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The reasoning given at the time on the Mac Pro was basically that Apple had painted itself into an architecture corner by being aggressively original on the design of the bullet/turbine/trash-can shaped casing and internal components of the current Mac Pro.
The reasoning given above allows one to prove that under the same assumptions this map is differentiable in the sense of Fréchet and the differential of this map is the double operator integral begin{aligned} iint frac{f(s_1 -f(s_1 -fs_2-s_2},dE_A(s_1)K,dE_A(s_2).
But the reasoning given by the US military lawyer was "dogmatic and wrong".
Again, the reasoning given was that of providing safe, hygienic housing.
The merits of the diverse routes are assessed and the reasoning given for which one was ultimately used for large-scale synthesis of 1.
One can summarize the reasoning given above as follows: Theorem 3. Let g ∈ C2(S R ), and let relation (5) hold.
Similar(52)
The only reasoning given in the report is, "The desire for a clear focus on energy coupled with the need for a number of attributes not found in LFEE, e.g., control of core central space, leads us to conclude that a new organization is needed at MIT". (p.38) Nothing is said about the feasibility of additional support of LFEE to address the non-specific perceived shortcomings.
We therefore ask whether better descriptions of auxin transport as well as the cellular embedding within the root layout affect the mathematical reasoning given above.
Moreover, the second formulation of the ambit of legal reasoning given above, i.e. that legal reasoning is about how judges should decide cases, is also ambiguous on some approaches to legal theory.
But Justice Danny K. Chun denied the request, noting that a jury had found Mr. Giuca guilty and an early appellate ruling had upheld the conviction — an odd bit of legal reasoning, given that the latest ruling cast doubt on the former and appeared to overturn the latter.
The ability of English to preserve the complex logical structure of abstract moral reasoning (given its syntactic and semantic structure) recommends it, as well as its infinite productivity.
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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