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The new equations read (12).
Maxwell's equations read ∇ ⋅ D = ρ, (1).
and the Lie equations read as f = ξ ( f, g ) = - g g =. ( f, g ) = f.
In a dimensional form, these equations read begin{array}rcl@ frac {partial widetilde{u}_{j}}{partial widetilde{x}_{j}} &=& 0, end{array} (16).
The well-known projective Riccati equations read as f^ xi =pf xi g xi), (9) g^{prime}(xi =R+pg^2 xi -rf xi), (10)where p ≠ 0 is a real constant, R and r are two real constants.
The terms, and correspond to the stimulated transitions 2 → 1, 2 → 0 and 2 → 4. The terms, and correspond to the spontaneous transitions 2 → 1, 2 → 0 and 2 → 4. The associated rate equations read: (6) (7) (8) (9) (10).
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"Shouldn't the second equation read 16 over pi?" asks Gabriella.
Published 12 September 2014 In the published article text, a term was omitted from Equation 2. This equation read: Pr [ Z = z | A = a, q ] = (2 z + a − 1 z ) q z + a (1 − q ) z It should have read: Pr [ Z = z | A = a, q ] = a a + z (2 z + a − 1 z ) q z + a (1 − q ) z The article has now been corrected.
The time-dependent Schrödinger equation reads The quantity i is the square root of −1.
Thus, the error equation reads mathcal{Q}_{k} e_{k+1}= e_{k}.
Thus, the integral equation reads as u = ∫ M d θ = ∫ 1 b θ − 1 d θ = 1 b log θ, (1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com