• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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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.

• Korean Journal of Optics and Photonics
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• v.13 no.6
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• pp.537-542
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• 2002

Null tests using two different kinds of null corrector have been discussed. A parabolic mirror was used as a surface under test. After designing, encoding, and fabricating the CGH (computer generated hologram), the null CGH test was performed. An autocollimation test was also performed using a flat mirror. The reliability of the null CGH test has been discussed by comparing the result obtained by both null tests.

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1991.10a
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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.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.1
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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.

• Honam Mathematical Journal
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• v.40 no.3
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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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• v.16 no.1
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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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• v.51 no.3
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• pp.262-266
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• 2008

Purpose : Glutathione S-transferase (GST) is a polymorphic supergene family of detoxification enzymes that are involved in the metabolism of numerous diseases. Several allelic variants of GSTs show impaired enzyme activity and are suspected to increase the susceptibility to diseases. Bilirubin is bound efficiently by GST members. The most commonly expressed gene in the liver is GSTM1, and GSTT1 is expressed predominantly in the liver and kidneys. To ascertain the relationship between GST and neonatal hyperbilirubinemia, the distribution of the polymorphisms of GSTT1 and GSTM1 were investigated in this study. Methods : Genomic DNA was isolated from 88 patients and 186 healthy controls. The genotypes were analyzed by polymerase chain reaction (PCR). Results : The overall frequency of the GSTM1 null was lower in patients compared to controls (P=0.0187, Odds ratio (OR) =0.52, 95% confidence interval (CI), 0.31-0.88). Also, the GSTT1 null was lower in patients compared to controls (P=0.0014, OR=0.41, 95% CI=0.24-0.70). Moreover, the frequency of the null type of both, in the combination of GSTM1 and GSTT1, was significantly reduced in jaundiced patients (P=0.0008, OR=0.31, 95% CI=0.17-0.61). Conclusion : We hypothesized that GSTM1 and GSTT1 might be associated with neonatal hyperbilirubinemia. However, the GSTT1 and GSTM1 null type was reduced in patients. Therefore the null GSTT1, null GSTM1, and null type of both in the combination of GSTM1 and GSTT1 may be not a risk factor of neonatal jaundice.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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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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• v.59 no.4
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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.