With the zero-covariance assumption, one can substitute (32) back into the equation for the expectation for each species, which yields (33) d d t E X s (t ) = ∑ r = 1 N r v r s k r Φ 1 - F s ∏ s = 1 N s μ s f r s for every s = 1,..., N s.
Algebraic equations are obtained for the expectations of some suitable excitation and response quantities.
According to the master equation (7), we can obtain the equation of motion for the expectation value of any physical operator O of the coupled system by calculating Ȯ ( t ) = Tr [ O ρ · ( t ) ].
The expectations appearing in the equations for the coefficients of the equivalent polynomials are calculated by a multi-dimensional Gram-Charlier expansion.
The regression equation for the models predicting the expectation of the logarithm of weekly GBS hospitalizations, Y, was where δy represents the coefficients for each year (y), S t) represents a smooth function of season (comprising 6 harmonics), and φ (holiday) is a term representing weeks with public holidays.
We use the basic equation for conditional expectations, i.e. E ( X ) = E ( E [ X | Y ] ), (6).
An issue arises from the statement in equation 2, which is required for the expectation of the score statistic U i to be equal to 0. This result implicitly assumes that the CNV intensity is linear with the discrete CNV genotype call.
His influential book "Systems Architecting: Creating and Building Complex Systems" (1991) was "an engineering text without equations that looked at the expectations for a product's performance, its materials and their cost, and the necessary balance between them," said F. Stan Settles, a professor of astronautics and industrial and systems engineering at the university.
The recursion for the expectation of the autosomal fraction of admixture, Equations 17 and 19, is equivalent to that derived by Verdu and Rosenberg (2011).
