• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.419-431
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• 2017

In this paper, we define a new kind of formal power series rings by using Gaussian binomial coefficients and investigate some properties. More precisely, we call such a ring a Gaussian series ring and study McCoy's theorem, Hermite properties and Noetherian properties.

• Proceedings of the Optical Society of Korea Conference
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• 2009.10a
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• pp.111-112
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• 2009

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.69-77
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• 2023

In this article we relate the six Prüfer conditions with the EM conditions. We use the EM-conditions to prove some cases of equivalence of the six Prüfer conditions. We also use the Prüfer conditions to answer some open problems concerning EM-rings.

• Kyungpook Mathematical Journal
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• v.57 no.4
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• pp.581-600
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• 2017

A classical result of A. Cohn states that, if we express a prime p in base 10 as $$p=a_n10^n+a_{n-1}10^{n-1}+{\cdots}+a_110+a_0$$, then the polynomial $f(x)=a_nx^n+a_{n-1}x^{n-1}+{\cdots}+a_1x+a_0$ is irreducible in ${\mathbb{Z}}[x]$. This problem was subsequently generalized to any base b by Brillhart, Filaseta, and Odlyzko. We establish this result of A. Cohn in $O_K[x]$, K an imaginary quadratic field such that its ring of integers, $O_K$, is a Euclidean domain. For a Gaussian integer ${\beta}$ with ${\mid}{\beta}{\mid}$ > $1+{\sqrt{2}}/2$, we give another representation for any Gaussian integer using a complete residue system modulo ${\beta}$, and then establish an irreducibility criterion in ${\mathbb{Z}}[i][x]$ by applying this result.

• Journal of the Optical Society of Korea
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• v.13 no.1
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• pp.146-151
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• 2009

A Gaussian beam of single mode fiber laser was changed into a ring-shaped pattern after it was transmitted through the hollow optical fiber. The ring-shaped beam was focused on a plane by an f-. lens and it was scanned by a Galvano-mirror. The spatial profile of laser energy incident on a plane had two peaks at both sides of the scanned linear track. The profile was compared with the result obtained when the Gaussian beam was dithered transversely by an acousto-optic modulator. It is found that hollow optical fiber beam shaper can replace acousto-optic beam dithering device which is employed in a laser induced thermal printing system.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.591-611
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• 2001

In this paper, we classify elliptic curve by isomorphism classes over some finite fields. We consider finite field as a quotient ring, saying $\mathbb{Z}[i]/{\pi}\mathbb{Z}[i]$ where $\pi$ is a prime element in $\mathbb{Z}[i]$. Here $\mathbb{Z}[i]$ is the ring of Gaussian integers.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.563-580
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• 2019

In this paper, we study the strong metric dimension of zero-divisor graph ${\Gamma}(R)$ associated to a ring R. This is done by transforming the problem into a more well-known problem of finding the vertex cover number ${\alpha}(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring ${\mathbb{Z}}_n$ of integers modulo n and the ring of Gaussian integers ${\mathbb{Z}}_n$[i] modulo n. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.

• Bulletin of the Society of Naval Architects of Korea
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• v.27 no.3
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• pp.38-46
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• 1990

A numerical solution method of the boundary integral equation for axisymmetric potential flows is presented. Those are represented by ring source and ring vorticity distribution. Strengths of ring source and ring vorticity are approximated by linear functions of a parameter $\zeta$ on a segment. The geometry of the body is represented by a cubic B-spline. Limiting integral expressions as the field point tends to the surface having ring source and ring vorticity distribution are derived upto the order of ${\zeta}ln{\zeta}$. In numerical calculations, the principal value integrals over the adjacent segments cancel each other exactly. Thus the singular part proportional to $\(\frac{1}{\zeta}\)$ can be subtracted off in the calculation of the induced velocity by singularities. And the terms proportional to $ln{\zeta}$ and ${\zeta}ln{\zeta}$ can be integrated analytically. Thus those are subtracted off in the numerical calculations and the numerical value obtained from the analytic integrations for $ln{\zeta}$ and ${\zeta}ln{\zeta}$ are added to the induced velocity. The four point Gaussian Quadrature formula was used to evaluate the higher order terms than ${\zeta}ln{\zeta}$ in the integration over the adjacent segments to the field points and the integral over the segments off the field points. The root mean square errors, $E_2$, are examined as a function of the number of nodes to determine convergence rates. The convergence rate of this method approaches 2.

• Journal of Advanced Navigation Technology
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• v.10 no.1
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• pp.13-19
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• 2006

In this paper, Gaussian impulse generator for DS-UWB was proposed and fabricated so that the frequency band allocated to WLAN, around 5 GHz, was suppressed in accordance with the regulation of radiation spectrum limitation defined by FCC. In order to transform an unipolar rectangular signal to a Gaussian impulse, the proposed impulse generator consists of two stage impulse generation parts; the first stage using dual SRD and the second stage using gain switching of semiconductor laser diode. The result shows a gaussian impulse as narrow as 180 psec in width. In addition, high order derivative Gaussian filter with a structure of 4 stage ring resonators was designed and fabricated so that DS-UWB impulse generator could reduce the frequency spectrum of WLAN by 25 dB compared to the spectral power of th adjacent UWB band.

• Asian Journal of Atmospheric Environment
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• v.12 no.3
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• pp.215-231
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• 2018

In order to understand the variation of air quality and the concentration of atmospheric particulates in Chengdu Second Ring Road renovation project, this paper starts to investigate the surrounding residents' opinions on the influenced environment and their daily lives via questionnaires. Then the study numerically simulates the change rule of atmospheric particulates in terms of time and space by using the Gaussian dispersion-deposition model and the compartment model. The optimized scientific scheme is selected by the improved fuzzy analytical hierarchy process(FAHP) to help decision making for the future urban reconstructions. Finally, the reduced emissions of atmospheric particulates are measured when the improvement scheme is provided. According to the study, it can be concluded that the concentration of atmospheric particulates increases rapidly in central Chengdu city during the renovation project, which results in worsening air quality in Chengdu during March 2012 to March 2013. Taking related measures on energy saving and emission reduction can effectively reduce the concentration of atmospheric particulates and promote economic, environmental and social coordination.