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As a consequence, the output of partial VRRM may only be a local minimum and not the global one.
The semiempirical methods also show the C2v symmetry to be a local minimum, though it is supposed to be a transition state by ab initio and DFT calculations.
The TH1 AC30 shows an interesting notch in the DIM distortion curve, indicating that there could be a local minimum of DIM distortion with input signals with a certain amplitude.
Proof Let x ¯ ∈ S be a local minimum; then there exists a neighborhood N ϵ ( x ¯ ) such that f ( x ¯ ) ≤ f ( x ) (5). for all x ∈ S ∩ N ϵ ( x ¯ ).
Hence the local extreme cannot be a local minimum, showing that K τ has no local minimum and therefore has at most one local maximum for 0 < τ < T because of its smoothness.
Lemma 1: (Karush-Kuhn-Tucker Conditions) Let y* be a local minimum of the following problem begin{array}{c}hfill kern0.96em min; f y)hfill hfill mathrm{subject};mathrm{t}mathrm{o};{g}_1 y)le 0, dots,;{g}_{mathrm{m}} y)le 0hfill end{array} (25).
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Thus, x = −1 is a local maximum, and x = 1 is a local minimum.
However, at these frequencies what is observed is a local minimum in the vertical spectral component, sometimes associated to local maxima in the horizontal components, whose visibility depend on the specific amount of SH and Love waves at the site.
For example, with m−n∈[1,2) and for suitable choices of the period and mean value, we find three fundamentally different steady-states. The first is a constant steady-state that is stable and is a local minimum of the energy.
If L is fixed, there is a local minimum at t/w = 1.
If H f α is positive definite, then f α is a local minimum point.
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Justyna Jupowicz-Kozak
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