introducing three principal methods of determining the solar orbital eccentricity in the ancient and medieval astronomy (i.e., the method of seasons, of mid-signs, of three–points), the accuracy of the results obtained from each is being investigated. in doing so, two main goals have been targeted: (1) to determine the accuracy and the intrinsic limitation of each method with regard to their st...

We consider particles with low free or proper eccentricity that are orbiting near planets on eccentric orbits. Via collisionless particle integration we numerically find the location of the boundary of the chaotic zone in the planet’s corotation region. We find that the distance in semi-major axis between the planet and boundary depends on the planet mass to the 2/7 power and is independent of ...

Factors underlying Weber's law for position were investigated by measuring spatial interval discrimination accuracy for spectrally narrow-band stimuli. These stimuli were positioned around an iso-eccentric arc in order to allow separation and eccentricity to be varied independently. We find that Weber's law occurs at individual spatial scales, and holds true not just for stimuli positioned eith...

The eccentricity of a vertex $v$ is the maximum distance between $v$ and anyother vertex. A vertex with maximum eccentricity is called a peripheral vertex.The peripheral Wiener index $ PW(G)$ of a graph $G$ is defined as the sum ofthe distances between all pairs of peripheral vertices of $G.$ In this paper, weinitiate the study of the peripheral Wiener index and we investigate its basicproperti...

The center (periphery) of a graph is the set of vertices with minimum (maximum) eccentricity. In this paper, the structure of centers and peripheries of some classes of composite graphs are determined. The relations between eccentricity, radius and diameter of such composite graphs are also investigated. As an application we determine the center and periphery of some chemical graphs such as nan...

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...

At least several percent of solar type stars possess giant planets. Surprisingly, most move on orbits of substantial eccentricity. We investigate the hypothesis that interactions between a giant planet and the disk from which it forms promote eccentricity growth. These interactions are concentrated at discrete Lindblad and corotation resonances. Interactions at principal Lindblad resonances cau...

let $g$ be a connected graph. the multiplicative zagreb eccentricity indices of $g$ are defined respectively as ${bf pi}_1^*(g)=prod_{vin v(g)}varepsilon_g^2(v)$ and ${bf pi}_2^*(g)=prod_{uvin e(g)}varepsilon_g(u)varepsilon_g(v)$, where $varepsilon_g(v)$ is the eccentricity of vertex $v$ in graph $g$ and $varepsilon_g^2(v)=(varepsilon_g(v))^2$. in this paper, we present some bounds of the multi...

Although synchronous generators are robust and long-lasting equipment of power plants, consistent electricity production depends on their health conditions. Static dynamic eccentricity faults among the prevalent that may have a costly effect. several methods been proposed in literature to detect static salient pole (SPSGs), they non-sensitive low degree failure require predefined threshold reco...