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The self-excitation can be realized because appropriate feedback gains can set two of the eigenvalues to be conjugate complex roots with a positive real part and the other eigenvalue to be a negative real root.
(2.13) The eigenvalue λ must be a negative real number.
For every (n inmathbb{N}), let (r_{n}) be a negative real number such that d_{n} x, Tfx leq d_{n} x,Tx) +r_{n} d_{n} x,fx) quadtextit{for all } x in X. (2) Then f has a fixed point z, that is, (z = fz).
Remark 2 In view of the definition for close-to-convex functions, if f ( z ) satisfies Re z f ′ ( z ) g ( z ) > 0 in D, then we can say that f ( z ) is close-to-convex in D. But c should be a negative real number in Theorem 2.
Due to the eigenvalue needing to be a negative real number, say (-lambda^{2}), we can now obtain that Eq. (13) becomes begin{aligned}& frac{X"(x)}{X x)} = -lambda^{2}, end{aligned} (15) begin{aligned}& -frac{Y y)}{Y y)}+frac{T t)}{T t)} = -lambda^{2}.
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What you need in this situation is a negative real interest rate — which means that you need some expected inflation, because nominal rates face the zero lower bound.
When the euro zone had 3% inflation and ultra-low interest rates, there was a negative real rate; now, with the main interest rate at 0.05% but inflation at -0.6%, the real rate is 0.65%.
A positive, imaginary inductance is a negative, real impedance, which may therefore provide gain.
(2.8) Clearly, (lambda=-b) is a negative real root of equation (2.8).
and z 0 p ′ ( z 0 ) is a negative real number.
This implies that z 0 p ′ ( z 0 ) is a negative real number and − z 0 p ′ ( z 0 ) ≧ k 2 ( 1 + | p ( z 0 ) | 2 ).
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