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The analysis of response speed showed the significance of the orientation factor (F[1,12] = 89.48; p < 0.0001), with faster responses to stimuli in standard (506 ms) than in rotated (534 ms) orientation.
Then we find and orient an edge set E (E1⊆E⊆E2) with in-degree m2 (m-orientation Sandwich Problem).
By Theorem 3 and Claim 2, E is a solution of the m-orientation Sandwich Problem.
We present a characterization and a polynomial-time algorithm for solving the m-orientation sandwich problem.
This result stands in contrast to the strongly connected m-orientation sandwich problem which we show is NP-complete.
We say that a subset F of E0 is feasible if (V,F∪E1) has an m-orientation.
In the analysis of the m-orientation workspace, a procedure for calculating this type of workspace was presented, and the relationship between this type of workspace and the requirement of rotational displacement was revealed.
If them-Orientation Sandwich Problemhas aYesanswer, then a subsetFofE0is feasible if and only ifFis a base of the matroid(M_{bar{m}}/E_{1}). Complexity: The condition (d) of Theorem 11 can be verified in polynomial time by Theorem 4, so the m-Orientation Sandwich Problem is in P. Optimization: The minimum cost version of the problem can be solved in polynomial time.
m-Orientation Sandwich ProblemInstance: Given undirected graphs G1= V,E1) and G2= V,E2) with E1⊆E2 and a non-negative integer vector m on V. Question: Does there exist a sandwich graph G= V,E) (E1⊆E⊆E2) that has an orientation (vec{G}) whose in-degree vector is m that is (d^_{vec{G}} v =m v)) for all v∈V?
In Sect. 5 we consider sandwich problems regarding an m-orientation, i.e., given undirected graphs G1= V,E1) and G2= V,E2) with E1⊆E2 and a non-negative integer vector m on V, we show that it is polynomial to decide whether there exists a sandwich graph G= V,E) (E1⊆E⊆E2) that has an orientation (vec{G}) whose in-degree vector is m that is (d^_{vec{G}} v =m v)) for all v∈V.
Local orientations measurements indicate that the scattering of the original T-M orientations within shear bands towards two, twin-related positions is due to the localised lattice rotation around the TD ‖ 〈011〉 axis.
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