• Kyungpook Mathematical Journal
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• 제57권3호
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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.

• 한국광학회:학술대회논문집
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• 한국광학회 2009년도 창립 20주년기념 특별학술발표회
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• pp.111-112
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• 2009

• 대한수학회논문집
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• 제38권1호
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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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• 제57권4호
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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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• 제13권1호
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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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• 제8권2호
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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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• 제27권3호
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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.

• 대한조선학회지
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• 제27권3호
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• pp.38-46
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• 1990

본 보에서는 축대칭포텐시얼유동에 대한 경계적분방정식의 해법이 제시된다. 이 문제는 고리용출점과 고리보오텍스에 의해서 표시되는데 이들의 세기는 한 구간내에서 매개변수 $\zeta$의 선형함수로 근사된다. 물체의 형상은 3차 B-spline으로 표시된다. 속도가 계산되는 점이 고리용출점이나 고리보오텍스에 접근할 때의 극한표현식이 $\zeta{ln}\zeta$항까지 유도된다. 수치계산에서 양 옆구간에 의한 주치적분은 정확하게 서로 상쇄되기 때문에 특이점에 의한 유기속도중 $\(\frac{1}{\zeta}\)$에 비례하는 항은 계산에서 제외된다. 그리고 ${ln}\zeta$에 비례하는 항과 $\zeta{ln}\zeta$에 비례하는 항은 해석적으로 적분이 가능하기 때문에 수치계산에서 이에 비례하는 항을 빼고 계산한 후 해석적으로 계산한 값을 더해 준다. 기타 수치적분은 4점 Gaussian Quadrature 공식에 의해서 수행되었다. 수렴률을 정하기 위하여 구간의 개수에 따른 평균자승근오차를 조사하였으며, 이 방법의 수렴률은 2에 접근점이 밝혀졌다.

• 한국항행학회논문지
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• 제10권1호
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• pp.13-19
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• 2006

본 논문에서는 FCC의 방사 스펙트럼 제한 규정에 따라 5 GHz-WLAN 주파수 대역을 억제한 DS-UWB 가우시안 임펄스 생성기를 제안하고, 이를 실험적으로 구현하였다. 단극 구형파를 가우시안 임펄스로 변환하기 위해 SRD를 이용한 첫 번째 임펄스 생성기와 반도체 레이저의 이득 스위칭을 이용한 두 번째 임펄스 생성기로 구성된 2단 구조의 임펄스 생성기를 사용하였다. 출력된 가우시안 임펄스의 폭은 약 180 psec로 매우 짧다. 또한 WLAN 주파수 대역을 제거하기 위해 4단 링 공진기 구조의 고차 미분 가우시안 필터를 설계 및 제작하여 최종적으로 WLAN 신호 대역은 약 25 dB의 억제 효과를 갖는 DS-UWB 신호의 발생기를 실험적으로 구현하였다.

• Asian Journal of Atmospheric Environment
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• 제12권3호
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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.