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In (Kerber, Kohlhase and Sorge 1998) the authors use the Ωmega planning system as the overall way to integrate theorem proving and symbolic computation.
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The constraint of underactuated AUVs is proved not to be integrated by the local integrability theorem, and the controllability of underactuated AUVs is verified through small-time local controllability (STLC).
The role of proofs, too, is transformed: they have not only to provide subjective certainty, but above all to integrate the theorems into the whole conceptual system.
(1) Sulkhan-Saba Orbeliani (1658 1726) integrates numerous theorems from Petrizi's Proclus work into his Georgian Dictionary.
On the other hand, there are truly promising attempts to integrate discursive symbolic theorem-proving with reasoning with image-like symbols.
Calculations are conducted by using a technique integrated the kinematic theorem of limit analysis with strength reduction concept.
Proof of Theorem 4.2 We integrate from −∞ to V F − α in (4.9) and let α tend to 0+ and use L'Hôpital's rule lim v → V F p ( v, t ) p ∞ ( v ) = lim v → V F ∂ p ∂ v ( v, t ) ∂ p ∞ ∂ v ( v ) = N ( t ) N ∞.
This inequality holds for all, and we can integrate it over and apply Fubini's theorem to obtain (3.7).
So, the fundamental theorem of calculus, not for line integrals, tells you if you integrate a derivative, then you get back the function.
By considering this source time function (11), we can use the residue theorem for integrating with respect to ω in Eq. (6).
was: integrate, integrate, integrate.
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