In a series of papers, we developed a technique for estimating the inner eccentricity in hierarchical triple systems, with the inner orbit being initially circular. However, for certain combinations of the masses and the orbital elements, the secular part of the solution failed. In the present paper, we derive a new solution for the secular part of the inner eccentricity, which corrects the pre...

This paper presents a computational method for detecting vibrations related to eccentricity in ultra precision rotation devices used for nano-scale manufacturing. The vibration is indirectly measured via a frequency domain analysis of the signal from a piezoelectric sensor attached to the stationary component of the rotating device. The algorithm searches for particular harmonic sequences assoc...

Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...

If the Moon’s spin evolved from faster prograde rates, it could have been captured into a higher spin–orbit resonance than the current 1:1 resonance. At the current value of orbital eccentricity, the probability of capture into the 3:2 resonance is as high as 0.6, but it strongly depends on the temperature and average viscosity of the Moon’s interior. A warmer, less viscous Moon on a higher ecc...

This paper proposes the eccentric problem in the coiling process of cold rolling mills. The wavelets multiresolution control method is designed: A wavelets multi-resolution controller is introduced in the control cycle of coiling tension control, whose purpose is to acquire the element caused by periodically change of the coiling eccentricity. Then the signal without effectiveness of the coilin...

Design of thinned elliptical antenna arrays of uniformly excited isotropic antennas using particle swarm optimization (PSO), is reported. Thinned arrays can generate directive beam with minimum side lobe level (SLL) without degrading the performance of fully populated antenna arrays significantly. Thinning of elliptical antenna arrays using PSO are optimized with different values of eccentricit...