let $g=(v,e)$ be a connected graph. the eccentric connectivity index of $g$, $xi^{c}(g)$, is defined as $xi^{c}(g)=sum_{vin v(g)}deg(v)ec(v)$, where $deg(v)$ is the degree of a vertex $v$ and $ec(v)$ is its eccentricity. the eccentric distance sum of $g$ is defined as $xi^{d}(g)=sum_{vin v(g)}ec(v)d(v)$, where $d(v)=sum_{uin v(g)}d_{g}(u,v)$ and $d_{g}(u,v)$ is the distance between $u$ and $v$ ...

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 ...

A topological index is a numeric quantity associated with chemical structure that attempts to link the various physicochemical properties, reactivity, or biological activity. Let R be commutative ring identity, and Z*(R) set of all non-zero zero divisors R. Then, Γ(R) said zero-divisor graph if only a·b=0, where a,b∈V(Γ(R))=Z*(R) (a,b)∈E(Γ(R)). We define a∼b a·b=0 a=b. ∼ always reflexive symmet...

For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as [Formula in text], where [Formula in text] is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as i...

Topological indices are empirical features of graphs that characterize the topology graph and, for most part, independent. An important branch theory is chemical theory. In theory, atoms corresponds vertices and edges covalent bonds. A topological index a numeric number represents underline structure. this article, we examined properties prism octahedron network dimension <math xmlns="http://ww...

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 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...

The use of wind turbines to generate electricity has increased in recent years. One of the most important parts of a wind turbine is the foundation, which should be designed accurately because it is influenced by difference forces. Soil cannot carry tension stress; thus, when a wind turbine foundation is applied eccentricity forces, a gap appears between the soil and foundation. The gap will ha...

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...