We introduce the Laplacian sum-eccentricity matrix LS_e} of a graph G, and its Laplacian sum-eccentricity energy LS_eE=sum_{i=1}^n |eta_i|, where eta_i=zeta_i-frac{2m}{n} and where zeta_1,zeta_2,ldots,zeta_n are the eigenvalues of LS_e}. Upper bounds for LS_eE are obtained. A graph is said to be twinenergetic if sum_{i=1}^n |eta_i|=sum_{i=1}^n |zeta_i|. Conditions ...

The paper presents a mathematical base modeling combined to Modified-Winding -Function-Approach (MWFA) for eccentricity fault detection of a round-rotor synchronous machine. For this aim, a 6-pole machine is considered, and the machine inductances are computed by MWFA in healthy and also under eccentricity fault. A numerical discrete-time method has been proposed to machine modeling in voltage-...

Direct displacement based design (DDBD) is a conceptual framework that directly design a structure to achieve an expected performance level under specified seismic intensity. In this study, two important issues relevant to torsional response of mass eccentric 8-story RC building designed with DDBD approach are investigated. These issues are including the effects of unbalanced mass distribution ...

the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

The Zagreb eccentricity indices are the eccentricity reformulation of the Zagreb indices. Let H be a simple graph. The first Zagreb eccentricity index (E1(H)) is defined to be the summation of squares of the eccentricity of vertices, i.e., E1(H) = ∑u∈V(H) Symmetry 2016, 9, 7; doi: 10.3390/sym9010007 www.mdpi.com/journal/symmetry Article First and Second Zagreb Eccentricity Indices of Thorny Gra...

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 ...

We postulate that stars in the Galactic field are born in aggregates of binary stars with half mass radii R 0.5 and number of binaries N bin which are dynamically equivalent to the dominant mode cluster (N bin , R 0.5) ≈ (200, 0.8 pc). Binary orbits are distributed according to an initial period distribution which is consistent with pre-main sequence data. Stellar masses are paired at random fr...

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...