The eccentric connectivity index ξ is a distance–based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum ξ among trees with a fixed maximum vertex degree, and characterize such trees with minimum ξ . In addition, we propose a simple linear algorithm for calculating ξ of trees.

In this paper we introduce a new facility location model, called backup multifacility location problem by considering the ideal radius for each customer. In this problem the location of clients are given in the plane. A radius is assigned to each client. We should find the location of new facilities, which some of them may fail with a given probability, such that the sum of weighted distances f...

We measured two- and three-line spatial interval and alignment thresholds for a wide range of separations and eccentricities. In order to avoid confounding the role of separation and eccentricity, the test lines were presented on iso-eccentric arcs, with radii between 0.625 and 10 deg. The iso-eccentric paradigm allows separation to be varied over a large range while holding eccentricity consta...

The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at l...

in this paper, a novel multi-objective bus stop location model is proposed, which considers not only the coverage of demand and minimization of access time but also the necessities of suitable stops for transit network design phase. three objective functions are considered including minimizing (i) sum of the total access distance (time), (ii) the weighted combination of stops, and (iii) the num...

PURPOSE To investigate the clinical characteristics and sensory mechanism of microtropia. METHODS Twenty patients with primary microtropia were studied. The patients were evaluated by the visuscope, Irvine prism test, Bagolini striated glasses test, Worth 4-dot test (W4D), TNO, and stereo-fly plate of the Titmus test. RESULTS The patients who had positive cover test and eccentric fixation s...

In this paper, a novel multi-objective bus stop location model is proposed, which considers not only the coverage of demand and minimization of access time but also the necessities of suitable stops for transit network design phase. Three objective functions are considered including minimizing (I) sum of the total access distance (time), (II) the weighted combination of stops, and (III) the num...

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 ...

This paper presents the first calculation of the gravitational self-force on a small compact object on an eccentric equatorial orbit around a Kerr black hole to first order in the mass-ratio. That is the pointwise correction to the object’s equations of motion (both conservative and dissipative) due to its own gravitational field, which is treated as a linear perturbation to the background Kerr...