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Now, recall our calculation of the expectations of the two dollar and three dollar gambles.
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The fast convergence of the series solutions allows the calculation of the expectation values of the kinetic energy potential energy 〈e Φ x)〉 and the total energy expectation value, yielding (8).
The calculation of the expectation value of a given operator O that conserves the particle-number is simplified by the use of the property[37]: Ψ m m ′ O Ψ m m ′ = 4 ( m + 1 ) ( m ′ + 1 ) C m m ′ Ψ O Ψ m m ′.
The following proposition will be useful for the calculation of the expectation in Equation 17: Proposition 4. h ~ j is chi-square distributed with 2m n degrees of freedom, where n and m are the number of transmit and receive antennas, respectively.
Finally, a correction in the calculation of the expectation values was established that results in a more reliable statistical analysis of PTMs.
Algorithm 1 shows the calculation process of the expectation with regard to the semantic relation.
The choice of an appropriate model for the calculation of additivity expectations is essential for assessments of mixture effects because it is in relation to these additivity expectations that combination effects are judged in terms of synergisms or antagonisms.
A generalised Brownian motion is an algebra of creation and annihilation operators acting on FV(H) for arbitrary Hilbert spaces H and having a prescription for the calculation of vacuum expectations in terms of a function t on pair partitions.
Rider et al. (2008) used historical data for the calculation of additivity expectations.
b) These data were used for the calculation of additivity expectations for a mixture of specific composition using "fixed mixture ratio design" (Altenburger et al. 2000; Hewlett and Plackett 1959).
Which is, according to the basic property of expectation value and variance in statistics, expectation calculation of the independent identically distributed Poisson distribution is a linear operation, and the variance is independent.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com