Statistics for Individual Crystallographic Orientation Measurements |
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Page 137
... representation property : = T ( 91 ) T ( 92 ) T ( 9192 ) ( A.1 ) For rotations in SO ( 3 ) only one representation is widely known , which simply maps a rotation to its " representation " as a 3 × 3 rotation matrix . However in ...
... representation property : = T ( 91 ) T ( 92 ) T ( 9192 ) ( A.1 ) For rotations in SO ( 3 ) only one representation is widely known , which simply maps a rotation to its " representation " as a 3 × 3 rotation matrix . However in ...
Page 138
... representations , motivated by complex valued representation theory , brings up two sources of unnecessary difficulties in tex- ture analysis . The first one is that these functions have values in the complex numbers C , but all ...
... representations , motivated by complex valued representation theory , brings up two sources of unnecessary difficulties in tex- ture analysis . The first one is that these functions have values in the complex numbers C , but all ...
Page 139
... representation is given by : TR ( g ) = B * Ti ( 9 ) B1 , _B1 = ( b'mm ' ) m = – ' mm ' ) m = -1 , ... , ! , m ' = - 1 , ... , ¡ € C2l + 1x24 + 1 √2 , m = m ' = 0 1 , m ' = m > 0 1 -1mi , -m ' = m > 0 - ' mm ' -i , m ' = m ...
... representation is given by : TR ( g ) = B * Ti ( 9 ) B1 , _B1 = ( b'mm ' ) m = – ' mm ' ) m = -1 , ... , ! , m ' = - 1 , ... , ¡ € C2l + 1x24 + 1 √2 , m = m ' = 0 1 , m ' = m > 0 1 -1mi , -m ' = m > 0 - ' mm ' -i , m ' = m ...
Common terms and phrases
approximation assumption bias Boogaart Bunge C-coefficients calculate the number CALIFORNIA Ccor CEF g confidence band cosets covariance function crystal symmetry crystallographic exponential family crystallographic orientation defined denotes diffraction EBSD empirical covariance function entropy equation ERSITY estimation error estimation variance exponential family formation process formula geostatistics given grain boundaries grain model gvar H₁ harmonic functions i,j)EDdo K(gi K(Si kernel density estimation lattice LIBRARIES SAN DIEGO linear functionals linear statistics Markov random fields maximum likelihood estimator measurement error measurement grid methods microstructure nmin npairs number of measurements orientation data orientation distribution orientation g orientation measurements parameterisation parameters parametric statistics physical property tensors rotation sample symmetry SAN DIEGO Schaeben simulation specimen stationary correlation model stochastically independent symmetry group texture analysis texture index texture regression theorem theory tion Tmn g unbiased estimators unbiasedly UNIVERSITY var(x vector X(gi μ ν ΣΣ