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Corollary 1 in the appendix states that if (mathsf {C}:mathcal {X}rightarrow mathcal {Y}) is a linear operator with closed range, and (mathcal {S}) is a subspace of the range of C, (mathcal {S} subset R(mathsf {C})), then (text {dim} {mathsf {C}}^{leftarrow }(mathcal {S}) = text {dim} N mathsf {C}) + text {dim}(mathcal {S})).
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The "Appendix" describes state-specific changes made to the original strong mandates in later periods.
Under Assumptions 1 and 2, it is shown in the Appendix that the state obeys the following recursion: x k ( j ) = ∑ i = 1 G f k ( ji ) x k - 1 ( i ), ∀ j ∈ [ 1, G ]. (3).
Like: here are the Top 10 Most Important States, and then here, at the back, in the appendix, are some other states that, you know, exist.
We confirm that this holds in the numerical solution of the problem, as discussed in the Appendix 2. The additional state variable, ({M^{e}_{t}},) is only used when maternity leave is available, which depends on a child being born that year and on the policy regime being analysed.
In the Appendix we describe the "coherent states" which motivate the definitions of these transforms.
This is in agreement with the Liblinear tutorial in the appendix of [ 44] which states that once the parameter C exceeds a certain value, the obtained models have a similar accuracy.
We would like to note that the 2002 Brisson paper, that lies at the base of all Brisson-alike papers, clearly states in the Appendix that 11 parameters were estimated.
The Appendix provides an aggregated discrete-state stochastic model used for reliability analysis, a typical continuous-state classical swing model used for transient stability analysis, and a typical electric transmission network model used for diagnosis.
The solution for these objects is provided in "Solving for the steady state" in the Appendix.
Some analogues of Theorem 1.2 will be stated in the Appendix.
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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