• Korean Journal of Mathematics
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• v.28 no.3
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• pp.405-419
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• 2020

The zeroth-order general Randić index ⁰R_α(G) of the graph G is defined as ∑_u∈V(G)d(u)^α, where d(u) is the degree of vertex u and α is an arbitrary real number. In this paper, the maximum value of zeroth-order general Randić index on the graphs of order n with a given clique number is presented for any α ≠ 0, 1 and α ∉ (2, 2n-1], where n = |V (G)|. The minimum value of zeroth-order general Randić index on the graphs with a given clique number is also obtained for any α ≠ 0, 1. Furthermore, the corresponding extremal graphs are characterized.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.20 no.9
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• pp.997-1002
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• 2009

This Letter presents a wideband ENG(Epsilon Negative) ZOR(Zeroth-Order Resonant) antenna designed on a microstrip line. It has a mushroom structure and its size is only $7.65{\times}1.31{\times}2.37\;mm$(or $0.306{\times}0.053{\times}0.095\;{\lambda}_0$ at 12 GHz) owing to zeroth-order resonance. The design procedures with closed form solutions are provided using transmission line theory considering radiation loss. The measured antenna bandwidth is about 20.0 % at 9.2 GHz and antenna gain is 7.1 dBi despite the compact size.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.44 no.7 s.361
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• pp.1-6
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• 2007

In this paper, the spiral zeroth-order resonance (ZOR) antenna using composite right- and left-handed (CRLH) transmission line is proposed. The zeroth-order resonant characteristics of the antenna are described by dispersion relation of a periodic structure. The size of the $2{\times}2$ spiral ZOR antenna is $0.155{\lambda}_{0}{\times}0.155{\lambda}_{0}$. By increasing shunt inductance of CRLH transmission line, the size of this antenna is reduced by 65% compared with that of a mushroom ZOR antenna. The radiation pattern of this antenna have omnidirectional pattern which is similar to that of mushroom ZOR antenna.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.22 no.1
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• pp.59-66
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• 2011

In this paper, a co-planar waveguide(CPW)-fed zeroth-order resonant(ZOR) antenna with an improved radiation efficiency was built and tested. The unit cell of the proposed antenna consists of a series metal-insulator-metal(MIM) capacitor and a shorted shunt stub inductor. In order to reduce the antenna size and to achieve the high radiation efficiency two shorted shunt stub arms bent by 90 degree were connected to the ground plane through the via. The proposed antenna consisting of two unit cells has an open ended composite right/left-handed(CRLH) transmission line structure. As a result the dominantly radiating parts of the antenna comes from shunt stub arms and vertical vias. The total size of the fabricated zeroth-order resonant antenna is $0.22\;{\lambda}_0{\times}0.22\;{\lambda}_0$. The measured gain and efficiency of the fabricated antenna have been enhanced by 3.07 dBi and 75 %, respectively, at the zeroth-order resonant frequency of 2.97 GHz.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.05a
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• pp.284-284
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• 2004

기존의 모빌리티 분석 방법은 크게 Grubler의 모빌리티 공식에 의한 zeroth-order 모빌리티 분석 방법, 관절 스크류를 활용한 일차 기구학 성질을 관절 스크류로서 활용한 first-order 모빌리티 분석 방법, 그리고 이차 기구학 특성을 활용하는 second-order 모빌리티 분석 방법으로 구분된다. 그러나, 많은 과다 구속 메커니즘의 경우 zeroth-order 또는 first-order 모빌리티 분석 방법에 의해서는 모빌리티의 분석이 불가능하며 현재까지 문헌에 소개된 second-order 모빌리티 분석 방법은 수치적인 방법에 의존하여 전체 메카니즘의 이차 기구학 특성을 분석하게 되므로 매우 복잡하여 활용하는데 매우 어려움이 있다.(중략)

• Journal of Power System Engineering
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• v.19 no.3
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• pp.55-62
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• 2015

This paper discusses a new model for investigating the micro-mechanical behavior of beam-like structures composed of various elastic moduli and complex geometries varying through the cross-sectional directions and also periodically-repeated along the axial directions. The original three-dimensional problem is first formulated in an unified and compact intrinsic form using the concept of decomposition of the rotation tensor. Taking advantage of two smallness of the cross-sectional dimension-to-length parameter and the micro-to-macro heterogeneity and performing homogenization along dimensional reduction simultaneously, the variational asymptotic method is used to rigorously construct an effective zeroth-order beam model, which is similar a generalized Timoshenko one (the first-order shear deformation model) capable of capturing the transverse shear deformations, but still carries out the zeroth-order approximation which can maximize simplicity and promote efficiency. Two examples available in literature are used to demonstrate the consistence and efficiency of this new model, especially for the structures, in which the effects of transverse shear deformations are significant.

• International journal of advanced smart convergence
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• v.13 no.2
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• pp.1-6
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• 2024

Reconfiguration and miniaturization of antennas have become key attributes in modern wireless communication systems. Reconfiguration of radiation pattern can alleviate the problems encountered in modern wireless communication systems such as multi-path problems. Physical limitation of miniaturization also can be overcome by using a zeroth-order resonance (ZOR) antenna based on metamaterial. In order to achieve reconfiguration and miniaturization of antennas at the same time, we propose a new pattern reconfigurable zeroth-order resonance (ZOR) antenna that reconfigures the radiation patterns by varying the position and the number of unit cells comprising the antenna. The antenna is fabricated in an equilateral triangular shaped symmetrical structure to increase pattern variety. This structure can easily provide eight different radiation patterns (two omnidirectional and six monopole like patterns).

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.747-756
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• 2018

We study a maximum principle for a uniformly elliptic second order differential operator in nondivergence form. We allow a bounded positive zeroth order coefficient in a certain type of unbounded domains. The results extend a result by J. Busca in a sense of domains, and we present a simple proof based on local maximum principle by Gilbarg and Trudinger with iterations.

• Journal of electromagnetic engineering and science
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• v.13 no.3
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• pp.189-191
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• 2013

This letter presents a compact metamaterial-based tunable zeroth-order resonant antenna. It is based on the double-negative unit cell with a function of tunable inductance realized by a varactor and impedance convertor in the shunt branch. The resonant frequency of the designed antenna ranges from 2.31 to 3.08 GHz, depending on the capacitance of the used varactor. Its size is very compact ($0.05{\lambda}_0{\times}0.2{\lambda}_0$) with a relatively wide tunable range of 29.1%. The impedance bandwidth of the antenna is from 20 to 50 MHz for the resonant center frequency. The measured maximum total realized gain is from -0.68 dBi (2.43 GHz) to 1.69 dBi (2.97 GHz). The EM-simulated and measured results are in good agreement.

• Journal of electromagnetic engineering and science
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• v.13 no.3
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• pp.195-197
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• 2013

A compact ($0.26{\times}0.05$ ${\lambda}_0$ at 2.27 GHz) metamaterial-based zeroth-order resonant antenna system consisting of epsilon-negative (ENG) and mu-negative (MNG) structures is proposed. Although the spacing between the ENG and MNG antennas is only 0.09 ${\lambda}_0$, the isolation is relatively high (27.6 dB at 2.27 GHz). Furthermore, the envelope correlation is only 0.015. The radiation efficiencies of the proposed two radiators are also very high (90% on average).