Since the shortest paths do not provide the unique solution on triangle meshes, we solve the initial value problem in an indirect manner: given a fixed point and an initial tangent direction on a triangle mesh M, we first compute a geodesic curve ˆγ on a piecewise smooth surface ˆM, which well approximates the input mesh M and can be constructed at little cost.
F is bounded for bounded s and p. Then the existence of a lower solution for the initial-value problem (3.1) provides the existence of the unique solution of the problem (3.1).
In particular, under appropriate assumptions, this theorem provides an approximation scheme to the unique solution of (1.1).
the sequence converges strongly to some point, provided that is firmly nonexpansive; is the unique solution of variational inequality (3.6).
for each, there is a unique such that (3.5). the sequence converges strongly to some point, provided that is firmly nonexpansive; is the unique solution of the following variational inequality (3.6).
The forward study enables the production of a unique plot of the hardness HIT vs. representative stress σr, where both are normalized by the Young's modulus E. The proposed reverse analysis provides a unique solution to the representative stress σr and the strain-hardening exponent, n, given that the Young's modulus is predetermined from the experimental hardness test.
The proposed reverse analysis provides a unique solution of the reduced Young's modulus E*, a representative stress σr, and the hardness pave.
Under the cooperative game situation, SV provides a unique solution with the desirable properties: (i) efficiency, (ii) symmetry, (iii) additivity, and (iv) dummy [5, 12].
This dual indenter reverse algorithm provides a unique solution of the reduced Young's modulus E∗, the hardness pave and two representative stresses (measured at two corresponding representative strains), which establish the basis for constructing power-law plastic material response.
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