R Notebook

AirPassengers [144] (ts)
BJsales [150] (ts)
BOD [6,2] (data.frame)
CO2 [84,5] (nfnGroupedData)
ChickWeight [578,4] (nfnGroupedData)
DNase [176,3] (nfnGroupedData)
EuStockMarkets [1860,4] (mts)
Formaldehyde [6,2] (data.frame)
HairEyeColor [4,4,2] (table)
Harman23.cor [c(8, 8); 8; 1 ] (list)
Harman74.cor [c(24, 24); 24; 1 ] (list)
Indometh [66,3] (nfnGroupedData)
InsectSprays [72,2] (data.frame)
JohnsonJohnson [84] (ts)
LakeHuron [98] (ts)
LifeCycleSavings [50,5] (data.frame)
Loblolly [84,3] (nfnGroupedData)
Nile [100] (ts)
Orange [35,3] (nfnGroupedData)
OrchardSprays [64,4] (data.frame)
PlantGrowth [30,2] (data.frame)
Puromycin [23,3] (data.frame)
Seatbelts [192,8] (mts)
Theoph [132,5] (nfnGroupedData)
Titanic [4,2,2,2] (table)
ToothGrowth [60,3] (data.frame)
UCBAdmissions [2,2,6] (table)
UKDriverDeaths [192] (ts)
UKgas [108] (ts)
USAccDeaths [72] (ts)
USArrests [50,4] (data.frame)
USJudgeRatings [43,12] (data.frame)
USPersonalExpenditure [5,5] (matrix)
UScitiesD [10,10] (dist)
VADeaths [5,4] (matrix)
WWWusage [100] (ts)
WorldPhones [7,7] (matrix)
ability.cov [c(6, 6); 6; 1 ] (list)
airmiles [24] (ts)
airquality [153,6] (data.frame)
anscombe [11,8] (data.frame)
attenu [182,5] (data.frame)
attitude [30,7] (data.frame)
austres [89] (ts)
cars [50,2] (data.frame)
chickwts [71,2] (data.frame)
co2 [468] (ts)
crimtab [42,22] (table)
discoveries [100] (ts)
esoph [88,5] (data.frame)
euro [11] (numeric)
eurodist [21,21] (dist)
faithful [272,2] (data.frame)
freeny [39,5] (data.frame)
infert [248,8] (data.frame)
iris [150,5] (data.frame)
iris3 [50,4,3] (array)
islands [48] (numeric)
lh [48] (ts)
longley [16,7] (data.frame)
lynx [114] (ts)
morley [100,3] (data.frame)
mtcars [32,11] (data.frame)
nhtemp [60] (ts)
nottem [240] (ts)
npk [24,5] (data.frame)
occupationalStatus [8,8] (table)
precip [70] (numeric)
presidents [120] (ts)
pressure [19,2] (data.frame)
quakes [1000,5] (data.frame)
randu [400,3] (data.frame)
rivers [141] (numeric)
rock [48,4] (data.frame)
sleep [20,3] (data.frame)
stackloss [21,4] (data.frame)
sunspot.month [3177] (ts)
sunspot.year [289] (ts)
sunspots [2820] (ts)
swiss [47,6] (data.frame)
treering [7980] (ts)
trees [31,3] (data.frame)
uspop [19] (ts)
volcano [87,61] (matrix)
warpbreaks [54,3] (data.frame)
women [15,2] (data.frame)
lakers [34624,13] (data.frame)

Přiřazení hodnoty proměnné

[1] FALSE

Sčítání, odčítání, násobení a dělení

[1] Inf
[1] Inf
[1] NaN
[1] NaN

Převod desetinných čísel na zlomky

3 / 4-167 is a prime!
-167 / 100

Mocniny a odmocniny

Attaching package: ‘numbers’

The following object is masked from ‘package:shiny’:

    div

[1] 12  2
[1] 2 3

Exponenty a logaritmy

Goniometrické funkce

Vypočítejte pH 0.001 M kyseliny chlorovodíkové, 0.01 M hydroxidu sodného, 0.15 M kyseliny octové (Ka = 1.75e-5) a 0.01 M amoniaku (Kb = 1.8e-5)

[1] 10.62764

Matematické konstanty

[1] 2.718282
[1] 2.7182818284590451

Vektory - generování řady čísel

Vektory - řada náhodných čísel z daného rozmezí

Indexy

[1] 18 94 87 47

Uspořádání vektoru

 [1]  7  8  5 11 12  6 19 18  9  3 14 13 10 16  4 17  1  2 15

Množiny

Vektorová aritmetika

diff(x)

 [1]   3 -38  33 -61  17 -25   2  32  33 -51   4  33  -7  29  -7
[16]   2 -39  -4

sign(x)

 [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Filtrování hodnot ve vektoru

numbers =c(4,23,4,23,5,43,54,56,657,67,67,435,453,435,7,65,34,435)
table(numbers)[2]==1

   5 
TRUE 

numbers[2]

[1] 23

sum(numbers==435)

[1] 3

Matice

matrix(x,nrow=6,ncol=3,byrow = TRUE)

     [,1] [,2] [,3]
[1,]   90   52   58
[2,]   71   27   17
[3,]   83   50   42
[4,]   61   45   15
[5,]   24   80   36
[6,]   63   33   43

matrix(x,nrow=6,ncol=3,byrow = FALSE)

     [,1] [,2] [,3]
[1,]   90   83   24
[2,]   52   50   80
[3,]   58   42   36
[4,]   71   61   63
[5,]   27   45   33
[6,]   17   15   43

Dataframes

Seznamy (lists)

[1] 23

Vypočítejte molekulové hmotnosti alkanů C1 - C12.

      1       2       3       4       5       6       7       8 
 16.043  30.070  44.097  58.124  72.151  86.178 100.205 114.232 
      9      10      11      12 
128.259 142.286 156.313 170.340 
$`1`
[1] 16.043

$`2`
[1] 30.07

$`3`
[1] 44.097

$`4`
[1] 58.124

$`5`
[1] 72.151

$`6`
[1] 86.178

$`7`
[1] 100.205

$`8`
[1] 114.232

$`9`
[1] 128.259

$`10`
[1] 142.286

$`11`
[1] 156.313

$`12`
[1] 170.34

Vliv 3 ůzných druhů krmiva na přírůstek živé váhy (v kg) prasat, rozdělených do 4 různých skupin.

        A    B    C
[1,]  7.0 14.0  8.5
[2,] 16.0 15.5 16.5
[3,] 10.5 15.0  9.5
[4,] 13.5 21.0 13.5

Pipe operator (%>%) v R

# pipe operator
library(magrittr)

Attaching package: ‘magrittr’

The following object is masked from ‘package:numbers’:

    mod

a = 3.14159
a %>% seq(10,3) %>% round(3)

[1] 3.142 6.142 9.142

Příkaz if-else

x = sample(12:99,18, replace = FALSE); x

ifelse(x<50,0,1)
x[x<50] = 0
x[x>=50] = 1
x

Vypocítejte vazebnou energii atomového jádra pomoci Bethe - Weiszackerovy rovnice B = 14.0 - 13.1A^(2/3) + 0.585Z(Z-1)/A^(1/3) - (18.1(A-2*Z)^2)/A + C/A, kde A - nukleonove cislo, Z - atomove cislo, C - konstanta, pro jádra se sudým počtem protonů i neutronů je rovna 132, pro jádra s lichým počtem protonů i neutronů je rovna -132, pro lichy počet protonů a sudý počet neutronů a naopak je rovna 0.

# alpha particle
A = 4 
Z = 2

# U-235
A = 235 
Z = 92

# funkce
N = A-Z
if (N%%2==0 & Z%%2==0){C = 132} else if (N%%2!=0 & Z%%2!=0){C = -132} else {C = 0}
B = 14.0 - 13.1*A^(2/3) + 0.585*Z*(Z-1)/A^(1/3) - (18.1*(A-2*Z)^2)/A + C/A
B # [MeV]
B/A # energie na 1 nukleon [MeV]

# polomer jadra: R = R0 * A^(1/3)
R0 = 1.4e-13 # [cm]
R = R0 * A^(1/3)
R = R*10e-15 
R   # [m]

Cyklus typu while

Vypočítejte molekulové hmotnosti alkanů C1 - C12 (while loop)

n = 1
Mhc = NULL
while(n <= 12){
  hc = n*12.011 + (2*n + 2)*1.008
  Mhc = c(Mhc,hc)
  n = n+1
}
names(Mhc) = c(1:12)
Mhc

      1       2       3       4       5       6       7       8 
 16.043  30.070  44.097  58.124  72.151  86.178 100.205 114.232 
      9      10      11      12 
128.259 142.286 156.313 170.340 

Cyklus typu for (for loop)

Vypočítejte molekulové hmotnosti alkanů C1 - C12

Mhc = NULL
for(n in c(1:12)){
  hc = n*12.011 + (2*n + 2)*1.008
  Mhc = c(Mhc,hc) 
}
names(Mhc) = c(1:12)
Mhc

      1       2       3       4       5       6       7       8 
 16.043  30.070  44.097  58.124  72.151  86.178 100.205 114.232 
      9      10      11      12 
128.259 142.286 156.313 170.340 

Vypočítejte střední kvadratickou rychlost molekul daných plynů v rozmezí teplot od 150 K do 500 K s krokem 50 K.

el = c("H2","He", "O2", "Kr")
M = c(2.0159, 4.0026, 31.9988, 83.8) # [g / mol]
Ts = seq(from=150, to=500, by=50) # [K]
R = 8314.34 # [J / kmol K]
MKV = NULL
for(tt in Ts){
  mkv= rep(0, length(M))
  for(ii in c(1:length(M))){
    mkv[ii] = (3*R*tt/M[ii])^(1/2)
  }
  MKV = rbind(MKV, mkv)   
}
colnames(MKV) = el
rownames(MKV) = Ts
MKV

          H2        He       O2       Kr
150 1362.340  966.8276 341.9427 211.2993
200 1573.095 1116.3964 394.8414 243.9875
250 1758.774 1248.1691 441.4461 272.7863
300 1926.640 1367.3007 483.5800 298.8224
350 2081.009 1476.8536 522.3261 322.7651
400 2224.693 1578.8229 558.3900 345.0504
450 2359.643 1674.5946 592.2621 365.9812
500 2487.282 1765.1777 624.2990 385.7780

plot(0,0,xlim=c(min(Ts),max(Ts)),ylim = c(min(MKV),max(MKV)), type ="n",xlab="T [K]",ylab="str. kv. rychlost [m/s]")
for(ii in c(1:length(M))){points(Ts,MKV[,ii], type="p",col=ii,pch=16)}

legend("topleft",legend=el,col=c(1:length(M)),pch=16,cex=.8)

Fyzikální konstanty

NULL

molweight("CH3CH2CHCHCH2CHCHCH2CHCHCH2CHCHCH2CHCH(CH2)3COOH") # eicosapentaenoic acid (EPA) 

CH3CH2CHCHCH2CHCHCH2CHCHCH2CHCHCH2CHCH(CH2)3COOH 
                                         302.451 

molweight("C20H30O2")

C20H30O2 
 302.451 

molweight(c("C2H5OH", "CO2", "H2O")) 

  C2H5OH      CO2      H2O 
46.06844 44.00950 18.01528 

molweight(c("SiOFH4", "NaHCO3", "C6H12O6", "Ca(HCO3)2", "Pb(NO3)2", "(NH4)2SO4"))

   SiOFH4    NaHCO3   C6H12O6 Ca(HCO3)2  Pb(NO3)2 (NH4)2SO4 
 67.11506  84.00661 180.15588 162.11168 331.20980 132.13952 

Určete délku měděného drátu o průměru 1.6 mm jehož hmotnost je 0.8 kg. Hustota mědi je 8900 kg/m3.

hm = 0.8 # kg
rho = 8900 # kg/m3
d = 1.6e-3 # m

V = hm/rho
S = pi*(d/2)^2
L = V/S; L

[1] 44.70644

Disociační konstanty

Izotopy

library(enviPat)
data(isotopes)
isotopes

library(ecipex)
nistiso
nistiso$mass
nistiso$abundance
nistiso$element

library(IsoSpecR)
data(isotopicData)
isotopicData

library(CIAAWconsensus)
ciaaw.mass.2003
ciaaw.mass.2012
ciaaw.mass.2016

Izotopové patterny

$Se
                m/z        abundance
   [1,] 72.92247640  0.000000000e+00
   [2,] 72.92895574  0.000000000e+00
   [3,] 72.93543507  0.000000000e+00
   [4,] 72.94191441  0.000000000e+00
   [5,] 72.94839374  0.000000000e+00
   [6,] 72.95487308  0.000000000e+00
   [7,] 72.96135241  0.000000000e+00
   [8,] 72.96783175  0.000000000e+00
   [9,] 72.97431108  0.000000000e+00
  [10,] 72.98079042  0.000000000e+00
  [11,] 72.98726975  0.000000000e+00
  [12,] 72.99374909  0.000000000e+00
  [13,] 73.00022842  0.000000000e+00
  [14,] 73.00670776  0.000000000e+00
  [15,] 73.01318709  0.000000000e+00
  [16,] 73.01966643  0.000000000e+00
  [17,] 73.02614576  0.000000000e+00
  [18,] 73.03262510  0.000000000e+00
  [19,] 73.03910443  0.000000000e+00
  [20,] 73.04558377  0.000000000e+00
  [21,] 73.05206310  0.000000000e+00
  [22,] 73.05854244  0.000000000e+00
  [23,] 73.06502177  0.000000000e+00
  [24,] 73.07150111  0.000000000e+00
  [25,] 73.07798044  0.000000000e+00
  [26,] 73.08445978  0.000000000e+00
  [27,] 73.09093911  0.000000000e+00
  [28,] 73.09741845  0.000000000e+00
  [29,] 73.10389779  0.000000000e+00
  [30,] 73.11037712  0.000000000e+00
  [31,] 73.11685646  0.000000000e+00
  [32,] 73.12333579  0.000000000e+00
  [33,] 73.12981513  0.000000000e+00
  [34,] 73.13629446  0.000000000e+00
  [35,] 73.14277380  0.000000000e+00
  [36,] 73.14925313  0.000000000e+00
  [37,] 73.15573247  0.000000000e+00
  [38,] 73.16221180  0.000000000e+00
  [39,] 73.16869114  0.000000000e+00
  [40,] 73.17517047  0.000000000e+00
  [41,] 73.18164981  0.000000000e+00
  [42,] 73.18812914  0.000000000e+00
  [43,] 73.19460848  0.000000000e+00
  [44,] 73.20108781  0.000000000e+00
  [45,] 73.20756715  0.000000000e+00
  [46,] 73.21404648  0.000000000e+00
  [47,] 73.22052582  0.000000000e+00
  [48,] 73.22700515  0.000000000e+00
  [49,] 73.23348449  0.000000000e+00
  [50,] 73.23996382  0.000000000e+00
  [51,] 73.24644316  0.000000000e+00
  [52,] 73.25292249  0.000000000e+00
  [53,] 73.25940183  0.000000000e+00
  [54,] 73.26588117  0.000000000e+00
  [55,] 73.27236050  0.000000000e+00
  [56,] 73.27883984  0.000000000e+00
  [57,] 73.28531917  0.000000000e+00
  [58,] 73.29179851  0.000000000e+00
  [59,] 73.29827784  0.000000000e+00
  [60,] 73.30475718  0.000000000e+00
  [61,] 73.31123651  0.000000000e+00
  [62,] 73.31771585  0.000000000e+00
  [63,] 73.32419518  0.000000000e+00
  [64,] 73.33067452  0.000000000e+00
  [65,] 73.33715385  0.000000000e+00
  [66,] 73.34363319  0.000000000e+00
  [67,] 73.35011252  0.000000000e+00
  [68,] 73.35659186  0.000000000e+00
  [69,] 73.36307119  0.000000000e+00
  [70,] 73.36955053  0.000000000e+00
  [71,] 73.37602986  0.000000000e+00
  [72,] 73.38250920  0.000000000e+00
  [73,] 73.38898853  0.000000000e+00
  [74,] 73.39546787  0.000000000e+00
  [75,] 73.40194720  0.000000000e+00
  [76,] 73.40842654  0.000000000e+00
  [77,] 73.41490587  0.000000000e+00
  [78,] 73.42138521  0.000000000e+00
  [79,] 73.42786454  0.000000000e+00
  [80,] 73.43434388  0.000000000e+00
  [81,] 73.44082322  0.000000000e+00
  [82,] 73.44730255  0.000000000e+00
  [83,] 73.45378189  0.000000000e+00
  [84,] 73.46026122  0.000000000e+00
  [85,] 73.46674056  0.000000000e+00
  [86,] 73.47321989  0.000000000e+00
  [87,] 73.47969923  0.000000000e+00
  [88,] 73.48617856  0.000000000e+00
  [89,] 73.49265790  0.000000000e+00
  [90,] 73.49913723  0.000000000e+00
  [91,] 73.50561657  0.000000000e+00
  [92,] 73.51209590  0.000000000e+00
  [93,] 73.51857524 9.881312917e-324
  [94,] 73.52505457 1.057540922e-313
  [95,] 73.53153391 1.427136826e-303
  [96,] 73.53801324 1.312563358e-293
  [97,] 73.54449258 8.227372688e-284
  [98,] 73.55097191 3.514700288e-274
  [99,] 73.55745125 1.023296892e-264
 [100,] 73.56393058 2.030491821e-255
 [101,] 73.57040992 2.745914849e-246
 [102,] 73.57688925 2.530807533e-237
 [103,] 73.58336859 1.589708158e-228
 [104,] 73.58984792 6.805529471e-220
 [105,] 73.59632726 1.985604127e-211
 [106,] 73.60280660 3.948295475e-203
 [107,] 73.60928593 5.350727785e-195
 [108,] 73.61576527 4.941994977e-187
 [109,] 73.62224460 3.110842144e-179
 [110,] 73.62872394 1.334565457e-171
 [111,] 73.63520327 3.902006759e-164
 [112,] 73.64168261 7.775393666e-157
 [113,] 73.64816194 1.055949107e-149
 [114,] 73.65464128 9.773493301e-143
 [115,] 73.66112061 6.165139156e-136
 [116,] 73.66759995 2.650465645e-129
 [117,] 73.67407928 7.765826913e-123
 [118,] 73.68055862 1.550741701e-116
 [119,] 73.68703795 2.110461608e-110
 [120,] 73.69351729 1.957499583e-104
 [121,] 73.69999662  1.237405757e-98
 [122,] 73.70647596  5.331001658e-93
 [123,] 73.71295529  1.565278913e-87
 [124,] 73.71943463  3.132282206e-82
 [125,] 73.72591396  4.271852647e-77
 [126,] 73.73239330  3.970615885e-72
 [127,] 73.73887263  2.515276419e-67
 [128,] 73.74535197  1.085924908e-62
 [129,] 73.75183130  3.195215111e-58
 [130,] 73.75831064  6.407470863e-54
 [131,] 73.76478997  8.757081874e-50
 [132,] 73.77126931  8.156773670e-46
 [133,] 73.77774865  5.178019067e-42
 [134,] 73.78422798  2.240242904e-38
 [135,] 73.79070732  6.605608144e-35
 [136,] 73.79718665  1.327445609e-31
 [137,] 73.80366599  1.818054489e-28
 [138,] 73.81014532  1.697005644e-25
 [139,] 73.81662466  1.079557826e-22
 [140,] 73.82310399  4.680527108e-20
 [141,] 73.82958333  1.383024429e-17
 [142,] 73.83606266  2.785166542e-15
 [143,] 73.84254200  3.822598800e-13
 [144,] 73.84902133  3.575629408e-11
 [145,] 73.85550067  2.279462823e-09
 [146,] 73.86198000  9.903729228e-08
 [147,] 73.86845934  2.932589223e-06
 [148,] 73.87493867  5.918204150e-05
 [149,] 73.88141801  8.139821508e-04
 [150,] 73.88789734  7.630026615e-03
 [151,] 73.89437668  4.874425708e-02
 [152,] 73.90085601  2.122301544e-01
 [153,] 73.90733535  6.297627314e-01
 [154,] 73.91381468  1.273600010e+00
 [155,] 73.92029402  1.755397126e+00
 [156,] 73.92677335  1.648936548e+00
 [157,] 73.93325269  1.055647045e+00
 [158,] 73.93973203  4.605955744e-01
 [159,] 73.94621136  1.369641847e-01
 [160,] 73.95269070  2.775750994e-02
 [161,] 73.95917003  3.833895076e-03
 [162,] 73.96564937  3.608994115e-04
 [163,] 73.97212870  2.315359094e-05
 [164,] 73.97860804  1.012364180e-06
 [165,] 73.98508737  3.016764548e-08
 [166,] 73.99156671  6.126780100e-10
 [167,] 73.99804604  8.480264574e-12
 [168,] 74.00452538  7.999682350e-14
 [169,] 74.01100471  5.143068570e-16
 [170,] 74.01748405  2.253502885e-18
 [171,] 74.02396338  6.729459036e-21
 [172,] 74.03044272  1.369583202e-23
 [173,] 74.03692205  1.899690800e-26
 [174,] 74.04340139  1.795823497e-29
 [175,] 74.04988072  1.156992681e-32
 [176,] 74.05636006  5.080235036e-36
 [177,] 74.06283939  1.520278769e-39
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 [403,] 75.52716915 1.942573463e-288
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 [499,] 76.14918533  6.869719067e-99
 [500,] 76.15566466 1.427925193e-104
 [ reached getOption("max.print") -- omitted 966 rows ]

$C6H6Cl6
               m/z        abundance
  [1,] 286.8600665 8.596420918e-130
  [2,] 286.8845572 1.827275087e-123
  [3,] 286.9090480 2.706474560e-117
  [4,] 286.9335388 2.793300896e-111
  [5,] 286.9580296 2.008839538e-105
  [6,] 286.9825204  1.006668617e-99
  [7,] 287.0070112  3.515131426e-94
  [8,] 287.0315020  8.552840247e-89
  [9,] 287.0559927  1.450083158e-83
 [10,] 287.0804835  1.713125628e-78
 [11,] 287.1049743  1.410260270e-73
 [12,] 287.1294651  8.089526190e-69
 [13,] 287.1539559  3.233409091e-64
 [14,] 287.1784467  9.005586044e-60
 [15,] 287.2029375  1.747740944e-55
 [16,] 287.2274282  2.363501576e-51
 [17,] 287.2519190  2.227144970e-47
 [18,] 287.2764098  1.462361800e-43
 [19,] 287.3009006  6.690752045e-40
 [20,] 287.3253914  2.133088099e-36
 [21,] 287.3498822  4.738669341e-33
 [22,] 287.3743730  7.335298186e-30
 [23,] 287.3988637  7.912120561e-27
 [24,] 287.4233545  5.946778666e-24
 [25,] 287.4478453  3.114471841e-21
 [26,] 287.4723361  1.136582063e-18
 [27,] 287.4968269  2.890220270e-16
 [28,] 287.5213177  5.121236623e-14
 [29,] 287.5458085  6.323135636e-12
 [30,] 287.5702992  5.440062741e-10
 [31,] 287.5947900  3.261287415e-08
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 [63,] 288.3784952  9.782407913e-31
 [64,] 288.4029860  9.938680697e-28
 [65,] 288.4274767  7.056362140e-25
 [66,] 288.4519675  3.499762871e-22
 [67,] 288.4764583  1.212557054e-19
 [68,] 288.5009491  2.934754160e-17
 [69,] 288.5254399  4.961893489e-15
 [70,] 288.5499307  5.860430321e-13
 [71,] 288.5744215  4.835241110e-11
 [72,] 288.5989122  2.786849605e-09
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 [74,] 288.6478938  3.155916584e-06
 [75,] 288.6723846  6.200726375e-05
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[466,] 298.2482819  1.709395467e-20
[467,] 298.2727727  5.687934986e-23
[468,] 298.2972634  1.353142439e-25
[469,] 298.3217542  2.301946395e-28
[470,] 298.3462450  2.960186378e-31
[471,] 298.3707358  1.304740724e-29
[472,] 298.3952266  7.644381721e-27
[473,] 298.4197174  3.203373812e-24
[474,] 298.4442082  9.600898285e-22
[475,] 298.4686989  2.058046148e-19
[476,] 298.4931897  3.155275909e-17
[477,] 298.5176805  3.459860325e-15
[478,] 298.5421713  2.713431010e-13
[479,] 298.5666621  1.522011710e-11
[480,] 298.5911529  6.105991509e-10
[481,] 298.6156437  1.751997131e-08
[482,] 298.6401344  3.595419567e-07
[483,] 298.6646252  5.277214621e-06
[484,] 298.6891160  5.539861775e-05
[485,] 298.7136068  4.159413461e-04
[486,] 298.7380976  2.233594078e-03
[487,] 298.7625884  8.578579858e-03
[488,] 298.7870792  2.356489667e-02
[489,] 298.8115699  4.629719439e-02
[490,] 298.8360607  6.505531734e-02
[491,] 298.8605515  6.538075302e-02
[492,] 298.8850423  4.699547344e-02
[493,] 298.9095331  2.416023379e-02
[494,] 298.9340239  8.883522939e-03
[495,] 298.9585147  2.336190837e-03
[496,] 298.9830054  4.394104658e-04
[497,] 299.0074962  5.911143052e-05
[498,] 299.0319870  5.687370681e-06
[499,] 299.0564778  3.913727578e-07
[500,] 299.0809686  1.926232218e-08
 [ reached getOption("max.print") -- omitted 92 rows ]

$C70
               m/z       abundance
  [1,] 839.0000000 4.378514092e-14
  [2,] 839.0702926 5.304472782e-12
  [3,] 839.1405853 4.530869679e-10
  [4,] 839.2108779 2.728630870e-08
  [5,] 839.2811706 1.158595607e-06
  [6,] 839.3514632 3.468509102e-05
  [7,] 839.4217559 7.321122463e-04
  [8,] 839.4920485 1.089522934e-02
  [9,] 839.5623412 1.143191412e-01
 [10,] 839.6326338 8.457176649e-01
 [11,] 839.7029265 4.411189578e+00
 [12,] 839.7732191 1.622220612e+01
 [13,] 839.8435117 4.206181217e+01
 [14,] 839.9138044 7.689355075e+01
 [15,] 839.9840970 9.910960020e+01
 [16,] 840.0543897 9.006693926e+01
 [17,] 840.1246823 5.770838977e+01
 [18,] 840.1949750 2.606972083e+01
 [19,] 840.2652676 8.303433159e+00
 [20,] 840.3355603 1.864684819e+00
 [21,] 840.4058529 2.954942266e-01
 [22,] 840.4761455 3.713079752e-02
 [23,] 840.5464382 5.049308911e-02
 [24,] 840.6167308 3.881539495e-01
 [25,] 840.6870235 2.217921202e+00
 [26,] 840.7573161 8.946082935e+00
 [27,] 840.8276088 2.546282720e+01
 [28,] 840.8979014 5.114063782e+01
 [29,] 840.9681941 7.247887858e+01
 [30,] 841.0384867 7.248407441e+01
 [31,] 841.1087794 5.115163703e+01
 [32,] 841.1790720 2.547195532e+01
 [33,] 841.2493646 8.950573042e+00
 [34,] 841.3196573 2.219348669e+00
 [35,] 841.3899499 3.883593783e-01
 [36,] 841.4602426 4.871344703e-02
 [37,] 841.5305352 1.384083335e-02
 [38,] 841.6008279 8.593807001e-02
 [39,] 841.6711205 5.365093931e-01
 [40,] 841.7414132 2.372450712e+00
 [41,] 841.8117058 7.409218633e+00
 [42,] 841.8819985 1.634158334e+01
 [43,] 841.9522911 2.545436729e+01
 [44,] 842.0225837 2.800121842e+01
 [45,] 842.0928764 2.175394378e+01
 [46,] 842.1631690 1.193563486e+01
 [47,] 842.2334617 4.624869648e+00
 [48,] 842.3037543 1.265610230e+00
 [49,] 842.3740470 2.445992555e-01
 [50,] 842.4443396 3.347534535e-02
 [51,] 842.5146323 4.469685146e-03
 [52,] 842.5849249 1.236070034e-02
 [53,] 842.6552175 8.325387131e-02
 [54,] 842.7255102 4.033925477e-01
 [55,] 842.7958028 1.381692131e+00
 [56,] 842.8660955 3.345036665e+00
 [57,] 842.9363881 5.723956024e+00
 [58,] 843.0066808 6.923050502e+00
 [59,] 843.0769734 5.918402754e+00
 [60,] 843.1472661 3.576163264e+00
 [61,] 843.2175587 1.527340839e+00
 [62,] 843.2878514 4.610631443e-01
 [63,] 843.3581440 9.837670207e-02
 [64,] 843.4284366 1.484414554e-02
 [65,] 843.4987293 1.698593459e-03
 [66,] 843.5690219 1.361238466e-03
 [67,] 843.6393146 9.326496749e-03
 [68,] 843.7096072 4.947222984e-02
 [69,] 843.7798999 1.857632132e-01
 [70,] 843.8501925 4.934281137e-01
 [71,] 843.9204852 9.271541799e-01
 [72,] 843.9907778 1.232377926e+00
 [73,] 844.0610705 1.158776664e+00
 [74,] 844.1313631 7.707605004e-01
 [75,] 844.2016557 3.626628243e-01
 [76,] 844.2719484 1.207120181e-01
 [77,] 844.3422410 2.842249491e-02
 [78,] 844.4125337 4.734611508e-03
 [79,] 844.4828263 5.662351829e-04
 [80,] 844.5531190 1.443309755e-04
 [81,] 844.6234116 8.058898793e-04
 [82,] 844.6937043 4.667794592e-03
 [83,] 844.7639969 1.920556207e-02
 [84,] 844.8342895 5.594657085e-02
 [85,] 844.9045822 1.153826948e-01
 [86,] 844.9748748 1.684723226e-01
 [87,] 845.0451675 1.741554735e-01
 [88,] 845.1154601 1.274577868e-01
 [89,] 845.1857528 6.604140394e-02
 [90,] 845.2560454 2.422628943e-02
 [91,] 845.3263381 6.291848530e-03
 [92,] 845.3966307 1.156912174e-03
 [93,] 845.4669234 1.510871428e-04
 [94,] 845.5372160 2.006063654e-05
 [95,] 845.6075086 5.639019512e-05
 [96,] 845.6778013 3.529465107e-04
 [97,] 845.7480939 1.590447033e-03
 [98,] 845.8183866 5.078745785e-03
 [99,] 845.8886792 1.149133058e-02
[100,] 845.9589719 1.842300099e-02
[101,] 846.0292645 2.092794778e-02
[102,] 846.0995572 1.684492654e-02
[103,] 846.1698498 9.607000433e-03
[104,] 846.2401425 3.882242951e-03
[105,] 846.3104351 1.111613564e-03
[106,] 846.3807277 2.255295426e-04
[107,] 846.4510204 3.244415121e-05
[108,] 846.5213130 3.624474669e-06
[109,] 846.5916057 3.398855023e-06
[110,] 846.6618983 2.200269245e-05
[111,] 846.7321910 1.085038151e-04
[112,] 846.8024836 3.796485913e-04
[113,] 846.8727763 9.419997726e-04
[114,] 846.9430689 1.657487627e-03
[115,] 847.0133615 2.068141605e-03
[116,] 847.0836542 1.829956334e-03
[117,] 847.1539468 1.148237329e-03
[118,] 847.2242395 5.109202019e-04
[119,] 847.2945321 1.612148219e-04
[120,] 847.3648248 3.607342179e-05
[121,] 847.4351174 5.724007457e-06
[122,] 847.5054101 6.440854982e-07

Izotopové poměry

Převody jednotek

[1] 180

Plynný systém mění svůj objem o 1200 ml za konstantního vnějšího tlaku 30 atm. Jakou práci vykoná plyn při expanzi? Vyjádřete v různých energetických jednotkách.

[1] 0.0012
[1] 3039750
[1] 3647.7
[1] 871.8212
[1] 3647.7
[1] 3.6477e+10

Kolik tepla se uvolní při průchodu náboje 26.43 C vodičem při potenciálovém spádu 2.432 V.

Pokus trval 7658 minut. Kolik je to dní, hodin a minut?

[1] "5d 7H 38M 0S"
[1] "5d 7H 38M 0S"

Zaokrouhlování čísel na daný pocet desetinných míst

      [,1]  [,2]
[1,]  1.76  3.76
[2,]  4.76  6.76
[3,]  7.76  8.76
[4,] 10.76 12.76
[5,] 15.76 16.76
      [,1]  [,2]
[1,]  1.77  3.76
[2,]  4.76  6.77
[3,]  7.77  8.77
[4,] 10.77 12.77
[5,] 15.77 16.77

Nejistoty a chyby měření

Attaching package: ‘errors’

The following object is masked from ‘package:seacarb’:

    errors

3.6020 ± 0.0080
3.6020(80)

Ze zásilky kaprolaktamu bylo odebráno 10 vzorku a byl u nich stanoven bod tání. Vypočítejte průměrnou hodnotu bodu tání v zásilce a její směrodatnou odchylku.

Error in string(print(e, digits = 2)) : could not find function "string"

Sireni chyb

$var.name
[1] "lambda.s"    "dbar.lambda" "delta.Cr"    "delta.Cnr"  
[5] "alpha.s"     "delta.alpha" "thetabar"    "Delta"      
[9] "delta.theta"

$unit
expression("nm", "nm", "nm", "nm", degree * 
    C^-1, degree * C^-1, degree * C, degree * C, degree * C)

$x.i
[1]  5.000062e+07  2.150000e+02  0.000000e+00  0.000000e+00
[5]  1.150000e-05  0.000000e+00 -1.000000e-01  0.000000e+00
[9]  0.000000e+00

$u.i
[1] 2.5e+01 5.8e+00 3.9e+00 6.7e+00 1.2e-06 5.8e-07 2.0e-01
[8] 3.5e-01 2.9e-02

$nu.i
[1]  18  24   5   8 Inf  50 Inf Inf   2

$type
[1] "B" "A" "B" "B" "B" "B" "B" "B" "B"

$distribution
[1] "Normal"        "Normal"        "Normal"       
[4] "Normal"        "Rectangular"   "Rectangular"  
[7] "Not Specified" "Arcsine"       "Rectangular"  

$measurement.fnc
[1] "(lambda.s*(1+alpha.s*(thetabar+Delta+delta.theta))+dbar.lambda+delta.Cr+delta.Cnr)/(1+(alpha.s+delta.alpha)*(thetabar+Delta))"

$correlation
      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
 [1,]    1    0    0    0    0    0    0    0    0
 [2,]    0    1    0    0    0    0    0    0    0
 [3,]    0    0    1    0    0    0    0    0    0
 [4,]    0    0    0    1    0    0    0    0    0
 [5,]    0    0    0    0    1    0    0    0    0
 [6,]    0    0    0    0    0    1    0    0    0
 [7,]    0    0    0    0    0    0    1    0    0
 [8,]    0    0    0    0    0    0    0    1    0
 [9,]    0    0    0    0    0    0    0    0    1

$shared.u.i
[1] "lambda.s"    "dbar.lambda" "delta.Cr"    "delta.Cnr"  
[5] "alpha.s"     "delta.alpha" "thetabar"    "Delta"      
[9] "delta.theta"

Vypočítejte hustotu a její chybu pro látku, u níž byla opakovaným měřením stanovena hmotnost 6.824 (0.008) g a objem 3.03 (0.01) ml.

Results from uncertainty propagation:

     Mean.1      Mean.2        sd.1        sd.2        2.5% 
2.252145215 2.252169745 0.007887829 0.007887910 2.236709711 
      97.5% 
2.267629780 

Results from Monte Carlo simulation:

       Mean          sd      Median         MAD        2.5% 
2.252147530 0.007865567 2.252134683 0.007849750 2.236838921 
      97.5% 
2.267579899 

Na píst o průměru 200 (0.05) mm působí pára tlakem 8.2 (0.1) atm. Jakou silou působí pára na píst?

Vypočítejte koeficient viskozity roztoku glycerinu Stokesovou metodou

Results from uncertainty propagation:

    Mean.1     Mean.2       sd.1       sd.2       2.5% 
0.66658893 0.66664378 0.01214241 0.01214272 0.64284446 
     97.5% 
0.69044310 

Results from Monte Carlo simulation:

      Mean         sd     Median        MAD       2.5% 
0.66662689 0.01214628 0.66655084 0.01211801 0.64300977 
     97.5% 
0.69063187 
          r     l    t     g    d0    d
[1,] 0.0112 31.23 62.1 980.1 13.55 1.28
[2,] 0.0001  0.05  0.2   0.0  0.00 0.00
    Mean.1     Mean.2       sd.1       sd.2       2.5% 
0.66658893 0.66664378 0.01214241 0.01214272 0.64284446 
     97.5% 
0.69044310 
      Mean         sd     Median        MAD       2.5% 
0.66662689 0.01214628 0.66655084 0.01211801 0.64300977 
     97.5% 
0.69063187 
          r     l    t
[1,] 0.0112 31.23 62.1
[2,] 0.0001  0.05  0.2
    Mean.1     Mean.2       sd.1       sd.2       2.5% 
0.66658893 0.66664378 0.01214241 0.01214272 0.64284446 
     97.5% 
0.69044310 
      Mean         sd     Median        MAD       2.5% 
0.66664227 0.01213821 0.66662723 0.01219665 0.64301492 
     97.5% 
0.69045151 
0.67 ± 0.01
0.67(1)

Vypočítejte koeficient viskozity roztoku glycerinu pomocí kapilárního viskozimetru.

[1] 3.141593

Results from uncertainty propagation:

     Mean.1      Mean.2        sd.1        sd.2        2.5% 
0.057476383 0.057485951 0.001211458 0.001211534 0.055111385 
      97.5% 
0.059860517 

Results from Monte Carlo simulation:

       Mean          sd      Median         MAD        2.5% 
0.057481093 0.001207036 0.057477011 0.001201292 0.055120264 
      97.5% 
0.059857552 
               p       r        l         V     t
[1,] 2682.446053 5.7e-04 0.010526 5.025e-06 27.34
[2,]    1.333224 3.0e-06 0.000005 1.000e-09  0.02
     Mean.1      Mean.2        sd.1        sd.2        2.5% 
0.057476383 0.057485951 0.001211458 0.001211534 0.055111385 
      97.5% 
0.059860517 
       Mean          sd      Median         MAD        2.5% 
0.057481093 0.001207036 0.057477011 0.001201292 0.055120264 
      97.5% 
0.059857552 
0.057 ± 0.001
0.057(1)

Součin rozpustnosti stříbrné soli AgX má hodnotu Ks = 4.0 (0.4) x 10^-8. Jaká je chyba vypočtené rovnovážné koncentrace stříbrných iontů ve vode?

Uncertainty evaluation

Call:
  uncert.function(obj = f, x = x, u = u, method = "NUM")

Expression: function (a) 

Evaluation method:  NUM 

Uncertainty budget:
  x     u     c    u.c  
a 4e-08 4e-09 2500 1e-05

   y:  2e-04
u(y):  1e-05 

Uncertainty evaluation

Call:
  uncert.formula(obj = ~a^0.5, x = x, u = u, method = "NUM")

Expression: ~a^0.5

Evaluation method:  NUM 

Uncertainty budget:
  x     u     c    u.c  
a 4e-08 4e-09 2500 1e-05

   y:  2e-04
u(y):  1e-05 

Nejistoty a korelace