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end{aligned} (3.8) The first term of right hand side is identically zero by Lemma 3.1 ii) for a mixed geodesic warped product submanifold.
The first term of right hand side is identically zero by (2.3), thus we get (ii), which proves the lemma completely.
end{aligned} Since M is mixed geodesic, the second term of right hand side is identically zero and break the above relation for the frames of (F TN_{theta})), (varphi TN_{perp})), and μ.
Using (4.1), the second term of right hand side is identically zero, then the above equation takes the form g ( ( ∇ ̄ U T Z Z, X ) = - g ( Z, ∇ P 2 U T X ) = - ( T X ln λ ) g ( Z, P 2 U ).
The term of right hand side of Eq. (5), ΔΕ pot, states the total change in the potential energy of the system during debonding, which equals to the difference between the recoverable energy stored in the beam before and after debonding.
The second term of right hand side is identically zero by the orthogonality of vector fields, thus we have g bigl(h X, Y), varphi Z bigr)=g bigl((widetilde{nabla}_{X} varphi Y, Z bigr)+g bigl(h X, Z), FY bigr).
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The second term of right-hand sides of (16) indicates the pilot contamination due to the use of the same pilot sequence set over all the user groups.
Since lim n μ n λ n β = 1 by (2) the first term and since S λ α − lim f k ( x ) = f ( x ) on A, the second term of right-hand side of above inequality tends to 0 as n → ∞. (Note that ( μ n λ n β − 1 ) ≥ 0 for all n ∈ N n o.) This implies that S λ α ( f ) ⊆ S μ β ( f ).
I always thought in terms of right and wrong.
Americans have on occasion been called moralists who often speak in terms of right and wrong.
I think of it in terms of right and wrong," Bowman told The Guardian in an interview.
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