3097:
4987:
2865:
954:
3092:{\displaystyle {\begin{aligned}P_{Avg}&=\left(I(t)^{2}R\right)_{Avg}&&{\text{where }}\left(\cdots \right)_{Avg}{\text{ denotes the temporal mean of a function}}\\&=\left(I(t)^{2}\right)_{Avg}R&&{\text{(as }}R{\text{ does not vary over time, it can be factored out)}}\\&=I_{\text{RMS}}^{2}R&&{\text{by definition of root-mean-square}}\end{aligned}}}
3970:
1836:
922:
831:
4204:
4970:
3673:
4329:
RMS quantities such as electric current are usually calculated over one cycle. However, for some purposes the RMS current over a longer period is required when calculating transmission power losses. The same principle applies, and (for example) a current of 10 amps used for 12 hours each 24-hour day
4474:
When two data sets — one set from theoretical prediction and the other from actual measurement of some physical variable, for instance — are compared, the RMS of the pairwise differences of the two data sets can serve as a measure of how far on average the error is from 0. The mean of the absolute
1646:
5272:
when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit. This is useful for electrical engineers in calculating the "AC only" RMS of a signal. Standard deviation being the RMS of a signal's
1577:
268:) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform. In physics, the RMS current value can also be defined as the "value of the direct current that dissipates the same power in a resistor."
1412:
806:
is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a sample consisting of equally spaced observations. Additionally, the RMS value of various waveforms can also be determined without
3981:
3658:
2586:
2223:
4760:
797:
4459:
of the gas in kilograms per mole. In physics, speed is defined as the scalar magnitude of velocity. For a stationary gas, the average speed of its molecules can be in the order of thousands of km/h, even though the average velocity of its molecules is zero.
467:
2689:
4475:
values of the pairwise differences could be a useful measure of the variability of the differences. However, the RMS of the differences is usually the preferred measure, probably due to mathematical convention and compatibility with other formulae.
665:
3470:
3965:{\displaystyle {\begin{aligned}I_{\text{RMS}}&=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{1-\cos(2\omega t) \over 2}\,dt}}}\\&=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}\left_{T_{1}}^{T_{2}}}}\end{aligned}}}
5256:
4686:
4326:, or about 170 volts. The peak-to-peak voltage, being double this, is about 340 volts. A similar calculation indicates that the peak mains voltage in Europe is about 325 volts, and the peak-to-peak mains voltage, about 650 volts.
1831:{\displaystyle y={\begin{cases}0&\operatorname {frac} (ft)<0.25\\A_{1}&0.25<\operatorname {frac} (ft)<0.5\\0&0.5<\operatorname {frac} (ft)<0.75\\-A_{1}&\operatorname {frac} (ft)>0.75\end{cases}}}
2855:), this formula must be extended to reflect the fact that the current (and thus the instantaneous power) is varying over time. If the function is periodic (such as household AC power), it is still meaningful to discuss the
1100:
1036:
2365:
1958:
2870:
4264:
1452:
3277:
3203:
3678:
1300:
4199:{\displaystyle I_{\text{RMS}}=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}\left_{T_{1}}^{T_{2}}}}=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}{{T_{2}-T_{1}} \over 2}}}={I_{\text{p}} \over {\sqrt {2}}}.}
2071:
5765:
4430:
3519:
2492:
2121:
4965:{\displaystyle {\text{RMS}}\{x\}={\sqrt {{\frac {1}{N}}\sum _{n}{x^{2}}}}={\sqrt {{\frac {1}{N^{2}}}\sum _{m}{{\bigl |}X{\bigr |}}^{2}}}={\sqrt {\sum _{m}{\left|{\frac {X}{N}}\right|^{2}}}}.}
1633:
676:
338:
4745:
2405:
1873:
1287:
2754:
2108:
1995:
346:
2721:
1250:
524:
2621:
224:
150:
115:
532:
2258:
973:
wave. However, this is not true for an arbitrary waveform, which may not be periodic or continuous. For a zero-mean sine wave, the relationship between RMS and peak-to-peak
5148:
5758:
5117:
4538:
2842:
1155:
3326:
916:
2482:
Waveforms made by summing known simple waveforms have an RMS value that is the root of the sum of squares of the component RMS values, if the component waveforms are
1441:
1184:
880:
943:
181:
80:
4345:(it is proportional to the square of the RMS voltage or RMS current in a resistive load). For a discussion of audio power measurements and their shortcomings, see
5168:
6160:
4558:
4298:
V in Europe) are almost always quoted in RMS values, and not peak values. Peak values can be calculated from RMS values from the above formula, which implies
5751:
4566:
5261:
From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the "error" / square deviation as well.
1050:
986:
5801:
2271:
5668:
2783:
5623:
1041:
For other waveforms, the relationships are not the same as they are for sine waves. For example, for either a triangular or sawtooth wave:
1886:
1572:{\displaystyle y=A_{0}+{\begin{cases}A_{1}&\operatorname {frac} (ft)<0.5\\-A_{1}&\operatorname {frac} (ft)>0.5\end{cases}}}
5477:
4376:
2486:(that is, if the average of the product of one simple waveform with another is zero for all pairs other than a waveform times itself).
4215:
2591:
Alternatively, for waveforms that are perfectly positively correlated, or "in phase" with each other, their RMS values sum directly.
5899:
5894:
5598:
5548:
5514:
5487:
1407:{\displaystyle y={\begin{cases}A_{1}&\operatorname {frac} (ft)<0.5\\-A_{1}&\operatorname {frac} (ft)>0.5\end{cases}}}
3313:
current, as is approximately true for mains power, the RMS value is easy to calculate from the continuous case equation above. If
3229:
3153:
5317:
3664:
6121:
5982:
5705:
2008:
3975:
but since the interval is a whole number of complete cycles (per definition of RMS), the sine terms will cancel out, leaving:
5806:
3653:{\displaystyle I_{\text{RMS}}=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{\sin ^{2}(\omega t)}\,dt}}}.}
2581:{\displaystyle {\text{RMS}}_{\text{Total}}={\sqrt {{\text{RMS}}_{1}^{2}+{\text{RMS}}_{2}^{2}+\cdots +{\text{RMS}}_{n}^{2}}}}
6072:
5816:
4385:
2218:{\displaystyle y={\begin{cases}A_{1}&\operatorname {frac} (ft)<D\\0&\operatorname {frac} (ft)>D\end{cases}}}
5831:
4319:, assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 Ă—
969:, the relationships between amplitudes (peak-to-peak, peak) and RMS are fixed and known, as they are for any continuous
3117:) is the constant current that yields the same power dissipation as the time-averaged power dissipation of the current
6038:
5967:
5904:
2610:
792:{\displaystyle f_{\text{RMS}}=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {2T}}{\int _{-T}^{T}{}^{2}\,{\rm {d}}t}}}.}
1583:
5851:
5826:
5811:
4469:
3290:
loads (that is, loads capable of not just dissipating energy but also storing it) are discussed under the topic of
2264:
250:
278:
5841:
5836:
5322:
4694:
2371:
5937:
5572:
1842:
1256:
462:{\displaystyle x_{\text{RMS}}={\sqrt {{\frac {1}{n}}\left({x_{1}}^{2}+{x_{2}}^{2}+\cdots +{x_{n}}^{2}\right)}}.}
2730:
2684:{\displaystyle {\text{RMS}}_{\text{AC+DC}}={\sqrt {{\text{V}}_{\text{DC}}^{2}+{\text{RMS}}_{\text{AC}}^{2}}}}
2077:
1964:
957:
Graph of a sine wave's voltage vs. time (in degrees), showing RMS, peak (PK), and peak-to-peak (PP) voltages.
6028:
5932:
5927:
5291:
2697:
1197:
6095:
3223:
By taking the square root of both these equations and multiplying them together, the power is found to be:
483:
5869:
5373:
5155:
4358:
660:{\displaystyle f_{\text{RMS}}={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{}^{2}\,{\rm {d}}t}}},}
188:
4986:
1639:
194:
120:
85:
4484:
2229:
6090:
5990:
5879:
5874:
5286:
3287:
2483:
2136:
1661:
1480:
1315:
5796:
5783:
4991:
3298:
2757:
234:
6116:
6082:
5962:
5791:
5634:
5327:
5269:
5151:
5126:
3465:{\displaystyle I_{\text{RMS}}={\sqrt {{1 \over {T_{2}-T_{1}}}\int _{T_{1}}^{T_{2}}\left^{2}dt}},}
5093:
4490:
2808:
1126:
6111:
6000:
5947:
5664:
5544:
5510:
5504:
5483:
5397:
3484:
885:
803:
246:
44:
5538:
4375:
is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is
1418:
1161:
852:
6134:
5919:
5884:
5774:
4751:
is the sample size, that is, the number of observations in the sample and DFT coefficients.
4330:
represents an average current of 5 amps, but an RMS current of 7.07 amps, in the long term.
2791:
970:
184:
5251:{\displaystyle x_{\text{rms}}^{2}={\overline {x}}^{2}+\sigma _{x}^{2}={\overline {x^{2}}}.}
928:
159:
58:
6067:
6010:
5889:
5120:
5033:
4754:
In this case, the RMS computed in the time domain is the same as in the frequency domain:
2775:
2461:
262:
3128:
Average power can also be found using the same method that in the case of a time-varying
2859:
power dissipated over time, which is calculated by taking the average power dissipation:
6155:
5302:
5297:
5044:
5022:
4681:{\displaystyle \sum _{n=1}^{N}{x^{2}}={\frac {1}{N}}\sum _{m=1}^{N}\left|X\right|^{2},}
4543:
2724:
1119:
819:
815:
238:
5743:
5685:
3282:
Both derivations depend on voltage and current being proportional (that is, the load,
6149:
5952:
5909:
5312:
5055:
3217:
2001:
1879:
846:
842:
5709:
5274:
4440:
5733:
953:
5573:"Determining the Effective or RMS Voltage of Various Waveforms without Calculus"
4346:
1293:
925:
A rectangular pulse wave of duty cycle D, the ratio between the pulse duration (
838:
52:
48:
20:
1095:{\displaystyle =2{\sqrt {3}}\times {\text{RMS}}\approx 3.5\times {\text{RMS}}.}
1031:{\displaystyle =2{\sqrt {2}}\times {\text{RMS}}\approx 2.8\times {\text{RMS}}.}
6046:
5957:
5942:
5386:
Using
Pythagoras' theorem, OC² = OG² + GC² ∴ GC = √
4456:
2446:
2114:
4337:
is sometimes erroneously used (e.g., in the audio industry) as a synonym for
5864:
5690:
3310:
3213:
2360:{\displaystyle y=A_{1}\sin(t)-A_{1}\sin \left(t-{\frac {2\pi }{3}}\right)\,}
1190:
974:
966:
834:
5277:
is removed (that is, RMS(signal) = stdev(signal) if the mean signal is 0).
4209:
A similar analysis leads to the analogous equation for sinusoidal voltage:
3220:, allowing us to calculate the mean power delivered into a specified load.
5159:
4981:
3291:
3209:
2769:
962:
808:
265:
242:
227:
5972:
5859:
5307:
4364:
4287:
4286:
Because of their usefulness in carrying out power calculations, listed
3129:
921:
830:
4448:
849:
waveforms. In each, the centerline is at 0, the positive peak is at
253:
of an estimator measures how far the estimator strays from the data.
1953:{\displaystyle y=\left|2A_{1}\operatorname {frac} (ft)-A_{1}\right|}
5738:
4985:
3513:
is a positive constant and was to be squared within the integral:
952:
920:
829:
472:
The corresponding formula for a continuous function (or waveform)
6051:
6023:
6018:
5995:
4259:{\displaystyle V_{\text{RMS}}={V_{\text{p}} \over {\sqrt {2}}},}
5747:
5624:"Make Better AC RMS Measurements with your Digital Multimeter"
4368:
5734:
A case for why RMS is a misnomer when applied to audio power
3272:{\displaystyle P_{\text{Avg}}=V_{\text{RMS}}I_{\text{RMS}}.}
3198:{\displaystyle P_{\text{Avg}}={V_{\text{RMS}}^{2} \over R}.}
2790:. It is easy to do the calculation when there is a constant
5599:"How to Derive the RMS Value of Pulse and Square Waveforms"
2211:
1824:
1565:
1400:
5509:. Macmillan International Higher Education. p. 185.
2066:{\displaystyle y=2A_{1}\operatorname {frac} (ft)-A_{1}\,}
5663:(2nd ed.). Cambridge University Press. p. 64.
4483:
The RMS can be computed in the frequency domain, using
3046: does not vary over time, it can be factored out)
5376:, QC² = QO² + OC² ∴ QC = √
5171:
5129:
5096:
4763:
4697:
4569:
4546:
4493:
4388:
4218:
3984:
3676:
3522:
3329:
3232:
3156:
2868:
2811:
2733:
2700:
2624:
2495:
2374:
2274:
2232:
2124:
2081:
2011:
1968:
1889:
1845:
1649:
1586:
1455:
1421:
1303:
1259:
1200:
1164:
1129:
1053:
989:
931:
888:
855:
679:
535:
486:
349:
281:
197:
162:
123:
88:
61:
4425:{\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
2847:
However, if the current is a time-varying function,
6104:
6081:
6060:
6037:
6009:
5981:
5918:
5850:
5782:
5540:
5273:variation about the mean, rather than about 0, the
2615:A special case of RMS of waveform combinations is:
5250:
5142:
5111:
4964:
4739:
4680:
4552:
4532:
4424:
4258:
4198:
3964:
3652:
3464:
3271:
3197:
3091:
2836:
2748:
2715:
2683:
2580:
2399:
2359:
2252:
2217:
2102:
2065:
1989:
1952:
1867:
1830:
1627:
1571:
1435:
1406:
1281:
1244:
1178:
1149:
1094:
1030:
937:
910:
874:
791:
659:
518:
461:
332:
218:
175:
144:
109:
74:
694:
1628:{\displaystyle {\sqrt {A_{0}^{2}+A_{1}^{2}}}\,}
5759:
4890:
4871:
2975: denotes the temporal mean of a function
8:
4784:
4769:
4734:
4719:
2774:Electrical engineers often need to know the
945:) and the period (T); illustrated here with
670:and the RMS for a function over all time is
333:{\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}
327:
282:
5659:Chris C. Bissell; David A. Chapman (1992).
4740:{\displaystyle X=\operatorname {DFT} \{x\}}
3208:This equation can be used for any periodic
2400:{\displaystyle A_{1}{\sqrt {\frac {3}{2}}}}
5766:
5752:
5744:
2727:(or average) component of the signal, and
1868:{\displaystyle {\frac {A_{1}}{\sqrt {2}}}}
1282:{\displaystyle {\frac {A_{1}}{\sqrt {2}}}}
5471:
5469:
5234:
5228:
5219:
5214:
5201:
5191:
5181:
5176:
5170:
5134:
5128:
5098:
5097:
5095:
4950:
4925:
4919:
4913:
4907:
4896:
4889:
4888:
4870:
4869:
4868:
4861:
4849:
4840:
4838:
4817:
4812:
4806:
4792:
4790:
4764:
4762:
4696:
4669:
4640:
4629:
4615:
4596:
4591:
4585:
4574:
4568:
4545:
4492:
4402:
4393:
4387:
4244:
4238:
4232:
4223:
4217:
4184:
4178:
4172:
4155:
4142:
4137:
4135:
4126:
4113:
4108:
4103:
4101:
4095:
4078:
4073:
4066:
4061:
4047:
4033:
4020:
4015:
4010:
4008:
4002:
3989:
3983:
3948:
3943:
3936:
3931:
3891:
3878:
3863:
3850:
3845:
3840:
3838:
3832:
3808:
3772:
3764:
3759:
3752:
3747:
3742:
3733:
3720:
3715:
3710:
3708:
3702:
3685:
3677:
3675:
3637:
3615:
3610:
3602:
3597:
3590:
3585:
3580:
3571:
3558:
3553:
3548:
3546:
3540:
3527:
3521:
3445:
3416:
3398:
3393:
3386:
3381:
3368:
3355:
3350:
3345:
3343:
3334:
3328:
3320:is defined to be the peak current, then:
3260:
3250:
3237:
3231:
3181:
3176:
3170:
3161:
3155:
3080:
3068:
3063:
3044:
3036:
3018:
3007:
2973:
2961:
2944:
2929:
2915:
2877:
2869:
2867:
2822:
2810:
2740:
2735:
2732:
2707:
2702:
2699:
2673:
2668:
2663:
2653:
2648:
2643:
2640:
2631:
2626:
2623:
2570:
2565:
2560:
2544:
2539:
2534:
2524:
2519:
2514:
2511:
2502:
2497:
2494:
2385:
2379:
2373:
2356:
2336:
2313:
2285:
2273:
2243:
2237:
2231:
2143:
2131:
2123:
2093:
2086:
2079:
2062:
2056:
2025:
2010:
1980:
1973:
1966:
1939:
1908:
1888:
1852:
1846:
1844:
1789:
1701:
1656:
1648:
1624:
1616:
1611:
1598:
1593:
1587:
1585:
1530:
1487:
1475:
1466:
1454:
1432:
1426:
1420:
1365:
1322:
1310:
1302:
1266:
1260:
1258:
1241:
1211:
1199:
1175:
1169:
1163:
1146:
1140:
1128:
1084:
1070:
1060:
1052:
1020:
1006:
996:
988:
930:
902:
887:
866:
854:
774:
773:
772:
766:
746:
739:
731:
726:
716:
711:
709:
697:
684:
678:
642:
641:
640:
634:
614:
605:
600:
593:
588:
583:
574:
561:
556:
551:
549:
540:
534:
510:
491:
485:
443:
436:
431:
415:
408:
403:
393:
386:
381:
365:
363:
354:
348:
321:
302:
289:
280:
241:that would dissipate the same power in a
203:
202:
196:
167:
161:
136:
125:
122:
94:
93:
87:
66:
60:
3667:to eliminate squaring of trig function:
2798:, through the resistance. For a load of
2749:{\displaystyle {\text{RMS}}_{\text{AC}}}
2449:or the proportion of the time period (1/
1104:
5465:
5339:
5264:Physical scientists often use the term
2103:{\displaystyle A_{1} \over {\sqrt {3}}}
1990:{\displaystyle A_{1} \over {\sqrt {3}}}
261:The RMS value of a set of values (or a
2716:{\displaystyle {\text{V}}_{\text{DC}}}
1245:{\displaystyle y=A_{1}\sin(2\pi ft)\,}
814:In the case of the RMS statistic of a
519:{\displaystyle T_{1}\leq t\leq T_{2}}
7:
6161:Statistical deviation and dispersion
5571:Cartwright, Kenneth V (Fall 2007).
4290:for power outlets (for example, 120
775:
704:
643:
226:and can be defined in terms of an
219:{\displaystyle f_{\mathrm {RMS} }}
210:
207:
204:
145:{\displaystyle \mathrm {RMS} _{x}}
132:
129:
126:
110:{\displaystyle x_{\mathrm {RMS} }}
101:
98:
95:
14:
5482:. Oxford University Press. 2009.
5079:of two distinct positive numbers
4447:is the temperature of the gas in
3082:by definition of root-mean-square
5318:Glossary of mathematical symbols
4976:Relationship to other statistics
4276:represents the peak current and
2253:{\displaystyle A_{1}{\sqrt {D}}}
6122:Pearson correlation coefficient
5479:A Dictionary of Physics (6 ed.)
230:of the square of the function.
152:. The RMS is also known as the
82:, its RMS is denoted as either
5603:MasteringElectronicsDesign.com
5503:Thompson, Sylvanus P. (1965).
5103:
4937:
4931:
4885:
4879:
4829:
4823:
4781:
4775:
4731:
4725:
4707:
4701:
4661:
4655:
4608:
4602:
4527:
4512:
4503:
4497:
4379:using the following equation:
3912:
3900:
3799:
3787:
3633:
3624:
3437:
3428:
3004:
2997:
2912:
2905:
2303:
2297:
2199:
2190:
2166:
2157:
2046:
2037:
1929:
1920:
1812:
1803:
1769:
1760:
1730:
1721:
1684:
1675:
1553:
1544:
1510:
1501:
1388:
1379:
1345:
1336:
1238:
1223:
762:
759:
753:
747:
701:
630:
627:
621:
615:
16:Square root of the mean square
1:
6061:Deep Learning Related Metrics
5739:A Java applet on learning RMS
4283:represents the peak voltage.
822:is used instead of the mean.
237:equals the value of constant
5240:
5196:
3503:is the period of the wave).
882:and the negative peak is at
480:) defined over the interval
235:alternating electric current
5905:Sensitivity and specificity
5661:Digital signal transmission
5143:{\displaystyle \sigma _{x}}
2611:Root mean square AC voltage
802:The RMS over all time of a
6177:
5476:"Root-mean-square value".
5112:{\displaystyle {\bar {x}}}
4979:
4470:Root-mean-square deviation
4467:
4356:
2767:
2608:
2439:is amplitude (peak value),
811:, as shown by Cartwright.
251:root-mean-square deviation
187:. The RMS of a continuous
6130:
5543:. Routledge. p. 48.
5388:OC² − OG²
5323:Mean squared displacement
4533:{\displaystyle x=x(t=nT)}
2837:{\displaystyle P=I^{2}R.}
2802:ohms, power is given by:
2760:component of the signal.
2600:In electrical engineering
2410:
1150:{\displaystyle y=A_{0}\,}
183:), a special case of the
4560:is the sampling period,
4443:, 8.314 J/(mol·K),
3286:, is purely resistive).
2764:Average electrical power
2478:In waveform combinations
2265:Phase-to-phase sine wave
911:{\displaystyle y=-A_{1}}
271:In the case of a set of
5933:Calinski-Harabasz index
5537:Jones, Alan R. (2018).
5292:Average rectified value
4487:. For a sampled signal
1447:DC-shifted square wave
1436:{\displaystyle A_{1}\,}
1179:{\displaystyle A_{0}\,}
1111:Variables and operators
875:{\displaystyle y=A_{1}}
5252:
5144:
5113:
5087:
4966:
4741:
4682:
4645:
4590:
4554:
4534:
4426:
4373:root-mean-square speed
4359:Root-mean-square speed
4260:
4200:
3966:
3665:trigonometric identity
3654:
3466:
3297:In the common case of
3273:
3199:
3093:
2838:
2750:
2717:
2685:
2582:
2401:
2361:
2254:
2219:
2104:
2067:
1991:
1954:
1869:
1832:
1629:
1573:
1437:
1408:
1283:
1246:
1180:
1151:
1096:
1032:
958:
950:
939:
918:
912:
876:
793:
661:
520:
463:
334:
220:
177:
146:
111:
76:
6096:Intra-list Similarity
5253:
5145:
5114:
4989:
4967:
4742:
4683:
4625:
4570:
4555:
4535:
4427:
4261:
4201:
3967:
3655:
3467:
3274:
3200:
3094:
2839:
2784:electrical resistance
2768:Further information:
2751:
2718:
2686:
2609:Further information:
2583:
2402:
2362:
2255:
2220:
2105:
2068:
1992:
1955:
1870:
1833:
1630:
1574:
1438:
1409:
1284:
1247:
1181:
1152:
1097:
1033:
956:
940:
938:{\displaystyle \tau }
924:
913:
877:
833:
794:
662:
521:
464:
335:
221:
178:
176:{\displaystyle M_{2}}
147:
112:
77:
75:{\displaystyle x_{i}}
5580:Technology Interface
5287:Pythagorean addition
5169:
5127:
5094:
4761:
4695:
4567:
4544:
4491:
4386:
4216:
3982:
3674:
3520:
3327:
3230:
3154:
2866:
2809:
2731:
2698:
2622:
2493:
2372:
2272:
2230:
2122:
2078:
2009:
1965:
1887:
1843:
1647:
1584:
1453:
1419:
1301:
1257:
1198:
1162:
1127:
1051:
987:
929:
886:
853:
677:
533:
484:
347:
279:
195:
160:
121:
86:
59:
5684:Weisstein, Eric W.
5597:Nastase, Adrian S.
5378:QO² + OC²
5374:Pythagoras' theorem
5224:
5186:
4992:proof without words
4479:In frequency domain
4294:V in the US, or 230
4085:
3955:
3771:
3609:
3405:
3299:alternating current
3186:
3102:So, the RMS value,
3073:
2782:, dissipated by an
2758:alternating current
2678:
2658:
2575:
2549:
2529:
1621:
1603:
826:In common waveforms
744:
612:
6117:Euclidean distance
6083:Recommender system
5963:Similarity measure
5777:evaluation metrics
5706:"ROOT, TH1:GetRMS"
5686:"Root-Mean-Square"
5640:on 15 January 2019
5506:Calculus Made Easy
5328:True RMS converter
5270:standard deviation
5248:
5210:
5172:
5152:standard deviation
5140:
5109:
5088:
4962:
4918:
4866:
4811:
4737:
4678:
4550:
4530:
4485:Parseval's theorem
4422:
4256:
4196:
4042:
3962:
3960:
3872:
3743:
3650:
3581:
3462:
3377:
3269:
3195:
3172:
3140:), with RMS value
3109:, of the function
3089:
3087:
3059:
2834:
2746:
2713:
2681:
2662:
2642:
2578:
2559:
2533:
2513:
2397:
2357:
2250:
2215:
2210:
2092:
2063:
1979:
1950:
1865:
1828:
1823:
1640:Modified sine wave
1625:
1607:
1589:
1569:
1564:
1433:
1404:
1399:
1279:
1242:
1176:
1147:
1092:
1028:
959:
951:
935:
919:
908:
872:
789:
727:
708:
657:
584:
516:
459:
330:
216:
173:
142:
107:
72:
47:of numbers is the
6143:
6142:
6112:Cosine similarity
5948:Hopkins statistic
5670:978-0-521-42557-5
5398:similar triangles
5268:as a synonym for
5243:
5199:
5179:
5106:
4957:
4944:
4909:
4902:
4857:
4855:
4833:
4802:
4800:
4767:
4623:
4553:{\displaystyle T}
4420:
4419:
4396:
4251:
4249:
4241:
4226:
4191:
4189:
4181:
4167:
4165:
4133:
4098:
4086:
4055:
4040:
4005:
3992:
3956:
3924:
3886:
3870:
3835:
3816:
3806:
3740:
3705:
3688:
3645:
3578:
3543:
3530:
3485:angular frequency
3457:
3419:
3375:
3337:
3263:
3253:
3240:
3218:sawtooth waveform
3190:
3179:
3164:
3083:
3066:
3047:
3039:
2976:
2947:
2743:
2738:
2710:
2705:
2679:
2671:
2666:
2651:
2646:
2634:
2629:
2576:
2563:
2537:
2517:
2505:
2500:
2475:
2474:
2395:
2394:
2349:
2248:
2100:
2098:
1987:
1985:
1863:
1862:
1622:
1277:
1276:
1087:
1073:
1065:
1023:
1009:
1001:
804:periodic function
784:
724:
693:
687:
652:
581:
543:
454:
373:
357:
247:estimation theory
6168:
6135:Confusion matrix
5910:Logarithmic Loss
5775:Machine learning
5768:
5761:
5754:
5745:
5721:
5720:
5718:
5717:
5708:. Archived from
5702:
5696:
5695:
5681:
5675:
5674:
5656:
5650:
5649:
5647:
5645:
5639:
5633:. Archived from
5628:
5620:
5614:
5613:
5611:
5609:
5594:
5588:
5587:
5577:
5568:
5562:
5561:
5559:
5557:
5534:
5528:
5527:
5525:
5523:
5500:
5494:
5493:
5473:
5453:
5447:
5445:
5444:
5441:
5438:
5431:
5429:
5428:
5425:
5422:
5415:
5413:
5412:
5409:
5406:
5389:
5379:
5344:
5266:root mean square
5257:
5255:
5254:
5249:
5244:
5239:
5238:
5229:
5223:
5218:
5206:
5205:
5200:
5192:
5185:
5180:
5177:
5149:
5147:
5146:
5141:
5139:
5138:
5118:
5116:
5115:
5110:
5108:
5107:
5099:
5078:
5063:
5052:
5041:
5030:
5019:
5012:root mean square
5008:
4971:
4969:
4968:
4963:
4958:
4956:
4955:
4954:
4949:
4945:
4940:
4926:
4917:
4908:
4903:
4901:
4900:
4895:
4894:
4893:
4875:
4874:
4865:
4856:
4854:
4853:
4841:
4839:
4834:
4832:
4822:
4821:
4810:
4801:
4793:
4791:
4768:
4765:
4746:
4744:
4743:
4738:
4687:
4685:
4684:
4679:
4674:
4673:
4668:
4664:
4644:
4639:
4624:
4616:
4611:
4601:
4600:
4589:
4584:
4559:
4557:
4556:
4551:
4539:
4537:
4536:
4531:
4431:
4429:
4428:
4423:
4421:
4415:
4404:
4403:
4398:
4397:
4394:
4325:
4324:
4318:
4317:
4297:
4293:
4265:
4263:
4262:
4257:
4252:
4250:
4245:
4243:
4242:
4239:
4233:
4228:
4227:
4224:
4205:
4203:
4202:
4197:
4192:
4190:
4185:
4183:
4182:
4179:
4173:
4168:
4166:
4161:
4160:
4159:
4147:
4146:
4136:
4134:
4132:
4131:
4130:
4118:
4117:
4104:
4102:
4100:
4099:
4096:
4087:
4084:
4083:
4082:
4072:
4071:
4070:
4060:
4056:
4048:
4041:
4039:
4038:
4037:
4025:
4024:
4011:
4009:
4007:
4006:
4003:
3994:
3993:
3990:
3971:
3969:
3968:
3963:
3961:
3957:
3954:
3953:
3952:
3942:
3941:
3940:
3930:
3926:
3925:
3923:
3915:
3892:
3887:
3879:
3871:
3869:
3868:
3867:
3855:
3854:
3841:
3839:
3837:
3836:
3833:
3821:
3817:
3815:
3807:
3802:
3773:
3770:
3769:
3768:
3758:
3757:
3756:
3741:
3739:
3738:
3737:
3725:
3724:
3711:
3709:
3707:
3706:
3703:
3690:
3689:
3686:
3659:
3657:
3656:
3651:
3646:
3644:
3636:
3620:
3619:
3608:
3607:
3606:
3596:
3595:
3594:
3579:
3577:
3576:
3575:
3563:
3562:
3549:
3547:
3545:
3544:
3541:
3532:
3531:
3528:
3494:
3471:
3469:
3468:
3463:
3458:
3450:
3449:
3444:
3440:
3421:
3420:
3417:
3404:
3403:
3402:
3392:
3391:
3390:
3376:
3374:
3373:
3372:
3360:
3359:
3346:
3344:
3339:
3338:
3335:
3278:
3276:
3275:
3270:
3265:
3264:
3261:
3255:
3254:
3251:
3242:
3241:
3238:
3204:
3202:
3201:
3196:
3191:
3185:
3180:
3177:
3171:
3166:
3165:
3162:
3098:
3096:
3095:
3090:
3088:
3084:
3081:
3078:
3072:
3067:
3064:
3052:
3048:
3045:
3040:
3037:
3034:
3029:
3028:
3017:
3013:
3012:
3011:
2981:
2977:
2974:
2972:
2971:
2960:
2948:
2945:
2942:
2940:
2939:
2928:
2924:
2920:
2919:
2888:
2887:
2843:
2841:
2840:
2835:
2827:
2826:
2755:
2753:
2752:
2747:
2745:
2744:
2741:
2739:
2736:
2722:
2720:
2719:
2714:
2712:
2711:
2708:
2706:
2703:
2690:
2688:
2687:
2682:
2680:
2677:
2672:
2669:
2667:
2664:
2657:
2652:
2649:
2647:
2644:
2641:
2636:
2635:
2632:
2630:
2627:
2587:
2585:
2584:
2579:
2577:
2574:
2569:
2564:
2561:
2548:
2543:
2538:
2535:
2528:
2523:
2518:
2515:
2512:
2507:
2506:
2503:
2501:
2498:
2418:is displacement,
2406:
2404:
2403:
2398:
2396:
2387:
2386:
2384:
2383:
2366:
2364:
2363:
2358:
2355:
2351:
2350:
2345:
2337:
2318:
2317:
2290:
2289:
2259:
2257:
2256:
2251:
2249:
2244:
2242:
2241:
2224:
2222:
2221:
2216:
2214:
2213:
2148:
2147:
2109:
2107:
2106:
2101:
2099:
2094:
2091:
2090:
2080:
2072:
2070:
2069:
2064:
2061:
2060:
2030:
2029:
1996:
1994:
1993:
1988:
1986:
1981:
1978:
1977:
1967:
1959:
1957:
1956:
1951:
1949:
1945:
1944:
1943:
1913:
1912:
1874:
1872:
1871:
1866:
1864:
1858:
1857:
1856:
1847:
1837:
1835:
1834:
1829:
1827:
1826:
1794:
1793:
1706:
1705:
1634:
1632:
1631:
1626:
1623:
1620:
1615:
1602:
1597:
1588:
1578:
1576:
1575:
1570:
1568:
1567:
1535:
1534:
1492:
1491:
1471:
1470:
1442:
1440:
1439:
1434:
1431:
1430:
1413:
1411:
1410:
1405:
1403:
1402:
1370:
1369:
1327:
1326:
1288:
1286:
1285:
1280:
1278:
1272:
1271:
1270:
1261:
1251:
1249:
1248:
1243:
1216:
1215:
1185:
1183:
1182:
1177:
1174:
1173:
1156:
1154:
1153:
1148:
1145:
1144:
1105:
1101:
1099:
1098:
1093:
1088:
1085:
1074:
1071:
1066:
1061:
1037:
1035:
1034:
1029:
1024:
1021:
1010:
1007:
1002:
997:
944:
942:
941:
936:
917:
915:
914:
909:
907:
906:
881:
879:
878:
873:
871:
870:
798:
796:
795:
790:
785:
783:
779:
778:
771:
770:
765:
743:
738:
725:
723:
712:
710:
707:
689:
688:
685:
666:
664:
663:
658:
653:
651:
647:
646:
639:
638:
633:
611:
610:
609:
599:
598:
597:
582:
580:
579:
578:
566:
565:
552:
550:
545:
544:
541:
525:
523:
522:
517:
515:
514:
496:
495:
468:
466:
465:
460:
455:
453:
449:
448:
447:
442:
441:
440:
420:
419:
414:
413:
412:
398:
397:
392:
391:
390:
374:
366:
364:
359:
358:
355:
339:
337:
336:
331:
326:
325:
307:
306:
294:
293:
225:
223:
222:
217:
215:
214:
213:
185:generalized mean
182:
180:
179:
174:
172:
171:
151:
149:
148:
143:
141:
140:
135:
116:
114:
113:
108:
106:
105:
104:
81:
79:
78:
73:
71:
70:
37:
36:
25:root mean square
6176:
6175:
6171:
6170:
6169:
6167:
6166:
6165:
6146:
6145:
6144:
6139:
6126:
6100:
6077:
6068:Inception score
6056:
6033:
6011:Computer Vision
6005:
5977:
5914:
5846:
5778:
5772:
5730:
5725:
5724:
5715:
5713:
5704:
5703:
5699:
5683:
5682:
5678:
5671:
5658:
5657:
5653:
5643:
5641:
5637:
5626:
5622:
5621:
5617:
5607:
5605:
5596:
5595:
5591:
5575:
5570:
5569:
5565:
5555:
5553:
5551:
5536:
5535:
5531:
5521:
5519:
5517:
5502:
5501:
5497:
5490:
5475:
5474:
5467:
5462:
5457:
5456:
5442:
5439:
5436:
5435:
5433:
5426:
5423:
5420:
5419:
5417:
5410:
5407:
5404:
5403:
5401:
5395:
5387:
5385:
5377:
5371:
5345:
5341:
5336:
5283:
5230:
5190:
5167:
5166:
5130:
5125:
5124:
5121:arithmetic mean
5092:
5091:
5065:
5054:
5043:
5034:arithmetic mean
5032:
5021:
5010:
4995:
4984:
4978:
4927:
4921:
4920:
4867:
4845:
4813:
4759:
4758:
4693:
4692:
4651:
4647:
4646:
4592:
4565:
4564:
4542:
4541:
4489:
4488:
4481:
4472:
4466:
4439:represents the
4405:
4389:
4384:
4383:
4371:molecules, the
4361:
4355:
4322:
4320:
4315:
4313:
4311:
4304:
4295:
4291:
4282:
4275:
4234:
4219:
4214:
4213:
4174:
4151:
4138:
4122:
4109:
4091:
4074:
4062:
4043:
4029:
4016:
3998:
3985:
3980:
3979:
3959:
3958:
3944:
3932:
3916:
3893:
3877:
3873:
3859:
3846:
3828:
3819:
3818:
3774:
3760:
3748:
3729:
3716:
3698:
3691:
3681:
3672:
3671:
3611:
3598:
3586:
3567:
3554:
3536:
3523:
3518:
3517:
3512:
3492:
3412:
3411:
3407:
3406:
3394:
3382:
3364:
3351:
3330:
3325:
3324:
3319:
3256:
3246:
3233:
3228:
3227:
3157:
3152:
3151:
3146:
3108:
3086:
3085:
3077:
3050:
3049:
3033:
3003:
2993:
2989:
2988:
2979:
2978:
2950:
2949:
2941:
2911:
2901:
2897:
2896:
2889:
2873:
2864:
2863:
2818:
2807:
2806:
2772:
2766:
2734:
2729:
2728:
2701:
2696:
2695:
2625:
2620:
2619:
2613:
2607:
2602:
2597:
2496:
2491:
2490:
2480:
2471:
2462:fractional part
2437:
2375:
2370:
2369:
2338:
2329:
2325:
2309:
2281:
2270:
2269:
2233:
2228:
2227:
2209:
2208:
2182:
2176:
2175:
2149:
2139:
2132:
2120:
2119:
2082:
2076:
2075:
2052:
2021:
2007:
2006:
1969:
1963:
1962:
1935:
1904:
1900:
1896:
1885:
1884:
1848:
1841:
1840:
1822:
1821:
1795:
1785:
1779:
1778:
1746:
1740:
1739:
1707:
1697:
1694:
1693:
1667:
1657:
1645:
1644:
1582:
1581:
1563:
1562:
1536:
1526:
1520:
1519:
1493:
1483:
1476:
1462:
1451:
1450:
1422:
1417:
1416:
1398:
1397:
1371:
1361:
1355:
1354:
1328:
1318:
1311:
1299:
1298:
1262:
1255:
1254:
1207:
1196:
1195:
1165:
1160:
1159:
1136:
1125:
1124:
1049:
1048:
985:
984:
927:
926:
898:
884:
883:
862:
851:
850:
828:
745:
680:
675:
674:
613:
601:
589:
570:
557:
536:
531:
530:
506:
487:
482:
481:
432:
430:
404:
402:
382:
380:
379:
375:
350:
345:
344:
317:
298:
285:
277:
276:
263:continuous-time
259:
198:
193:
192:
163:
158:
157:
124:
119:
118:
89:
84:
83:
62:
57:
56:
34:
33:
17:
12:
11:
5:
6174:
6172:
6164:
6163:
6158:
6148:
6147:
6141:
6140:
6138:
6137:
6131:
6128:
6127:
6125:
6124:
6119:
6114:
6108:
6106:
6102:
6101:
6099:
6098:
6093:
6087:
6085:
6079:
6078:
6076:
6075:
6070:
6064:
6062:
6058:
6057:
6055:
6054:
6049:
6043:
6041:
6035:
6034:
6032:
6031:
6026:
6021:
6015:
6013:
6007:
6006:
6004:
6003:
5998:
5993:
5987:
5985:
5979:
5978:
5976:
5975:
5970:
5965:
5960:
5955:
5950:
5945:
5940:
5938:Davies-Bouldin
5935:
5930:
5924:
5922:
5916:
5915:
5913:
5912:
5907:
5902:
5897:
5892:
5887:
5882:
5877:
5872:
5867:
5862:
5856:
5854:
5852:Classification
5848:
5847:
5845:
5844:
5839:
5834:
5829:
5824:
5819:
5814:
5809:
5804:
5799:
5794:
5788:
5786:
5780:
5779:
5773:
5771:
5770:
5763:
5756:
5748:
5742:
5741:
5736:
5729:
5728:External links
5726:
5723:
5722:
5697:
5676:
5669:
5651:
5615:
5589:
5586:(1): 20 pages.
5563:
5549:
5529:
5515:
5495:
5488:
5464:
5463:
5461:
5458:
5455:
5454:
5338:
5337:
5335:
5332:
5331:
5330:
5325:
5320:
5315:
5310:
5305:
5303:Geometric mean
5300:
5298:Central moment
5295:
5289:
5282:
5279:
5259:
5258:
5247:
5242:
5237:
5233:
5227:
5222:
5217:
5213:
5209:
5204:
5198:
5195:
5189:
5184:
5175:
5137:
5133:
5105:
5102:
5045:geometric mean
5023:quadratic mean
4977:
4974:
4973:
4972:
4961:
4953:
4948:
4943:
4939:
4936:
4933:
4930:
4924:
4916:
4912:
4906:
4899:
4892:
4887:
4884:
4881:
4878:
4873:
4864:
4860:
4852:
4848:
4844:
4837:
4831:
4828:
4825:
4820:
4816:
4809:
4805:
4799:
4796:
4789:
4786:
4783:
4780:
4777:
4774:
4771:
4736:
4733:
4730:
4727:
4724:
4721:
4718:
4715:
4712:
4709:
4706:
4703:
4700:
4689:
4688:
4677:
4672:
4667:
4663:
4660:
4657:
4654:
4650:
4643:
4638:
4635:
4632:
4628:
4622:
4619:
4614:
4610:
4607:
4604:
4599:
4595:
4588:
4583:
4580:
4577:
4573:
4549:
4529:
4526:
4523:
4520:
4517:
4514:
4511:
4508:
4505:
4502:
4499:
4496:
4480:
4477:
4468:Main article:
4465:
4462:
4433:
4432:
4418:
4414:
4411:
4408:
4401:
4392:
4357:Main article:
4354:
4351:
4309:
4302:
4280:
4273:
4267:
4266:
4255:
4248:
4237:
4231:
4222:
4207:
4206:
4195:
4188:
4177:
4171:
4164:
4158:
4154:
4150:
4145:
4141:
4129:
4125:
4121:
4116:
4112:
4107:
4094:
4090:
4081:
4077:
4069:
4065:
4059:
4054:
4051:
4046:
4036:
4032:
4028:
4023:
4019:
4014:
4001:
3997:
3988:
3973:
3972:
3951:
3947:
3939:
3935:
3929:
3922:
3919:
3914:
3911:
3908:
3905:
3902:
3899:
3896:
3890:
3885:
3882:
3876:
3866:
3862:
3858:
3853:
3849:
3844:
3831:
3827:
3824:
3822:
3820:
3814:
3811:
3805:
3801:
3798:
3795:
3792:
3789:
3786:
3783:
3780:
3777:
3767:
3763:
3755:
3751:
3746:
3736:
3732:
3728:
3723:
3719:
3714:
3701:
3697:
3694:
3692:
3684:
3680:
3679:
3661:
3660:
3649:
3643:
3640:
3635:
3632:
3629:
3626:
3623:
3618:
3614:
3605:
3601:
3593:
3589:
3584:
3574:
3570:
3566:
3561:
3557:
3552:
3539:
3535:
3526:
3510:
3491: = 2
3473:
3472:
3461:
3456:
3453:
3448:
3443:
3439:
3436:
3433:
3430:
3427:
3424:
3415:
3410:
3401:
3397:
3389:
3385:
3380:
3371:
3367:
3363:
3358:
3354:
3349:
3342:
3333:
3317:
3280:
3279:
3268:
3259:
3249:
3245:
3236:
3206:
3205:
3194:
3189:
3184:
3175:
3169:
3160:
3144:
3106:
3100:
3099:
3079:
3076:
3071:
3062:
3058:
3055:
3053:
3051:
3043:
3035:
3032:
3027:
3024:
3021:
3016:
3010:
3006:
3002:
2999:
2996:
2992:
2987:
2984:
2982:
2980:
2970:
2967:
2964:
2959:
2956:
2953:
2943:
2938:
2935:
2932:
2927:
2923:
2918:
2914:
2910:
2907:
2904:
2900:
2895:
2892:
2890:
2886:
2883:
2880:
2876:
2872:
2871:
2845:
2844:
2833:
2830:
2825:
2821:
2817:
2814:
2765:
2762:
2725:direct current
2723:refers to the
2692:
2691:
2676:
2661:
2656:
2639:
2606:
2603:
2601:
2598:
2596:
2593:
2589:
2588:
2573:
2568:
2558:
2555:
2552:
2547:
2542:
2532:
2527:
2522:
2510:
2479:
2476:
2473:
2472:
2470:
2469:
2454:
2440:
2435:
2431:
2425:
2419:
2412:
2408:
2407:
2393:
2390:
2382:
2378:
2367:
2354:
2348:
2344:
2341:
2335:
2332:
2328:
2324:
2321:
2316:
2312:
2308:
2305:
2302:
2299:
2296:
2293:
2288:
2284:
2280:
2277:
2267:
2261:
2260:
2247:
2240:
2236:
2225:
2212:
2207:
2204:
2201:
2198:
2195:
2192:
2189:
2186:
2183:
2181:
2178:
2177:
2174:
2171:
2168:
2165:
2162:
2159:
2156:
2153:
2150:
2146:
2142:
2138:
2137:
2135:
2130:
2127:
2117:
2111:
2110:
2097:
2089:
2085:
2073:
2059:
2055:
2051:
2048:
2045:
2042:
2039:
2036:
2033:
2028:
2024:
2020:
2017:
2014:
2004:
1998:
1997:
1984:
1976:
1972:
1960:
1948:
1942:
1938:
1934:
1931:
1928:
1925:
1922:
1919:
1916:
1911:
1907:
1903:
1899:
1895:
1892:
1882:
1876:
1875:
1861:
1855:
1851:
1838:
1825:
1820:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1792:
1788:
1784:
1781:
1780:
1777:
1774:
1771:
1768:
1765:
1762:
1759:
1756:
1753:
1750:
1747:
1745:
1742:
1741:
1738:
1735:
1732:
1729:
1726:
1723:
1720:
1717:
1714:
1711:
1708:
1704:
1700:
1696:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1671:
1668:
1666:
1663:
1662:
1660:
1655:
1652:
1642:
1636:
1635:
1619:
1614:
1610:
1606:
1601:
1596:
1592:
1579:
1566:
1561:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1537:
1533:
1529:
1525:
1522:
1521:
1518:
1515:
1512:
1509:
1506:
1503:
1500:
1497:
1494:
1490:
1486:
1482:
1481:
1479:
1474:
1469:
1465:
1461:
1458:
1448:
1444:
1443:
1429:
1425:
1414:
1401:
1396:
1393:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1368:
1364:
1360:
1357:
1356:
1353:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1329:
1325:
1321:
1317:
1316:
1314:
1309:
1306:
1296:
1290:
1289:
1275:
1269:
1265:
1252:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1214:
1210:
1206:
1203:
1193:
1187:
1186:
1172:
1168:
1157:
1143:
1139:
1135:
1132:
1122:
1116:
1115:
1112:
1109:
1103:
1102:
1091:
1083:
1080:
1077:
1069:
1064:
1059:
1056:
1039:
1038:
1027:
1019:
1016:
1013:
1005:
1000:
995:
992:
934:
905:
901:
897:
894:
891:
869:
865:
861:
858:
827:
824:
820:expected value
816:random process
800:
799:
788:
782:
777:
769:
764:
761:
758:
755:
752:
749:
742:
737:
734:
730:
722:
719:
715:
706:
703:
700:
696:
692:
683:
668:
667:
656:
650:
645:
637:
632:
629:
626:
623:
620:
617:
608:
604:
596:
592:
587:
577:
573:
569:
564:
560:
555:
548:
539:
513:
509:
505:
502:
499:
494:
490:
470:
469:
458:
452:
446:
439:
435:
429:
426:
423:
418:
411:
407:
401:
396:
389:
385:
378:
372:
369:
362:
353:
329:
324:
320:
316:
313:
310:
305:
301:
297:
292:
288:
284:
258:
255:
243:resistive load
239:direct current
233:The RMS of an
212:
209:
206:
201:
170:
166:
154:quadratic mean
139:
134:
131:
128:
103:
100:
97:
92:
69:
65:
55:. Given a set
15:
13:
10:
9:
6:
4:
3:
2:
6173:
6162:
6159:
6157:
6154:
6153:
6151:
6136:
6133:
6132:
6129:
6123:
6120:
6118:
6115:
6113:
6110:
6109:
6107:
6103:
6097:
6094:
6092:
6089:
6088:
6086:
6084:
6080:
6074:
6071:
6069:
6066:
6065:
6063:
6059:
6053:
6050:
6048:
6045:
6044:
6042:
6040:
6036:
6030:
6027:
6025:
6022:
6020:
6017:
6016:
6014:
6012:
6008:
6002:
5999:
5997:
5994:
5992:
5989:
5988:
5986:
5984:
5980:
5974:
5971:
5969:
5966:
5964:
5961:
5959:
5956:
5954:
5953:Jaccard index
5951:
5949:
5946:
5944:
5941:
5939:
5936:
5934:
5931:
5929:
5926:
5925:
5923:
5921:
5917:
5911:
5908:
5906:
5903:
5901:
5898:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5857:
5855:
5853:
5849:
5843:
5840:
5838:
5835:
5833:
5830:
5828:
5825:
5823:
5820:
5818:
5815:
5813:
5810:
5808:
5805:
5803:
5800:
5798:
5795:
5793:
5790:
5789:
5787:
5785:
5781:
5776:
5769:
5764:
5762:
5757:
5755:
5750:
5749:
5746:
5740:
5737:
5735:
5732:
5731:
5727:
5712:on 2017-06-30
5711:
5707:
5701:
5698:
5693:
5692:
5687:
5680:
5677:
5672:
5666:
5662:
5655:
5652:
5636:
5632:
5625:
5619:
5616:
5604:
5600:
5593:
5590:
5585:
5581:
5574:
5567:
5564:
5552:
5550:9781351661386
5546:
5542:
5541:
5533:
5530:
5518:
5516:9781349004874
5512:
5508:
5507:
5499:
5496:
5491:
5489:9780199233991
5485:
5481:
5480:
5472:
5470:
5466:
5459:
5451:
5432:∴ HC =
5399:
5393:
5383:
5375:
5369:
5366:, and radius
5365:
5361:
5357:
5353:
5349:
5343:
5340:
5333:
5329:
5326:
5324:
5321:
5319:
5316:
5314:
5313:Least squares
5311:
5309:
5306:
5304:
5301:
5299:
5296:
5293:
5290:
5288:
5285:
5284:
5280:
5278:
5276:
5271:
5267:
5262:
5245:
5235:
5231:
5225:
5220:
5215:
5211:
5207:
5202:
5193:
5187:
5182:
5173:
5165:
5164:
5163:
5161:
5157:
5153:
5135:
5131:
5122:
5100:
5086:
5082:
5076:
5072:
5068:
5061:
5057:
5056:harmonic mean
5050:
5046:
5039:
5035:
5028:
5024:
5017:
5013:
5006:
5002:
4998:
4993:
4988:
4983:
4975:
4959:
4951:
4946:
4941:
4934:
4928:
4922:
4914:
4910:
4904:
4897:
4882:
4876:
4862:
4858:
4850:
4846:
4842:
4835:
4826:
4818:
4814:
4807:
4803:
4797:
4794:
4787:
4778:
4772:
4757:
4756:
4755:
4752:
4750:
4728:
4722:
4716:
4713:
4710:
4704:
4698:
4675:
4670:
4665:
4658:
4652:
4648:
4641:
4636:
4633:
4630:
4626:
4620:
4617:
4612:
4605:
4597:
4593:
4586:
4581:
4578:
4575:
4571:
4563:
4562:
4561:
4547:
4524:
4521:
4518:
4515:
4509:
4506:
4500:
4494:
4486:
4478:
4476:
4471:
4463:
4461:
4458:
4454:
4450:
4446:
4442:
4438:
4416:
4412:
4409:
4406:
4399:
4390:
4382:
4381:
4380:
4378:
4374:
4370:
4366:
4360:
4352:
4350:
4348:
4344:
4343:average power
4340:
4336:
4331:
4327:
4312: Ă—
4308:
4305: =
4301:
4289:
4284:
4279:
4272:
4253:
4246:
4235:
4229:
4220:
4212:
4211:
4210:
4193:
4186:
4175:
4169:
4162:
4156:
4152:
4148:
4143:
4139:
4127:
4123:
4119:
4114:
4110:
4105:
4092:
4088:
4079:
4075:
4067:
4063:
4057:
4052:
4049:
4044:
4034:
4030:
4026:
4021:
4017:
4012:
3999:
3995:
3986:
3978:
3977:
3976:
3949:
3945:
3937:
3933:
3927:
3920:
3917:
3909:
3906:
3903:
3897:
3894:
3888:
3883:
3880:
3874:
3864:
3860:
3856:
3851:
3847:
3842:
3829:
3825:
3823:
3812:
3809:
3803:
3796:
3793:
3790:
3784:
3781:
3778:
3775:
3765:
3761:
3753:
3749:
3744:
3734:
3730:
3726:
3721:
3717:
3712:
3699:
3695:
3693:
3682:
3670:
3669:
3668:
3666:
3647:
3641:
3638:
3630:
3627:
3621:
3616:
3612:
3603:
3599:
3591:
3587:
3582:
3572:
3568:
3564:
3559:
3555:
3550:
3537:
3533:
3524:
3516:
3515:
3514:
3509:
3504:
3502:
3498:
3490:
3486:
3482:
3478:
3459:
3454:
3451:
3446:
3441:
3434:
3431:
3425:
3422:
3413:
3408:
3399:
3395:
3387:
3383:
3378:
3369:
3365:
3361:
3356:
3352:
3347:
3340:
3331:
3323:
3322:
3321:
3316:
3312:
3308:
3304:
3300:
3295:
3293:
3289:
3285:
3266:
3257:
3247:
3243:
3234:
3226:
3225:
3224:
3221:
3219:
3215:
3211:
3192:
3187:
3182:
3173:
3167:
3158:
3150:
3149:
3148:
3143:
3139:
3135:
3131:
3126:
3124:
3120:
3116:
3112:
3105:
3074:
3069:
3060:
3056:
3054:
3041:
3030:
3025:
3022:
3019:
3014:
3008:
3000:
2994:
2990:
2985:
2983:
2968:
2965:
2962:
2957:
2954:
2951:
2936:
2933:
2930:
2925:
2921:
2916:
2908:
2902:
2898:
2893:
2891:
2884:
2881:
2878:
2874:
2862:
2861:
2860:
2858:
2854:
2850:
2831:
2828:
2823:
2819:
2815:
2812:
2805:
2804:
2803:
2801:
2797:
2793:
2789:
2785:
2781:
2777:
2771:
2763:
2761:
2759:
2726:
2674:
2659:
2654:
2637:
2618:
2617:
2616:
2612:
2604:
2599:
2594:
2592:
2571:
2566:
2556:
2553:
2550:
2545:
2540:
2530:
2525:
2520:
2508:
2489:
2488:
2487:
2485:
2477:
2467:
2463:
2459:
2455:
2453:) spent high,
2452:
2448:
2444:
2441:
2438:
2432:
2430:is frequency,
2429:
2426:
2423:
2420:
2417:
2414:
2413:
2409:
2391:
2388:
2380:
2376:
2368:
2352:
2346:
2342:
2339:
2333:
2330:
2326:
2322:
2319:
2314:
2310:
2306:
2300:
2294:
2291:
2286:
2282:
2278:
2275:
2268:
2266:
2263:
2262:
2245:
2238:
2234:
2226:
2205:
2202:
2196:
2193:
2187:
2184:
2179:
2172:
2169:
2163:
2160:
2154:
2151:
2144:
2140:
2133:
2128:
2125:
2118:
2116:
2113:
2112:
2095:
2087:
2083:
2074:
2057:
2053:
2049:
2043:
2040:
2034:
2031:
2026:
2022:
2018:
2015:
2012:
2005:
2003:
2002:Sawtooth wave
2000:
1999:
1982:
1974:
1970:
1961:
1946:
1940:
1936:
1932:
1926:
1923:
1917:
1914:
1909:
1905:
1901:
1897:
1893:
1890:
1883:
1881:
1880:Triangle wave
1878:
1877:
1859:
1853:
1849:
1839:
1818:
1815:
1809:
1806:
1800:
1797:
1790:
1786:
1782:
1775:
1772:
1766:
1763:
1757:
1754:
1751:
1748:
1743:
1736:
1733:
1727:
1724:
1718:
1715:
1712:
1709:
1702:
1698:
1690:
1687:
1681:
1678:
1672:
1669:
1664:
1658:
1653:
1650:
1643:
1641:
1638:
1637:
1617:
1612:
1608:
1604:
1599:
1594:
1590:
1580:
1559:
1556:
1550:
1547:
1541:
1538:
1531:
1527:
1523:
1516:
1513:
1507:
1504:
1498:
1495:
1488:
1484:
1477:
1472:
1467:
1463:
1459:
1456:
1449:
1446:
1445:
1427:
1423:
1415:
1394:
1391:
1385:
1382:
1376:
1373:
1366:
1362:
1358:
1351:
1348:
1342:
1339:
1333:
1330:
1323:
1319:
1312:
1307:
1304:
1297:
1295:
1292:
1291:
1273:
1267:
1263:
1253:
1235:
1232:
1229:
1226:
1220:
1217:
1212:
1208:
1204:
1201:
1194:
1192:
1189:
1188:
1170:
1166:
1158:
1141:
1137:
1133:
1130:
1123:
1121:
1118:
1117:
1113:
1110:
1107:
1106:
1089:
1081:
1078:
1075:
1067:
1062:
1057:
1054:
1047:
1044:
1043:
1042:
1025:
1017:
1014:
1011:
1003:
998:
993:
990:
983:
980:
979:
978:
976:
972:
968:
964:
955:
948:
932:
923:
903:
899:
895:
892:
889:
867:
863:
859:
856:
848:
844:
840:
836:
832:
825:
823:
821:
817:
812:
810:
805:
786:
780:
767:
756:
750:
740:
735:
732:
728:
720:
717:
713:
698:
690:
681:
673:
672:
671:
654:
648:
635:
624:
618:
606:
602:
594:
590:
585:
575:
571:
567:
562:
558:
553:
546:
537:
529:
528:
527:
511:
507:
503:
500:
497:
492:
488:
479:
475:
456:
450:
444:
437:
433:
427:
424:
421:
416:
409:
405:
399:
394:
387:
383:
376:
370:
367:
360:
351:
343:
342:
341:
340:, the RMS is
322:
318:
314:
311:
308:
303:
299:
295:
290:
286:
274:
269:
267:
264:
256:
254:
252:
248:
244:
240:
236:
231:
229:
199:
190:
186:
168:
164:
155:
137:
90:
67:
63:
54:
51:of the set's
50:
46:
42:
38:
30:
26:
22:
5821:
5714:. Retrieved
5710:the original
5700:
5689:
5679:
5660:
5654:
5642:. Retrieved
5635:the original
5630:
5618:
5606:. Retrieved
5602:
5592:
5583:
5579:
5566:
5554:. Retrieved
5539:
5532:
5520:. Retrieved
5505:
5498:
5478:
5449:
5391:
5381:
5367:
5363:
5359:
5355:
5351:
5347:
5342:
5275:DC component
5265:
5263:
5260:
5089:
5084:
5080:
5074:
5070:
5066:
5059:
5048:
5037:
5026:
5015:
5011:
5004:
5000:
4996:
4753:
4748:
4690:
4482:
4473:
4452:
4444:
4441:gas constant
4436:
4434:
4372:
4362:
4342:
4338:
4334:
4332:
4328:
4306:
4299:
4285:
4277:
4270:
4268:
4208:
3974:
3662:
3507:
3505:
3500:
3496:
3488:
3480:
3479:is time and
3476:
3474:
3314:
3306:
3302:
3296:
3283:
3281:
3222:
3212:, such as a
3207:
3141:
3137:
3133:
3127:
3122:
3118:
3114:
3110:
3103:
3101:
2856:
2852:
2848:
2846:
2799:
2795:
2787:
2779:
2773:
2693:
2614:
2590:
2481:
2465:
2457:
2450:
2442:
2433:
2427:
2421:
2415:
1046:Peak-to-peak
1045:
1040:
982:Peak-to-peak
981:
960:
946:
813:
801:
669:
477:
473:
471:
272:
270:
260:
232:
153:
40:
32:
28:
24:
18:
4347:Audio power
2946:where
1294:Square wave
191:is denoted
53:mean square
49:square root
21:mathematics
6150:Categories
6105:Similarity
6047:Perplexity
5958:Rand index
5943:Dunn index
5928:Silhouette
5920:Clustering
5784:Regression
5716:2013-07-18
5644:15 January
5608:21 January
5460:References
5370:= QO = OG.
5156:population
4990:Geometric
4980:See also:
4457:molar mass
4377:calculated
4339:mean power
3311:sinusoidal
3214:sinusoidal
2484:orthogonal
2447:duty cycle
2115:Pulse wave
965:is a pure
257:Definition
5875:Precision
5827:RMSE/RMSD
5691:MathWorld
5350:and BC =
5241:¯
5212:σ
5197:¯
5132:σ
5104:¯
4911:∑
4859:∑
4804:∑
4717:
4627:∑
4572:∑
4335:RMS power
4333:The term
4149:−
4120:−
4027:−
3921:ω
3907:ω
3898:
3889:−
3857:−
3794:ω
3785:
3779:−
3745:∫
3727:−
3628:ω
3622:
3583:∫
3565:−
3432:ω
3426:
3379:∫
3362:−
3038:(as
2955:⋯
2554:⋯
2460:) is the
2343:π
2334:−
2323:
2307:−
2295:
2188:
2155:
2050:−
2035:
1933:−
1918:
1801:
1783:−
1758:
1719:
1673:
1542:
1524:−
1499:
1377:
1359:−
1334:
1230:π
1221:
1191:Sine wave
1082:×
1076:≈
1068:×
1018:×
1012:≈
1004:×
975:amplitude
967:sine wave
933:τ
896:−
733:−
729:∫
705:∞
702:→
586:∫
568:−
504:≤
498:≤
425:⋯
312:…
156:(denoted
27:(abbrev.
6091:Coverage
5870:Accuracy
5631:Keysight
5437:GC²
5346:If AC =
5281:See also
5162:, then:
5160:waveform
5069: (
4999: (
4982:Accuracy
4540:, where
4288:voltages
3663:Using a
3499:, where
3292:AC power
3288:Reactive
3210:waveform
2770:AC power
2424:is time,
1108:Waveform
971:periodic
963:waveform
847:sawtooth
843:triangle
809:calculus
266:waveform
228:integral
189:function
5983:Ranking
5973:SimHash
5860:F-score
5446:
5434:
5430:
5418:
5414:
5402:
5354:. OC =
5308:L2 norm
5150:is the
5119:is the
4455:is the
4449:kelvins
4365:physics
4363:In the
4321:√
4314:√
3483:is the
3309:) is a
3130:voltage
2857:average
2792:current
2756:is the
2605:Voltage
2445:is the
2411:where:
961:If the
275:values
43:) of a
5880:Recall
5667:
5556:5 July
5547:
5522:5 July
5513:
5486:
5396:Using
5372:Using
4691:where
4451:, and
4435:where
4296:
4292:
4269:where
3506:Since
3475:where
2694:where
845:, and
839:square
818:, the
249:, the
23:, the
6156:Means
5885:Kappa
5802:sMAPE
5638:(PDF)
5627:(PDF)
5576:(PDF)
5334:Notes
5294:(ARV)
5158:or a
5154:of a
5064:>
5053:>
5042:>
5031:>
5009:>
4994:that
4464:Error
4353:Speed
3301:when
2776:power
2633:AC+DC
2504:Total
2456:frac(
245:. In
6052:BLEU
6024:SSIM
6019:PSNR
5996:NDCG
5817:MSPE
5812:MASE
5807:MAPE
5665:ISBN
5646:2019
5610:2015
5558:2020
5545:ISBN
5524:2020
5511:ISBN
5484:ISBN
5362:and
5123:and
5083:and
4747:and
2595:Uses
2203:>
2185:frac
2170:<
2152:frac
2032:frac
1915:frac
1819:0.75
1816:>
1798:frac
1776:0.75
1773:<
1755:frac
1752:<
1734:<
1716:frac
1713:<
1710:0.25
1691:0.25
1688:<
1670:frac
1557:>
1539:frac
1514:<
1496:frac
1392:>
1374:frac
1349:<
1331:frac
1114:RMS
977:is:
949:= 1.
835:Sine
6073:FID
6039:NLP
6029:IoU
5991:MRR
5968:SMC
5900:ROC
5895:AUC
5890:MCC
5842:MAD
5837:MDA
5822:RMS
5797:MAE
5792:MSE
5358:of
5178:rms
5090:If
5067:min
5020:or
5016:RMS
4997:max
4766:RMS
4714:DFT
4395:RMS
4369:gas
4367:of
4341:or
4310:RMS
4225:RMS
3991:RMS
3895:sin
3782:cos
3687:RMS
3613:sin
3529:RMS
3423:sin
3336:RMS
3262:RMS
3252:RMS
3239:Avg
3216:or
3178:RMS
3163:Avg
3145:RMS
3125:).
3107:RMS
3065:RMS
2737:RMS
2665:RMS
2628:RMS
2562:RMS
2536:RMS
2516:RMS
2499:RMS
2464:of
2320:sin
2292:sin
1749:0.5
1737:0.5
1560:0.5
1517:0.5
1395:0.5
1352:0.5
1218:sin
1086:RMS
1079:3.5
1072:RMS
1022:RMS
1015:2.8
1008:RMS
695:lim
686:RMS
542:RMS
526:is
356:RMS
117:or
45:set
41:rms
39:or
35:RMS
29:RMS
19:In
6152::
6001:AP
5865:P4
5688:.
5629:.
5601:.
5582:.
5578:.
5468:^
5450:HM
5448:=
5443:OC
5427:OC
5421:GC
5416:=
5411:GC
5405:HC
5400:,
5392:GM
5390:=
5382:QM
5380:=
5356:AM
5060:HM
5049:GM
5038:AM
5027:QM
4349:.
3294:.
3147:,
3132:,
2794:,
2786:,
2778:,
2742:AC
2709:DC
2670:AC
2650:DC
1120:DC
841:,
837:,
31:,
5832:R
5767:e
5760:t
5753:v
5719:.
5694:.
5673:.
5648:.
5612:.
5584:8
5560:.
5526:.
5492:.
5452:.
5440:/
5424:/
5408:/
5394:.
5384:.
5368:r
5364:b
5360:a
5352:b
5348:a
5246:.
5236:2
5232:x
5226:=
5221:2
5216:x
5208:+
5203:2
5194:x
5188:=
5183:2
5174:x
5136:x
5101:x
5085:b
5081:a
5077:)
5075:b
5073:,
5071:a
5062:)
5058:(
5051:)
5047:(
5040:)
5036:(
5029:)
5025:(
5018:)
5014:(
5007:)
5005:b
5003:,
5001:a
4960:.
4952:2
4947:|
4942:N
4938:]
4935:m
4932:[
4929:X
4923:|
4915:m
4905:=
4898:2
4891:|
4886:]
4883:m
4880:[
4877:X
4872:|
4863:m
4851:2
4847:N
4843:1
4836:=
4830:]
4827:n
4824:[
4819:2
4815:x
4808:n
4798:N
4795:1
4788:=
4785:}
4782:]
4779:n
4776:[
4773:x
4770:{
4749:N
4735:}
4732:]
4729:n
4726:[
4723:x
4720:{
4711:=
4708:]
4705:m
4702:[
4699:X
4676:,
4671:2
4666:|
4662:]
4659:m
4656:[
4653:X
4649:|
4642:N
4637:1
4634:=
4631:m
4621:N
4618:1
4613:=
4609:]
4606:n
4603:[
4598:2
4594:x
4587:N
4582:1
4579:=
4576:n
4548:T
4528:)
4525:T
4522:n
4519:=
4516:t
4513:(
4510:x
4507:=
4504:]
4501:n
4498:[
4495:x
4453:M
4445:T
4437:R
4417:M
4413:T
4410:R
4407:3
4400:=
4391:v
4323:2
4316:2
4307:V
4303:P
4300:V
4281:P
4278:V
4274:P
4271:I
4254:,
4247:2
4240:p
4236:V
4230:=
4221:V
4194:.
4187:2
4180:p
4176:I
4170:=
4163:2
4157:1
4153:T
4144:2
4140:T
4128:1
4124:T
4115:2
4111:T
4106:1
4097:p
4093:I
4089:=
4080:2
4076:T
4068:1
4064:T
4058:]
4053:2
4050:t
4045:[
4035:1
4031:T
4022:2
4018:T
4013:1
4004:p
4000:I
3996:=
3987:I
3950:2
3946:T
3938:1
3934:T
3928:]
3918:4
3913:)
3910:t
3904:2
3901:(
3884:2
3881:t
3875:[
3865:1
3861:T
3852:2
3848:T
3843:1
3834:p
3830:I
3826:=
3813:t
3810:d
3804:2
3800:)
3797:t
3791:2
3788:(
3776:1
3766:2
3762:T
3754:1
3750:T
3735:1
3731:T
3722:2
3718:T
3713:1
3704:p
3700:I
3696:=
3683:I
3648:.
3642:t
3639:d
3634:)
3631:t
3625:(
3617:2
3604:2
3600:T
3592:1
3588:T
3573:1
3569:T
3560:2
3556:T
3551:1
3542:p
3538:I
3534:=
3525:I
3511:p
3508:I
3501:T
3497:T
3495:/
3493:Ď€
3489:ω
3487:(
3481:ω
3477:t
3460:,
3455:t
3452:d
3447:2
3442:]
3438:)
3435:t
3429:(
3418:p
3414:I
3409:[
3400:2
3396:T
3388:1
3384:T
3370:1
3366:T
3357:2
3353:T
3348:1
3341:=
3332:I
3318:p
3315:I
3307:t
3305:(
3303:I
3284:R
3267:.
3258:I
3248:V
3244:=
3235:P
3193:.
3188:R
3183:2
3174:V
3168:=
3159:P
3142:V
3138:t
3136:(
3134:V
3123:t
3121:(
3119:I
3115:t
3113:(
3111:I
3104:I
3075:R
3070:2
3061:I
3057:=
3042:R
3031:R
3026:g
3023:v
3020:A
3015:)
3009:2
3005:)
3001:t
2998:(
2995:I
2991:(
2986:=
2969:g
2966:v
2963:A
2958:)
2952:(
2937:g
2934:v
2931:A
2926:)
2922:R
2917:2
2913:)
2909:t
2906:(
2903:I
2899:(
2894:=
2885:g
2882:v
2879:A
2875:P
2853:t
2851:(
2849:I
2832:.
2829:R
2824:2
2820:I
2816:=
2813:P
2800:R
2796:I
2788:R
2780:P
2704:V
2675:2
2660:+
2655:2
2645:V
2638:=
2572:2
2567:n
2557:+
2551:+
2546:2
2541:2
2531:+
2526:2
2521:1
2509:=
2468:.
2466:r
2458:r
2451:f
2443:D
2436:i
2434:A
2428:f
2422:t
2416:y
2392:2
2389:3
2381:1
2377:A
2353:)
2347:3
2340:2
2331:t
2327:(
2315:1
2311:A
2304:)
2301:t
2298:(
2287:1
2283:A
2279:=
2276:y
2246:D
2239:1
2235:A
2206:D
2200:)
2197:t
2194:f
2191:(
2180:0
2173:D
2167:)
2164:t
2161:f
2158:(
2145:1
2141:A
2134:{
2129:=
2126:y
2096:3
2088:1
2084:A
2058:1
2054:A
2047:)
2044:t
2041:f
2038:(
2027:1
2023:A
2019:2
2016:=
2013:y
1983:3
1975:1
1971:A
1947:|
1941:1
1937:A
1930:)
1927:t
1924:f
1921:(
1910:1
1906:A
1902:2
1898:|
1894:=
1891:y
1860:2
1854:1
1850:A
1813:)
1810:t
1807:f
1804:(
1791:1
1787:A
1770:)
1767:t
1764:f
1761:(
1744:0
1731:)
1728:t
1725:f
1722:(
1703:1
1699:A
1685:)
1682:t
1679:f
1676:(
1665:0
1659:{
1654:=
1651:y
1618:2
1613:1
1609:A
1605:+
1600:2
1595:0
1591:A
1554:)
1551:t
1548:f
1545:(
1532:1
1528:A
1511:)
1508:t
1505:f
1502:(
1489:1
1485:A
1478:{
1473:+
1468:0
1464:A
1460:=
1457:y
1428:1
1424:A
1389:)
1386:t
1383:f
1380:(
1367:1
1363:A
1346:)
1343:t
1340:f
1337:(
1324:1
1320:A
1313:{
1308:=
1305:y
1274:2
1268:1
1264:A
1239:)
1236:t
1233:f
1227:2
1224:(
1213:1
1209:A
1205:=
1202:y
1171:0
1167:A
1142:0
1138:A
1134:=
1131:y
1090:.
1063:3
1058:2
1055:=
1026:.
999:2
994:2
991:=
947:a
904:1
900:A
893:=
890:y
868:1
864:A
860:=
857:y
787:.
781:t
776:d
768:2
763:]
760:)
757:t
754:(
751:f
748:[
741:T
736:T
721:T
718:2
714:1
699:T
691:=
682:f
655:,
649:t
644:d
636:2
631:]
628:)
625:t
622:(
619:f
616:[
607:2
603:T
595:1
591:T
576:1
572:T
563:2
559:T
554:1
547:=
538:f
512:2
508:T
501:t
493:1
489:T
478:t
476:(
474:f
457:.
451:)
445:2
438:n
434:x
428:+
422:+
417:2
410:2
406:x
400:+
395:2
388:1
384:x
377:(
371:n
368:1
361:=
352:x
328:}
323:n
319:x
315:,
309:,
304:2
300:x
296:,
291:1
287:x
283:{
273:n
211:S
208:M
205:R
200:f
169:2
165:M
138:x
133:S
130:M
127:R
102:S
99:M
96:R
91:x
68:i
64:x
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