5 "Definition/congruence" "" }{TEXT -1 13 " of the form " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 22 1 "f" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 25 ") is congruent to 0 (mod " } {TEXT 22 1 "m" } {TEXT -1 2 ") " } } {PARA 0 "> " 0 "" {TEXT -1 6 "where " } {TEXT 22 2 "f " } {TEXT -1 5 "is a " } {HYPERLNK 45 "quadratic" 5 "Definition/quadratic" "" }{TEXT -1 1 " " } {HYPERLNK 45 "polynomial" 5 "Definition/polynomial" "" }{TEXT -1 36 " with integer coefficients. Compare " } {HYPERLNK 45 "quadratic residue" 5 "Definition/quadraticresidue" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "linear congruence" 5 "Definition/linearcongruence" "" }{TEXT -1 2 ". " } } } aU{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 14 "oblique angle," } } {PARA 0 "> " 0 "" {TEXT 22 3 "n. " } {TEXT -1 75 "any angle that is neither a right angle nor any multiple of a right angle. " } } } nit interval by the formula f[n](x) = (-1)^(i+1) if (i-1)/2^n <= x < i/2^n for each positive integer " } {TEXT 22 2 "n." } {TEXT -1 16 " Alternatively, " } {TEXT 22 4 "f[n]" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 42 ") can be defined to be the sign of sin(2^(" } {TEXT 22 1 "n" } {TEXT -1 3 ")pi" } {TEXT 22 1 "x" } {TEXT -1 30 "), for a non-negative integer " } {TEXT 22 2 "n." } {TEXT -1 59 " (Named after the German-born analyst and number theorist, " } {TEXT 22 22 "Hans Adolph Rademacher" } {TEXT -1 75 " (1892-1969), who was persecuted by the Nazis and took refuge in the USA.) " } } } dictionary,Synthetic_geometry synthetic geometry definitiondictionary,Synthetic_methodsynthetic proof definitiondictionary,Synthetic_proofsynthetic proof definition!dictionary,Synthetic_substitution synthetic division definitiondictionary,Syntheticdivision synthetic division definitiondictionary,Syntheticgeometry synthetic geometry definitiondictionary,Syntheticmethodsynthetic proof definitiondictionary,Syntheticproofsynthetic proof definitionMathdictionary,quadric quadric definitionMathdictionary,quadrilateralqquadrilateral definitionMathdictionary,quadrinomialquadrinomial definition#Mathdictionary,qualitative_identity"[qualitative identity definition"Mathdictionary,qualitativeidentity"[qualitative identity definitionMathdictionary,quality_control quality control definitionMathdictionary,qualitycontrol quality control definitionMathdictionary,quantic2]quantic definitionMathdictionary,quantifier quantifier definitiondefinition,quadraticconvergence#Gquadratic convergence definitiondefinition,quadraticequation quadratic equation definitiondefinition,quadraticformHquadratic form definitiondefinition,quadraticprogramming#iquadratic programming definitiondefinition,quadraticreciprocity#mhquadratic reciprocity definitiondefinition,quadraticresidueOQquadratic residue definitiondefinition,quadraticsquadratics definitiondefinition,quadratureequadrature definition#Quadraticprogramming,mathdictionaryiQuadraticreciprocity,DefinitionmhQuadraticreciprocity,Dictionarymh#Quadraticreciprocity,MathDictionarymh#Quadraticreciprocity,MathdictionarymhQuadraticreciprocity,definitionmhQuadraticreciprocity,dictionarymh#Quadraticreciprocity,mathdictionarymhQuadraticresidue,DefinitionOQQuadraticresidue,DictionaryOQQuadraticresidue,MathDictionaryOQQuadraticresidue,MathdictionaryOQQuadraticresidue,definitionOQQuadratic_Form,dictionaryHQuadratic_Form,mathdictionaryH Quadratic_Programming,Definitioni 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 22 "quadratic convergence," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "rate of convergence" 5 "Definition/rateofconvergence" "" }{TEXT -1 2 ". " } } } dictionary,quadratic_convergence#Gquadratic convergence definitiondictionary,quadratic_equation quadratic equation definitiondictionary,quadratic_formHquadratic form definition dictionary,quadratic_programming#iquadratic programming definition dictionary,quadratic_reciprocity#mhquadratic reciprocity definitiondictionary,quadratic_residueOQquadratic residue definitiondictionary,quadraticcongruence"*quadratic congruence definitiondictionary,quadraticconvergence#Gquadratic convergence definitiondictionary,quadraticequation quadratic equation definitiondictionary,quadraticformHquadratic form definitionDefinition,Quadratic_equation quadratic equation definitionDefinition,Quadratic_formHquadratic form definition Definition,Quadratic_programming#iquadratic programming definition Definition,Quadratic_reciprocity#mhquadratic reciprocity definitionDefinition,Quadratic_residueOQquadratic residue definitionDefinition,Quadraticcongruence"*quadratic congruence 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quality_control,Dictionary quality_control,MathDictionary quality_control,Mathdictionary quality_control,definition quality_control,dictionary quality_control,mathdictionary qualitycontrol,Definition qualitycontrol,Dictionary qualitycontrol,MathDictionary qualitycontrol,Mathdictionary qualitycontrol,definition qualitycontrol,dictionary qualitycontrol,mathdictionary 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quality control definitiondefinition,Quantic2]quantic definitiondefinition,Quantifier quantifier definitiondefinition,Quantify!quantify definitiondefinition,Quantityoquantity definitiondefinition,Quantizequantize definitiondefinition,Quarticquartic definitiondefinition,Quartilequartile definitiondefinition,Quasi quasi- definitiondefinition,Quasi- quasi- definitiondefinition,Quasi-Concaveq~quasi-concave definitionary,QuadraticProgrammingMathdictionary,QuadraticProgrammingmathdictionary,QuadraticProgrammingMathDictionary,Quadratic_ProgrammingMathdictionary,Quadratic_Programmingmathdictionary,Quadratic_ProgrammingMathDictionary,QuadraticprogrammingMathdictionary,Quadraticprogrammingmathdictionary,QuadraticprogrammingMathDictionary,Quadratic_programmingMathdictionary,Quadratic_programmingmathdictionary,Quadratic_programmingmingdictionary,quadraticprogrammingDictionary,quadratic_programmingdictionary,quadratic_programmingDictionary,QuadraticProgrammingdictionary,QuadraticProgrammingDictionary,Quadratic_Programmingdictionary,Quadratic_ProgrammingDictionary,Quadraticprogrammingdictionary,QuadraticprogrammingDictionary,Quadratic_programmingdictionary,Quadratic_programmingMathDictionary,quadraticprogrammingMathdictionary,quadraticprogrammingmathdictionary,quadraticprogrammingMathDictionary,quadratic_programmingMathdictionary,quadratic_programmingmathdictionary,quadratic_programmingMathDictionmhs{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "quadratic reciprocity" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 20 "Gaussian reciprocity" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 47 " the important number-theoretic result that if " } {TEXT 22 1 "p" } {TEXT -1 5 " and " } {TEXT 22 1 "q" } {TEXT -1 33 " are distinct odd prime numbers, " } {TEXT 22 1 "p" } {TEXT -1 6 " is a " } {HYPERLNK 45 "quadratic residue" 5 "Definition/quadraticresidue" "" }{TEXT -1 4 " of " } {TEXT 22 1 "q" } {TEXT -1 16 " if and only if " } {TEXT 22 1 "q" } {TEXT -1 27 " is a quadratic residue of " } {TEXT 22 1 "p" } {TEXT -1 18 ", unless both are " } {HYPERLNK 45 "congruent" 5 "Definition/congruent" "" }{TEXT -1 68 " to 3 modulo 4, in which case the opposite holds: in that one case, " } {TEXT 22 1 "p" } {TEXT -1 27 " is a quadratic residue of " } {TEXT 22 1 "q" } {TEXT -1 16 " if and only if " } {TEXT 22 2 "q " } {TEXT -1 30 "is not a quadratic residue of " } {TEXT 22 2 "p." } {TEXT -1 1 " " } } } -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 21 "quadratic reciprocity" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 20 "Gaussian reciprocity" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 47 " the important number-theoretic result that if " } {TEXT 22 1 "p" } {TEXT -1 5 " and " } {TEXT 22 1 "q" } {TEXT -1 33 " are distinct odd prime numbers, " } {TEXT 22 1 "p" } {TEXT -1 6 " is a " } {HYPERLNK 45 "quadratic residue" 5 "Definition/quadraticresidue" "" }{TEXT -1 4 " of " } {TEXT 22 1 "q" } {TEXT -1 16 " if and only if " } {TEXT 22 1 "q" } {TEXT -1 27 " is a quadratic residue of " } {TEXT 22 1 "p" } {TEXT -1 18 ", unless both are " } {HYPERLNK 45 "congruent" 5 "Definition/congruent" "" }{TEXT -1 68 " to 3 modulo 4, in which case the opposite holds: in that one case, " } {TEXT 22 1 "p" } {TEXT -1 27 " is a quadratic residue of " } {TEXT 22 1 "q" } {TEXT -1 definition,Radius_of_torsionradius of torsion definitiondefinition,Radius_vector/radius vector definitiondefinition,Radiusofconvergence#/radius of convergence definitiondefinition,Radiusofcurvature!Kradius of curvature definitiondefinition,Radiusofgyration hradius of gyration definition"definition,Radiusofnormalcurvature(~radius of normal curvature definitiondefinition,Radiusoftorsionradius of torsion definitiondefinition,Radiusvector/radius vector definition Dictionary,Quasi_Linear_Equation#Tquasi-linear equation definitionDictionary,Quasi_Metrictquasi-metric definitionDictionary,Quasi_Newton_Method!ېquasi-Newton method definitionDictionary,Quasi_Orderingquasi-ordering definitionDictionary,Quasi_Quotationwquasi-quotation definitionDictionary,Quasi_Tautologyquasi-tautology definitionDictionary,Quasi_concaveq~quasi-concave definitionDictionary,Quasi_convexwquasi-convex definitionDictionary,Quasi_groupquasi-group definitionDictionary,Qualitycontrol quality control 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programming definition#MathDictionary,Quadraticreciprocity#mhquadratic reciprocity definitionMathDictionary,QuadraticresidueOQquadratic residue definitionMathDictionary,Quadraticsquadratics definitionMathDictionary,Quadratureequadrature definitionMathDictionary,Quadric quadric definitionMathDictionary,Quadrilateralqquadrilateral definition#Mathdictionary,QuadraticReciprocity#mhquadratic reciprocity definitionMathdictionary,QuadraticResidueOQquadratic residue definition#Mathdictionary,Quadratic_Congruence"*quadratic congruence definition$Mathdictionary,Quadratic_Convergence#Gquadratic convergence definition!Mathdictionary,Quadratic_Equation quadratic equation definitionMathdictionary,Quadratic_FormHquadratic form definition$Mathdictionary,Quadratic_Programming#iquadratic programming definition$Mathdictionary,Quadratic_Reciprocity#mhquadratic reciprocity definition Mathdictionary,Quadratic_ResidueOQquadratic residue definition#Mathdictionary,Quadratic_congruence"*quadratic congruence definition#mathdictionary,Quadraticconvergence#Gquadratic convergence definition mathdictionary,Quadraticequation quadratic equation definitionmathdictionary,QuadraticformHquadratic form definition#mathdictionary,Quadraticprogramming#iquadratic programming definition#mathdictionary,Quadraticreciprocity#mhquadratic reciprocity definitionmathdictionary,QuadraticresidueOQquadratic residue definitionmathdictionary,Quadraticsquadratics definitionmathdictionary,Quadratureequadrature definitionDefinition,gaussianplane8)DGaussian plane definition5Argand diagram definitionDefinition,gaussianreciprocityEYGaussian reciprocity definitionmhquadratic reciprocity definition!Definition,gaussjordaneliminationFGauss-Jordan elimination definitioniJordan elimination definitionDefinition,gausslemmavQ_Expansion,DictionaryQ_binomial,definitionYQbinomial,DictionarytQef,mathdictionaryFQr_Algorithm,DefinitionQseries,MathdictionaryQuadrant,dictionaryQuadratic,DefinitionQuadraticConvergence,Definitionȝ QuadraticEquation,mathdictionaryQuadraticProgramming,dictionaryQuadratic_Congruence,Definitionԝ Quadratic_Convergence,dictionaryɝQuadratic_Form,definitionݝ$Quadratic_Reciprocity,MathDictionary $Quasi-Linear_Equation,mathdictionaryTQuasi-Metric,DefinitiontQuasi-Metric,DictionarytQuasi-Metric,MathDictionarytQuasi-Metric,MathdictionarytQuasi-Metric,definitiontQuasi-Metric,dictionarytQuasi-Metric,mathdictionarytQuasi-NewtonMethod,DefinitionېQuasi-NewtonMethod,Dictionaryې!Quasi-NewtonMethod,MathDictionaryې!Quasi-NewtonMethod,MathdictionaryېQuasi-NewtonMethod,definitionېQuasi-NewtonMethod,dictionaryېe{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "quadrature," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 1 " " } {TEXT 39 2 "1." } {TEXT -1 109 " the construction of a square with the same area as a given figure or surface, especially a circle. See also " } {HYPERLNK 45 "constructible" 5 "Definition/constructible" "" }{TEXT -1 2 ". " } {TEXT 39 3 "2. " } {TEXT -1 85 "the calculation of planar areas by repeated use of quadrature in the previous sense. " } {TEXT 39 2 "3." } {TEXT -1 1 " " } {TEXT 39 21 "numerical quadrature." } {TEXT -1 137 " the evaluation of a definite integral by a formula involving weighted sums of function values at given points. The rule is said to have " } {TEXT 22 7 "order n" } {TEXT -1 52 " if it is exact for polynomials of that degree. The " } {HYPERLNK 45 "trapezoidal rule" 5 "Definition/trapezoidalrule" "" }{TEXT -1 19 " has or der 1 while " } {HYPERLNK 45 "Simpson's rule" 5 "Definition/Simpsonsrule" "" }{TEXT -1 14 " has order 3. " } {TEXT 39 2 "4." } {TEXT -1 1 " " } {TEXT 39 26 "integration by quadrature." } {TEXT -1 50 " symbolic integration in terms of known functions." } } } 1 " " } {TEXT 39 2 "1." } {TEXT -1 109 " the construction of a square with the same area as a given figure or surface, especially a circle. See also " } {HYPERLNK 45 "constructible" 5 "Definition/constructible" "" }{TEXT -1 2 ". " } {TEXT 39 3 "2. " } {TEXT -1 85 "the calculation of planar areas by repeated use of quadrature in the previous sense. " } {TEXT 39 2 "3." } {TEXT -1 1 " " } {TEXT 39 21 "numerical quadrature." } {TEXT -1 137 " the evaluation of a definite integral by a formula involving weighted sums of function values at given points. The rule is said to have " } {TEXT 22 7 "order n" } {TEXT -1 52 " if it is exact for polynomials of that degree. The " } {HYPERLNK 45 "trapezoidal rule" 5 "Definition/trapezoidalrule" "" }{TEXT -1 19 " has or Queueingtheory,DictionaryGQueueingtheory,MathDictionaryGQueueingtheory,MathdictionaryGQueueingtheory,definitionGQueueingtheory,dictionaryGQueueingtheory,mathdictionaryGQuinary,DefinitionhQuinary,DictionaryhQuinary,MathDictionaryhQuinary,MathdictionaryhQuinary,definitionhQuinary,dictionaryhQuinary,mathdictionaryhQuindecagon,DefinitionQuindecagon,DictionaryQuindecagon,MathDictionaryquantify,dictionary!quantify,mathdictionary!quantity,Definitionoquantity,Dictionaryoquantity,MathDictionaryoquantity,Mathdictionaryoquantity,definitionoquantity,dictionaryoquantity,mathdictionaryoquantize,Definitionquantize,Dictionaryquantize,MathDictionaryquantize,Mathdictionaryquantize,definitionquantize,dictionaryquantize,mathdictionaryquartic,Definition Dictionary,QuodEratDemonstrandum%(quod erat demonstrandum definitionDictionary,QuodEratFaciendum!Vquod erat faciendum 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quasi,definition quasi,dictionary Qualitativeidentity,Dictionary["Qualitativeidentity,MathDictionary["Qualitativeidentity,Mathdictionary[Qualitativeidentity,definition[Qualitativeidentity,dictionary["Qualitativeidentity,mathdictionary[QualityControl,Definition QualityControl,Dictionary QualityControl,MathDictionary QualityControl,Mathdictionary QualityControl,definition QualityControl,dictionary QualityControl,mathdictionary Quality_Control,Definition Quality_Control,Dictionary Quality_Control,MathDictionary Quality_Control,Mathdictionary Quality_Control,definition Quality_Control,dictionary Quality_Control,mathdictionary Quality_control,Definition Quality_control,Dictionary Quality_control,MathDictionary Quality_control,Mathdictionary Quality_control,definition Quality_control,dictionary Quality_control,mathdictionary Qualitycontrol,Definition Qualitycontrol,Dictionary Qualitycontrol,MathDictionary Qualitycontrol,Mathdictionary Qualitycontrol,definition Qualitycontrol,dictionary Qualitycontrol,mathdictionary Quantic,Definition2]Quantic,Dictionary2]Quantic,MathDictionary2]Quantic,Mathdictionary2]Quantic,definition2]Quantic,dictionary2]{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "quartile," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 10 "Statistics" } {TEXT -1 137 ") any of the three values of a variable that divide its distribution into four intervals with equal probability; the 25th, 50th, or 75th " } {HYPERLNK 45 "percentiles" 5 "Definition/percentile" "" }{TEXT -1 53 ". 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identity definitionmathdictionary,quality_control quality control definitionmathdictionary,qualitycontrol quality control definitionmathdictionary,quantic2]quantic definitionmathdictionary,quantifier quantifier definition΀orderwithequinumerouthusfunctrangmembermathdictionardictionardefinitioniindexsequencinfinitinfinitesequencdefinit cbasiwithdefinmathdictionardictionardefinitioncindextensorcartesiancartesiantensordefinit alsosuchlogicextendanalogouanyrealallexamplquantificatspecifnecessarformulasemanticlogicianwrittenrenderoccurgeneralitindicatvariablcontainsymbolmathdictionardictionardefinitionqindexquantifidefinit%Omathdictionardictionardefinitiondindexperiodicdoubdoublyperiodicdefinit Definition,undefinedelementdefinition,undefinedelementDefinition,undefined_elementdefinition,undefined_elementDefinition,UndefinedElementdefinition,UndefinedElementDefinition,Undefined_Elementdefinition,Undefined_ElementDefinition,Undefinedelementdefinition,UndefinedelementDefinition,Undefined_elementdefinition,Undefined_elementDictionary,undefinedelementdictionary,undefinedelementDictionary,undefined_elementdictionary,undefined_elementDictionary,UndefinedElementdictionary,UndefinedElementDictionary,Undefined_Elementdictionary,Undefined_ElementDictionary,Undefinedelementdictionary,UndefinedelementDictionary,Undefined_elementdictionary,Undefined_elementMathDictionary,undefinedelementMathdictionary,undefinedelementmathdictionary,undefinedelementMathDictionary,undefined_elementMathdictionary,undefined_elementmathdictionary,undefined_elementMathDictionary,UndefinedElementMathdictionary,UndefinedElementmathdictionary,UndefinedElementMathDictionary,Undefined_ElementMalionary,QualitycontrolMathdictionary,Qualitycontrolmathdictionary,QualitycontrolMathDictionary,Quality_controlMathdictionary,Quality_controlmathdictionary,Quality_controlion,Quality_Controldefinition,Quality_ControlDefinition,Qualitycontroldefinition,QualitycontrolDefinition,Quality_controldefinition,Quality_controlDictionary,qualitycontroldictionary,qualitycontrolDictionary,quality_controldictionary,quality_controlDictionary,QualityControldictionary,QualityControlDictionary,Quality_Controldictionary,Quality_ControlDictionary,Qualitycontroldictionary,QualitycontrolDictionary,Quality_controldictionary,Quality_controlMathDictionary,qualitycontrolMathdictionary,qualitycontrolmathdictionary,qualitycontrolMathDictionary,quality_controlMathdictionary,quality_controlmathdictionary,quality_controlMathDictionary,QualityControlMathdictionary,QualityControlmathdictionary,QualityControlMathDictionary,Quality_ControlMathdictionary,Quality_Controlmathdictionary,Quality_ControlMathDict#2]c{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 8 "quantic," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 113 " a homogeneous function of two or more variables in a form with rational and integral coefficients, especially a " } {HYPERLNK 45 "quadratic form" 5 "Definition/quadraticform" "" }{TEXT -1 15 "; for example, " } {TEXT 22 1 "x" } {TEXT -1 6 "^2 + 3" } {TEXT 22 4 "xyz " } {TEXT -1 2 "+ " } {TEXT 22 1 "y" } {TEXT -1 33 "^2 is a ternary quadric quantic. " } } } [3Definition,planegeometryplane geometry definition\CDefinition,Riemann-LebesguelemmaRiemann-Lebesgue lemma definition+\JDefinition,generalizeddeltafunctiongeneralized delta function definitionB\$Definition,randomrandom definitionJ\=Definition,trivialultrafiltertrivial ultrafilter definition_\&Definition,densitydensity definitionh\1Definition,excessdemandexcess demand definition\/Definition,integerpartinteger part definition\"Definition,tonnetonne definition\5Definition,descentmethodsdescent methods definition\,Definition,serpentineserpentine definition\;Definition,indicatorfunctionindicator function definition\/Definition,factorgroupfactor group definition\ Definition,walkwalk definition\-Definition,convexhullconvex hull definition\@Definition,partiallyorderedsetpartially ordered set definition\=Definition,functionalanalysisfunctional analysis definition\=Definition,indirectproportionindirect proportion definition ]1Definition,aliquantpartaliquant part definition ]9Definition,priorprobabilityprior probability definition ]Definition,aea.e. definition]1Definition,solublegroupsoluble group definition(]2Definition,reciprocationreciprocation definition2]&Definition,quanticquantic definition5]EDefinition,characteristicfunctioncharacteristic function definitionQuartic,definitionQuartic,dictionaryQuartic,mathdictionaryQuartile,DefinitionQuartile,DictionaryQuartile,MathDictionaryQuartile,MathdictionaryQuartile,definitionQuartile,dictionaryQuartile,mathdictionaryQuasi,Definition Quasi,Dictionary Quasi,MathDictionary Quasi,Mathdictionary Quasi,definition Quasi,dictionary Quasi,mathdictionary Scmathdictionary,Quotient_Ruledmathdictionary,Quotientgroupfmathdictionary,R_moduleQ mathdictionary,RacecourseParadoxu!mathdictionary,Rademacher_Theoremmathdictionary,Radial_componentɟmathdictionary,Radical_Centermathdictionary,Radicalfraction$mathdictionary,Radius_Of_Convergence !mathdictionary,Radius_of_gyration&&mathdictionary,Radiusofnormalcurvature(mathdictionary,Radix_point~%mathdictionary,RadonNikodymDerivative~Definition,rademacherfunctions"bRademacher functions definitionDefinition,rademachertheorem  Rademacher theorem definitionDefinition,radial]radial definitionDefinition,radial_componentradial component definitionDefinition,radialcomponentradial component definitionDefinition,radianradian definitionDefinition,radical radical definitionDefinition,radical_axis8radical axis definitionDefinition,radical_centerradical center definitionDefinition,quasi-orderingDefinition,quasiorderingdefinition,quasiorderingDefinition,quasi_orderingdefinition,quasi_orderingDefinition,QuasiOrderingdefinition,QuasiOrderingDefinition,Quasi_Orderingdefinition,Quasi_OrderingDefinition,Quasiorderingdefinition,QuasiorderingDefinition,Quasi_orderingdefinition,Quasi_orderingDictionary,quasiorderingdictionary,quasiorderingDictionary,quasi_orderingdictionary,quasi_orderingDictionary,QuasiOrderingdictionary,QuasiOrderingDictionary,Quasi_Orderingdictionary,Quasi_OrderingDictionary,Quasiorderingdictionary,QuasiorderingDictionary,Quasi_orderingdictionary,Quasi_orderingMathDictionary,quasiorderingMathdictionary,quasiorderingmathdictionary,quasiorderingMathDictionary,quasi_orderingMathdictionary,quasi_orderingmathdictionary,quasi_orderingMathDictionary,QuasiOrderingMathdictionary,QuasiOrderingmathdictionary,QuasiOrderingMathDictionary,Quasi_OrderingMathdictionary,Quasi_Orderingmathdictionary,Quasi_OrderingMathDictionary,Qua؞ ]precedusualextractquantitnumbmathdictionardictionardefinitionrindexradicanddefinit comparspacrepresentatrightleftpointgraphdimensionalverticalconventionalsystemaxesmathdictionardictionaryaxidefinitionindexaxisdefinit circlpointexamplzeroparametcoefficisettobtainoftensimplequivalentittypesomecaselimitmathdictionardictionardefinitiondindexdegeneratdefinit writtenusualmainthemonlyfalscomponbotheithtruesentencformenglishcorrespondconnectsententialbinarbiconditionalcallalsootherimpleachtheystatementbetweenholdrelatmathdictionardictionardefinitionindexequivalencdefinitq{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 14 "quadrilateral," } } {PARA 0 "> " 0 "" {TEXT 39 2 "1." } {TEXT -1 1 " " } {TEXT 22 4 "adj." } {TEXT -1 33 " having or formed by four sides. " } } {PARA 0 "> " 0 "" {TEXT 39 3 "2a." } {TEXT -1 1 " " } {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 14 "as substantive" } {TEXT -1 21 ") more rarely called " } {TEXT 39 8 "tetragon" } {TEXT -1 160 ", a four-sided polygon; a plane figure bounded by four straight line segments, each joining two vertices and not intersecting elsewhere between the vertices. A " } {HYPERLNK 45 "quadrangle" 5 "Definition/quadrangle" "" }{TEXT -1 44 " is thus not a quadrilateral unless it is a " } {HYPERLNK 45 "polygon" 5 "Definition/polygon" "" }{TEXT -1 2 ". " } {TEXT 39 2 "b." } {TEXT -1 1 " " } {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "complete quadrilateral" 5 "Definition/complete-quadrilateral" "" }{TEXT -1 154 " that consists of four infinite lines, all six of their points of intersection, and three diagonals on which opposite pairs of these points lie. See also " } {HYPERLNK 45 "dual" 5 "Definition/dual" "" }{TEXT -1 2 ". " } } } -1 1 " " } {TEXT 22 4 "adj." } {TEXT -1 33 " having or formed by four sides. " } } {PARA 0 "> " 0 "" {TEXT 39 3 "2a." } {TEXT -1 1 " " } {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 14 "as substantive" } {TEXT -1 21 ") more rarely called " } {TEXT 39 8 "tetragon" } {TEXT -1 160 ", a four-sided polygon; a plane figure bounded by four straight line segments, each joining two vertices and not intersecting elsewhere between the vertices. A " } {HYPERLNK 45 "quadrangle" 5 "Definition/quadrangle" "" }{TEXT -1 44 " is thus not a quadrilateral unless it is a " } {HYPERLNK 45 "polygon" 5 "Definition/polygon" "" }{TEXT -1 2 ". " } {TEXT 39 2 "b." } {TEXT -1 1 " " } {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "complete quadrilateral" 5 "Definition/complete-uDefinition,queuedefinition,queueDefinition,Queuedefinition,QueueDictionary,queuedictionary,queueDictionary,Queuedictionary,QueueMathDictionary,queueMathdictionary,queuemathdictionary,queueMathDictionary,QueueMathdictionary,Queuemathdictionary,Queuedictionary,Quotientspace6a^quotient space definitionfactor space definitiondictionary,Quotienttopologyquotient topology definition dictionary,R7iR definitionreal number definitionyr definitiondictionary,R-Module5eR-module definitiondictionary,RModule5eR-module definitiondictionary,R_Module5eR-module definitiondictionary,R_module5eR-module definitiondictionary,RaabeTestRaabe's test definitiondictionary,Raabe_TestRaabe's test definitiondictionary,Raabe_testRaabe's test definitiondictionary,RaabesTestRaabe's test definitionDefinition,Rate_of_change rate of change definitionDefinition,Rate_of_convergence![rate of convergence definitionDefinition,Rateofchange rate of change definitionDefinition,Rateofconvergence![rate of convergence definitionDefinition,Ratioratio definitionDefinition,RatioOfSimilitude!Vratio of similitude definitionDefinition,RatioScale!ratio scale definitionDefinition,RatioTestWratio test definitionDefinition,RatioTheorem8 Xratio theorem definitionsection formula definitionDefinition,Ratio_Of_Similitude!Vratio of similitude definitionDefinition,Ratio_Scale!ratio scale definitionDefinition,Ratio_TestWratio test definitionDefinition,Ratio_Theorem8 Xratio theorem definitionsection formula definitionDefinition,Ratio_of_similitude!Vratio of similitude definitionMathdictionary,Quasi- quasi- definitionMathdictionary,Quasi-Concaveq~quasi-concave definitionMathdictionary,Quasi-Convexwquasi-convex definitionMathdictionary,Quasi-Groupquasi-group definitionMathdictionary,Quasi-Linearqquasi-linear definition#Mathdictionary,Quasi-LinearEquation#Tquasi-linear equation definition$Mathdictionary,Quasi-Linear_Equation#Tquasi-linear equation definitionMathdictionary,Quasi-Metrictquasi-metric definition!Mathdictionary,Quasi-NewtonMethod!ېquasi-Newton method definition"Mathdictionary,Quasi-Newton_Method!ېquasi-Newton method definitionMathdictionary,Quasi-Orderingquasi-ordering definitionMathdictionary,Quasi-Quotationwquasi-quotation definitionMathdictionary,Quasi-Tautologyquasi-tautology definition$Mathdictionary,Quasi-linear_equation#Tquasi-linear equation definition#Mathdictionary,Quasi-linearequation#Tquasi-linear equation definition#MathDictionary,qualitative_identity"[qualitative identity definition"MathDictionary,qualitativeidentity"[qualitative identity definitionMathDictionary,quality_control quality control definitionMathDictionary,qualitycontrol quality control definitionMathDictionary,quantic2]quantic definitionMathDictionary,quantifier quantifier definitionMathDictionary,quantify!quantify definitionMathDictionary,quantityoquantity definitionMathDictionary,quantizequantize definitionMathDictionary,Qualitycontrol quality control definitionMathDictionary,Quantic2]quantic definitionMathDictionary,Quantifier quantifier definitionMathDictionary,Quantify!quantify definitionMathDictionary,Quantityoquantity definitionMathDictionary,Quantizequantize definitionMathDictionary,Quarticquartic definitionMathDictionary,Quartilequartile definitionMathDictionary,Quasi quasi- definitionMathDictionary,Quasi- quasi- definitiono={VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "quantity," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 1 " " } {TEXT 39 3 "1. " } {TEXT -1 51 "an entity that has a magnitude or numerical value. " } {TEXT 39 2 "2." } {TEXT -1 62 " a numerical expression; a variable that ranges over numbers. " } {TEXT 39 2 "3." } {TEXT -1 2 " (" } {TEXT 22 5 "Logic" } {TEXT -1 56 ") the property of being either universal or particular. " } } }  H {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "quantifier," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 5 "Logic" } {TEXT -1 2 ") " } {TEXT 39 2 "1." } {TEXT -1 13 " a symbol of " } {HYPERLNK 45 "predicate calculus" 5 "Definition/predicatecalculus" "" }{TEXT -1 62 " that contains a variable and indicates the generality of the " } {HYPERLNK 45 "open sentence" 5 "Definition/opensentence" "" }{TEXT -1 36 " in which that variable occurs. The " } {HYPERLNK 45 "existential quantifier" 5 "Definition/existentialquantifier" "" }{TEXT -1 13 " is rendered " } {TEXT 22 17 "there exists an F" } {TEXT -1 2 ", " } {TEXT 22 12 "something Fs" } {TEXT -1 2 ", " } {TEXT 22 8 "Fs exist" } {TEXT -1 5 ", or " } {TEXT 22 17 "something is an F" } {TEXT -1 6 ". The " } {HYPERLNK 45 "universal quantifier" 5 "Definition/universalquantifier" "" }{TEXT -1 13 " is bcitydictionary,Gaussian_ReciprocityDictionary,Gaussianreciprocitydictionary,GaussianreciprocityDictionary,Gaussian_reciprocitydictionary,Gaussian_reciprocityMathDictionary,gaussianreciprocityMathdictionary,gaussianreciprocitymathdictionary,gaussianreciprocityMathDictionary,gaussian_reciprocityMathdictionary,gaussian_reciprocitymathdictionary,gaussian_reciprocityMathDictionary,GaussianReciprocityMathdictionary,GaussianReciprocitymathdictionary,GaussianReciprocityMathDictionary,Gaussian_ReciprocityMathdictionary,Gaussian_Reciprocitymathdictionary,Gaussian_ReciprocityMathDictionary,GaussianreciprocityMathdictionary,Gaussianreciprocitymathdictionary,GaussianreciprocityMathDictionary,Gaussian_reciprocityMathdictionary,Gaussian_reciprocitymathdictionary,Gaussian_reciprocitytyDictionary,gaussianreciprocitydictionary,gaussianreciprocityDictionary,gaussian_reciprocitydictionary,gaussian_reciprocityDictionary,GaussianReciprocitydictionary,GaussianReciprocityDictionary,Gaussian_Recipro6OQ{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 18 "quadratic residue," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 10 " a number " } {HYPERLNK 45 "congruent" 5 "Definition/congruent" "" }{TEXT -1 41 " to a perfect square to a given modulus; " } {TEXT 22 2 "a " } {TEXT -1 28 "is a quadratic residue (mod " } {TEXT 22 1 "n" } {TEXT -1 17 ") if and only if " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 22 1 "x" } {TEXT -1 22 "^(2 ) is congruent to " } {TEXT 22 2 "a " } {TEXT -1 5 "(mod " } {TEXT 22 1 "n" } {TEXT -1 26 ") is soluble for integral " } {TEXT 22 2 "x." } {TEXT -1 6 " When " } {TEXT 22 2 "n " } {TEXT -1 40 "is prime, this holds precisely when the " } {HYPERLNK 45 "Legendre symbol" 5 "Definition/Legendresymbol" "" }{TEXT -1 3 ", (" } {TEXT 22 1 "a" } {TEXT -1 1 "|" } {TEXT 22 1 "n" } {TEXT -1 13 "), is unity. " } } } Dictionary,quasi_convexwquasi-convex definitionDictionary,quasi_groupquasi-group definitionDictionary,quasi_linearqquasi-linear definition Dictionary,quasi_linear_equation#Tquasi-linear equation definitionDictionary,quasi_metrictquasi-metric definitionDictionary,quasi_newton_method!ېquasi-Newton method definitionDictionary,quasi_orderingquasi-ordering definitionDictionary,quasi_quotationwquasi-quotation definitionDictionary,quasi_tautologyquasi-tautology definitionDictionary,quasiconcaveq~quasi-concave definitionDictionary,quasiconvexwquasi-convex definition#Definition,Ramified_Theory_Of_Types&ramified theory of types definition#Definition,Ramified_theory_of_types&ramified theory of types definition Definition,Ramifiedtheoryoftypes&ramified theory of types definitionDefinition,RamseyNumbersRamsey numbers definitionDefinition,RamseyTheoremG Ramsey theorem definitionDefinition,Ramsey_NumbersRamsey numbers definitionDefinition,Ramsey_TheoremG Ramsey theorem definitionDefinition,Ramsey_numbersRamsey numbers definition"Dictionary,radiusofnormalcurvature(~radius of normal curvature definitionDictionary,radiusoftorsionradius of torsion definitionDictionary,radiusvector/radius vector definitionDictionary,radixradix definitionDictionary,radix_fractionVradix fraction definitionDictionary,radix_point0radix point definitionDictionary,radixfractionVradix fraction definitionDictionary,radixpoint0radix point definition#Dictionary,radon-nikodym_derivative&Radon-Nikodym derivative definition Dictionary,radon-nikodym_theorem##Radon-Nikodym theorem definition"Dictionary,radon-nikodymderivative&Radon-Nikodym derivative definitionDictionary,radon-nikodymtheorem##Radon-Nikodym theorem definitionDictionary,radon_measureBbbRadon measure definition*Riemann-Stieltjes measure definition#Dictionary,radon_nikodym_derivative&Radon-Nikodym derivative definitionDefinition,Radm " 0 "" {TEXT -1 9 "quantize," } } {PARA 0 "> " 0 "" {TEXT 22 3 "vb." } {TEXT -1 88 " to restrict a quantity or variable to values that are integral multiples of some unit. " } } } =Ζcomparsequencinfinitdoubsummablsquarspacdefinoperatorlinearmathdictionardictionardefinitionbindexshiftbilateralbilateralshiftdefinit>΁betweendistinguishavoidorigindifferhavingregardgeneralsuchtheorrusselsolvablformsamesuperficialalthoughonlyfollowlongbutsincshortexamplthemselvdescribdoworddescriptdefinresultmathematiciangermandiscoversemanticheterologicalheterologicalparadoxgrellingmathdictionardictionargrellingparadoxdefinitiongindexparadoxgrellgrellingsparadoxdefinitiodicdefinit!2{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 9 "quantify," } } {PARA 0 "> " 0 "" {TEXT 22 3 "vb." } {TEXT -1 1 " " } {TEXT 39 3 "1. " } {TEXT -1 56 "to discover a numerical value or to express a quantity. " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 39 2 "2." } {TEXT -1 2 " (" } {TEXT 22 5 "Logic" } {TEXT -1 25 ") to use a quantifier to " } {HYPERLNK 45 "bind" 5 "Definition/bind" "" }{TEXT -1 13 " a variable. " } } } KwDefinition,quotientgroupdefinition,quotientgroupDefinition,quotient_groupdefinition,quotient_groupDefinition,QuotientGroupdefinition,QuotientGroupDefinition,Quotient_Groupdefinition,Quotient_GroupDefinition,Quotientgroupdefinition,QuotientgroupDefinition,Quotient_groupdefinition,Quotient_groupDictionary,quotientgroupdictionary,quotientgroupDictionary,quotient_groupdictionary,quotient_groupDictionary,QuotientGroupdictionary,QuotientGroupDictionary,Quotient_Groupdictionary,Quotient_GroupDictionary,Quotientgroupdictionary,QuotientgroupDictionary,Quotient_groupdictionary,Quotient_groupMathDictionary,quotientgroupMathdictionary,quotientgroupmathdictionary,quotientgroupMathDictionary,quotient_groupMathdictionary,quotient_groupmathdictionary,quotient_groupMathDictionary,QuotientGroupMathdictionary,QuotientGroupmathdictionary,QuotientGroupMathDictionary,Quotient_GroupMathdictionary,Quotient_Groupmathdictionary,Quotient_GroupMathDictionary,QuotientgroupMathdictionary,definition,QuasiConvexwquasi-convex definitiondefinition,QuasiGroupquasi-group definitiondefinition,QuasiLinearqquasi-linear definitiondefinition,QuasiLinearEquation#Tquasi-linear equation definitiondefinition,QuasiMetrictquasi-metric definitiondefinition,QuasiNewtonMethod!ېquasi-Newton method definitiondefinition,QuasiOrderingquasi-ordering definitiondefinition,QuasiQuotationwquasi-quotation definitiondefinition,QuasiTautologyquasi-tautology definitiondefinition,Quasi_Concaveq~quasi-concave definitiondefinition,Quasi_Convexwquasi-convex definitiondefinition,Quasi_Groupquasi-group definitiondefinition,Quasi_Linearqquasi-linear definitiondefinition,quasilinearequation#Tquasi-linear equation definitiondefinition,quasimetrictquasi-metric definitiondefinition,quasinewtonmethod!ېquasi-Newton method definitiondefinition,quasiorderingquasi-ordering definitiondefinition,quasiquotationwquasi-quotation definitiondefinition,quasitautologyquasi-tautology definitiondefinition,quaternaryquaternary definitiondefinition,quaternion݃quaternion definitiondefinition,quatrefoil0quatrefoil definitionto determine the expected queue lengths, waiting times, etc. in a steady state of the system. " } } } 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "queueing theory," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 44 " the mathematical study of waiting lines or " } {TEXT 22 7 "queues." } {TEXT -1 206 " A typical model considers customers entering a queue, often when the time between successive customers is exponentially distributed, in which case the number of customers per unit time is distributed as a " } {HYPERLNK 45 "Poisson distribution" 5 "Definition/Poissondistribution" "" }{TEXT -1 252 ". The queue has a finite or infinite bound, and there is some mechanism for serving customers (often first come, first served) in a number of parallel service channels. The service time for each customer is also described probabilistically, often by a " } {HYPERLNK 45 "gamma distribution" 5 "Definition/gammadistribution" "" }{TEXT -1 121 ". The theory then attempts Cdefinition,Rational_polynomial!#jrational polynomial definition definition,Rational_root_theorem#4rational root theorem definitiondefinition,Rationalelement8rational element definitiondefinition,Rationalform0rational form definitiondefinition,Rationalfunctionmrational function definitiondefinition,Rationalizerationalize definitiondefinition,Rationalnumber.+rational number definitiondefinition,Rationalpolynomial!#jrational polynomial definitionMathDictionary,quarticquartic definitionMathDictionary,quartilequartile definitionMathDictionary,quasi quasi- definitionMathDictionary,quasi- quasi- definitionMathDictionary,quasi-concaveq~quasi-concave definitionMathDictionary,quasi-convexwquasi-convex definitionMathDictionary,quasi-groupquasi-group definitionMathDictionary,quasi-linearqquasi-linear definition$MathDictionary,quasi-linear_equation#Tquasi-linear equation definition$Quasi-linear_equation,mathdictionaryTQuasi-linearequation,DefinitionTQuasi-linearequation,DictionaryT#Quasi-linearequation,MathDictionaryT#Quasi-linearequation,MathdictionaryTQuasi-linearequation,definitionTQuasi-linearequation,dictionaryT#Quasi-linearequation,mathdictionaryTQuasi-newton_method,DefinitionېQuasi-newton_method,Dictionaryې"Quasi-newton_method,MathDictionaryې"Quasi-newton_method,MathdictionaryېQuasi-newton_method,definitionېQuasi_Group,mathdictionaryQuasi_Linear,DefinitionqQuasi_Linear,DictionaryqQuasi_Linear,MathDictionaryqQuasi_Linear,MathdictionaryqQuasi_Linear,definitionqQuasi_Linear,dictionaryqQuasi_Linear,mathdictionaryq Quasi_Linear_Equation,DefinitionT Quasi_Linear_Equation,DictionaryT$Quasi_Linear_Equation,MathDictionaryT$Quasi_Linear_Equation,MathdictionaryT Quasi_Linear_Equation,definitionT Quasi_Linear_Equation,dictionaryTQuadraticresidue,dictionaryOQQuadraticresidue,mathdictionaryOQQuadratics,DefinitionQuadratics,DictionaryQuadratics,MathDictionaryQuadratics,MathdictionaryQuadratics,definitionQuadratics,dictionaryQuadratics,mathdictionaryQuadrature,DefinitioneQuadrature,DictionaryeQuadrature,MathDictionaryeQuadrature,MathdictionaryeQuadrature,definitioneQuadrature,dictionaryeM 0Definition,negationdefinition,negationDefinition,Negationdefinition,NegationDictionary,negationdictionary,negationDictionary,Negationdictionary,NegationMathDictionary,negationMathdictionary,negationmathdictionary,negationMathDictionary,NegationMathdictionary,Negationmathdictionary,Negationa 0Definition,sistroiddefinition,sistroidDefinition,Sistroiddefinition,SistroidDictionary,sistroiddictionary,sistroidDictionary,Sistroiddictionary,SistroidMathDictionary,sistroidMathdictionary,sistroidmathdictionary,sistroidMathDictionary,SistroidMathdictionary,Sistroidmathdictionary,Sistroidthdictionary,Quadratic_Residuemathdictionary,Quadratic_ResidueMathDictionary,QuadraticresidueMathdictionary,Quadraticresiduemathdictionary,QuadraticresidueMathDictionary,Quadratic_residueMathdictionary,Quadratic_residuemathdictionary,Quadratic_residueesiduedefinition,QuadraticresidueDefinition,Quadratic_residuedefinition,Quadratic_residueDictionary,quadraticresiduedictionary,quadraticresidueDictionary,quadratic_residuedictionary,quadratic_residueDictionary,QuadraticResiduedictionary,QuadraticResidueDictionary,Quadratic_Residuedictionary,Quadratic_ResidueDictionary,Quadraticresiduedictionary,QuadraticresidueDictionary,Quadratic_residuedictionary,Quadratic_residueMathDictionary,quadraticresidueMathdictionary,quadraticresiduemathdictionary,quadraticresidueMathDictionary,quadratic_residueMathdictionary,quadratic_residuemathdictionary,quadratic_residueMathDictionary,QuadraticResidueMathdictionary,QuadraticResiduemathdictionary,QuadraticResidueMathDictionary,Quadratic_ResidueMaJ#mathdictionary,quadraticconvergence#Gquadratic convergence definition mathdictionary,quadraticequation quadratic equation definitionmathdictionary,quadraticformHquadratic form definition#mathdictionary,quadraticprogramming#iquadratic programming definition#mathdictionary,quadraticreciprocity#mhquadratic reciprocity definitionmathdictionary,quadraticresidueOQquadratic residue definitionmathdictionary,quadraticsquadratics definitionmathdictionary,quadratureequadrature definitionn{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 8 "quartic," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 1 " " } } {PARA 0 "> " 0 "" {TEXT 39 3 "1a." } {TEXT -1 34 " polynomial of the fourth degree. " } } {PARA 0 "> " 0 "" {TEXT 39 3 "b. " } {TEXT -1 106 " characterized by an algebraic equation of the fourth degree, usually in two or three variables. See also " } {HYPERLNK 45 "biquadratic" 5 "Definition/biquadratic" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "biquadrate" 5 "Definition/biquadrate" "" }{TEXT -1 2 ". " } {TEXT 39 2 "2." } {TEXT -1 2 " (" } {TEXT 22 14 "as substantive" } {TEXT -1 45 ") a quartic curve, surface, or function. See " } {HYPERLNK 45 "Cardano's formula" 5 "Definition/Cardanosformula" "" }{TEXT -1 2 ". " } } } Quadrinomial,DictionaryQuadrinomial,MathDictionaryQuadrinomial,MathdictionaryQuadrinomial,definitionQuadrinomial,dictionaryQuadrinomial,mathdictionaryQualitativeIdentity,Definition[QualitativeIdentity,Dictionary["QualitativeIdentity,MathDictionary["QualitativeIdentity,Mathdictionary[QualitativeIdentity,definition[QualitativeIdentity,dictionary["QualitativeIdentity,mathdictionary[quadrinomial,dictionaryquadrinomial,mathdictionaryqualitative_identity,Definition[qualitative_identity,Dictionary[#qualitative_identity,MathDictionary[#qualitative_identity,Mathdictionary[qualitative_identity,definition[qualitative_identity,dictionary[#qualitative_identity,mathdictionary[qualitativeidentity,Definition[qualitativeidentity,Dictionary["qualitativeidentity,MathDictionary["qualitativeidentity,Mathdictionary[qualitativeidentity,definition[qualitativeidentity,dictionary["qualitativeidentity,mathdictionary[Quantity,DictionaryoQuantity,MathDictionaryoQuantity,MathdictionaryoQuantity,definitionoQuantity,dictionaryoQuantity,mathdictionaryoQuantize,DefinitionQuantize,DictionaryQuantize,MathDictionaryQuantize,MathdictionaryQuantize,definitionQuantize,dictionaryQuantize,mathdictionaryQuartic,DefinitionQuartic,DictionaryQuartic,MathDictionaryQuartic,MathdictionaryDefinition,Rademachertheorem  Rademacher theorem definitionDefinition,Radial]radial definitionDefinition,RadialComponentradial component definitionDefinition,Radial_Componentradial component definitionDefinition,Radial_componentradial component definitionDefinition,Radialcomponentradial component definitionDefinition,Radianradian definitionDefinition,Radical radical definitionDefinition,RadicalAxis8radical axis definitiondictionary,radm " 0 "" {TEXT -1 14 "quasi-concave," } } {PARA 0 "> " 0 "" {TEXT 22 4 "adj." } {TEXT -1 24 " (of a function) having " } {HYPERLNK 45 "convex" 5 "Definition/convex" "" }{TEXT -1 7 " upper " } {HYPERLNK 45 "level sets" 5 "Definition/levelset" "" }{TEXT -1 33 "; that is, all sets of the form {" } {TEXT 22 1 "x" } {TEXT -1 3 " : " } {TEXT 22 1 "f" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 5 ") >= " } {TEXT 22 1 "r" } {TEXT -1 21 "} are convex for all " } {TEXT 22 1 "r" } {TEXT -1 10 ". Compare " } {HYPERLNK 45 "concave" 5 "Definition/concave" "" }{TEXT -1 2 ", " } {HYPERLNK 45 "quasi-convex" 5 "Definition/quasi-convex" "" }{TEXT -1 1 "." } } } Mathdictionary,Randomwalk random walk definitionMathdictionary,Rangerange definition"Mathdictionary,RangeOfSignificance#range of significance definition$Mathdictionary,Range_Of_Significance#range of significance definition$Mathdictionary,Range_of_significance#range of significance definition"Mathdictionary,Rangeofsignificance#range of significance definitionMathdictionary,Rankִrank definition)Mathdictionary,RankCorrelationCoefficient*~rank correlation coefficient 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falslatttrueincludwaysmanywrittencanbelowgivenenglishcorrespondanothsentencformoperatorsententialmonadicmathdictionardictionardefinitionindexnegatdefinita acomparcurvintersectsideconvexbetweencontainmathdictionardictionarindexsistroiddefinitd Vsensteststatisticalmathdictionardictionardefinitiondindexdiscriminatordefinit derivatanygeneralmorerepresentrespectwithfunctpointsameintervalendpointbothlimittendcontinuousunitpertimedifferatquantitvariablvalubetweendifferencratiomathdictionardictionardefinitionrindexchangraterateofchangdefinitDictionary,Quasi-Convexwquasi-convex definitionDictionary,Quasi-Groupquasi-group definitionDictionary,Quasi-Linearqquasi-linear definitionDictionary,Quasi-LinearEquation#Tquasi-linear equation definition Dictionary,Quasi-Linear_Equation#Tquasi-linear equation definitionDictionary,Quasi-Metrictquasi-metric definitionDictionary,Quasi-NewtonMethod!ېquasi-Newton method definitionDictionary,Quasi-Newton_Method!ېquasi-Newton method definition quadrilateral+Md 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In a semantic " } {HYPERLNK 45 "interpretation" 5 "Definition/interpretation" "" }{TEXT -1 54 " of quantified formulae, it is necessary to specify a " } {HYPERLNK 45 "range" 5 "Definition/range" "" }{TEXT -1 32 " of quantification. For example," } } {PARA 0 "> " 0 "" {TEXT -1 14 "`For all real " } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "x" } {TEXT -1 42 "^2 >= 0' would be written by logicians as " } } {PARA 0 "> " 0 "" {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 3 ")((" } {TEXT 22 1 "x" } {TEXT -1 4 " in " } {TEXT 39 1 "R" } {TEXT -1 6 ") -> (" } {TEXT 22 1 "x" } {TEXT -1 11 "^2 >= 0)). " } {TEXT 39 2 "2." } {TEXT -1 53 " any analogous symbol in an extended logic, such as (" } {TEXT 22 2 "Mx" } {TEXT -1 2 ")F" } {TEXT 22 1 "x" } {TEXT -1 5 " for " } {TEXT 22 12 "most x are F" } {TEXT -1 5 ", or " } {HYPERLNK 45 "restricted cquantifiers" 5 "Definition/restrictedquantifier" "" }{TEXT -1 10 " such as (" } {TEXT 22 1 "x" } {TEXT -1 3 " : " } {TEXT 22 2 "Fx" } {TEXT -1 1 ")" } {TEXT 22 2 "Gx" } {TEXT -1 5 " for " } {TEXT 22 13 "all Fs are Gs" } {TEXT -1 11 ". See also " } {HYPERLNK 45 "numerical quantifier" 5 "Definition/numericalquantifier" "" }{TEXT -1 2 ". " } } } range" 5 "Definition/range" "" }{TEXT -1 32 " of quantification. For example," } } {PARA 0 "> " 0 "" {TEXT -1 14 "`For all real " } {TEXT 22 1 "x" } {TEXT -1 2 ", " } {TEXT 22 1 "x" } {TEXT -1 42 "^2 >= 0' would be written by logicians as " } } {PARA 0 "> " 0 "" {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 3 ")((" } {TEXT 22 1 "x" } {TEXT -1 4 " in " } {TEXT 39 1 "R" } {TEXT -1 6 ") -> (" } {TEXT 22 1 "x" } {TEXT -1 11 "^2 >= 0)). " } {TEXT 39 2 "2." } {TEXT -1 53 " any analogous symbol in an extended logic, such as (" } {TEXT 22 2 "Mx" } {TEXT -1 2 ")F" } {TEXT 22 1 "x" } {TEXT -1 5 " for " } {TEXT 22 12 "most x are F" } {TEXT -1 5 ", or " } {HYPERLNK 45 "restricted cMathdictionary,quasi_convexwquasi-convex definitionMathdictionary,quasi_groupquasi-group definitionMathdictionary,quasi_linearqquasi-linear definition$Mathdictionary,quasi_linear_equation#Tquasi-linear equation definitionMathdictionary,quasi_metrictquasi-metric definition"Mathdictionary,quasi_newton_method!ېquasi-Newton method definitionMathdictionary,quasi_orderingquasi-ordering definitionMathdictionary,quasi_quotationwquasi-quotation definitionMathdictionary,quasi_tautologyquasi-tautology definitionMathdictionary,quasiconcaveq~quasi-concave definitionMathdictionary,quasiconvexwquasi-convex 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definition"Definition,quarticdefinition,quarticDefinition,Quarticdefinition,QuarticDictionary,quarticdictionary,quarticDictionary,Quarticdictionary,QuarticMathDictionary,quarticMathdictionary,quarticmathdictionary,quarticMathDictionary,QuarticMathdictionary,Quarticmathdictionary,Quartic+/Hkk623+4J51STuw$|y}b`ՍEE[ZAhƙ&5,t_$ ).!8YUX8,a/'dORtX 5ǚlJʚu*̚;ΚdxҚg욚!Q -89+/!"d&:d>(BE\!Quadratic_equation,MathDictionaryʝ Quadratic_programming,Dictionaryޝ$Quadratic_reciprocity,mathdictionaryQuadraticconvergence,Definition 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definitiondictionary,Quasi-Groupquasi-group definitiondictionary,Quasi-Linearqquasi-linear definitiondictionary,Quasi-LinearEquation#Tquasi-linear equation definition dictionary,Quasi-Linear_Equation#Tquasi-linear equation definitiondictionary,Quasi-Metrictquasi-metric definitiondictionary,Quasi-NewtonMethod!ېquasi-Newton method definitiondictionary,Quasi-Newton_Method!ېquasi-Newton method definition"Quasi_newton_method,mathdictionaryېQuasi_ordering,DefinitionQuasi_ordering,DictionaryQuasi_ordering,MathDictionaryQuasi_ordering,MathdictionaryQuasi_ordering,definitionQuasi_ordering,dictionaryQuasi_ordering,mathdictionaryQuasi_quotation,DefinitionwQuasi_quotation,DictionarywQuasi_quotation,MathDictionarywQuasi_quotation,MathdictionarywQuasi_quotation,definitionwQuasi_quotation,dictionaryw"Mathdictionary,Quasi-newton_method!ېquasi-Newton method definition!Mathdictionary,Quasi-newtonmethod!ېquasi-Newton method definitionMathdictionary,QuasiConcaveq~quasi-concave definitionMathdictionary,QuasiConvexwquasi-convex definitionMathdictionary,QuasiGroupquasi-group definitionMathdictionary,QuasiLinearqquasi-linear definition"Mathdictionary,QuasiLinearEquation#Tquasi-linear equation definitionMathdictionary,QuasiMetrictquasi-metric definition Mathdictionary,QuasiNewtonMethod!ېquasi-Newton method definitionMathdictionary,QuasiOrderingquasi-ordering definitionMathdictionary,QuasiQuotationwquasi-quotation definitionMathdictionary,QuasiTautologyquasi-tautology definitionMathdictionary,Quasi_Concaveq~quasi-concave definitionMathdictionary,Quasi_Convexwquasi-convex definitionMathdictionary,Quasi_Groupquasi-group definitionDefinition,quadraticformHquadratic form definitionDefinition,quadraticformula quadratic equation definitionDefinition,quadraticprogramming#iquadratic programming definitionDefinition,quadraticreciprocity#mhquadratic reciprocity definitionDefinition,quadraticresidueOQquadratic residue definitionDefinition,quadraticsquadratics definitionDefinition,quadratureequadrature definitionDefinition,quadric quadric definitionDefinition,quadrilateralqquadrilateral definitionQualitative_Identity,Definition[Qualitative_Identity,Dictionary[#Qualitative_Identity,MathDictionary[#Qualitative_Identity,Mathdictionary[Qualitative_Identity,definition[Qualitative_Identity,dictionary[#Qualitative_Identity,mathdictionary[Qualitative_identity,Definition[Qualitative_identity,Dictionary[#Qualitative_identity,MathDictionary[#Qualitative_identity,Mathdictionary[Qualitative_identity,definition[Qualitative_identity,dictionary[#Qualitative_identity,mathdictionary[Qualitativeidentity,Definition[ctionary,QualitativeIdentitymathdictionary,QualitativeIdentityMathDictionary,Qualitative_IdentityMathdictionary,Qualitative_Identitymathdictionary,Qualitative_IdentityMathDictionary,QualitativeidentityMathdictionary,Qualitativeidentitymathdictionary,QualitativeidentityMathDictionary,Qualitative_identityMathdictionary,Qualitative_identitymathdictionary,Qualitative_identitytyDictionary,qualitativeidentitydictionary,qualitativeidentityDictionary,qualitative_identitydictionary,qualitative_identityDictionary,QualitativeIdentitydictionary,QualitativeIdentityDictionary,Qualitative_Identitydictionary,Qualitative_IdentityDictionary,Qualitativeidentitydictionary,QualitativeidentityDictionary,Qualitative_identitydictionary,Qualitative_identityMathDictionary,qualitativeidentityMathdictionary,qualitativeidentitymathdictionary,qualitativeidentityMathDictionary,qualitative_identityMathdictionary,qualitative_identitymathdictionary,qualitative_identityMathDictionary,QualitativeIdentityMathdip {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "quality control," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 10 "Statistics" } {TEXT -1 101 ") the application of statistical sampling techniques to the maintenance of the quality of a product. " } } } Definition,Recurringdecimal!recurring decimal definitionDefinition,Recursion& recursion definitionDefinition,RecursionClauserecursion formula definitionDefinition,RecursionFormularecursion formula definitionDefinition,Recursion_Clauserecursion formula definitionDefinition,Recursion_Formularecursion formula definitionDefinition,Recursion_clauserecursion formula definitionDefinition,Recursion_formularecursion formula 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definitionDefinition,Quasilinearqquasi-linear definitionDefinition,Quasilinearequation#Tquasi-linear equation definitionDefinition,Quasimetrictquasi-metric definitionDefinition,Quasinewtonmethod!ېquasi-Newton method definitionDefinition,Quasiorderingquasi-ordering definitionDefinition,Quasiquotationwquasi-quotation definitionDefinition,Quasitautologyquasi-tautology definitionDefinition,Quaternaryquaternary definitionDictionary,QuasiConvexwquasi-convex definitionDictionary,QuasiGroupquasi-group definitionDictionary,QuasiLinearqquasi-linear definitionDictionary,QuasiLinearEquation#Tquasi-linear equation definitionDictionary,QuasiMetrictquasi-metric definitionDictionary,QuasiNewtonMethod!ېquasi-Newton method definitionDictionary,QuasiOrderingquasi-ordering definitionDictionary,QuasiQuotationwquasi-quotation definitionDictionary,QuasiTautologyquasi-tautology definitionDictionary,Quasi_Concaveq~quasi-concave definitionDictionary,Quasi_Convexwquasi-convex 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definitionmathdictionary,Quasi_convexwquasi-convex definitionmathdictionary,Quasi_groupquasi-group definitionmathdictionary,Quasi_linearqquasi-linear definitionmathdictionary,quantify!quantify definitionmathdictionary,quantityoquantity definitionmathdictionary,quantizequantize definitionmathdictionary,quarticquartic definitionmathdictionary,quartilequartile definitionmathdictionary,quasi quasi- definitionmathdictionary,quasi- quasi- definitionmathdictionary,quasi-concaveq~quasi-concave definitionmathdictionary,quasi-convexwquasi-convex definitionmathdictionary,quasi-groupquasi-group definitionQuasi_group,mathdictionaryQuasi_linear,DefinitionqQuasi_linear,DictionaryqQuasi_linear,MathDictionaryqQuasi_linear,MathdictionaryqQuasi_linear,definitionqQuasi_linear,dictionaryqQuasi_linear,mathdictionaryq Quasi_linear_equation,DefinitionT Quasi_linear_equation,DictionaryT$Quasi_linear_equation,MathDictionaryT$Quasi_linear_equation,MathdictionaryT Quasi_linear_equation,definitionT 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 12 "quasi-group," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 3 " a " } {HYPERLNK 45 "groupoid" 5 "Definition/groupoid" "" }{TEXT -1 47 " in which every element has both a unique left " } {HYPERLNK 45 "inverse" 5 "Definition/inverse" "" }{TEXT -1 186 " and a unique right inverse, which need not be equal unless the associative law holds. 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 20 "quasi-Newton method," } } {PARA 0 "> " 0 "" {TEXT 22 3 "n. " } {TEXT -1 1 "(" } {TEXT 22 18 "Numerical analysis" } {TEXT -1 63 ") any of a class of methods for solving nonlinear equations or " } {HYPERLNK 45 "unconstrained optimization" 5 "Definition/constrainedoptimization" "" }{TEXT -1 20 " problems, based on " } {HYPERLNK 45 "Newton's method" 5 "Definition/Newtonsmethod" "" }{TEXT -1 34 " but using rough estimates of the " } {HYPERLNK 45 "Hessians" 5 "Definition/Hessian" "" }{TEXT -1 4 " or " } {HYPERLNK 45 "Jacobians" 5 "Definition/Jacobian" "" }{TEXT -1 131 " involved to reduce computational cost. These estimates are often recursively estimated and are refined during the calculation. In " } {TEXT 22 25 "quasi-Newton minimization" } {TEXT -1 37 " procedures, the approximate Hessian " } {TEXT 22 1 "H" } {TEXTž -1 20 " is usually given a " } {HYPERLNK 45 "rank" 5 "Definition/rank" "" }{TEXT -1 31 " one or rank two update, and a " } {HYPERLNK 45 "line search method" 5 "Definition/linesearchmethod" "" }{TEXT -1 35 " is then used in the direction of -" } {TEXT 22 1 "H" } {TEXT -1 6 " grad " } {TEXT 22 1 "f" } {TEXT -1 1 "(" } {TEXT 22 1 "x" } {TEXT -1 32 ") to produce the next estimate. " } } } } {HYPERLNK 45 "unconstrained optimization" 5 "Definition/constrainedoptimization" "" }{TEXT -1 20 " problems, based on " } {HYPERLNK 45 "Newton's method" 5 "Definition/Newtonsmethod" "" }{TEXT -1 34 " but using rough estimates of the " } {HYPERLNK 45 "Hessians" 5 "Definition/Hessian" "" }{TEXT -1 4 " or " } {HYPERLNK 45 "Jacobians" 5 "Definition/Jacobian" "" }{TEXT -1 131 " involved to reduce computational cost. These estimates are often recursively estimated and are refined during the calculation. 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4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "quasi-quotation," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 269 " a device, written '....', whereby it is possible to refer to generalized expressions, some parts of which are variables and others which are operators that appear in their own right. For example, it is not possible to state the truth conditions for a conjunction as " } } {PARA 0 "> " 0 "" {TEXT -1 50 " `P and Q' if and only if P is true and Q is true " } } {PARA 0 "> " 0 "" {TEXT -1 364 "in a way that is consistent with the fundamental principle of any notation that variables be uniformly replaced by their instances, since, if the variables stand for unquoted sentences, the second clause is ill-formed, while if they represent quoted sentences, the conjunction is ill-formed. Instead we require that the variables represent quoted expressionڞs, but " } {HYPERLNK 45 "concatenate" 5 "Definition/concatenate" "" }{TEXT -1 365 " P, the symbol `&', and Q, in such a way that we delete the final quotation mark in the replacement of the first variable with the quotation mark preceding the ampersand, and the initial quotation mark in the replacement of the second variable with the quotation mark following the ampersand. The quasi-quotation 'P & Q' is then defined to be this concatenation, " } } {PARA 0 "> " 0 "" {TEXT -1 13 "P ^ `&' ^ Q, " } } {PARA 0 "> " 0 "" {TEXT -1 50 "and is the required quotation of the conjunction. " } } } nly if P is true and Q is true " } } {PARA 0 "> " 0 "" {TEXT -1 364 "in a way that is consistent with the fundamental principle of any notation that variables be uniformly replaced by their instances, since, if the variables stand for unquoted sentences, the second clause is ill-formed, while if they represent quoted sentences, the conjunction is ill-formed. Instead we require that the variables represent quoted expressionڞMathDictionary,RatioTestWratio test definitionMathDictionary,RatioTheorem8 Xratio theorem definitionsection formula definition"MathDictionary,Ratio_Of_Similitude!Vratio of similitude definitionMathDictionary,Ratio_Scale!ratio scale definitionMathDictionary,Ratio_TestWratio test definitionMathDictionary,Ratio_Theorem8 Xratio theorem definitionsection formula definition"MathDictionary,Ratio_of_similitude!Vratio of similitude definitionMathDictionary,Ratio_scale!ratio scale definitionMathDictionary,Ratio_testWratio test definitionMathDictionary,Ratio_theorem8 Xratio theorem definitionsection formula definitionMathDictionary,Rational3.+rational number definitionϳrational definitionMathDictionary,RationalElement8rational element definitionLDefinition,quaternarydefinition,quaternaryDefinition,Quaternarydefinition,QuaternaryDictionary,quaternarydictionary,quaternaryDictionary,Quaternarydictionary,QuaternaryMathDictionary,quaternaryMathdictionary,quaternarymathdictionary,quaternaryMathDictionary,QuaternaryMathdictionary,Quaternarymathdictionary,QuaternaryQuasi-Ordering,dictionaryQuasi-Ordering,mathdictionaryQuasi-Quotation,DefinitionwQuasi-Quotation,DictionarywQuasi-Quotation,MathDictionarywQuasi-Quotation,MathdictionarywQuasi-Quotation,definitionwQuasi-Quotation,dictionarywQuasi-Quotation,mathdictionarywQuasi-Tautology,DefinitionQuasi-Tautology,DictionaryQuasi-Tautology,MathDictionaryQuasi-Tautology,MathdictionaryQuasi-Tautology,definitionQuasi-Tautology,dictionaryQuasi-Tautology,mathdictionary Quasi-linear_equation,DefinitionT Quasi-linear_equation,DictionaryT$Quasi-linear_equation,MathDictionaryT$Quasi-linear_equation,MathdictionaryT Quasi-linear_equation,definitionT Quasi-linear_equation,dictionaryT(comparlittlsaidinfinitabslimitthetaothereachcaseidentifoftensimilarohbigreadwritweallsuchconstantgivenequalitinequalitreplacusefulsetfunctionanoththossequencelementbetweencomparisonindicatmathdictionardictionardefinitionoindexnotatorderordernotatdefinitcomparalsootherreturnboldnecessariteratbranchitselfordereachindifferotherwisrightleftdowntopreadobtainrepresentatexpressstructurrepresnodeatdiagramtreebinarusesacccunambiguousthuswrittenexamplargumenttheirbeforespecialoperatorwritbracketneedwithdispenslogicalprefixprefixnotatmathdictionardictionardefinitionpindexnotatpolishpolishnotatdefinititry,Quasi_QuotationMathDictionary,QuasiquotationMathdictionary,Quasiquotationmathdictionary,QuasiquotationMathDictionary,Quasi_quotationMathdictionary,Quasi_quotationmathdictionary,Quasi_quotationdefinition,quasi-quotationDefinition,Quasi-Quotationdefinition,Quasi-QuotationDictionary,quasi-quotationdictionary,quasi-quotationDictionary,Quasi-Quotationdictionary,Quasi-QuotationMathDictionary,quasi-quotationMathdictionary,quasi-quotationmathdictionary,quasi-quotationMathDictionary,Quasi-QuotationMathdictionary,Quasi-Quotationmathdictionary,Quasi-Quotation,Quasiquotationdictionary,QuasiquotationDictionary,Quasi_quotationdictionary,Quasi_quotationMathDictionary,quasiquotationMathdictionary,quasiquotationmathdictionary,quasiquotationMathDictionary,quasi_quotationMathdictionary,quasi_quotationmathdictionary,quasi_quotationMathDictionary,QuasiQuotationMathdictionary,QuasiQuotationmathdictionary,QuasiQuotationMathDictionary,Quasi_QuotationMathdictionary,Quasi_Quotationmathdictionaߞ{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 16 "quasi-tautology," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 5 "Logic" } {TEXT -1 4 ") a " } {HYPERLNK 45 "tautological consequence" 5 "Definition/tautologicalconsequence" "" }{TEXT -1 51 " of instances of identity and equality axioms in a " } {HYPERLNK 45 "theory" 5 "Definition/theory" "" }{TEXT -1 2 ". 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The queue has a finite or infinite bound, and there is some mechanism for serving customers (often first come, first served) in a number of parallel service channels. The service time for each customer is also described probabilistically, often by a " } {HYPERLNK 45 "gamma distribution" 5 "Definition/gammadistribution" "" }{TEXT -1 121 ". The theory then attempts 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Definition,Quasi_Linear_Equation#Tquasi-linear equation definitionDefinition,Quasi_Metrictquasi-metric definitionDefinition,Quasi_Newton_Method!ېquasi-Newton method definitionDefinition,Quasi_Orderingquasi-ordering definitionDefinition,Quasi_Quotationwquasi-quotation definitionDefinition,Quasi_Tautologyquasi-tautology definitionDefinition,Quasi_concaveq~quasi-concave definitionDefinition,Quasi_convexwquasi-convex definitionDefinition,Quasi_groupquasi-group definitionDefinition,Quasi_linearqquasi-linear definition Definition,Quasi_linear_equation#Tquasi-linear equation definitionDefinition,Quasi_metrictquasi-metric definitionDefinition,Quasi_newton_method!ېquasi-Newton method definitionDefinition,Quasi_orderingquasi-ordering definitionDefinition,Quasi_quotationwquasi-quotation definitionDefinition,Quasi_tautologyquasi-tautology definitionDefinition,Quasiconcaveq~quasi-concave definitionDefinition,Quasiconvexwquasi-convex definitiondefinition,Quasi_linearqquasi-linear definition 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" } } } 0 "" {TEXT -1 26 "variance-covariance matrix" } } {PARA 0 "> " 0 "" {TEXT -1 3 "or " } {TEXT 39 17 "covariance matrix" } {TEXT -1 2 ", " } {TEXT 22 2 "n." } {TEXT -1 2 " (" } {TEXT 22 10 "Statistics" } {TEXT -1 22 ") (for a sequence, {X[" } {TEXT 22 1 "i" } {TEXT -1 7 "]}, of " } {HYPERLNK 45 "random variables" 5 "Definition/randomvariable" "" }{TEXT -1 6 ") the " } {TEXT 22 1 "n" } {TEXT -1 3 " x " } {TEXT 22 1 "n" } {TEXT -1 45 " matrix, usually denoted Sigma, of which the " } {TEXT 22 1 "i" } {TEXT -1 1 "," } {TEXT 22 1 "j" } {TEXT -1 22 "^( th) entry is Cov(X[" } {TEXT 22 1 "i" } {TEXT -1 5 "], X[" } {TEXT 22 1 "j" } {TEXT -1 8 "]), the " } {HYPERLNK 45 "covariance" 5 "Definition/covariance" "" }{TEXT -1 6 " of X[" } {TEXT 22 1 "i" } {TEXT -1 8 "] and X[" } {TEXT 22 1 "j" } {TEXT -1 94 "]; the matrix is then symmetrical and nDefinition,Quasi-Orderingquasi-ordering definitionDefinition,Quasi-Quotationwquasi-quotation definitionDefinition,Quasi-Tautologyquasi-tautology 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Radical,Dictionary Radical,MathDictionary Radical,Mathdictionary Radical,definition Radical,dictionary Radical,mathdictionary RadicalAxis,Definition8RadicalAxis,Dictionary8RadicalAxis,MathDictionary8RadicalAxis,Mathdictionary8RadicalAxis,definition8RadicalAxis,dictionary8RadicalAxis,mathdictionary8MathDictionary,RadixfractionVradix fraction definitionMathDictionary,Radixpoint0radix point definition&MathDictionary,Radon-NikodymDerivative&Radon-Nikodym derivative definition#MathDictionary,Radon-NikodymTheorem##Radon-Nikodym theorem definition'MathDictionary,Radon-Nikodym_Derivative&Radon-Nikodym derivative definition$MathDictionary,Radon-Nikodym_Theorem##Radon-Nikodym theorem definition'MathDictionary,Radon-nikodym_derivative&Radon-Nikodym derivative definitionDefinition,Radixpoint0radix point definition"Definition,Radon-NikodymDerivative&Radon-Nikodym derivative definitionDefinition,Radon-NikodymTheorem##Radon-Nikodym theorem definition#Definition,Radon-Nikodym_Derivative&Radon-Nikodym derivative definition Definition,Radon-Nikodym_Theorem##Radon-Nikodym theorem definition"Definition,Radon-Nikodymderivative&Radon-Nikodym derivative definitionDefinition,Radon-Nikodymtheorem##Radon-Nikodym theorem definition#Definition,Radon-nikodym_derivative&Radon-Nikodym derivative definition Definition,Radon-nikodym_theorem##Radon-Nikodym theorem definition"Definition,Radon-nikodymderivative&Radon-Nikodym derivative definition݃{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "quaternion," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 31 " a generalized complex number, " } {TEXT 22 1 "x" } {TEXT -1 42 ", consisting of four components such that " } } {PARA 0 "> " 0 "" {TEXT 22 5 "x = x" } {TEXT -1 6 "[0] + " } {TEXT 22 1 "x" } {TEXT -1 3 "[1]" } {TEXT 39 2 "i " } {TEXT -1 3 " + " } {TEXT 22 1 "x" } {TEXT -1 3 "[2]" } {TEXT 39 2 "j " } {TEXT -1 3 " + " } {TEXT 22 1 "x" } {TEXT -1 3 "[3]" } {TEXT 39 1 "k" } {TEXT -1 2 ", " } } {PARA 0 "> " 0 "" {TEXT -1 11 " where the " } {TEXT 22 4 "x[i]" } {TEXT -1 22 " are real numbers and " } {TEXT 39 1 "i" } {TEXT -1 2 ", " } {TEXT 39 1 "j" } {TEXT -1 2 ", " } {TEXT 39 1 "k" } {TEXT -1 5 " are " } {HYPERLNK 45 "hypercomplex numbers" 5 "Definition/hypercomplexnumbers" "" }{TEXT -1 11 " for which " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 39 1 "i" } {TEXT -1 5 "^2 = " } {TEXT 39 1 "j" } {TEXT -1 6 " ^2 = " } {TEXT 39 1 "k" } {TEXT -1 6 " ^2 = " } {TEXT 39 3 "ijk" } {TEXT -1 6 " = -1 " } } {PARA 0 "> " 0 "" {TEXT -1 41 "The set of all quaternions is denoted by " } {TEXT 39 2 "IH" } {TEXT -1 14 ", and forms a " } {HYPERLNK 45 "division ring" 5 "Definition/divisionring" "" }{TEXT -1 4 " (a " } {HYPERLNK 45 "skew field" 5 "Definition/skewfield" "" }{TEXT -1 7 "). The " } {TEXT 22 16 "quaternion group" } {TEXT -1 12 " is the set " } } {PARA 0 "> " 0 "" {TEXT -1 11 "{ +/-1, +/-" } {TEXT 39 1 "i" } {TEXT -1 5 ", +/-" } {TEXT 39 1 "j" } {TEXT -1 5 ", +/-" } {TEXT 39 2 "k " } {TEXT -1 2 "} " } } {PARA 0 "> " 0 "" {TEXT -1 60 "with respect to the multiplication of the unit quaternions. " } } } " } {TEXT 39 1 "i" } {TEXT -1 2 ", " } {TEXT 39 1 "j" } {TEXT -1 2 ", " } {TEXT 39 1 "k" } {TEXT -1 5 " are " } {HYPERLNK 45 "hypercomplex numbers" 5 "Definition/hypercomplexnumbers" "" }{TEXT -1 11 " for which " } } {PARA 0 "> " 0 "" {TEXT -1 1 " " } {TEXT 39 1 Definition,quoderatdemonstrandum%(quod erat demonstrandum definitionDefinition,quoderatfaciendum!Vquod erat faciendum definitionDefinition,quotientFquotient definitionDefinition,quotient_group6Kquotient group definition\factor group definitionDefinition,quotient_ring4*factor ring definitionquotient ring definitionDefinition,quotient_rule-quotient rule definitionDefinition,quotient_space6a^quotient space definitionfactor space definitionionmathdictionary,Quintic*quintic definition$mathdictionary,QuodEratDemonstrandum%(quod erat demonstrandum definition mathdictionary,QuodEratFaciendum!Vquod erat faciendum definition&mathdictionary,Quod_Erat_Demonstrandum%(quod erat demonstrandum 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Theta_function,DictionarywTheta_function,MathDictionarywTheta_function,MathdictionarywTheta_function,definitionwTheta_function,dictionarywTheta_function,mathdictionarywTheta_notation,DefinitionU=Theta_notation,DictionaryU=Theta_notation,MathDictionaryU=Theta_notation,MathdictionaryU=Theta_notation,definitionU=Theta_notation,dictionaryU=Theta_notation,mathdictionaryU='Theta_transformation_formula,DefinitionkSY{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 10 "injection," } } {PARA 0 "> " 0 "" {TEXT 22 2 "n." } {TEXT -1 4 " an " } {HYPERLNK 45 "injective" 5 "Definition/injective" "" }{TEXT -1 10 " mapping. " } } } {VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 15 "quasi-ordering," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "ordering" 5 "Definition/ordering" "" }{TEXT -1 2 ". " } } } queue,MathDictionaryuqueue,Mathdictionaryuqueue,definitionuqueue,dictionaryuqueue,mathdictionaryuqueueing_theory,DefinitionGqueueing_theory,DictionaryGqueueing_theory,MathDictionaryGqueueing_theory,MathdictionaryGqueueing_theory,definitionGqueueing_theory,dictionaryGqueueing_theory,mathdictionaryGqueueingtheory,DefinitionGqueueingtheory,DictionaryGqueueingtheory,MathDictionaryGqueueingtheory,MathdictionaryGqueueingtheory,definitionGqueueingtheory,dictionaryG0?{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 11 "quatrefoil," } } {PARA 0 "> " 0 "" {TEXT -1 4 "see " } {HYPERLNK 45 "multifoil" 5 "Definition/multifoil" "" }{TEXT -1 2 ". " } } } Definition,quasilinearqquasi-linear definitionDefinition,quasilinearequation#Tquasi-linear equation definitionDefinition,quasimetrictquasi-metric definitionDefinition,quasinewtonmethod!ېquasi-Newton method definitionDefinition,quasiorderingquasi-ordering definitionDefinition,quasiquotationwquasi-quotation definitionDefinition,quasitautologyquasi-tautology definitionDefinition,quaternaryquaternary definitionDefinition,quaternion݃quaternion definition"MathDictionary,Quod_erat_faciendum!Vquod erat faciendum definition$MathDictionary,Quoderatdemonstrandum%(quod erat demonstrandum definition MathDictionary,Quoderatfaciendum!Vquod erat faciendum definitionMathDictionary,QuotientFquotient definitionMathDictionary,QuotientGroup6Kquotient group definition\factor group definitionMathDictionary,QuotientRing4*factor ring definitionquotient ring definitionMathDictionary,QuotientRule-quotient rule definitionQuotient_Group,dictionaryK\Quotient_Group,mathdictionaryK\Quotient_Ring,Definition*Quotient_Ring,Dictionary*Quotient_Ring,MathDictionary*Quotient_Ring,Mathdictionary*Quotient_Ring,definition*Quotient_Ring,dictionary*Quotient_Ring,mathdictionary*Quotient_Rule,Definition-Quotient_Rule,Dictionary-Quotient_Rule,MathDictionary-Quotient_Rule,Mathdictionary-Quotient_Rule,definition-Quotient_Rule,dictionary-Quotient_Rule,mathdictionary-Quotient_Space,Definitiona^Quotient_Space,Dictionarya^"Quod_Erat_Demonstrandum,dictionary(&Quod_Erat_Demonstrandum,mathdictionary(Quod_Erat_Faciendum,DefinitionVQuod_Erat_Faciendum,DictionaryV"Quod_Erat_Faciendum,MathDictionaryV"Quod_Erat_Faciendum,MathdictionaryVQuod_Erat_Faciendum,definitionVQuod_Erat_Faciendum,dictionaryV"Quod_Erat_Faciendum,mathdictionaryV"Quod_erat_demonstrandum,Definition("Quod_erat_demonstrandum,Dictionary(&Quod_erat_demonstrandum,MathDictionary(&Quod_erat_demonstrandum,Mathdictionary("Quod_erat_demonstrandum,definition(*{VERSION 4 0 "HELP" "4.0"} {USTYLETAB {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 10 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 3 "> " 0 "" {TEXT -1 8 "quintic," } } {PARA 0 "> " 0 "" {TEXT 22 5 "adj. " } {TEXT -1 38 "of or relating to the fifth degree. A " } {TEXT 22 16 "quintic equation" } {TEXT -1 31 " is not in general amenable to " } {HYPERLNK 45 "solution by radicals" 5 "Definition/solutionbyradicals" "" }{TEXT -1 2 ". " } } } Definition,Ramsey_theoremG Ramsey theorem definitionDefinition,RamseynumbersRamsey numbers definitionDefinition,RamseytheoremG Ramsey theorem definitionDefinition,RandomB\random definitionDefinition,RandomErrorzrandom error definition Definition,RandomNumberGenerator%random number generator definitionDefinition,RandomNumbersrandom numbers definitionDefinition,RandomSampleӦrandom sample definitionDefinition,RandomVariablerandom variable definitiondefinition,Realnumberreal number definitiondefinition,Realpart]ereal part definitiondefinition,Realsymmetricreal-symmetric definitiondefinition,Realvaluedreal-valued definitiondefinition,Realvariable|real variable definitiondefinition,Rearrangementf0rearrangement definitiondefinition,Reciprocalreciprocal definitiondefinition,ReciprocalPolarCurve$Qreciprocal polar curve definition definition,ReciprocalPolarFigure%reciprocal polar figure definitiondefinition,ReciprocalVariationBfreciprocal variation definitionoinverse proportion definitionDictionary,Realnumberreal number definitionDictionary,Realpart]ereal part definitionDictionary,Realsymmetricreal-symmetric definitionDictionary,Realvaluedreal-valued definitionDictionary,Realvariable|real variable definitionDictionary,Rearrangementf0rearrangement definitionDictionary,Reciprocalreciprocal definitionDictionary,ReciprocalPolarCurve$Qreciprocal polar curve definition Dictionary,ReciprocalPolarFigure%reciprocal polar figure definitionDictionary,ReciprocalVariationBfreciprocal variation definitionoinverse proportion definitiondictionary,Realnumberreal number definitiondictionary,Realpart]ereal part definitiondictionary,Realsymmetricreal-symmetric definitiondictionary,Realvaluedreal-valued definitiondictionary,Realvariable|real variable definitiondictionary,Rearrangementf0rearrangement definitiondictionary,Reciprocalreciprocal definitiondictionary,ReciprocalPolarCurve$Qreciprocal polar curve definition dictionary,ReciprocalPolarFigure%reciprocal polar figure 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