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Null computer generated hologram test for measurement of parabolic mirror (Null CGH를 이용한 포물면경 형상 측정)

  • 김태희;김성하;문일권;이윤우
    • 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.

POLYTOPES OF MINIMAL NULL DESIGNS

  • Cho, Soo-Jin
    • 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.

BERTRAND CURVES IN NON-FLAT 3-DIMENSIONAL (RIEMANNIAN OR LORENTZIAN) SPACE FORMS

  • Lucas, Pascual;Ortega-Yagues, Jose Antonio
    • 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.

GEOMETRY OF ISOPARAMETRIC NULL HYPERSURFACES OF LORENTZIAN MANIFOLDS

  • Ssekajja, Samuel
    • 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.

Distributions of the GSTM1 and GSTT1 Null Genotypes Worldwide are Characterized by Latitudinal Clines

  • Saitou, Marie;Ishida, Takafumi
    • 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.

NOTE ON BERTRAND B-PAIRS OF CURVES IN MINKOWSKI 3-SPACE

  • Ilarslan, Kazim;Ucum, Ali;Aslan, Nihal Kilic;Nesovic, Emilija
    • 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.

Glutathione S-transferase polymorphism of neonatal hyperbilirubinemia in Korean neonates (한국인 신생아 황달과 Glutathione S-transferase 다형성에 관한 연구)

  • Kang, Chang Seok;Hong, Seung Su;Kim, Ji Sook;Kim, Eun Ryoung
    • 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.

DIRECTIONAL ASSOCIATED CURVES OF A NULL CURVE IN MINKOWSKI 3-SPACE

  • Qian, Jinhua;Kim, Young Ho
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.1
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    • pp.183-200
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    • 2015
  • In this paper, we define the directional associated curve and the self-associated curve of a null curve in Minkowski 3-space. We study the properties and relations between the null curve, its directional associated curve and its self-associated curve. At the same time, by solving certain differential equations, we get the explicit representations of some null curves.

NOTE ON NULL HELICES IN $\mathbb{E}_1^3$

  • Choi, Jin Ho;Kim, Young Ho
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.3
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    • pp.885-899
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    • 2013
  • In this paper, we study null helices, null slant helices and Cartan slant helices in $\mathb{E}^3_1$. Using some associated curves, we characterize the null helices and the Cartan slant helices and construct them. Also, we study a space-like curve with the principal normal vector field which is a degenerate plane curve.

ON NULL SCROLLS SATISFYING THE CONDITION ${\triangle}$H = AH

  • Pak, Jin-Suk;Yoon, Dae-Won
    • Communications of the Korean Mathematical Society
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    • v.15 no.3
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    • pp.533-540
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    • 2000
  • In the present paper, we study a non-degenrate ruled surface along a null curve in a 3-dimensional Minkowski space E31, which is called a null scroll, an investigate some characterizations of null scrolls satisfying the condition H=AH, A Mat(3, ), where denotes the Laplacian of the surface with respect to the induced metric, H the mean curvature vector and Mat(3, ) the set of 3$\times$3-real matrices.

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