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Unlike spike-layered solutions, whose concentration occurs around minimum points of V, the solutions we are going to study concentrate around minimum points of an auxiliary potential.
The minimum points of the histogram are used for data embedding.
Our proofs use Brouwer's fixed point theorem and properties of minimum points of convex functions.
To find the minimum points of TC, we survey its condition as below.
Using to find the local optimum solutions (that is, the local minimum points) of (24).
Fig. 4 Minimum points of C total (k optimal) according to N and k.
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When, the unique minimum point of the function satisfies (3.13).
Since is the minimum point of, we have.
Take as the global maximum point and global minimum point of on, respectively, then (3.28).
Let t ¯ be the global minimum point of x ( t ) on [ 0, T ].
In other words, the minimum point of the ΔΦ − VEFM curve should be located at zero.
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