Expression 10: sine left parenthesis, pi "x" , right parenthesis sine left parenthesis, pi "y" , right parenthesis equals 0sinπxsinπy=0
10
f(u) = cos(θ), -1<=u<=1
11
Expression 12: "f" left parenthesis, "u" , right parenthesis equals 1 half StartFraction, left parenthesis, 1 minus "g" squared , right parenthesis Over left parenthesis, 1 plus "g" squared minus 2 "g" "u" , right parenthesis Superscript, 3 halves , Baseline , EndFraction left brace, negative 1 less than or equal to "u" less than or equal to 1 , right bracefu=121−g21+g2−2gu32−1≤u≤1
12
Expression 13: "F" left parenthesis, "u" , right parenthesis equals 1 half StartFraction, left parenthesis, 1 minus "g" squared , right parenthesis Over "g" StartRoot, 1 plus "g" squared minus 2 "g" "u" , EndRoot , EndFraction minus StartFraction, 1 minus "g" Over 2 "g" , EndFraction left brace, negative 1 less than or equal to "u" less than or equal to 1 , right braceFu=121−g2g1+g2−2gu−1−g2g−1≤u≤1
13
Expression 14: "F" Subscript, "i" "n" "v" , Baseline left parenthesis, "x" , right parenthesis equals StartFraction, 1 Over 2 "g" , EndFraction left parenthesis, 1 plus "g" squared minus left parenthesis, StartFraction, left parenthesis, 1 minus "g" squared , right parenthesis Over 2 "g" left parenthesis, "x" plus StartNestedFraction, 1 minus "g" NestedOver 2 "g" , EndNestedFraction , right parenthesis , EndFraction , right parenthesis squared , right parenthesis left brace, 0 less than or equal to "x" less than or equal to 1 , right braceFinvx=12g1+g2−1−g22gx+1−g2g20≤x≤1
14
Expression 15: "N" equals 1000N=1000
11
10001000
15
Expression 16: "u" Subscript, "s" , Baseline equals "F" Subscript, "i" "n" "v" , Baseline left parenthesis, random left parenthesis, "N" , right parenthesis , right parenthesisus=FinvrandomN
equals=
negative 0.4 8 6 7 6 8 0 1 3 9 1 4−0.486768013914
0.8 1 3 6 9 7 1 3 8 0 7 10.813697138071
0.8 7 8 5 0 9 1 1 7 2 1 30.878509117213
0.9 5 0 8 0 9 9 7 4 9 2 70.950809974927
0.9 9 5 8 0 6 4 1 4 1 2 30.995806414123
negative 0.2 7 4 5 2 7 8 4 6 0 6 8−0.274527846068
0.8 7 6 1 4 6 5 0 7 7 8 20.876146507782
0.9 8 0 4 9 0 2 7 8 9 2 90.980490278929
0.9 5 3 7 0 0 5 3 8 8 80.95370053888
0.7 1 4 2 6 8 3 6 1 8 30.71426836183
0.4 7 4 6 7 8 9 1 6 4 7 10.474678916471
0.7 0 4 0 4 1 5 3 2 5 3 40.704041532534
0.9 9 5 4 3 3 1 2 9 4 4 10.995433129441
0.8 4 2 7 4 6 8 0 2 4 7 60.842746802476
0.9 0 3 2 2 0 5 0 1 9 2 60.903220501926
1000 element list
16
Expression 17: theta Subscript, "s" , Baseline equals arc cosine left parenthesis, "u" Subscript, "s" , Baseline , right parenthesisθs=arccosus
equals=
2.0 7 9 1 8 2 3 4 0 4 22.07918234042
0.6 2 0 3 1 1 9 9 3 1 3 80.620311993138
0.4 9 8 0 6 3 9 3 1 5 70.49806393157
0.3 1 4 9 5 6 1 1 2 9 5 80.314956112958
0.0 9 1 6 1 3 5 3 8 1 5 40.091613538154
1.8 4 8 8 9 4 9 7 5 4 31.84889497543
0.5 0 2 9 8 7 2 0 1 6 1 30.502987201613
0.1 9 7 8 5 5 9 6 4 7 8 80.197855964788
0.3 0 5 4 8 7 1 9 2 2 0 10.305487192201
0.7 7 5 2 1 8 1 6 7 3 8 20.775218167382
1.0 7 6 1 9 7 1 3 2 71.0761971327
0.7 8 9 7 2 3 7 3 7 8 20.78972373782
0.0 9 5 6 0 7 0 1 6 9 9 4 90.0956070169949
0.5 6 8 4 3 0 6 6 3 2 8 80.568430663288
0.4 4 3 5 8 1 1 7 3 0 4 50.443581173045
1000 element list
17
Expression 18: phi Subscript, "s" , Baseline equals 2 pi random left parenthesis, "N" , right parenthesisϕs=2πrandomN
equals=
3.2 7 3 2 5 1 3 7 9 5 83.27325137958
1.0 9 1 7 4 1 0 2 3 9 61.09174102396
4.2 0 5 2 9 4 2 6 4 3 44.20529426434
3.5 2 4 1 5 9 1 0 4 7 33.52415910473
4.1 6 6 3 0 2 4 3 1 7 34.16630243173
2.7 6 3 0 4 6 1 7 8 6 42.76304617864
1.4 4 7 6 5 4 8 2 7 0 21.44765482702
2.9 7 0 5 0 5 8 5 1 4 72.97050585147
3.6 5 2 1 7 9 7 4 9 6 73.65217974967
6.2 5 5 7 5 4 0 7 0 56.2557540705
4.3 8 1 2 7 2 0 5 6 0 74.38127205607
5.1 9 3 3 6 3 1 0 8 35.1933631083
1.0 9 1 7 8 7 5 6 0 0 21.09178756002
2.3 8 7 4 4 9 0 2 0 0 22.38744902002
1.8 1 6 9 8 2 1 1 1 2 41.81698211124
1000 element list
18
Hidden Label: left parenthesis, "X" Subscript, "s" , Baseline left parenthesis, cos left parenthesis, phi Subscript, "s" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , sin left parenthesis, phi Subscript, "s" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , cos left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , right parenthesis , "Y" Subscript, "s" , Baseline left parenthesis, cos left parenthesis, phi Subscript, "s" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , sin left parenthesis, phi Subscript, "s" , Baseline , right parenthesis sin left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , cos left parenthesis, theta Subscript, "s" , Baseline , right parenthesis , right parenthesis , right parenthesisXscosϕssinθs,sinϕssinθs,cosθs,Yscosϕssinθs,sinϕssinθs,cosθs
Label
equals=
left parenthesis, 0.8 5 1 , negative 0.5 2 5 , right parenthesis0.851,−0.525
left parenthesis, negative 0.4 3 2 2 , 0.6 2 4 6 , right parenthesis−0.4322,0.6246
left parenthesis, 0.3 6 4 , 0.9 3 1 2 , right parenthesis0.364,0.9312
left parenthesis, 0.3 0 9 7 , 0.8 9 2 4 , right parenthesis0.3097,0.8924
left parenthesis, 0.0 7 1 9 6 , 0.9 5 1 9 , right parenthesis0.07196,0.9519
left parenthesis, 0.7 1 1 6 , negative 0.4 8 4 8 , right parenthesis0.7116,−0.4848
left parenthesis, negative 0.2 2 3 6 , 0.6 6 9 5 , right parenthesis−0.2236,0.6695
left parenthesis, 0.1 6 9 6 , 0.8 8 2 6 , right parenthesis0.1696,0.8826
left parenthesis, 0.2 9 7 3 , 0.9 0 8 5 , right parenthesis0.2973,0.9085
left parenthesis, negative 0.6 4 8 2 , 0.7 6 1 4 , right parenthesis−0.6482,0.7614
left parenthesis, 0.5 6 0 5 , 0.6 8 3 3 , right parenthesis0.5605,0.6833
left parenthesis, negative 0.0 8 6 2 6 , 0.9 0 7 2 , right parenthesis−0.08626,0.9072
left parenthesis, negative 0.0 7 0 9 7 , 0.9 0 9 1 , right parenthesis−0.07097,0.9091
left parenthesis, 0.2 3 7 8 , 0.6 1 8 6 , right parenthesis0.2378,0.6186
left parenthesis, negative 0.0 4 8 4 , 0.6 9 5 1 , right parenthesis−0.0484,0.6951
