• 대한수학회지
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• 제46권5호
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• pp.895-905
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• 2009

Let $B^{n+1}$ be the unit ball in the complex vector space $\mathbb{C}^{n+1}$ with the standard Hermitian metric. Let ${\Sigma}^n={\partial}B^{n+1}=S^{2n+1}$ be the boundary sphere with the induced CR structure. Let f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$ be a local CR immersion. If N < 3n - 1, the asymptotic vectors of the CR second fundamental form of f at each point form a subspace of the CR(horizontal) tangent space of ${\Sigma}^n$ of codimension at most 1. We study the higher order derivatives of this relation, and we show that a linearly full local CR immersion f : ${\Sigma}^n{\hookrightarrow}{\Sigma}^N$, N $\leq$ 3n-2, can only occur when N = n, 2n, or 2n + 1. As a consequence, it gives an extension of the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{2n+2}$ by Hamada to the classification of the rational proper holomorphic maps from $B^{n+1}$ to $B^{3n+1}$.

• 한국안전학회지
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• 제34권1호
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• pp.34-39
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• 2019

Flash point is the important indicator to determine fire and explosion hazards of liquid solutions. In this study, flash points of n-propanol+n-hexanol and n-butanol+n-hexanol systems were obtained by Seta flash tester. The methods based on UNIFAC equation and multiple regression analysis were used to calculate flash point. The calculated flash point was compared with the experimental flash point. Absolute average errors of flash points calculated by UNIFAC equation are $2.9^{\circ}C$ and $0.6^{\circ}C$ for n-propanol+n-hexanol and n-butanol+n-hexanol, respectively. Absolute average errors of flash points calculated by multiple regression analysis are $0.5^{\circ}C$ and $0.2^{\circ}C$ for n-propanol+ n-hexanol and n-butanol+n-hexanol, respectively. As can be seen from AAE, the values calculated by multiple regression analysis are noticed to be better than the values by the method based on UNIFAC eauation.

• 한국인터넷방송통신학회논문지
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• 제13권6호
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• pp.221-228
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• 2013

큰 반소수 n=pq의 소인수 p,q를 나눗셈 시행법으로 직접 찾는 것은 현실적으로 거의 불가능하다. 따라서 대부분의 소인수분해 알고리즘은$a^2{\equiv}b^2$ (mod n)의 제곱합동을 찾아 p=GCD(a-b, n), q=GCD(a+b, n)의 소인수를 찾는 간접 방법을 적용하고 있다. n = pq에 대해 p와 q를 선택한 영역은 $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$의 [$10{\cdots}01$, $99{\cdots}9$] 범위에서 $\sqrt{n}$을 기준으로 $10{\cdots}00$ < p < $\sqrt{n}$과 $\sqrt{n}$ < q < $99{\cdots}9$에 존재한다는 사실만이 밝혀졌다. 본 논문은 n으로 부터 획득한 정보를 이용하여 p의 범위를 보다 축소시키는 방법을 제안한다. 제안 방법은 $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$으로 분할하여 $p_{min}=n_{LR}$, $q_{min}=n_{RL}$로 설정하는 방법을 적용하였다. 본 논문에서 제안한 n의 정보로 p의 범위를 축소하는 방법은 $\sqrt{n}$의 정보로 p의 범위 축소 방법에 비해 최소 17.79%에서 최대 90.17%의 범위 축소 효과를 얻었다.

• Journal of Nutrition and Health
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• 제29권7호
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• pp.788-805
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• 1996

This study was performed to investigate effects of examination-stress and protein supplementation on nitrogen metabolism and blood protein levels of Korean college students. Experiment was conducted at the beginning of a academic term and during midterm examination. During midterm examination, subjects were classified into two groups randomly : protein supplemental group(male n=6, female n=10) and placebo group(male n=4, female n=9). Protein capsules(2g/day) above 10% of indispensible amino acids requirement estimates were given to supplemental group for 10 days. At the begining of the term, male students(n=12) ingested 223.15mgN/kg/d, excreted 20.7mgN/kg/d in feces, and excreted 94.31mgN/kg/d in urine. Their apparent protein protein digestibility was 90.72%, true N balance was +100.11mgN/kg/d, and the mean maintenance N requirement of mixed Korena diet calculated was 112.13mgN/kg/d. Female students(n=19) ingested 171.44mgN/kg/d, excreted 22.13mgN/kg/d in feces, and excreted 122.92mgN/kg/d in urine. Their apparent protein digestibility was 86.76%, true N blance was + 18.39mgN/kg/d, and the mean maintenance N requirement calculated was 135.31mgN/kg/d. Blood levels of serum total protein, albumin, and BUN were within normal range. During midterm examination, fecal and urinary N excretions of female subjects(n=19) were increased, especially urea N markedly, and urea N/creatinine N ratio was augumented significantly. Apparent protein digestibility of male subjects(n=10) was decreased. Examination-stress showed 8.05mgN/kg/d (7.2%) increase of mean maintenance N requirement in male and 8.55mgN/kg/d(6.3%) increase in female students in comparison with that of the beginning of the term. Serum total protein and albumin levels showed no significant change, but serum transferrin level of female were decreased significantly. During midterm examination, females supplemented with protein capsules(2g/d)had no significant increase in fecal and urinary N excretions.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.349-355
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• 2016

For any integer $n{\geq}2$, each palindrome of n induces a circulant graph of order n. It is known that for each integer $n{\geq}2$, there is a one-to-one correspondence between the set of (resp. aperiodic) palindromes of n and the set of (resp. connected) circulant graphs of order n (cf. [2]). This bijection gives a one-to-one correspondence of the palindromes ${\sigma}$ with $gcd({\sigma})=1$ to the connected circulant graphs. It was also shown that the number of palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ is the same number of aperiodic palindromes of n. Let $a_n$ (resp. $b_n$) be the number of aperiodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). Let $c_n$ (resp. $d_n$) be the number of periodic palindromes ${\sigma}$ of n with $gcd({\sigma})=1$ (resp. $gcd({\sigma}){\neq}1$). In this paper, we calculate the numbers $a_n$, $b_n$, $c_n$, $d_n$ in two ways. In Theorem 2.3, we $n_d$ recurrence relations for $a_n$, $b_n$, $c_n$, $d_n$ in terms of $a_d$ for $d{\mid}n$ and $d{\neq}n$. Afterwards, we nd formulae for $a_n$, $b_n$, $c_n$, $d_n$ explicitly in Theorem 2.5.

• 한국재료학회지
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• 제18권10호
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• pp.558-563
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• 2008

TiAlN films were deposited on WC-5Co substrates with different buffer layers by D.C. magnetron sputtering. The films were evaluated by microstructural observations and measuring of preferred orientation, hardness value, and adhesion force. As a process variable, various buffer layers were used such as TiAlN single layer, TiAlN/TiAl, TiAlN/TiN and TiAlN/CrN. TiAlN coating layer showed columnar structures which grew up at a right angle to the substrates. The thickness of the TiAlN coating layer was about $1.8{\mu}m$, which was formed for 200 minutes at $300^{\circ}$. XRD analysis showed that the preferred orientation of TiAlN layer with TiN buffer layer was (111) and (200), and the specimens of TiAlN/TiAl, TiAlN/CrN, TiAlN single layer have preferred orientation of (111), respectively. TiAlN single layer and TiAlN/TiAl showed good adhesion properties, showing an over 80N adhesion force, while TiAlN/TiN film showed approximately 13N and the TiAlN/CrN was the worst case, in which the layer was destroyed because of high internal residual stress. The value of micro vickers hardness of the TiAlN single layer, TiAlN/TiAl and TiAlN/TiN layers were 2711, 2548 and 2461 Hv, respectively.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.455-462
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• 2012

The cyclic group $Cn={\langle}(12{\cdots}n){\rangle}$ acts on the set ($^{[n]}_k$) of all $k$-subsets of [$n$]. In this action of $C_n$ the number of orbits of size $d$, for $d|n$, is $$O^{n,k}_d=\frac{1}{d}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})(^{n/s}_{k/s})$$. Stanton and White[7] generalized the above identity to construct the orbit polynomials $$O^{n,k}_d(q)=\frac{1}{[d]_{q^{n/d}}}\sum_{\frac{n}{d}|s|n}{\mu}(\frac{ds}{n})[^{n/s}_{k/s}]{_q}^s$$ and conjectured that $O^{n,k}_d(q)$ have non-negative coefficients. In this paper we give a combinatorial proof for the positivity of coefficients of the orbit polynomial $O^{n,3}_d(q)$.

• Nuclear Engineering and Technology
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• 제52권9호
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• pp.2034-2040
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• 2020

The gas evolution from mixtures consisting of 0.2 M solution of N,N,N',N'-tetra-n-octyldiglycolamide (TODGA) in n-alcohol (n-decanol or n-nonanol) with Isopar-M diluent was investigated during thermal oxidation. The effect of ionizing radiation on their thermal stability has been studied. It has been determined that the volume of gaseous thermolysis products increases by 260% in the case of n-nonanol and 80% in the case of n-decanol compared to non-irradiated solutions. It has been shown that the gas evolution rate and gas volume increase when the irradiated mixture saturated with nitric acid is heated. However, there are no prerequisites for the development of autocatalytic oxidation.

• East Asian mathematical journal
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• 제33권3호
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• pp.257-263
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• 2017

Let n be any positive integer and ${\mathbb{Z}}_n=\{0,1,{\cdots},n-1\}$ be the ring of integers modulo n. Let $X_n$ be the set of all nonzero, nonunits of ${\mathbb{Z}}_n$, and $G_n$ be the group of all units of ${\mathbb{Z}}_n$. In this paper, by investigating the regular action on $X_n$ by $G_n$, the following are proved : (1) The number of orbits under the regular action (resp. the number of annihilators in $X_n$) is equal to the number of all divisors (${\neq}1$, n) of n; (2) For any positive integer n, ${\sum}_{g{\in}G_n}\;g{\equiv}0$ (mod n); (3) For any orbit o(x) ($x{\in}X_n$) with ${\mid}o(x){\mid}{\geq}2$, ${\sum}_{y{\in}o(x)}\;y{\equiv}0$ (mod n).

• 한국정보과학회논문지:시스템및이론
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• 제27권2호
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• pp.209-215
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• 2000

본 논문에서는 n개의 노드로 이루어진 이진트리를 평면에 그리는 한 방법인 평면 다각선 상향 순서보존 그리드 방법을 이용하여 높이 0(n), 폭 0(log n), 면적 O(n log n)은 기존의 결과와 같게 유지하면서, 굴곡점의 수를 (n)에서 (n/logn)으로 줄이는 알고리즘을 제시한다.