• 한국안광학회지
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• 제6권2호
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• pp.65-70
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• 2001

두 개의 토로이드 면이 서로 직각인 토릭렌즈의 두 곡률의 합($C_x+C_y$)는 $$C_x+C_y=\frac{x^2+y^2}{2r_1}+\frac{x^2}{2}(\frac{1}{r_2}-\frac{1}{r_1})$$이며, 사축인 토릭렌즈의 두 곡률의 합 ($C_a+C_b$)은 $$(C_a+C_b)=\frac{x^2cos^2{\alpha}_1}{2r_1}+\frac{x^2cos^2{\alpha}_2}{2r_2}+\frac{y^2sin^2{\alpha}_1}{2r_1}+\frac{y^2sin^2{\alpha}_2}{2r_2}$$이다. $(C_1+C_2)+(C_1+C_2)_{90^{\circ}}$는 구면의 곡률 합$S_{S_1}+S_{S_2}$과 같은 값을 얻었다. 표면 곡률(Cx, Cy) 값을 포함한 사축 토릭렌즈의 합성 굴절력의 parameter S, C, ${\theta}$ 값을 다음과 같다. $$S=(n-1)\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]-\frac{C}{2},\;C=-\frac{2(n-1)}{sin2{\theta}}\[\frac{C_x}{x^2}+\frac{C_y}{y^2}\]$$ $${\theta}=\frac{1}{2}tan^{-1}\[-\frac{{C_xy^2sin2{\theta}_1}+{C_yx^2sin2{\theta}_2}}{{C_xy^2cos2{\theta}_1}+{C_yx^2cos2{\theta}_2}}\]$$.

• Kyungpook Mathematical Journal
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• 제56권3호
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• pp.781-791
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• 2016

Let $d_*(1,w)^2 ={\mathbb{R}}^2$ with the octagonal norm of weight w. It is the two dimensional real predual of Lorentz sequence space. In this paper we classify the smooth points of the unit ball of the space of symmetric bilinear forms on $d_*(1,w)^2$. We also show that the unit sphere of the space of symmetric bilinear forms on $d_*(1,w)^2$ is the disjoint union of the sets of smooth points, extreme points and the set A as follows: $$S_{{\mathcal{L}}_s(^2d_*(1,w)^2)}=smB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}extB_{{\mathcal{L}}_s(^2d_*(1,w)^2)}{\bigcup}A$$, where the set A consists of $ax_1x_2+by_1y_2+c(x_1y_2+x_2y_1)$ with (a = b = 0, $c={\pm}{\frac{1}{1+w^2}}$), ($a{\neq}b$, $ab{\geq}0$, c = 0), (a = b, 0 < ac, 0 < ${\mid}c{\mid}$ < ${\mid}a{\mid}$), ($a{\neq}{\mid}c{\mid}$, a = -b, 0 < ac, 0 < ${\mid}c{\mid}$), ($a={\frac{1-w}{1+w}}$, b = 0, $c={\frac{1}{1+w}}$), ($a={\frac{1+w+w(w^2-3)c}{1+w^2}}$, $b={\frac{w-1+(1-3w^2)c}{w(1+w^2)}}$, ${\frac{1}{2+2w}}$ < c < ${\frac{1}{(1+w)^2(1-w)}}$, $c{\neq}{\frac{1}{1+2w-w^2}}$), ($a={\frac{1+w(1+w)c}{1+w}}$, $b={\frac{-1+(1+w)c}{w(1+w)}}$, 0 < c < $\frac{1}{2+2w}$) or ($a={\frac{1=w(1+w)c}{1+w}}$, $b={\frac{1-(1+w)c}{1+w}}$, $\frac{1}{1+w}$ < c < $\frac{1}{(1+w)^2(1-w)}$).

• Journal of Korean Neurosurgical Society
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• 제41권2호
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• pp.141-144
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• 2007

A vertebral arte [VA] injury presents a difficult problem in atlantoaxial fixation. Recent technical reports described posterior C2 fixation using bilateral, crossing C2 laminar screws. The translaminar screw technique has the advantages of producing little risk of VA injury and the unconstrained screw placement. In addition, biomechanical studies have demonstrated the potential of the translaminar screw technique to provide a firmer construct that is equivalent to methods currently used. We report the successful treatment of C1-2 instability with a left-side high-riding VA. Because of the potential risk of VA injury, we performed a posterior C1-2 fixation with a combination of pedicle screws and a laminar screw in C2. We first placed bilateral C1 lateral mass screws and a right-side C2 pedicle screw. However, placement of the left- side C2 pedicle screw was technically difficult due to a narrow isthmus and pedicle. A laminar screw was inserted instead and authors believe that this posterior C1-C2 fixation with a combination of pedicle screws and a laminar screw in C2 can be a useful alternative technique for the treatment of C1-C2 instability in the presence of a unilateral high-riding VA.

• Asian Pacific Journal of Cancer Prevention
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• 제13권10호
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• pp.4915-4921
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• 2012

Published data on any association between the CYP2E1 RsaI/PstI (c1/c2) polymorphism and liver cancer risk among east Asians are inconclusive. The aim of this Human Genome Epidemiology (HuGE) review and meta-analysis was to derive a more precise estimation of the relationship. A literature search of Pubmed, Embase, Web of science and CBM databases from inception through July 2012 was conducted. Twelve case-control studies were included with a total of 1,552 liver cancer cases and 1,763 healthy controls. Crude odds ratios (ORs) with 95% confidence intervals (CIs) were used to assess the strength of association under five genetic models. When all the eligible studies were pooled into the meta-analysis, the results showed that the c2 allele and the c2 carrier (c2/c2 + c2/c1) of RsaI/PstI polymorphism were associated with decreased risk of liver cancer among east Asians (c2 vs. c1: OR = 0.75, 95%CI: 0.59-0.95, P = 0.016; c2/c2 + c2/c1 vs. c1/c1: OR = 0.76, 95%CI: 0.58-1.00, P = 0.050). In the stratified analysis by country, significant associations were observed between RsaI/PstI polymorphism and decreased risk of liver cancer among the Chinese population (c2 vs. c1: OR = 0.70, 95%CI: 0.54-0.91, P = 0.007; c2/c2 + c2/c1 vs. c1/c1: OR = 0.72, 95%CI: 0.54-0.95, P = 0.020), but not among Japanese and Korean populations. Results from the current meta-analysis indicates that the c2 allele of CYP2E1 RsaI/PstI (c1/c2) polymorphism may be a protective factor for HCC among east Asians, especially among China populations.

• 한국수산과학회지
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• 제19권3호
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• pp.257-264
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• 1986

우리나라 남부지방에 서식하는 기름종개속 어류의 5종 및 아종, Cobitis taenia taenia, C.taenia lutheri, C.taenia striata, C.koreensis, C.longicorpus의 핵형 분석 결과, 2n의 수, karyotype form (metacentric-submeta centric-acrocentric chromosome), AN(arm number)은 다음과 같다. C. longicorpus, 2n=50, 12m-8sm-30a, AN=70; C. koreensis, 2n=50, 10m-l2sm-28a, AN=72; C. taenia taenia, 2n=48,14m-4sm-30a, AN=66; C. taenia striata, 2n=50,10m-6sm-34a, AN=66; C. taenia lutheri, 2n=50,10m-6sm-34a, AN=66. 이 가운데 C.t.lutheri는 2n=48, 49 및 51도 높은 빈도로 나타나고, 각각의 AN이 66인 점으로 미루어 Robertsonian 염색체 다형현상을 나타내었다. 그리고 본 조사에서 특히 주목되는 것은 C.taenia taenia의 핵형은 2n=48로서 종전의 결과와는 아주 다르고, 또 본 조사집단의 반문등 형태적 특징에 있어서도 유럽산 C.t.taenia와 구분되기때문에 이 개체군은 분류학적으로 별종이 된다고 사료된다. 그리고 본 조사결과 각 종의 집단이나 개체내에서는 현저한 변이는 없었으나, diploid number와 arm number를 이용하여 유연관계를 본 바 다음 3가지의species group으로 나눌 수 있었다. 1) C. taenia taenia, C. taenia lutheri 및 C. taenia striata 2) C. koreensis, C. longicorpus 및 C. rotundicaudata 3) C. granoei

• Korean Journal of Mathematics
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• 제27권2호
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• pp.437-444
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• 2019

For c > -1, let ${\nu}_c$ denote a weighted radial measure on ${\mathbb{C}}$ normalized so that ${\nu}_c(D)=1$. For $c_1,c_2>-1$ and $f{\in}L^1(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$, we define the weighted Berezin transform $B_{c_1,c_2}f$ on $D^2$ by $$(B_{c_1,c_2})f(z,w)={\displaystyle{\smashmargin2{\int\nolimits_D}{\int\nolimits_D}}}f({\varphi}_z(x),\;{\varphi}_w(y))\;d{\nu}_{c_1}(x)d{\upsilon}_{c_2}(y)$$. This paper is about the space $M^p_{c_1,c_2}$ of function $f{\in}L^p(D^2,\;{\nu}_{c_1}{\times}{\nu}_{c_2})$ ) satisfying $B_{c_1,c_2}f=f$ for $1{\leq}p<{\infty}$. We find the identity operator on $M^p_{c_1,c_2}$ by using invariant Laplacians and we characterize some special type of functions in $M^p_{c_1,c_2}$.

• Journal of Korean Neurosurgical Society
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• 제61권2호
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• pp.194-200
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• 2018

Objective : Sometimes a vertebral artery (VA) enters the spinal canal via the C1-2 intervertebral space, a variation regarded as a C2 segmental-type VA. This paper describes the anatomy of the C2 segmental-type VA and reviews its clinical importance. Methods : Between March 2014 and November 2015, 3386 patients underwent computed tomographic angiography. I identified C2 segmental-type VAs, associated vascular variation, the origin of ipsilateral posterior inferior cerebellar arteries (PICAs), and the clinical symptoms associated with C2 segmental-type VAs. The origin of an ipsilateral PICA is divided into 5 types. A type 1 PICA originates from ipsilateral VAs coursing suboccipitally (IVASO), a type 2 originates from ipsilateral proximal C2 segmental-type VAs, a type 3 originates from ipsilateral distal C2 segmental-type VAs. For type 4, the PICA does not originate from an ipsilateral VA. For type 5, the PICA is the terminal end of an ipsilateral C2 segmental-type VA. Results : One hundred thirteen patients had 121 C2 segmental-type VAs; 47 were associated with an IVASO, and 74 were not. Four type 1, 13 type 2, 60 type 3, 42 type 4, and two type 5 PICAs were identified. Only one patient showed symptoms associated with a C2 segmental-type VA, being a 71-year-old man presenting with a C2 segmental-type VA infarction. Conclusion : For C2 segmental-type VAs, the ipsilateral IVASO and origin of the PICA are important for predicting the outcome of this type of VA infarction.

• Journal of Korean Neurosurgical Society
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• 제64권6호
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• pp.913-921
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• 2021

Objective : Accurate measurement of T1 slope (a component of T1s minus cervical lordosis [CL]) is often constrained by anatomical limitations. In this situation, efforts should be made to find the exact meaning of T1s-CL and whether there are any alternatives to it. Methods : We enrolled 117 patients who received two-level anterior cervical discectomy and fusion (ACDF). Occipital slope, C2 slope (C2s), C7 slope (C7s), T1, O-C2 angle (O-C2A), C2-7 angle (C2-7A), O-C7 angle (O-C7A), T1s-CL, C7-T1 angle (C7-T1A), and C2-7 sagittal vertical axis were measured. We determined 16° (T1s-CL) as the reference point for dividing subjects into the mismatch group and the balance group, and a comparative analysis was performed. Results : The mean value of C7-T1A was constantly maintained within 2.6° peri-operatively. In addition, C2s and T1s-CL showed the same absolute change (Δ|0.8|°). The mean values of T1s-CL of the mismatch and balance groups were 23.0° and 7.6°, respectively. The five factors with the largest differences between the two groups were as follows : C2s (Δ13.3°), T1s-CL (Δ15.4°), O-C2A (Δ8.7°), C2-7A (Δ14.7°), and segmental angle (Δ7.9°) before surgery. Only four factors showed statistically significant change between the two groups after ACDF : T1s-CL (Δ4.0° vs. Δ0.2°), C2s (Δ3.2° vs. Δ0.7°), O-C2A (Δ2.6° vs. Δ1.3°), C2-7A (Δ6.3° vs. Δ1.3°). A very strong correlation between T1s-CL and C2s was also found (r=|0.88-0.96|). Conclusion : C2s itself may be the essential key to represent T1s-CL. The amounts and directions of change of these two factors (T1s-CL and C2s) were also almost identical. The above phenomenon was re-confirmed once again through the correlation analysis.

• 한국결정학회지
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• 제5권1호
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• pp.1-6
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• 1994

화합물 VP6N3018C243H60의 두 가지 가능한 공간군은 PT,a=14.O22(1), b=12.644(2), c=12.640(1)A, a=80.38(1), β=102.12(1), y =102.16(1), V=2124.1A3, Z=2, u=0.47cm-1,d==1.46g/cm3, Fo>4c IfoI인 3350윤의 독립반사강도에 대하여 R=0.083 과 C2/c, a=19.32(2), b=16.32(2), c=14.02(1)A, β= 105.98(5), V=4348.2A3, Z=4, Fo>4o IFoI인 1590개의 독립반사강도에 대하여 R=0.083 이다. 주간군 Pi의 경우 단위포내에 두 분자가 있는데 각 분자내의 바나둠 원자가 특수치치에 있어 중심대칭에 의하여 한 분자를 이루고 있으므로 단위포내의 비대칭단위는 두개의 bis(timetalhosphate)vanadate 반분자와 3개의 tetraethylammDnium분자로 되어있다. 공문군 C2/c의 경우 bis(trimetaphosphate)vanadate 한분자의 vanadium 원자가 중심대1칭을 갖는 변광단동치에 있으며, 3개의 tetrethylammonium 분자중 한 분자내의 CL2, N2, C25 원자들을 2-회회전대칭축이 지나므로 bis(trimetaphosphate)vanadate 반분자와 tetraethylammonium 3/2 분자가 비대칭단위를 이루고 있다. 두 경우 공히 vanadium원자를 배위하고 있는 6개의 산소원자가 8함체를 이루며 nitrogen원자와 결합하고 있는 4개의 carbon 원자들은 모두 disorder되어 있어 nitrogen원자의 주권에 있는 8개의 carbon 원자들은 불규칙한 12면체를 이루고 있다.

• Bulletin of the Korean Chemical Society
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• 제18권4호
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• pp.402-405
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• 1997

Olefinic and cyclopropyl group substituted arenes (C6H5Y) react with [Cp*Ir(CH3COCH3)3]A2 (A=ClO4-, OTf-) to give η6-arene complexes, [Cp*Ir(η6-C6H5Y)]2+ (1a: Y=-CH=CH2 (a),-CH=CHCH3 (b),-C(CH3)=CH2 (c),-CH-CH2-CH2 (d)). Complex 1b-1d are readily converted into η3-allyl complexes, [Cp*(CH3CN)Ir(η3-CH(C6H5)CHCH2)]+ (2a) and [Cp*(CH3CN)Ir(η3-CH2(C6H5)CH2)]+ (2b), in the presence of Na2CO3 in CH3CN. The η6-styrene complex, 1a reacts with NaBH4 to give η5-cyclohexadienyl complex, [Cp*Ir(η5-C6H6-CH=CH2)]+ (3), while with H2 it gives η6-ethylbenzene complex [Cp*Ir(η6-C6H5CH2CH3)]2+ (4). Complex 1a and 1c react with HCl to give [Cp*Ir(η6-C6H5CH2CH2Cl)]2+ (5a) and [Cp*Ir(η6-C6H5CH(CH3)CH2Cl]2+ (5b), respectively.