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Based on radar amplitude data, the outer units seem to be highly inclined (Figs. 2 and 4) and partially folded (Fig. 4b).
Join the outer units together by closing the locks.
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where and are derivatives with respect to the outer unit normal of.
The directional derivative, is the outer unit-normal vector on ; the function is defined as for ; denotes the trace operator.
(rho(x)) is a smooth positive function in Ω̅ satisfying (partial_{nu}rho(x vert_{partialOmega}=0), ν is the outer unit normal vector on ∂Ω.
where is an outer unit vector normal to an undeformed body, is the permutation symbol, and means the jump in any field quantity across the discontinuity surface.
where are constants, is the Laplace operator with respect to the space variables, and is the outer unit normal derivative to boundary.
end{aligned} (5.36)Note that when E is a smooth open subset of (mathbb {S}^n), the unit vector (nu _E x in T_xmathbb {S}^n) coincides with the outer unit normal vector to (partial E) at x.
where Ω ⊂ R n ( n ≥ 3 ) is a bounded domain with smooth boundary Γ, ν denotes the outer unit normal on Γ, p ≥ 2, the nonlinearity f and the external force g satisfy some conditions specified later.
where Ω ⊂ R N (N ≥ 2) is a bounded domain with boundary of class C1. ν is the outer unit normal to ∂Ω, λ, μ ≥ 0 are real numbers.
In the case of a geodesic ball (B_{vartheta }(p)) it can be easily checked that the outer unit normal vector field along its boundary is given by begin{aligned} nu _{B_{vartheta }(p)}(x) = frac{(xcdot p x-p}{sqrt{1- xcdot p x-p}{sqrt{1- xcdot
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