3084:
4974:
2876:
3079:{\displaystyle {\begin{aligned}P_{\text{Avg}}&=\left(I(t)^{2}R\right)_{\text{Avg}}&&{\text{where }}\left(\cdots \right)_{\text{Avg}}{\text{ denotes the temporal mean of a function}}\\&=\left(I(t)^{2}\right)_{\text{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}}}
965:
3957:
1847:
933:
842:
4191:
4957:
3660:
4316:
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
4461:
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
1657:
5259:
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
1588:
279:) 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."
1423:
817:
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
3968:
3645:
2597:
2234:
4747:
808:
4446:
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.
478:
2700:
4462:
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.
676:
3457:
3952:{\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}}}
5243:
4673:
4313:, 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.
1842:{\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}}}
2866:), 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
1111:
1047:
2376:
1969:
2881:
4251:
1463:
3264:
3190:
3665:
1311:
4186:{\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}}}.}
2082:
5752:
4417:
3506:
2503:
2132:
4952:{\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}}}}.}
1644:
687:
349:
4732:
2416:
1884:
1298:
2765:
2119:
2006:
357:
2732:
1261:
535:
2632:
235:
161:
126:
543:
2269:
984:
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
5135:
5745:
5104:
4525:
2853:
1166:
3313:
927:
2493:
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
1452:
1195:
891:
954:
192:
91:
4332:(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
5155:
6147:
4545:
4285:
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
5738:
4553:
5248:
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.
1061:
997:
5788:
2282:
5655:
2794:
5610:
1052:
For other waveforms, the relationships are not the same as they are for sine waves. For example, for either a triangular or sawtooth wave:
1897:
1583:{\displaystyle y=A_{0}+{\begin{cases}A_{1}&\operatorname {frac} (ft)<0.5\\-A_{1}&\operatorname {frac} (ft)>0.5\end{cases}}}
5464:
4363:
2497:(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).
4202:
2602:
Alternatively, for waveforms that are perfectly positively correlated, or "in phase" with each other, their RMS values sum directly.
5886:
5881:
5585:
5535:
5501:
5474:
1418:{\displaystyle y={\begin{cases}A_{1}&\operatorname {frac} (ft)<0.5\\-A_{1}&\operatorname {frac} (ft)>0.5\end{cases}}}
3300:
current, as is approximately true for mains power, the RMS value is easy to calculate from the continuous case equation above. If
3216:
3140:
5304:
3651:
6108:
5969:
5692:
2019:
3962:
but since the interval is a whole number of complete cycles (per definition of RMS), the sine terms will cancel out, leaving:
5793:
3640:{\displaystyle I_{\text{RMS}}=I_{\text{p}}{\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{\sin ^{2}(\omega t)}\,dt}}}.}
2592:{\displaystyle {\text{RMS}}_{\text{Total}}={\sqrt {{\text{RMS}}_{1}^{2}+{\text{RMS}}_{2}^{2}+\cdots +{\text{RMS}}_{n}^{2}}}}
6059:
5803:
4372:
2229:{\displaystyle y={\begin{cases}A_{1}&\operatorname {frac} (ft)<D\\0&\operatorname {frac} (ft)>D\end{cases}}}
5818:
4306:, assuming the source is a pure sine wave. Thus the peak value of the mains voltage in the USA is about 120 Ă—
980:, the relationships between amplitudes (peak-to-peak, peak) and RMS are fixed and known, as they are for any continuous
3104:) is the constant current that yields the same power dissipation as the time-averaged power dissipation of the current
6025:
5954:
5891:
2621:
803:{\displaystyle f_{\text{RMS}}=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {2T}}{\int _{-T}^{T}{}^{2}\,{\rm {d}}t}}}.}
1594:
5838:
5813:
5798:
4456:
3277:
loads (that is, loads capable of not just dissipating energy but also storing it) are discussed under the topic of
2275:
261:
289:
5828:
5823:
5309:
4681:
2382:
5924:
5559:
1853:
1267:
473:{\displaystyle x_{\text{RMS}}={\sqrt {{\frac {1}{n}}\left({x_{1}}^{2}+{x_{2}}^{2}+\cdots +{x_{n}}^{2}\right)}}.}
2741:
2695:{\displaystyle {\text{RMS}}_{\text{AC+DC}}={\sqrt {{\text{V}}_{\text{DC}}^{2}+{\text{RMS}}_{\text{AC}}^{2}}}}
2088:
1975:
968:
Graph of a sine wave's voltage vs. time (in degrees), showing RMS, peak (PK), and peak-to-peak (PP) voltages.
6015:
5919:
5914:
5278:
2708:
1208:
6082:
3210:
By taking the square root of both these equations and multiplying them together, the power is found to be:
494:
5856:
5360:
5142:
4345:
671:{\displaystyle f_{\text{RMS}}={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{}^{2}\,{\rm {d}}t}}},}
199:
4973:
1650:
205:
131:
96:
4471:
2240:
6077:
5977:
5866:
5861:
5273:
3274:
2494:
2147:
1672:
1491:
1326:
5783:
5770:
4978:
3285:
2768:
245:
6103:
6069:
5949:
5778:
5621:
5314:
5256:
5138:
5113:
3452:{\displaystyle I_{\text{RMS}}={\sqrt {{1 \over {T_{2}-T_{1}}}\int _{T_{1}}^{T_{2}}\left^{2}dt}},}
5080:
4477:
2819:
1137:
6098:
5987:
5934:
5651:
5531:
5497:
5491:
5470:
5384:
3471:
896:
814:
257:
55:
5525:
4362:
is defined as the square root of the average squared-speed. The RMS speed of an ideal gas is
1429:
1172:
863:
6121:
5906:
5871:
5761:
4738:
is the sample size, that is, the number of observations in the sample and DFT coefficients.
4317:
represents an average current of 5 amps, but an RMS current of 7.07 amps, in the long term.
2802:
981:
195:
5238:{\displaystyle x_{\text{rms}}^{2}={\overline {x}}^{2}+\sigma _{x}^{2}={\overline {x^{2}}}.}
939:
170:
69:
6054:
5997:
5876:
5107:
5020:
4741:
In this case, the RMS computed in the time domain is the same as in the frequency domain:
2786:
2472:
273:
3115:
Average power can also be found using the same method that in the case of a time-varying
2870:
power dissipated over time, which is calculated by taking the average power dissipation:
6142:
5289:
5284:
5031:
5009:
4668:{\displaystyle \sum _{n=1}^{N}{x^{2}}={\frac {1}{N}}\sum _{m=1}^{N}\left|X\right|^{2},}
4530:
2735:
1130:
830:
826:
249:
5730:
5672:
3269:
Both derivations depend on voltage and current being proportional (that is, the load,
6136:
5939:
5896:
5299:
5042:
3204:
2012:
1890:
857:
853:
5696:
5261:
4427:
5720:
964:
5560:"Determining the Effective or RMS Voltage of Various Waveforms without Calculus"
4333:
1304:
936:
A rectangular pulse wave of duty cycle D, the ratio between the pulse duration (
849:
63:
59:
31:
17:
1106:{\displaystyle =2{\sqrt {3}}\times {\text{RMS}}\approx 3.5\times {\text{RMS}}.}
1042:{\displaystyle =2{\sqrt {2}}\times {\text{RMS}}\approx 2.8\times {\text{RMS}}.}
6033:
5944:
5929:
5373:
Using
Pythagoras' theorem, OC² = OG² + GC² ∴ GC = √
4443:
2457:
2125:
4324:
is sometimes erroneously used (e.g., in the audio industry) as a synonym for
5851:
5677:
3297:
3200:
2371:{\displaystyle y=A_{1}\sin(t)-A_{1}\sin \left(t-{\frac {2\pi }{3}}\right)\,}
1201:
985:
977:
845:
5264:
is removed (that is, RMS(signal) = stdev(signal) if the mean signal is 0).
4196:
A similar analysis leads to the analogous equation for sinusoidal voltage:
3207:, allowing us to calculate the mean power delivered into a specified load.
5146:
4968:
3278:
3196:
2780:
973:
819:
276:
253:
238:
5959:
5846:
5294:
4351:
4274:
4273:
Because of their usefulness in carrying out power calculations, listed
3116:
932:
841:
4435:
860:
waveforms. In each, the centerline is at 0, the positive peak is at
264:
of an estimator measures how far the estimator strays from the data.
1964:{\displaystyle y=\left|2A_{1}\operatorname {frac} (ft)-A_{1}\right|}
5725:
4972:
3500:
is a positive constant and was to be squared within the integral:
963:
931:
840:
483:
The corresponding formula for a continuous function (or waveform)
6038:
6010:
6005:
5982:
4246:{\displaystyle V_{\text{RMS}}={V_{\text{p}} \over {\sqrt {2}}},}
5734:
5611:"Make Better AC RMS Measurements with your Digital Multimeter"
4355:
5721:
A case for why RMS is a misnomer when applied to audio power
3259:{\displaystyle P_{\text{Avg}}=V_{\text{RMS}}I_{\text{RMS}}.}
3185:{\displaystyle P_{\text{Avg}}={V_{\text{RMS}}^{2} \over R}.}
2801:. It is easy to do the calculation when there is a constant
5586:"How to Derive the RMS Value of Pulse and Square Waveforms"
2222:
1835:
1576:
1411:
5496:. Macmillan International Higher Education. p. 185.
2077:{\displaystyle y=2A_{1}\operatorname {frac} (ft)-A_{1}\,}
5650:(2nd ed.). Cambridge University Press. p. 64.
4470:
The RMS can be computed in the frequency domain, using
3033: does not vary over time, it can be factored out)
5363:, QC² = QO² + OC² ∴ QC = √
5158:
5116:
5083:
4750:
4684:
4556:
4533:
4480:
4375:
4205:
3971:
3663:
3509:
3316:
3219:
3143:
2879:
2822:
2744:
2711:
2635:
2506:
2385:
2285:
2243:
2135:
2092:
2022:
1979:
1900:
1856:
1660:
1597:
1466:
1432:
1314:
1270:
1211:
1175:
1140:
1064:
1000:
942:
899:
866:
690:
546:
497:
360:
292:
208:
173:
134:
99:
72:
4412:{\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}}
2858:
However, if the current is a time-varying function,
6091:
6068:
6047:
6024:
5996:
5968:
5905:
5837:
5769:
5527:
5260:variation about the mean, rather than about 0, the
2626:A special case of RMS of waveform combinations is:
5237:
5129:
5098:
4951:
4726:
4667:
4539:
4519:
4411:
4245:
4185:
3951:
3639:
3451:
3258:
3184:
3078:
2847:
2759:
2726:
2694:
2591:
2410:
2370:
2263:
2228:
2113:
2076:
2000:
1963:
1878:
1841:
1638:
1582:
1446:
1417:
1292:
1255:
1189:
1160:
1105:
1041:
948:
921:
885:
802:
670:
529:
472:
343:
229:
186:
155:
120:
85:
705:
1639:{\displaystyle {\sqrt {A_{0}^{2}+A_{1}^{2}}}\,}
5746:
4877:
4858:
2968: denotes the temporal mean of a function
8:
4771:
4756:
4721:
4706:
2785:Electrical engineers often need to know the
956:) and the period (T); illustrated here with
681:and the RMS for a function over all time is
344:{\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}
338:
293:
5646:Chris C. Bissell; David A. Chapman (1992).
4727:{\displaystyle X=\operatorname {DFT} \{x\}}
3195:This equation can be used for any periodic
2411:{\displaystyle A_{1}{\sqrt {\frac {3}{2}}}}
5753:
5739:
5731:
2738:(or average) component of the signal, and
1879:{\displaystyle {\frac {A_{1}}{\sqrt {2}}}}
1293:{\displaystyle {\frac {A_{1}}{\sqrt {2}}}}
5458:
5456:
5221:
5215:
5206:
5201:
5188:
5178:
5168:
5163:
5157:
5121:
5115:
5085:
5084:
5082:
4937:
4912:
4906:
4900:
4894:
4883:
4876:
4875:
4857:
4856:
4855:
4848:
4836:
4827:
4825:
4804:
4799:
4793:
4779:
4777:
4751:
4749:
4683:
4656:
4627:
4616:
4602:
4583:
4578:
4572:
4561:
4555:
4532:
4479:
4389:
4380:
4374:
4231:
4225:
4219:
4210:
4204:
4171:
4165:
4159:
4142:
4129:
4124:
4122:
4113:
4100:
4095:
4090:
4088:
4082:
4065:
4060:
4053:
4048:
4034:
4020:
4007:
4002:
3997:
3995:
3989:
3976:
3970:
3935:
3930:
3923:
3918:
3878:
3865:
3850:
3837:
3832:
3827:
3825:
3819:
3795:
3759:
3751:
3746:
3739:
3734:
3729:
3720:
3707:
3702:
3697:
3695:
3689:
3672:
3664:
3662:
3624:
3602:
3597:
3589:
3584:
3577:
3572:
3567:
3558:
3545:
3540:
3535:
3533:
3527:
3514:
3508:
3432:
3403:
3385:
3380:
3373:
3368:
3355:
3342:
3337:
3332:
3330:
3321:
3315:
3307:is defined to be the peak current, then:
3247:
3237:
3224:
3218:
3168:
3163:
3157:
3148:
3142:
3067:
3055:
3050:
3031:
3023:
3011:
3000:
2966:
2960:
2943:
2934:
2920:
2888:
2880:
2878:
2833:
2821:
2751:
2746:
2743:
2718:
2713:
2710:
2684:
2679:
2674:
2664:
2659:
2654:
2651:
2642:
2637:
2634:
2581:
2576:
2571:
2555:
2550:
2545:
2535:
2530:
2525:
2522:
2513:
2508:
2505:
2396:
2390:
2384:
2367:
2347:
2324:
2296:
2284:
2254:
2248:
2242:
2154:
2142:
2134:
2104:
2097:
2090:
2073:
2067:
2036:
2021:
1991:
1984:
1977:
1950:
1919:
1899:
1863:
1857:
1855:
1800:
1712:
1667:
1659:
1635:
1627:
1622:
1609:
1604:
1598:
1596:
1541:
1498:
1486:
1477:
1465:
1443:
1437:
1431:
1376:
1333:
1321:
1313:
1277:
1271:
1269:
1252:
1222:
1210:
1186:
1180:
1174:
1157:
1151:
1139:
1095:
1081:
1071:
1063:
1031:
1017:
1007:
999:
941:
913:
898:
877:
865:
785:
784:
783:
777:
757:
750:
742:
737:
727:
722:
720:
708:
695:
689:
653:
652:
651:
645:
625:
616:
611:
604:
599:
594:
585:
572:
567:
562:
560:
551:
545:
521:
502:
496:
454:
447:
442:
426:
419:
414:
404:
397:
392:
376:
374:
365:
359:
332:
313:
300:
291:
252:that would dissipate the same power in a
214:
213:
207:
178:
172:
147:
136:
133:
105:
104:
98:
77:
71:
3654:to eliminate squaring of trig function:
2809:, through the resistance. For a load of
2760:{\displaystyle {\text{RMS}}_{\text{AC}}}
2460:or the proportion of the time period (1/
1115:
5452:
5326:
5251:Physical scientists often use the term
2114:{\displaystyle A_{1} \over {\sqrt {3}}}
2001:{\displaystyle A_{1} \over {\sqrt {3}}}
272:The RMS value of a set of values (or a
2727:{\displaystyle {\text{V}}_{\text{DC}}}
1256:{\displaystyle y=A_{1}\sin(2\pi ft)\,}
825:In the case of the RMS statistic of a
530:{\displaystyle T_{1}\leq t\leq T_{2}}
7:
6148:Statistical deviation and dispersion
5558:Cartwright, Kenneth V (Fall 2007).
4277:for power outlets (for example, 120
786:
715:
654:
237:and can be defined in terms of an
230:{\displaystyle f_{\mathrm {RMS} }}
221:
218:
215:
156:{\displaystyle \mathrm {RMS} _{x}}
143:
140:
137:
121:{\displaystyle x_{\mathrm {RMS} }}
112:
109:
106:
25:
5469:. Oxford University Press. 2009.
5066:of two distinct positive numbers
4434:is the temperature of the gas in
3069:by definition of root-mean-square
5305:Glossary of mathematical symbols
4963:Relationship to other statistics
4263:represents the peak current and
2264:{\displaystyle A_{1}{\sqrt {D}}}
6109:Pearson correlation coefficient
5466:A Dictionary of Physics (6 ed.)
241:of the square of the function.
163:. The RMS is also known as the
93:, its RMS is denoted as either
5590:MasteringElectronicsDesign.com
5490:Thompson, Sylvanus P. (1965).
5090:
4924:
4918:
4872:
4866:
4816:
4810:
4768:
4762:
4718:
4712:
4694:
4688:
4648:
4642:
4595:
4589:
4514:
4499:
4490:
4484:
4366:using the following equation:
3899:
3887:
3786:
3774:
3620:
3611:
3424:
3415:
2997:
2990:
2917:
2910:
2314:
2308:
2210:
2201:
2177:
2168:
2057:
2048:
1940:
1931:
1823:
1814:
1780:
1771:
1741:
1732:
1695:
1686:
1564:
1555:
1521:
1512:
1399:
1390:
1356:
1347:
1249:
1234:
773:
770:
764:
758:
712:
641:
638:
632:
626:
27:Square root of the mean square
1:
6048:Deep Learning Related Metrics
5726:A Java applet on learning RMS
4270:represents the peak voltage.
833:is used instead of the mean.
248:equals the value of constant
5227:
5183:
3490:is the period of the wave).
893:and the negative peak is at
491:) defined over the interval
246:alternating electric current
5892:Sensitivity and specificity
5648:Digital signal transmission
5130:{\displaystyle \sigma _{x}}
2622:Root mean square AC voltage
813:The RMS over all time of a
6164:
5463:"Root-mean-square value".
5099:{\displaystyle {\bar {x}}}
4966:
4457:Root-mean-square deviation
4454:
4343:
2778:
2619:
2450:is amplitude (peak value),
822:, as shown by Cartwright.
262:root-mean-square deviation
198:. The RMS of a continuous
6117:
5530:. Routledge. p. 48.
5375:OC² − OG²
5310:Mean squared displacement
4520:{\displaystyle x=x(t=nT)}
2848:{\displaystyle P=I^{2}R.}
2813:ohms, power is given by:
2771:component of the signal.
2611:In electrical engineering
2421:
1161:{\displaystyle y=A_{0}\,}
194:), a special case of the
4547:is the sampling period,
4430:, 8.314 J/(mol·K),
3273:, is purely resistive).
2775:Average electrical power
2489:In waveform combinations
2276:Phase-to-phase sine wave
922:{\displaystyle y=-A_{1}}
282:In the case of a set of
5920:Calinski-Harabasz index
5524:Jones, Alan R. (2018).
5279:Average rectified value
4474:. For a sampled signal
1458:DC-shifted square wave
1447:{\displaystyle A_{1}\,}
1190:{\displaystyle A_{0}\,}
1122:Variables and operators
886:{\displaystyle y=A_{1}}
5239:
5131:
5100:
5074:
4953:
4728:
4669:
4632:
4577:
4541:
4521:
4413:
4360:root-mean-square speed
4346:Root-mean-square speed
4247:
4187:
3953:
3652:trigonometric identity
3641:
3453:
3284:In the common case of
3260:
3186:
3080:
2849:
2761:
2728:
2696:
2593:
2412:
2372:
2265:
2230:
2115:
2078:
2002:
1965:
1880:
1843:
1640:
1584:
1448:
1419:
1294:
1257:
1191:
1162:
1107:
1043:
969:
961:
950:
929:
923:
887:
804:
672:
531:
474:
345:
231:
188:
157:
122:
87:
6083:Intra-list Similarity
5240:
5132:
5101:
4976:
4954:
4729:
4670:
4612:
4557:
4542:
4522:
4414:
4248:
4188:
3954:
3642:
3454:
3261:
3187:
3081:
2850:
2795:electrical resistance
2779:Further information:
2762:
2729:
2697:
2620:Further information:
2594:
2413:
2373:
2266:
2231:
2116:
2079:
2003:
1966:
1881:
1844:
1641:
1585:
1449:
1420:
1295:
1258:
1192:
1163:
1108:
1044:
967:
951:
949:{\displaystyle \tau }
935:
924:
888:
844:
805:
673:
532:
475:
346:
232:
189:
187:{\displaystyle M_{2}}
158:
123:
88:
86:{\displaystyle x_{i}}
5567:Technology Interface
5274:Pythagorean addition
5156:
5114:
5081:
4748:
4682:
4554:
4531:
4478:
4373:
4203:
3969:
3661:
3507:
3314:
3217:
3141:
2877:
2820:
2742:
2709:
2633:
2504:
2383:
2283:
2241:
2133:
2089:
2020:
1976:
1898:
1854:
1658:
1595:
1464:
1430:
1312:
1268:
1209:
1173:
1138:
1062:
998:
940:
897:
864:
688:
544:
495:
358:
290:
206:
171:
132:
97:
70:
5671:Weisstein, Eric W.
5584:Nastase, Adrian S.
5365:QO² + OC²
5361:Pythagoras' theorem
5211:
5173:
4979:proof without words
4466:In frequency domain
4281:V in the US, or 230
4072:
3942:
3758:
3596:
3392:
3286:alternating current
3173:
3089:So, the RMS value,
3060:
2793:, dissipated by an
2769:alternating current
2689:
2669:
2586:
2560:
2540:
1632:
1614:
837:In common waveforms
755:
623:
6104:Euclidean distance
6070:Recommender system
5950:Similarity measure
5764:evaluation metrics
5693:"ROOT, TH1:GetRMS"
5673:"Root-Mean-Square"
5627:on 15 January 2019
5493:Calculus Made Easy
5315:True RMS converter
5257:standard deviation
5235:
5197:
5159:
5139:standard deviation
5127:
5096:
5075:
4949:
4905:
4853:
4798:
4724:
4665:
4537:
4517:
4472:Parseval's theorem
4409:
4243:
4183:
4029:
3949:
3947:
3859:
3730:
3637:
3568:
3449:
3364:
3256:
3182:
3159:
3127:), with RMS value
3096:, of the function
3076:
3074:
3046:
2845:
2757:
2724:
2692:
2673:
2653:
2589:
2570:
2544:
2524:
2408:
2368:
2261:
2226:
2221:
2103:
2074:
1990:
1961:
1876:
1839:
1834:
1651:Modified sine wave
1636:
1618:
1600:
1580:
1575:
1444:
1415:
1410:
1290:
1253:
1187:
1158:
1103:
1039:
970:
962:
946:
930:
919:
883:
800:
738:
719:
668:
595:
527:
470:
341:
227:
184:
153:
118:
83:
58:of numbers is the
6130:
6129:
6099:Cosine similarity
5935:Hopkins statistic
5657:978-0-521-42557-5
5385:similar triangles
5255:as a synonym for
5230:
5186:
5166:
5093:
4944:
4931:
4896:
4889:
4844:
4842:
4820:
4789:
4787:
4754:
4610:
4540:{\displaystyle T}
4407:
4406:
4383:
4238:
4236:
4228:
4213:
4178:
4176:
4168:
4154:
4152:
4120:
4085:
4073:
4042:
4027:
3992:
3979:
3943:
3911:
3873:
3857:
3822:
3803:
3793:
3727:
3692:
3675:
3632:
3565:
3530:
3517:
3472:angular frequency
3444:
3406:
3362:
3324:
3250:
3240:
3227:
3205:sawtooth waveform
3177:
3166:
3151:
3070:
3053:
3034:
3026:
3014:
2969:
2963:
2946:
2937:
2891:
2754:
2749:
2721:
2716:
2690:
2682:
2677:
2662:
2657:
2645:
2640:
2587:
2574:
2548:
2528:
2516:
2511:
2486:
2485:
2406:
2405:
2360:
2259:
2111:
2109:
1998:
1996:
1874:
1873:
1633:
1288:
1287:
1098:
1084:
1076:
1034:
1020:
1012:
815:periodic function
795:
735:
704:
698:
663:
592:
554:
465:
384:
368:
258:estimation theory
16:(Redirected from
6155:
6122:Confusion matrix
5897:Logarithmic Loss
5762:Machine learning
5755:
5748:
5741:
5732:
5708:
5707:
5705:
5704:
5695:. Archived from
5689:
5683:
5682:
5668:
5662:
5661:
5643:
5637:
5636:
5634:
5632:
5626:
5620:. Archived from
5615:
5607:
5601:
5600:
5598:
5596:
5581:
5575:
5574:
5564:
5555:
5549:
5548:
5546:
5544:
5521:
5515:
5514:
5512:
5510:
5487:
5481:
5480:
5460:
5440:
5434:
5432:
5431:
5428:
5425:
5418:
5416:
5415:
5412:
5409:
5402:
5400:
5399:
5396:
5393:
5376:
5366:
5331:
5253:root mean square
5244:
5242:
5241:
5236:
5231:
5226:
5225:
5216:
5210:
5205:
5193:
5192:
5187:
5179:
5172:
5167:
5164:
5136:
5134:
5133:
5128:
5126:
5125:
5105:
5103:
5102:
5097:
5095:
5094:
5086:
5065:
5050:
5039:
5028:
5017:
5006:
4999:root mean square
4995:
4958:
4956:
4955:
4950:
4945:
4943:
4942:
4941:
4936:
4932:
4927:
4913:
4904:
4895:
4890:
4888:
4887:
4882:
4881:
4880:
4862:
4861:
4852:
4843:
4841:
4840:
4828:
4826:
4821:
4819:
4809:
4808:
4797:
4788:
4780:
4778:
4755:
4752:
4733:
4731:
4730:
4725:
4674:
4672:
4671:
4666:
4661:
4660:
4655:
4651:
4631:
4626:
4611:
4603:
4598:
4588:
4587:
4576:
4571:
4546:
4544:
4543:
4538:
4526:
4524:
4523:
4518:
4418:
4416:
4415:
4410:
4408:
4402:
4391:
4390:
4385:
4384:
4381:
4312:
4311:
4305:
4304:
4284:
4280:
4252:
4250:
4249:
4244:
4239:
4237:
4232:
4230:
4229:
4226:
4220:
4215:
4214:
4211:
4192:
4190:
4189:
4184:
4179:
4177:
4172:
4170:
4169:
4166:
4160:
4155:
4153:
4148:
4147:
4146:
4134:
4133:
4123:
4121:
4119:
4118:
4117:
4105:
4104:
4091:
4089:
4087:
4086:
4083:
4074:
4071:
4070:
4069:
4059:
4058:
4057:
4047:
4043:
4035:
4028:
4026:
4025:
4024:
4012:
4011:
3998:
3996:
3994:
3993:
3990:
3981:
3980:
3977:
3958:
3956:
3955:
3950:
3948:
3944:
3941:
3940:
3939:
3929:
3928:
3927:
3917:
3913:
3912:
3910:
3902:
3879:
3874:
3866:
3858:
3856:
3855:
3854:
3842:
3841:
3828:
3826:
3824:
3823:
3820:
3808:
3804:
3802:
3794:
3789:
3760:
3757:
3756:
3755:
3745:
3744:
3743:
3728:
3726:
3725:
3724:
3712:
3711:
3698:
3696:
3694:
3693:
3690:
3677:
3676:
3673:
3646:
3644:
3643:
3638:
3633:
3631:
3623:
3607:
3606:
3595:
3594:
3593:
3583:
3582:
3581:
3566:
3564:
3563:
3562:
3550:
3549:
3536:
3534:
3532:
3531:
3528:
3519:
3518:
3515:
3481:
3458:
3456:
3455:
3450:
3445:
3437:
3436:
3431:
3427:
3408:
3407:
3404:
3391:
3390:
3389:
3379:
3378:
3377:
3363:
3361:
3360:
3359:
3347:
3346:
3333:
3331:
3326:
3325:
3322:
3265:
3263:
3262:
3257:
3252:
3251:
3248:
3242:
3241:
3238:
3229:
3228:
3225:
3191:
3189:
3188:
3183:
3178:
3172:
3167:
3164:
3158:
3153:
3152:
3149:
3085:
3083:
3082:
3077:
3075:
3071:
3068:
3065:
3059:
3054:
3051:
3039:
3035:
3032:
3027:
3024:
3021:
3016:
3015:
3012:
3010:
3006:
3005:
3004:
2974:
2970:
2967:
2965:
2964:
2961:
2959:
2947:
2944:
2941:
2939:
2938:
2935:
2933:
2929:
2925:
2924:
2893:
2892:
2889:
2854:
2852:
2851:
2846:
2838:
2837:
2766:
2764:
2763:
2758:
2756:
2755:
2752:
2750:
2747:
2733:
2731:
2730:
2725:
2723:
2722:
2719:
2717:
2714:
2701:
2699:
2698:
2693:
2691:
2688:
2683:
2680:
2678:
2675:
2668:
2663:
2660:
2658:
2655:
2652:
2647:
2646:
2643:
2641:
2638:
2598:
2596:
2595:
2590:
2588:
2585:
2580:
2575:
2572:
2559:
2554:
2549:
2546:
2539:
2534:
2529:
2526:
2523:
2518:
2517:
2514:
2512:
2509:
2429:is displacement,
2417:
2415:
2414:
2409:
2407:
2398:
2397:
2395:
2394:
2377:
2375:
2374:
2369:
2366:
2362:
2361:
2356:
2348:
2329:
2328:
2301:
2300:
2270:
2268:
2267:
2262:
2260:
2255:
2253:
2252:
2235:
2233:
2232:
2227:
2225:
2224:
2159:
2158:
2120:
2118:
2117:
2112:
2110:
2105:
2102:
2101:
2091:
2083:
2081:
2080:
2075:
2072:
2071:
2041:
2040:
2007:
2005:
2004:
1999:
1997:
1992:
1989:
1988:
1978:
1970:
1968:
1967:
1962:
1960:
1956:
1955:
1954:
1924:
1923:
1885:
1883:
1882:
1877:
1875:
1869:
1868:
1867:
1858:
1848:
1846:
1845:
1840:
1838:
1837:
1805:
1804:
1717:
1716:
1645:
1643:
1642:
1637:
1634:
1631:
1626:
1613:
1608:
1599:
1589:
1587:
1586:
1581:
1579:
1578:
1546:
1545:
1503:
1502:
1482:
1481:
1453:
1451:
1450:
1445:
1442:
1441:
1424:
1422:
1421:
1416:
1414:
1413:
1381:
1380:
1338:
1337:
1299:
1297:
1296:
1291:
1289:
1283:
1282:
1281:
1272:
1262:
1260:
1259:
1254:
1227:
1226:
1196:
1194:
1193:
1188:
1185:
1184:
1167:
1165:
1164:
1159:
1156:
1155:
1116:
1112:
1110:
1109:
1104:
1099:
1096:
1085:
1082:
1077:
1072:
1048:
1046:
1045:
1040:
1035:
1032:
1021:
1018:
1013:
1008:
955:
953:
952:
947:
928:
926:
925:
920:
918:
917:
892:
890:
889:
884:
882:
881:
809:
807:
806:
801:
796:
794:
790:
789:
782:
781:
776:
754:
749:
736:
734:
723:
721:
718:
700:
699:
696:
677:
675:
674:
669:
664:
662:
658:
657:
650:
649:
644:
622:
621:
620:
610:
609:
608:
593:
591:
590:
589:
577:
576:
563:
561:
556:
555:
552:
536:
534:
533:
528:
526:
525:
507:
506:
479:
477:
476:
471:
466:
464:
460:
459:
458:
453:
452:
451:
431:
430:
425:
424:
423:
409:
408:
403:
402:
401:
385:
377:
375:
370:
369:
366:
350:
348:
347:
342:
337:
336:
318:
317:
305:
304:
236:
234:
233:
228:
226:
225:
224:
196:generalized mean
193:
191:
190:
185:
183:
182:
162:
160:
159:
154:
152:
151:
146:
127:
125:
124:
119:
117:
116:
115:
92:
90:
89:
84:
82:
81:
48:
47:
36:root mean square
21:
18:Root Mean Square
6163:
6162:
6158:
6157:
6156:
6154:
6153:
6152:
6133:
6132:
6131:
6126:
6113:
6087:
6064:
6055:Inception score
6043:
6020:
5998:Computer Vision
5992:
5964:
5901:
5833:
5765:
5759:
5717:
5712:
5711:
5702:
5700:
5691:
5690:
5686:
5670:
5669:
5665:
5658:
5645:
5644:
5640:
5630:
5628:
5624:
5613:
5609:
5608:
5604:
5594:
5592:
5583:
5582:
5578:
5562:
5557:
5556:
5552:
5542:
5540:
5538:
5523:
5522:
5518:
5508:
5506:
5504:
5489:
5488:
5484:
5477:
5462:
5461:
5454:
5449:
5444:
5443:
5429:
5426:
5423:
5422:
5420:
5413:
5410:
5407:
5406:
5404:
5397:
5394:
5391:
5390:
5388:
5382:
5374:
5372:
5364:
5358:
5332:
5328:
5323:
5270:
5217:
5177:
5154:
5153:
5117:
5112:
5111:
5108:arithmetic mean
5079:
5078:
5052:
5041:
5030:
5021:arithmetic mean
5019:
5008:
4997:
4982:
4971:
4965:
4914:
4908:
4907:
4854:
4832:
4800:
4746:
4745:
4680:
4679:
4638:
4634:
4633:
4579:
4552:
4551:
4529:
4528:
4476:
4475:
4468:
4459:
4453:
4426:represents the
4392:
4376:
4371:
4370:
4358:molecules, the
4348:
4342:
4309:
4307:
4302:
4300:
4298:
4291:
4282:
4278:
4269:
4262:
4221:
4206:
4201:
4200:
4161:
4138:
4125:
4109:
4096:
4078:
4061:
4049:
4030:
4016:
4003:
3985:
3972:
3967:
3966:
3946:
3945:
3931:
3919:
3903:
3880:
3864:
3860:
3846:
3833:
3815:
3806:
3805:
3761:
3747:
3735:
3716:
3703:
3685:
3678:
3668:
3659:
3658:
3598:
3585:
3573:
3554:
3541:
3523:
3510:
3505:
3504:
3499:
3479:
3399:
3398:
3394:
3393:
3381:
3369:
3351:
3338:
3317:
3312:
3311:
3306:
3243:
3233:
3220:
3215:
3214:
3144:
3139:
3138:
3133:
3095:
3073:
3072:
3064:
3037:
3036:
3020:
2996:
2986:
2982:
2981:
2972:
2971:
2949:
2948:
2940:
2916:
2906:
2902:
2901:
2894:
2884:
2875:
2874:
2829:
2818:
2817:
2783:
2777:
2745:
2740:
2739:
2712:
2707:
2706:
2636:
2631:
2630:
2624:
2618:
2613:
2608:
2507:
2502:
2501:
2491:
2482:
2473:fractional part
2448:
2386:
2381:
2380:
2349:
2340:
2336:
2320:
2292:
2281:
2280:
2244:
2239:
2238:
2220:
2219:
2193:
2187:
2186:
2160:
2150:
2143:
2131:
2130:
2093:
2087:
2086:
2063:
2032:
2018:
2017:
1980:
1974:
1973:
1946:
1915:
1911:
1907:
1896:
1895:
1859:
1852:
1851:
1833:
1832:
1806:
1796:
1790:
1789:
1757:
1751:
1750:
1718:
1708:
1705:
1704:
1678:
1668:
1656:
1655:
1593:
1592:
1574:
1573:
1547:
1537:
1531:
1530:
1504:
1494:
1487:
1473:
1462:
1461:
1433:
1428:
1427:
1409:
1408:
1382:
1372:
1366:
1365:
1339:
1329:
1322:
1310:
1309:
1273:
1266:
1265:
1218:
1207:
1206:
1176:
1171:
1170:
1147:
1136:
1135:
1060:
1059:
996:
995:
938:
937:
909:
895:
894:
873:
862:
861:
839:
756:
691:
686:
685:
624:
612:
600:
581:
568:
547:
542:
541:
517:
498:
493:
492:
443:
441:
415:
413:
393:
391:
390:
386:
361:
356:
355:
328:
309:
296:
288:
287:
274:continuous-time
270:
209:
204:
203:
174:
169:
168:
135:
130:
129:
100:
95:
94:
73:
68:
67:
45:
44:
28:
23:
22:
15:
12:
11:
5:
6161:
6159:
6151:
6150:
6145:
6135:
6134:
6128:
6127:
6125:
6124:
6118:
6115:
6114:
6112:
6111:
6106:
6101:
6095:
6093:
6089:
6088:
6086:
6085:
6080:
6074:
6072:
6066:
6065:
6063:
6062:
6057:
6051:
6049:
6045:
6044:
6042:
6041:
6036:
6030:
6028:
6022:
6021:
6019:
6018:
6013:
6008:
6002:
6000:
5994:
5993:
5991:
5990:
5985:
5980:
5974:
5972:
5966:
5965:
5963:
5962:
5957:
5952:
5947:
5942:
5937:
5932:
5927:
5925:Davies-Bouldin
5922:
5917:
5911:
5909:
5903:
5902:
5900:
5899:
5894:
5889:
5884:
5879:
5874:
5869:
5864:
5859:
5854:
5849:
5843:
5841:
5839:Classification
5835:
5834:
5832:
5831:
5826:
5821:
5816:
5811:
5806:
5801:
5796:
5791:
5786:
5781:
5775:
5773:
5767:
5766:
5760:
5758:
5757:
5750:
5743:
5735:
5729:
5728:
5723:
5716:
5715:External links
5713:
5710:
5709:
5684:
5663:
5656:
5638:
5602:
5576:
5573:(1): 20 pages.
5550:
5536:
5516:
5502:
5482:
5475:
5451:
5450:
5448:
5445:
5442:
5441:
5325:
5324:
5322:
5319:
5318:
5317:
5312:
5307:
5302:
5297:
5292:
5290:Geometric mean
5287:
5285:Central moment
5282:
5276:
5269:
5266:
5246:
5245:
5234:
5229:
5224:
5220:
5214:
5209:
5204:
5200:
5196:
5191:
5185:
5182:
5176:
5171:
5162:
5124:
5120:
5092:
5089:
5032:geometric mean
5010:quadratic mean
4964:
4961:
4960:
4959:
4948:
4940:
4935:
4930:
4926:
4923:
4920:
4917:
4911:
4903:
4899:
4893:
4886:
4879:
4874:
4871:
4868:
4865:
4860:
4851:
4847:
4839:
4835:
4831:
4824:
4818:
4815:
4812:
4807:
4803:
4796:
4792:
4786:
4783:
4776:
4773:
4770:
4767:
4764:
4761:
4758:
4723:
4720:
4717:
4714:
4711:
4708:
4705:
4702:
4699:
4696:
4693:
4690:
4687:
4676:
4675:
4664:
4659:
4654:
4650:
4647:
4644:
4641:
4637:
4630:
4625:
4622:
4619:
4615:
4609:
4606:
4601:
4597:
4594:
4591:
4586:
4582:
4575:
4570:
4567:
4564:
4560:
4536:
4516:
4513:
4510:
4507:
4504:
4501:
4498:
4495:
4492:
4489:
4486:
4483:
4467:
4464:
4455:Main article:
4452:
4449:
4420:
4419:
4405:
4401:
4398:
4395:
4388:
4379:
4344:Main article:
4341:
4338:
4296:
4289:
4267:
4260:
4254:
4253:
4242:
4235:
4224:
4218:
4209:
4194:
4193:
4182:
4175:
4164:
4158:
4151:
4145:
4141:
4137:
4132:
4128:
4116:
4112:
4108:
4103:
4099:
4094:
4081:
4077:
4068:
4064:
4056:
4052:
4046:
4041:
4038:
4033:
4023:
4019:
4015:
4010:
4006:
4001:
3988:
3984:
3975:
3960:
3959:
3938:
3934:
3926:
3922:
3916:
3909:
3906:
3901:
3898:
3895:
3892:
3889:
3886:
3883:
3877:
3872:
3869:
3863:
3853:
3849:
3845:
3840:
3836:
3831:
3818:
3814:
3811:
3809:
3807:
3801:
3798:
3792:
3788:
3785:
3782:
3779:
3776:
3773:
3770:
3767:
3764:
3754:
3750:
3742:
3738:
3733:
3723:
3719:
3715:
3710:
3706:
3701:
3688:
3684:
3681:
3679:
3671:
3667:
3666:
3648:
3647:
3636:
3630:
3627:
3622:
3619:
3616:
3613:
3610:
3605:
3601:
3592:
3588:
3580:
3576:
3571:
3561:
3557:
3553:
3548:
3544:
3539:
3526:
3522:
3513:
3497:
3478: = 2
3460:
3459:
3448:
3443:
3440:
3435:
3430:
3426:
3423:
3420:
3417:
3414:
3411:
3402:
3397:
3388:
3384:
3376:
3372:
3367:
3358:
3354:
3350:
3345:
3341:
3336:
3329:
3320:
3304:
3267:
3266:
3255:
3246:
3236:
3232:
3223:
3193:
3192:
3181:
3176:
3171:
3162:
3156:
3147:
3131:
3093:
3087:
3086:
3066:
3063:
3058:
3049:
3045:
3042:
3040:
3038:
3030:
3022:
3019:
3009:
3003:
2999:
2995:
2992:
2989:
2985:
2980:
2977:
2975:
2973:
2958:
2955:
2952:
2942:
2932:
2928:
2923:
2919:
2915:
2912:
2909:
2905:
2900:
2897:
2895:
2887:
2883:
2882:
2856:
2855:
2844:
2841:
2836:
2832:
2828:
2825:
2776:
2773:
2736:direct current
2734:refers to the
2703:
2702:
2687:
2672:
2667:
2650:
2617:
2614:
2612:
2609:
2607:
2604:
2600:
2599:
2584:
2579:
2569:
2566:
2563:
2558:
2553:
2543:
2538:
2533:
2521:
2490:
2487:
2484:
2483:
2481:
2480:
2465:
2451:
2446:
2442:
2436:
2430:
2423:
2419:
2418:
2404:
2401:
2393:
2389:
2378:
2365:
2359:
2355:
2352:
2346:
2343:
2339:
2335:
2332:
2327:
2323:
2319:
2316:
2313:
2310:
2307:
2304:
2299:
2295:
2291:
2288:
2278:
2272:
2271:
2258:
2251:
2247:
2236:
2223:
2218:
2215:
2212:
2209:
2206:
2203:
2200:
2197:
2194:
2192:
2189:
2188:
2185:
2182:
2179:
2176:
2173:
2170:
2167:
2164:
2161:
2157:
2153:
2149:
2148:
2146:
2141:
2138:
2128:
2122:
2121:
2108:
2100:
2096:
2084:
2070:
2066:
2062:
2059:
2056:
2053:
2050:
2047:
2044:
2039:
2035:
2031:
2028:
2025:
2015:
2009:
2008:
1995:
1987:
1983:
1971:
1959:
1953:
1949:
1945:
1942:
1939:
1936:
1933:
1930:
1927:
1922:
1918:
1914:
1910:
1906:
1903:
1893:
1887:
1886:
1872:
1866:
1862:
1849:
1836:
1831:
1828:
1825:
1822:
1819:
1816:
1813:
1810:
1807:
1803:
1799:
1795:
1792:
1791:
1788:
1785:
1782:
1779:
1776:
1773:
1770:
1767:
1764:
1761:
1758:
1756:
1753:
1752:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1725:
1722:
1719:
1715:
1711:
1707:
1706:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1682:
1679:
1677:
1674:
1673:
1671:
1666:
1663:
1653:
1647:
1646:
1630:
1625:
1621:
1617:
1612:
1607:
1603:
1590:
1577:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1544:
1540:
1536:
1533:
1532:
1529:
1526:
1523:
1520:
1517:
1514:
1511:
1508:
1505:
1501:
1497:
1493:
1492:
1490:
1485:
1480:
1476:
1472:
1469:
1459:
1455:
1454:
1440:
1436:
1425:
1412:
1407:
1404:
1401:
1398:
1395:
1392:
1389:
1386:
1383:
1379:
1375:
1371:
1368:
1367:
1364:
1361:
1358:
1355:
1352:
1349:
1346:
1343:
1340:
1336:
1332:
1328:
1327:
1325:
1320:
1317:
1307:
1301:
1300:
1286:
1280:
1276:
1263:
1251:
1248:
1245:
1242:
1239:
1236:
1233:
1230:
1225:
1221:
1217:
1214:
1204:
1198:
1197:
1183:
1179:
1168:
1154:
1150:
1146:
1143:
1133:
1127:
1126:
1123:
1120:
1114:
1113:
1102:
1094:
1091:
1088:
1080:
1075:
1070:
1067:
1050:
1049:
1038:
1030:
1027:
1024:
1016:
1011:
1006:
1003:
945:
916:
912:
908:
905:
902:
880:
876:
872:
869:
838:
835:
831:expected value
827:random process
811:
810:
799:
793:
788:
780:
775:
772:
769:
766:
763:
760:
753:
748:
745:
741:
733:
730:
726:
717:
714:
711:
707:
703:
694:
679:
678:
667:
661:
656:
648:
643:
640:
637:
634:
631:
628:
619:
615:
607:
603:
598:
588:
584:
580:
575:
571:
566:
559:
550:
524:
520:
516:
513:
510:
505:
501:
481:
480:
469:
463:
457:
450:
446:
440:
437:
434:
429:
422:
418:
412:
407:
400:
396:
389:
383:
380:
373:
364:
340:
335:
331:
327:
324:
321:
316:
312:
308:
303:
299:
295:
269:
266:
254:resistive load
250:direct current
244:The RMS of an
223:
220:
217:
212:
181:
177:
165:quadratic mean
150:
145:
142:
139:
114:
111:
108:
103:
80:
76:
66:. Given a set
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6160:
6149:
6146:
6144:
6141:
6140:
6138:
6123:
6120:
6119:
6116:
6110:
6107:
6105:
6102:
6100:
6097:
6096:
6094:
6090:
6084:
6081:
6079:
6076:
6075:
6073:
6071:
6067:
6061:
6058:
6056:
6053:
6052:
6050:
6046:
6040:
6037:
6035:
6032:
6031:
6029:
6027:
6023:
6017:
6014:
6012:
6009:
6007:
6004:
6003:
6001:
5999:
5995:
5989:
5986:
5984:
5981:
5979:
5976:
5975:
5973:
5971:
5967:
5961:
5958:
5956:
5953:
5951:
5948:
5946:
5943:
5941:
5940:Jaccard index
5938:
5936:
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5916:
5913:
5912:
5910:
5908:
5904:
5898:
5895:
5893:
5890:
5888:
5885:
5883:
5880:
5878:
5875:
5873:
5870:
5868:
5865:
5863:
5860:
5858:
5855:
5853:
5850:
5848:
5845:
5844:
5842:
5840:
5836:
5830:
5827:
5825:
5822:
5820:
5817:
5815:
5812:
5810:
5807:
5805:
5802:
5800:
5797:
5795:
5792:
5790:
5787:
5785:
5782:
5780:
5777:
5776:
5774:
5772:
5768:
5763:
5756:
5751:
5749:
5744:
5742:
5737:
5736:
5733:
5727:
5724:
5722:
5719:
5718:
5714:
5699:on 2017-06-30
5698:
5694:
5688:
5685:
5680:
5679:
5674:
5667:
5664:
5659:
5653:
5649:
5642:
5639:
5623:
5619:
5612:
5606:
5603:
5591:
5587:
5580:
5577:
5572:
5568:
5561:
5554:
5551:
5539:
5537:9781351661386
5533:
5529:
5528:
5520:
5517:
5505:
5503:9781349004874
5499:
5495:
5494:
5486:
5483:
5478:
5476:9780199233991
5472:
5468:
5467:
5459:
5457:
5453:
5446:
5438:
5419:∴ HC =
5386:
5380:
5370:
5362:
5356:
5353:, and radius
5352:
5348:
5344:
5340:
5336:
5330:
5327:
5320:
5316:
5313:
5311:
5308:
5306:
5303:
5301:
5300:Least squares
5298:
5296:
5293:
5291:
5288:
5286:
5283:
5280:
5277:
5275:
5272:
5271:
5267:
5265:
5263:
5258:
5254:
5249:
5232:
5222:
5218:
5212:
5207:
5202:
5198:
5194:
5189:
5180:
5174:
5169:
5160:
5152:
5151:
5150:
5148:
5144:
5140:
5122:
5118:
5109:
5087:
5073:
5069:
5063:
5059:
5055:
5048:
5044:
5043:harmonic mean
5037:
5033:
5026:
5022:
5015:
5011:
5004:
5000:
4993:
4989:
4985:
4980:
4975:
4970:
4962:
4946:
4938:
4933:
4928:
4921:
4915:
4909:
4901:
4897:
4891:
4884:
4869:
4863:
4849:
4845:
4837:
4833:
4829:
4822:
4813:
4805:
4801:
4794:
4790:
4784:
4781:
4774:
4765:
4759:
4744:
4743:
4742:
4739:
4737:
4715:
4709:
4703:
4700:
4697:
4691:
4685:
4662:
4657:
4652:
4645:
4639:
4635:
4628:
4623:
4620:
4617:
4613:
4607:
4604:
4599:
4592:
4584:
4580:
4573:
4568:
4565:
4562:
4558:
4550:
4549:
4548:
4534:
4511:
4508:
4505:
4502:
4496:
4493:
4487:
4481:
4473:
4465:
4463:
4458:
4450:
4448:
4445:
4441:
4437:
4433:
4429:
4425:
4403:
4399:
4396:
4393:
4386:
4377:
4369:
4368:
4367:
4365:
4361:
4357:
4353:
4347:
4339:
4337:
4335:
4331:
4330:average power
4327:
4323:
4318:
4314:
4299: Ă—
4295:
4292: =
4288:
4276:
4271:
4266:
4259:
4240:
4233:
4222:
4216:
4207:
4199:
4198:
4197:
4180:
4173:
4162:
4156:
4149:
4143:
4139:
4135:
4130:
4126:
4114:
4110:
4106:
4101:
4097:
4092:
4079:
4075:
4066:
4062:
4054:
4050:
4044:
4039:
4036:
4031:
4021:
4017:
4013:
4008:
4004:
3999:
3986:
3982:
3973:
3965:
3964:
3963:
3936:
3932:
3924:
3920:
3914:
3907:
3904:
3896:
3893:
3890:
3884:
3881:
3875:
3870:
3867:
3861:
3851:
3847:
3843:
3838:
3834:
3829:
3816:
3812:
3810:
3799:
3796:
3790:
3783:
3780:
3777:
3771:
3768:
3765:
3762:
3752:
3748:
3740:
3736:
3731:
3721:
3717:
3713:
3708:
3704:
3699:
3686:
3682:
3680:
3669:
3657:
3656:
3655:
3653:
3634:
3628:
3625:
3617:
3614:
3608:
3603:
3599:
3590:
3586:
3578:
3574:
3569:
3559:
3555:
3551:
3546:
3542:
3537:
3524:
3520:
3511:
3503:
3502:
3501:
3496:
3491:
3489:
3485:
3477:
3473:
3469:
3465:
3446:
3441:
3438:
3433:
3428:
3421:
3418:
3412:
3409:
3400:
3395:
3386:
3382:
3374:
3370:
3365:
3356:
3352:
3348:
3343:
3339:
3334:
3327:
3318:
3310:
3309:
3308:
3303:
3299:
3295:
3291:
3287:
3282:
3280:
3276:
3272:
3253:
3244:
3234:
3230:
3221:
3213:
3212:
3211:
3208:
3206:
3202:
3198:
3179:
3174:
3169:
3160:
3154:
3145:
3137:
3136:
3135:
3130:
3126:
3122:
3118:
3113:
3111:
3107:
3103:
3099:
3092:
3061:
3056:
3047:
3043:
3041:
3028:
3017:
3007:
3001:
2993:
2987:
2983:
2978:
2976:
2956:
2953:
2950:
2930:
2926:
2921:
2913:
2907:
2903:
2898:
2896:
2885:
2873:
2872:
2871:
2869:
2865:
2861:
2842:
2839:
2834:
2830:
2826:
2823:
2816:
2815:
2814:
2812:
2808:
2804:
2800:
2796:
2792:
2788:
2782:
2774:
2772:
2770:
2737:
2685:
2670:
2665:
2648:
2629:
2628:
2627:
2623:
2615:
2610:
2605:
2603:
2582:
2577:
2567:
2564:
2561:
2556:
2551:
2541:
2536:
2531:
2519:
2500:
2499:
2498:
2496:
2488:
2478:
2474:
2470:
2466:
2464:) spent high,
2463:
2459:
2455:
2452:
2449:
2443:
2441:is frequency,
2440:
2437:
2434:
2431:
2428:
2425:
2424:
2420:
2402:
2399:
2391:
2387:
2379:
2363:
2357:
2353:
2350:
2344:
2341:
2337:
2333:
2330:
2325:
2321:
2317:
2311:
2305:
2302:
2297:
2293:
2289:
2286:
2279:
2277:
2274:
2273:
2256:
2249:
2245:
2237:
2216:
2213:
2207:
2204:
2198:
2195:
2190:
2183:
2180:
2174:
2171:
2165:
2162:
2155:
2151:
2144:
2139:
2136:
2129:
2127:
2124:
2123:
2106:
2098:
2094:
2085:
2068:
2064:
2060:
2054:
2051:
2045:
2042:
2037:
2033:
2029:
2026:
2023:
2016:
2014:
2013:Sawtooth wave
2011:
2010:
1993:
1985:
1981:
1972:
1957:
1951:
1947:
1943:
1937:
1934:
1928:
1925:
1920:
1916:
1912:
1908:
1904:
1901:
1894:
1892:
1891:Triangle wave
1889:
1888:
1870:
1864:
1860:
1850:
1829:
1826:
1820:
1817:
1811:
1808:
1801:
1797:
1793:
1786:
1783:
1777:
1774:
1768:
1765:
1762:
1759:
1754:
1747:
1744:
1738:
1735:
1729:
1726:
1723:
1720:
1713:
1709:
1701:
1698:
1692:
1689:
1683:
1680:
1675:
1669:
1664:
1661:
1654:
1652:
1649:
1648:
1628:
1623:
1619:
1615:
1610:
1605:
1601:
1591:
1570:
1567:
1561:
1558:
1552:
1549:
1542:
1538:
1534:
1527:
1524:
1518:
1515:
1509:
1506:
1499:
1495:
1488:
1483:
1478:
1474:
1470:
1467:
1460:
1457:
1456:
1438:
1434:
1426:
1405:
1402:
1396:
1393:
1387:
1384:
1377:
1373:
1369:
1362:
1359:
1353:
1350:
1344:
1341:
1334:
1330:
1323:
1318:
1315:
1308:
1306:
1303:
1302:
1284:
1278:
1274:
1264:
1246:
1243:
1240:
1237:
1231:
1228:
1223:
1219:
1215:
1212:
1205:
1203:
1200:
1199:
1181:
1177:
1169:
1152:
1148:
1144:
1141:
1134:
1132:
1129:
1128:
1124:
1121:
1118:
1117:
1100:
1092:
1089:
1086:
1078:
1073:
1068:
1065:
1058:
1055:
1054:
1053:
1036:
1028:
1025:
1022:
1014:
1009:
1004:
1001:
994:
991:
990:
989:
987:
983:
979:
975:
966:
959:
943:
934:
914:
910:
906:
903:
900:
878:
874:
870:
867:
859:
855:
851:
847:
843:
836:
834:
832:
828:
823:
821:
816:
797:
791:
778:
767:
761:
751:
746:
743:
739:
731:
728:
724:
709:
701:
692:
684:
683:
682:
665:
659:
646:
635:
629:
617:
613:
605:
601:
596:
586:
582:
578:
573:
569:
564:
557:
548:
540:
539:
538:
522:
518:
514:
511:
508:
503:
499:
490:
486:
467:
461:
455:
448:
444:
438:
435:
432:
427:
420:
416:
410:
405:
398:
394:
387:
381:
378:
371:
362:
354:
353:
352:
351:, the RMS is
333:
329:
325:
322:
319:
314:
310:
306:
301:
297:
285:
280:
278:
275:
267:
265:
263:
259:
255:
251:
247:
242:
240:
210:
201:
197:
179:
175:
166:
148:
101:
78:
74:
65:
62:of the set's
61:
57:
53:
49:
41:
37:
33:
19:
5808:
5701:. Retrieved
5697:the original
5687:
5676:
5666:
5647:
5641:
5629:. Retrieved
5622:the original
5617:
5605:
5593:. Retrieved
5589:
5579:
5570:
5566:
5553:
5541:. Retrieved
5526:
5519:
5507:. Retrieved
5492:
5485:
5465:
5436:
5378:
5368:
5354:
5350:
5346:
5342:
5338:
5334:
5329:
5262:DC component
5252:
5250:
5247:
5076:
5071:
5067:
5061:
5057:
5053:
5046:
5035:
5024:
5013:
5002:
4998:
4991:
4987:
4983:
4740:
4735:
4677:
4469:
4460:
4439:
4431:
4428:gas constant
4423:
4421:
4359:
4349:
4329:
4325:
4321:
4319:
4315:
4293:
4286:
4272:
4264:
4257:
4255:
4195:
3961:
3649:
3494:
3492:
3487:
3483:
3475:
3467:
3466:is time and
3463:
3461:
3301:
3293:
3289:
3283:
3270:
3268:
3209:
3199:, such as a
3194:
3128:
3124:
3120:
3114:
3109:
3105:
3101:
3097:
3090:
3088:
2867:
2863:
2859:
2857:
2810:
2806:
2798:
2790:
2784:
2704:
2625:
2601:
2492:
2476:
2468:
2461:
2453:
2444:
2438:
2432:
2426:
1057:Peak-to-peak
1056:
1051:
993:Peak-to-peak
992:
971:
957:
824:
812:
680:
488:
484:
482:
283:
281:
271:
243:
164:
51:
43:
39:
35:
29:
4334:Audio power
2945:where
1305:Square wave
202:is denoted
64:mean square
60:square root
32:mathematics
6137:Categories
6092:Similarity
6034:Perplexity
5945:Rand index
5930:Dunn index
5915:Silhouette
5907:Clustering
5771:Regression
5703:2013-07-18
5631:15 January
5595:21 January
5447:References
5357:= QO = OG.
5143:population
4977:Geometric
4967:See also:
4444:molar mass
4364:calculated
4326:mean power
3298:sinusoidal
3201:sinusoidal
2495:orthogonal
2458:duty cycle
2126:Pulse wave
976:is a pure
268:Definition
5862:Precision
5814:RMSE/RMSD
5678:MathWorld
5337:and BC =
5228:¯
5199:σ
5184:¯
5119:σ
5091:¯
4898:∑
4846:∑
4791:∑
4704:
4614:∑
4559:∑
4322:RMS power
4320:The term
4136:−
4107:−
4014:−
3908:ω
3894:ω
3885:
3876:−
3844:−
3781:ω
3772:
3766:−
3732:∫
3714:−
3615:ω
3609:
3570:∫
3552:−
3419:ω
3413:
3366:∫
3349:−
3025:(as
2954:⋯
2565:⋯
2471:) is the
2354:π
2345:−
2334:
2318:−
2306:
2199:
2166:
2061:−
2046:
1944:−
1929:
1812:
1794:−
1769:
1730:
1684:
1553:
1535:−
1510:
1388:
1370:−
1345:
1241:π
1232:
1202:Sine wave
1093:×
1087:≈
1079:×
1029:×
1023:≈
1015:×
986:amplitude
978:sine wave
944:τ
907:−
744:−
740:∫
716:∞
713:→
597:∫
579:−
515:≤
509:≤
436:⋯
323:…
167:(denoted
38:(abbrev.
6078:Coverage
5857:Accuracy
5618:Keysight
5424:GC²
5333:If AC =
5268:See also
5149:, then:
5147:waveform
5056: (
4986: (
4969:Accuracy
4527:, where
4275:voltages
3650:Using a
3486:, where
3279:AC power
3275:Reactive
3197:waveform
2781:AC power
2435:is time,
1119:Waveform
982:periodic
974:waveform
858:sawtooth
854:triangle
820:calculus
277:waveform
239:integral
200:function
5970:Ranking
5960:SimHash
5847:F-score
5433:
5421:
5417:
5405:
5401:
5389:
5341:. OC =
5295:L2 norm
5137:is the
5106:is the
4442:is the
4436:kelvins
4352:physics
4350:In the
4308:√
4301:√
3470:is the
3296:) is a
3117:voltage
2868:average
2803:current
2767:is the
2616:Voltage
2456:is the
2422:where:
972:If the
286:values
54:) of a
5867:Recall
5654:
5543:5 July
5534:
5509:5 July
5500:
5473:
5383:Using
5359:Using
4678:where
4438:, and
4422:where
4283:
4279:
4256:where
3493:Since
3462:where
2705:where
856:, and
850:square
829:, the
260:, the
34:, the
6143:Means
5872:Kappa
5789:sMAPE
5625:(PDF)
5614:(PDF)
5563:(PDF)
5321:Notes
5281:(ARV)
5145:or a
5141:of a
5051:>
5040:>
5029:>
5018:>
4996:>
4981:that
4451:Error
4340:Speed
3288:when
2787:power
2644:AC+DC
2515:Total
2467:frac(
256:. In
6039:BLEU
6011:SSIM
6006:PSNR
5983:NDCG
5804:MSPE
5799:MASE
5794:MAPE
5652:ISBN
5633:2019
5597:2015
5545:2020
5532:ISBN
5511:2020
5498:ISBN
5471:ISBN
5349:and
5110:and
5070:and
4734:and
2606:Uses
2214:>
2196:frac
2181:<
2163:frac
2043:frac
1926:frac
1830:0.75
1827:>
1809:frac
1787:0.75
1784:<
1766:frac
1763:<
1745:<
1727:frac
1724:<
1721:0.25
1702:0.25
1699:<
1681:frac
1568:>
1550:frac
1525:<
1507:frac
1403:>
1385:frac
1360:<
1342:frac
1125:RMS
988:is:
960:= 1.
846:Sine
6060:FID
6026:NLP
6016:IoU
5978:MRR
5955:SMC
5887:ROC
5882:AUC
5877:MCC
5829:MAD
5824:MDA
5809:RMS
5784:MAE
5779:MSE
5345:of
5165:rms
5077:If
5054:min
5007:or
5003:RMS
4984:max
4753:RMS
4701:DFT
4382:RMS
4356:gas
4354:of
4328:or
4297:RMS
4212:RMS
3978:RMS
3882:sin
3769:cos
3674:RMS
3600:sin
3516:RMS
3410:sin
3323:RMS
3249:RMS
3239:RMS
3226:Avg
3203:or
3165:RMS
3150:Avg
3132:RMS
3112:).
3094:RMS
3052:RMS
3013:Avg
2962:Avg
2936:Avg
2890:Avg
2748:RMS
2676:RMS
2639:RMS
2573:RMS
2547:RMS
2527:RMS
2510:RMS
2475:of
2331:sin
2303:sin
1760:0.5
1748:0.5
1571:0.5
1528:0.5
1406:0.5
1363:0.5
1229:sin
1097:RMS
1090:3.5
1083:RMS
1033:RMS
1026:2.8
1019:RMS
706:lim
697:RMS
553:RMS
537:is
367:RMS
128:or
56:set
52:rms
50:or
46:RMS
40:RMS
30:In
6139::
5988:AP
5852:P4
5675:.
5616:.
5588:.
5569:.
5565:.
5455:^
5437:HM
5435:=
5430:OC
5414:OC
5408:GC
5403:=
5398:GC
5392:HC
5387:,
5379:GM
5377:=
5369:QM
5367:=
5343:AM
5047:HM
5036:GM
5025:AM
5014:QM
4336:.
3281:.
3134:,
3119:,
2805:,
2797:,
2789:,
2753:AC
2720:DC
2681:AC
2661:DC
1131:DC
852:,
848:,
42:,
5819:R
5754:e
5747:t
5740:v
5706:.
5681:.
5660:.
5635:.
5599:.
5571:8
5547:.
5513:.
5479:.
5439:.
5427:/
5411:/
5395:/
5381:.
5371:.
5355:r
5351:b
5347:a
5339:b
5335:a
5233:.
5223:2
5219:x
5213:=
5208:2
5203:x
5195:+
5190:2
5181:x
5175:=
5170:2
5161:x
5123:x
5088:x
5072:b
5068:a
5064:)
5062:b
5060:,
5058:a
5049:)
5045:(
5038:)
5034:(
5027:)
5023:(
5016:)
5012:(
5005:)
5001:(
4994:)
4992:b
4990:,
4988:a
4947:.
4939:2
4934:|
4929:N
4925:]
4922:m
4919:[
4916:X
4910:|
4902:m
4892:=
4885:2
4878:|
4873:]
4870:m
4867:[
4864:X
4859:|
4850:m
4838:2
4834:N
4830:1
4823:=
4817:]
4814:n
4811:[
4806:2
4802:x
4795:n
4785:N
4782:1
4775:=
4772:}
4769:]
4766:n
4763:[
4760:x
4757:{
4736:N
4722:}
4719:]
4716:n
4713:[
4710:x
4707:{
4698:=
4695:]
4692:m
4689:[
4686:X
4663:,
4658:2
4653:|
4649:]
4646:m
4643:[
4640:X
4636:|
4629:N
4624:1
4621:=
4618:m
4608:N
4605:1
4600:=
4596:]
4593:n
4590:[
4585:2
4581:x
4574:N
4569:1
4566:=
4563:n
4535:T
4515:)
4512:T
4509:n
4506:=
4503:t
4500:(
4497:x
4494:=
4491:]
4488:n
4485:[
4482:x
4440:M
4432:T
4424:R
4404:M
4400:T
4397:R
4394:3
4387:=
4378:v
4310:2
4303:2
4294:V
4290:P
4287:V
4268:P
4265:V
4261:P
4258:I
4241:,
4234:2
4227:p
4223:V
4217:=
4208:V
4181:.
4174:2
4167:p
4163:I
4157:=
4150:2
4144:1
4140:T
4131:2
4127:T
4115:1
4111:T
4102:2
4098:T
4093:1
4084:p
4080:I
4076:=
4067:2
4063:T
4055:1
4051:T
4045:]
4040:2
4037:t
4032:[
4022:1
4018:T
4009:2
4005:T
4000:1
3991:p
3987:I
3983:=
3974:I
3937:2
3933:T
3925:1
3921:T
3915:]
3905:4
3900:)
3897:t
3891:2
3888:(
3871:2
3868:t
3862:[
3852:1
3848:T
3839:2
3835:T
3830:1
3821:p
3817:I
3813:=
3800:t
3797:d
3791:2
3787:)
3784:t
3778:2
3775:(
3763:1
3753:2
3749:T
3741:1
3737:T
3722:1
3718:T
3709:2
3705:T
3700:1
3691:p
3687:I
3683:=
3670:I
3635:.
3629:t
3626:d
3621:)
3618:t
3612:(
3604:2
3591:2
3587:T
3579:1
3575:T
3560:1
3556:T
3547:2
3543:T
3538:1
3529:p
3525:I
3521:=
3512:I
3498:p
3495:I
3488:T
3484:T
3482:/
3480:Ď€
3476:ω
3474:(
3468:ω
3464:t
3447:,
3442:t
3439:d
3434:2
3429:]
3425:)
3422:t
3416:(
3405:p
3401:I
3396:[
3387:2
3383:T
3375:1
3371:T
3357:1
3353:T
3344:2
3340:T
3335:1
3328:=
3319:I
3305:p
3302:I
3294:t
3292:(
3290:I
3271:R
3254:.
3245:I
3235:V
3231:=
3222:P
3180:.
3175:R
3170:2
3161:V
3155:=
3146:P
3129:V
3125:t
3123:(
3121:V
3110:t
3108:(
3106:I
3102:t
3100:(
3098:I
3091:I
3062:R
3057:2
3048:I
3044:=
3029:R
3018:R
3008:)
3002:2
2998:)
2994:t
2991:(
2988:I
2984:(
2979:=
2957:)
2951:(
2931:)
2927:R
2922:2
2918:)
2914:t
2911:(
2908:I
2904:(
2899:=
2886:P
2864:t
2862:(
2860:I
2843:.
2840:R
2835:2
2831:I
2827:=
2824:P
2811:R
2807:I
2799:R
2791:P
2715:V
2686:2
2671:+
2666:2
2656:V
2649:=
2583:2
2578:n
2568:+
2562:+
2557:2
2552:2
2542:+
2537:2
2532:1
2520:=
2479:.
2477:r
2469:r
2462:f
2454:D
2447:i
2445:A
2439:f
2433:t
2427:y
2403:2
2400:3
2392:1
2388:A
2364:)
2358:3
2351:2
2342:t
2338:(
2326:1
2322:A
2315:)
2312:t
2309:(
2298:1
2294:A
2290:=
2287:y
2257:D
2250:1
2246:A
2217:D
2211:)
2208:t
2205:f
2202:(
2191:0
2184:D
2178:)
2175:t
2172:f
2169:(
2156:1
2152:A
2145:{
2140:=
2137:y
2107:3
2099:1
2095:A
2069:1
2065:A
2058:)
2055:t
2052:f
2049:(
2038:1
2034:A
2030:2
2027:=
2024:y
1994:3
1986:1
1982:A
1958:|
1952:1
1948:A
1941:)
1938:t
1935:f
1932:(
1921:1
1917:A
1913:2
1909:|
1905:=
1902:y
1871:2
1865:1
1861:A
1824:)
1821:t
1818:f
1815:(
1802:1
1798:A
1781:)
1778:t
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1772:(
1755:0
1742:)
1739:t
1736:f
1733:(
1714:1
1710:A
1696:)
1693:t
1690:f
1687:(
1676:0
1670:{
1665:=
1662:y
1629:2
1624:1
1620:A
1616:+
1611:2
1606:0
1602:A
1565:)
1562:t
1559:f
1556:(
1543:1
1539:A
1522:)
1519:t
1516:f
1513:(
1500:1
1496:A
1489:{
1484:+
1479:0
1475:A
1471:=
1468:y
1439:1
1435:A
1400:)
1397:t
1394:f
1391:(
1378:1
1374:A
1357:)
1354:t
1351:f
1348:(
1335:1
1331:A
1324:{
1319:=
1316:y
1285:2
1279:1
1275:A
1250:)
1247:t
1244:f
1238:2
1235:(
1224:1
1220:A
1216:=
1213:y
1182:0
1178:A
1153:0
1149:A
1145:=
1142:y
1101:.
1074:3
1069:2
1066:=
1037:.
1010:2
1005:2
1002:=
958:a
915:1
911:A
904:=
901:y
879:1
875:A
871:=
868:y
798:.
792:t
787:d
779:2
774:]
771:)
768:t
765:(
762:f
759:[
752:T
747:T
732:T
729:2
725:1
710:T
702:=
693:f
666:,
660:t
655:d
647:2
642:]
639:)
636:t
633:(
630:f
627:[
618:2
614:T
606:1
602:T
587:1
583:T
574:2
570:T
565:1
558:=
549:f
523:2
519:T
512:t
504:1
500:T
489:t
487:(
485:f
468:.
462:)
456:2
449:n
445:x
439:+
433:+
428:2
421:2
417:x
411:+
406:2
399:1
395:x
388:(
382:n
379:1
372:=
363:x
339:}
334:n
330:x
326:,
320:,
315:2
311:x
307:,
302:1
298:x
294:{
284:n
222:S
219:M
216:R
211:f
180:2
176:M
149:x
144:S
141:M
138:R
113:S
110:M
107:R
102:x
79:i
75:x
20:)
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