• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.221-229
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• 2018

The first Zagreb eccentricity index $E_1(G)$ of a graph G is defined as the sum of squares of the eccentricities of the vertices. In this paper some bounds for the first Zagreb eccentricity index and first Zagreb degree eccentricity index are computed.

• Journal of the Earthquake Engineering Society of Korea
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• v.17 no.5
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• pp.237-243
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• 2013

In the Korean Building Code (KBC), the Design Eccentricity involves the torsional amplification factor (TAF), and the inherent and accidental eccentricities. When a structure of less than 6-stories and assigned to seismic design category C or D is designed using equivalent static analysis method, both KBC-2006 and KBC-2009 use the TAF but apply different calculation methods for the of design eccentricity. The design eccentricity in KBC-2006 is calculated by multiplying the sum of inherent eccentricity and accidental eccentricity at each level by a TAF but that in KBC-2009 is calculated by multiplying only the accidental eccentricity by a TAF. In this paper, the damage indices of a building with planar structural irregularity designed by different design eccentricities are compared and the relationship between the earthquake damage and design eccentricity of the building is evaluated. On the basis of this study, the increment of design eccentricity results in the decrement of final eccentricity and global damage index of structure. It is observed that design eccentricity in KBC-2006 reduces the vulnerability of torsional irregular building compared to design eccentricity in KBC-2009.

• Current Optics and Photonics
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• v.2 no.6
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• pp.525-531
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• 2018

The effect of eccentricity on dispersion and nonlinear properties of a photonic crystal fiber having elliptical air holes is investigated using a fully vectorial effective index method. It is found that the effective refractive index increases with increase of eccentricity. The dependence of dispersion and nonlinear properties of the PCF on the eccentricity of the air hole is investigated. It is revealed that eccentricity of the air hole affects the zero dispersion wavelength. Further, the nonlinear properties such as mode field area, nonlinear coefficient and self phase modulation of the Photonic crystal fibers are analyzed. The mode field area increases and the nonlinear coefficient decreases with increase in eccentricity. The variation of the self phase modulation with elliptical air hole is also discussed.

• Kyungpook Mathematical Journal
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• v.61 no.1
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• pp.61-74
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• 2021

Let G = (V, E) be a connected graph. The eccentric connectivity index of G is defined by ��C (G) = ∑u∈V (G) deg(u)e(u), where deg(u) and e(u) denote the degree and eccentricity of the vertex u in G, respectively. In this paper, we introduce a new formulation of ��C that will be called the distance eccentric connectivity index of G and defined by $${\xi}^{De}(G)\;=\;{\sum\limits_{u{\in}V(G)}}\;deg^{De}(u)e(u)$$ where degDe(u) denotes the distance eccentricity degree of the vertex u in G. The aim of this paper is to introduce and study this new topological index. The values of the eccentric connectivity index is calculated for some fundamental graph classes and also for some graph operations. Some inequalities giving upper and lower bounds for this index are obtained.

• Proceedings of the KIEE Conference
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• 2002.07b
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• pp.706-708
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• 2002

Vibration, giving rise to acoustical noise, is an important index of motor performance. The unbalance force due to rotor eccentricity caused by manufacturing imprecision or bearing defects is one possible source of excitation to vibration. With the advent of new high-energy magnetic material together with high precision motor applications, magnetic sources of vibration are becoming more serious. This paper introduces two types of high-speed slotless permanent magnet (PM) machine for electro-mechanical battery and investigates unbalance force due to static eccentricity with finite element method.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.3
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• pp.49-57
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• 2010

Most previous research on the seismic response of structures with plan irregularities have focused on the relationship between the eccentricity and the amount of torsion. This approach cannot provide the direct relationship between the irregularity and the damage. Therefore, an investigation on the relationship between the eccentricities of buildings with plan irregularities and the damage index was performed. Inelastic dynamic time-history analyses were performed on one-story buildings with various eccentricities. For the damage assessment, a 3D damage index was adopted to reflect the effect of the bi-directional response and torsion. Based on the analysis results, buildings with eccentricities of 10%, 20% and 30% will suffer 3~5%, 13~18%, and 33~47% more damage than their regular counterparts, respectively.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.24.1-24.1
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• 2008

We examine the eccentricity parameter (EP) of Coronal Mass Ejections (CMEs). For this, we select 298 front-side CMEs from SOHO LASCO CMEs whose speed is larger than 1000km/s and angular width is greater than $120^{\circ}$ during from 1997 to 2007. These are thought to be the most plausible candidate of geoeffective CMEs. We examine the relation between CMEs eccentricity parameter and the minimum value of the Dst index. We find that strong geomagnetic storms (Dst < -200nT) are well correlated with the EP from the scattered plot. We also find that CMEs have high geoeffectiveness when they occurred near the center of the solar disk with the small EP and they have the small speed with the small EP. These results indicate that the CME EP also can be an important indicator to forecast CME geoeffectiveness such as Earthward direction parameter (Moon et al. 2005, Kim et al. 2008).

• Journal of Astronomy and Space Sciences
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• v.25 no.4
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• pp.383-394
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• 2008

We examine geoeffective directional parameters of coronal mass ejections (CMEs). We select 30 front-side halo CMEs from SOHO LASCO CMEs whose speed is larger than 1000km/s and longitude is less than ${\pm}30^{\circ}$. These are thought to be the most plausible candidate of geoeffective CMEs. We examine the relation between CMEs directional parameters (Earthward direction, eccentricity, ${\Delta}$ distance and central angle parameter) and the minimum value of the Dst index. We have found that the Earthward direction parameter has a good correlation with the Dst index, the eccentricity parameter has a much better correlation with the Dst index. The bo distance and central angle parameter has a poor correlation with the Dst index. It's, however, well correlated with the Dst index in very strong geomagnetic storms. Most of CMEs causing very strong storms (Dst ${\leq}$-200nT) are found to have large Earthward direction parameter $({\geq}0.6)$, small eccentricity, bo distance and central angle parameters $(E{\leq}0.4,\;{\Delta}X\;and\;sin\;{\theta}{\leq}0.2)$. These directional parameters are very important parameters that control the geoeffectiveness of very fast front-side halo CMEs.

• Earthquakes and Structures
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• v.9 no.1
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• pp.145-171
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• 2015

Due to earthquakes, many structures suffered extensive damages that were attributed to the torsional effect caused by mass, stiffness or strength eccentricity. Due to this type of asymmetry torsional moments are generated that are imposed by means of additional shear forces developed at the vertical resisting structural elements of the buildings. Although the torsional effect on the response of reinforced concrete buildings was the subject of extensive research over the last decades, a quantitative index measuring the amplification of the shear forces developed at the vertical resisting elements due to lateral-torsional coupling valid for both elastic and elastoplastic response states is still missing. In this study a reliable index capable of assessing the torsional effect is proposed. The performance of the proposed index is evaluated and its correlation with structural response quantities like displacements, interstorey drift, base torque, shear forces and upper diaphragm's rotation is presented. Torsionally stiff, mass eccentric single-story and multistory structures, subjected to bidirectional excitation, are considered and nonlinear dynamic analyses are performed using natural records selected for three hazard levels. It was found that the proposed index provides reliable prediction of the magnitude of torsional effect for all test examples considered.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.48.2-48.2
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• 2019

Tidal disruption events (TDEs) provide evidence for quiescent supermassive black holes (SMBHs) in the centers of inactive galaxies. TDEs occur when a star on a parabolic orbit approaches close enough to a SMBH to be disrupted by the tidal force of the SMBH. The subsequent super-Eddington accretion of stellar debris falling back to the SMBH produces a characteristic flare lasting several months. It is theoretically expected that the bolometric light curve decays with time as proportional to $t^{-5/3}$. However, some of the observed X-ray light curves deviate from the $t^{-5/3}$ decay rate, while some of them are overall in good agreement with the $t^{-5/3}$ law. Therefore, it is required to construct the theoretical model for explaining these light curve variations consistently. In this paper, we revisit the mass fallback rates semi-analytically by taking account of the stellar internal structure, orbital eccentricity and penetration factor. We find that the mass fallback rate is shallower than the standard $t^{-5/3}$ decay rate independently of the polytropic index, and the orbital eccentricity only changes the magnitude of the mass fallback rate. Furthermore, the penetration factor significantly can modify the magnitude and variation of mass fallback rate. We confirm these results by performing the computational hydrodynamic simulations. We also discuss the relevance of our model by comparing these results with the observed light curves.