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Lately, growth within the iteration of squeezed states of sunshine, often characterised via a discounted noise estate, has encouraged very important paintings when it comes to their capability use to enhance the sensitivity of optical communique platforms. those notes are dedicated to the detection and data processing of optical indications at very low degrees of strength.
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Additional resources for Brownian motion and classical potential theory
3 Discontinuity Mappings 45 Fig. 6. 40 Hz. Closed circles (•)belong to the upward scan of the excitation amplitude and open circles ( ) for the downward scan, . in the bifurcation diagram shown in Fig. 7 for the case of p4 ←→ p4/2 . It was reported that the additional impact occurred at the turning point that immediately preceded the primary impact. This turning point was the closest to the barrier. At bifurcation, the motion between these two impacts experienced signiﬁcant changes. In terms of discontinuity mapping, De Weger et al  explicitly showed that the square-root also survives soft impacts with a soft barrier.
3 Discontinuity Mappings 33 invariant. The dynamics of a piecewise linear oscillator close to grazing has been experimentally examined by Ing et al . The experimental results revealed the occurrence of higher periodic responses after grazing. The complex dynamics associated with high-dimensional mapping as applied to vibro-impact systems has been considered in several studies. For example, the four-dimensional Poincar´e map of the vibro-impact system was reduced to a two-dimensional normal form using a center manifold reduction and a normal form technique .
According to Stronge , they deﬁned what is known as the energetic coeﬃcient of restitution, e∗ , which is obtained by equating the total work done by the normal force, FN , during restitution, Fn νdt, to the work done by the normal v<0 force during compression times, −e∗2 Fn νdt, where v is the velocity. 4 Border–Collision or C–Bifurcation Border bifurcation occurs when a ﬁxed point or a periodic orbit of a piecewise smooth system crosses or collides one of the boundaries between diﬀerent phase spaces as a system parameter varies in quasi–statically manner .