• 대한수학회보
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• 제60권5호
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• pp.1265-1280
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• 2023

The aim of this paper is to investigate Betchov-Da Rios equation by using null Cartan, pseudo null and partially null curve in Minkowski spacetime. Time derivative formulas of frame of s parameter null Cartan, pseudo null and partially null curve are examined, respectively. By using the obtained derivative formulas, new results are given about the solution of Betchov-Da Rios equation. The differential geometric properties of these solutions are obtained with respect to Lorentzian causal character of s parameter curve. For a solution of Betchov-Da Rios equation, it is seen that null Cartan s parameter curves are space curves in three-dimensional Minkowski space. Then all points of the soliton surface are flat points of the surface for null Cartan and partially null curve. Thus, it is seen from the results obtained that there is no surface corresponding to the solution of Betchov-Da Rios equation by using the pseudo null s parameter curve.

• 한국광학회지
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• 제13권6호
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• pp.537-542
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• 2002

서로 다른 null optics를 사용하는 null test의 측정결과를 상호 비교함으로써 null CGH test 신뢰성을 알아보았다. 회전대칭 포물면경(90mm, F/0.76) 형상측정 및 측정장치 정렬용 null CGH를 설계, encoding, 제작 후 null CGH test를 실시하였다. 결과를 평면경을 null optics로 사용하는 autocollimation test측정치와 비교하여 null CGH test의 정확성을 평가하였다.

• 한국통신학회:학술대회논문집
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• 한국통신학회 1991년도 추계종합학술발표회논문집
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• pp.123-126
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• 1991

A generalization of null-spectrum for use in the estimation of directions of arrival of signal sources is considered in this paper. The upper and lower bounds of the generalized null-spectrum, the maximum and minimum null-spectra, are also derived. We observed that the maximum null-spectrum has higher resolution capability than other null-spectra including the two well-known null-spectra, the multiple signal classification null-spectrum and the Min-Norm null-spectrum.

• 대한수학회논문집
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• 제17권1호
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• pp.143-153
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• 2002

Null designs form a vector space and there are only finite number of minimal null designs(up to scalar multiple), hence it is natural to look at the convex polytopes of minimal null designs. For example, when t = 0, k = 1, the convex polytope of minimal null designs is the polytope of roofs of type An. In this article, we look at the convex polytopes of minimal null designs and find many general properties on the vertices, edges, dimension, and some structural properties that might help to understand the structure of polytopes for big n, t through the structure of smaller n, t.

• 대한수학회지
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• 제57권1호
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• pp.195-213
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• 2020

We define two types of null hypersurfaces as; isoparametric and quasi isoparametric null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi isoparametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.

• 호남수학학술지
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• 제40권3호
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• pp.561-576
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• 2018

In this paper, we define null Cartan and pseudo null Bertrand curves in Minkowski space ${\mathbb{E}}^3_1$ according to their Bishop frames. We obtain the necessary and sufficient conditions for pseudo null curves to be Bertand B-curves in terms of their Bishop curvatures. We prove that there are no null Cartan curves in Minkowski 3-space which are Bertrand B-curves, by considering the cases when their Bertrand B-mate curves are spacelike, timelike, null Cartan and pseudo null curves. Finally, we give some examples of pseudo null Bertrand B-curve pairs.

• Asian Pacific Journal of Cancer Prevention
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• 제16권1호
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• pp.355-361
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• 2015

Background: Deletion types of genetic variants of glutathione S-transferase (GST) M1 and T1, the GSTM1 null and GSTT1 null which are risk factors for certain cancers, have been ubiquitously found in human populations but their worldwide distribution pattern is unclear. Materials and Methods: To perform a meta-analysis, a systematic search for the literature on GSTM1 and GSTT1 null genotypes was done to identify 63 reports for 81 human populations. Relationships between the GSTM1 and GSTT1 null genotype frequencies and the absolute latitude of 81 populations were tested by Spearman's rank correlation coefficient. Results: A significant positive correlation was detected between the GSTM1 null genotype frequency and the absolute latitude (r=0.28, p-value <0.05), whereas the GSTT1 null genotype frequency and absolute latitude showed a significant negative correlation (r= -0.41 p-value <0.01). There was no correlation between the frequencies of GSTM1 and GSTT1 null genotype in each population (r= -0.029, p-value=0.80). Conclusions: Latitudinal clines of the distribution of the GSTM1 and GSTT1 null genotypes may be attributed to the result of gene-environmental adaptation. No functional compensation between GSTM1 and GSTT1 was suggested by the lack of correlation between the null frequencies for GSTM1 and GSTT1.

• Clinical and Experimental Pediatrics
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• 제51권3호
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• pp.262-266
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• 2008

목 적 : GSTs는 glutathione과 친전자성 화합물의 결합을 촉매하여 생체내에 독성 물질로부터 조직을 보호하는 효소로, 여러 다형성이 확인 되었으며 일부 GSTs의 null 유전자형을 가진 사람은 GSTs 단백을 생성하지 못하여 다양한 질병의 감수성에 영향을 미친다고 보고 되었다. 이것은 빌리루빈과 같은 non-substrate ligand와 결합하여 세포내로 운반하는 역할을 하는 대표적인 ligandin이며 빌리루빈을 간세포 내 소포체로 이동시켜 UGT를 통해 glucuronidation 시키는 역할을 한다. 이 연구에서는 빌리루빈 대사의 ligandin인 GSTs 중 GSTM1, GSTT1과 신생아 황달과 연관성이 있는 지 알아보고자 본 연구를 시행하였다. 방 법 : 혈청 빌리루빈 수치가 12 mg/dL 이상인 건강하고 위험인자가 없는 만삭아 중 신생아 고빌리루빈혈증 환아 88명, 대조군은 186명을 대상으로 혈액 0.5 cc를 채혈하여 DNA를 분류하였고 중합효소 연쇄 반응을 수행하여 DNA band를 확인하였다. 결 과 : 대조군의 GSTM1 null 유전형 58.1%, GSTT1의 null 유전형 53.2%였다. 환자군에서 GSTM1 null 유전형은 42% (P=0.0187), GSTT1 null 유전형은 31.8% (P=0.0014)로 통계학적 연관성이 있었다. GSTM1/GSTT1 null/null인 경우, 환자군에서 20명(22.7%)(P=0.0008), GSTM1/GSTT1 null/present인 경우 환자군에서 17명(19.3%) (P=0.0470), GSTM1/GSTT1 present/null인 경우 환자군에서 8명(9.1%) (P=0.0066)으로 나타났다 결 론 : GSTM1과 GSTT1 모두 환자군에서 null 유전형이 대조군에 비하여 더 적게 나타나 GSTs null 유전형이 신생아 고빌리루빈혈증의 위험인자는 아니었다.

• 대한수학회보
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• 제50권4호
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• pp.1109-1126
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• 2013

Let $\mathbb{M}^3_q(c)$ denote the 3-dimensional space form of index $q=0,1$, and constant curvature $c{\neq}0$. A curve ${\alpha}$ immersed in $\mathbb{M}^3_q(c)$ is said to be a Bertrand curve if there exists another curve ${\beta}$ and a one-to-one correspondence between ${\alpha}$ and ${\beta}$ such that both curves have common principal normal geodesics at corresponding points. We obtain characterizations for both the cases of non-null curves and null curves. For non-null curves our theorem formally agrees with the classical one: non-null Bertrand curves in $\mathbb{M}^3_q(c)$ correspond with curves for which there exist two constants ${\lambda}{\neq}0$ and ${\mu}$ such that ${\lambda}{\kappa}+{\mu}{\tau}=1$, where ${\kappa}$ and ${\tau}$ stand for the curvature and torsion of the curve. As a consequence, non-null helices in $\mathbb{M}^3_q(c)$ are the only twisted curves in $\mathbb{M}^3_q(c)$ having infinite non-null Bertrand conjugate curves. In the case of null curves in the 3-dimensional Lorentzian space forms, we show that a null curve is a Bertrand curve if and only if it has non-zero constant second Frenet curvature. In the particular case where null curves are parametrized by the pseudo-arc length parameter, null helices are the only null Bertrand curves.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.783-795
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• 2019

We prove that a Lorentzian concircular structure (LCS)-manifold does not admit any null hypersurface which is tangential or transversal to its characteristic vector field. Due to the above, we focus on its ascreen null hypersurfaces and show that such hypersurfaces admit a symmetric Ricci tensor. Furthermore, we prove that there are no totally geodesic ascreen null hypersurfaces of a conformally flat (LCS)-manifold.