In this paper we present the design of tow robust nonlinear controllers for two mechanical problems of rejecting disturbances such as eccentricity and friction compensation. In the eccentricity compensation problem, the considered disturbances are here assumed to be produced by eccentricity in mechanical systems and drives, the frequency and amplitude of this disturbance is unknown. The objecti...

For a vertex v and a (k−1)-element subset P of vertices of a graph, one can define the distance from v to P in various ways, including the minimum, average, and maximum distance from v to P . Associated with each of these distances, one can define the keccentricity of the vertex v as the maximum distance over all P , and the k-eccentricity of the set P as the maximum distance over all v. If k =...

The extrasolar planets discovered to date possess unexpected orbital elements. Most orbit their host stars with larger eccentricities and smaller semi-major axes than similarly sized planets in our own solar system do. It is generally agreed that the interaction between giant planets and circumstellar disks (Type II migration) drives these planets inward to small radii, but the effect of these ...

Exoplanet habitability is traditionally assessed by comparing a planet’s semi-major axis to the location of its host star’s “habitable zone,” the shell around a star for which Earth-like planets can possess liquid surface water. The Kepler space telescope has discovered numerous planet candidates near the habitable zone, and many more are expected from missions such as K2, TESS and PLATO. These...

The known population of exoplanets exhibits a much wider range of orbital eccentricities than Solar System planets and has a much higher average eccentricity. These facts have been widely interpreted to indicate that the Solar System is an atypical member of the overall population of planetary systems. We report here on a strong anticorrelation of orbital eccentricity with multiplicity (number ...

Based on astrometry from an orbit derived byHubble Space Telescope imagery, Charon’s orbital eccentricity has been reported to be in the range of 0.003–0.008. Solar and planetary tides are orders of magnitude too small to induce the reported eccentricity. This nonzero value, if correct, therefore indicates some significant forcing against the two-body tidal equilibrium value, which should forma...

Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index of a connected graph G=(V,E) and defined as where d denotes the degree of vertex v of G, that introduced by Furtula v and et.al. Also, in 1997, Sharma, Goswami and Madan introduced the eccentric connectivity index of the molecular ...

We survey the literature on the eccentricity sequence of a connected graph and make the following contribution. The eccentricity sequence of a graph G is the list of its eccentricities in non-increasing order. Two graphs G1 and G2 are co-eccentric when they have the same eccentricity sequence. Then, we say that G1 and G2 are co-eccentric mates. We characterize the eccentricity sequence of almos...

Eccentricity-dependent resolution losses are sometimes compensated for in psychophysical experiments by magnifying (scaling) stimuli at each eccentricity. The use of either pre-selected scaling factors or unscaled stimuli sometimes leads to non-monotonic changes in performance as a function of eccentricity. We argue that such non-monotonic changes arise when performance is limited by more than ...