• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.895-905
• /
• 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 $B^{3n+1}$.

• Journal of the Korean Society of Safety
• /
• v.34 no.1
• /
• pp.34-39
• /
• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.13 no.6
• /
• pp.221-228
• /
• 2013

It is impossible directly to find a prime number p,q of a large semiprime n = pq using Trial Division method. So the most of the factorization algorithms use the indirection method which finds a prime number of p = GCD(a-b, n), q=GCD(a+b, n); get with a congruence of squares of $a^2{\equiv}b^2$ (mod n). It is just known the fact which the area that selects p and q about n=pq is between $10{\cdots}00$ < p < $\sqrt{n}$ and $\sqrt{n}$ < q < $99{\cdots}9$ based on $\sqrt{n}$ in the range, [$10{\cdots}01$, $99{\cdots}9$] of $l(p)=l(q)=l(\sqrt{n})=0.5l(n)$. This paper proposes the method that reduces the range of p using information obtained from n. The proposed method uses the method that sets to $p_{min}=n_{LR}$, $q_{min}=n_{RL}$; divide into $n=n_{LR}+n_{RL}$, $l(n_{LR})=l(n_{RL})=l(\sqrt{n})$. The proposed method is more effective from minimum 17.79% to maxmimum 90.17% than the method that reduces using $\sqrt{n}$ information.

• Journal of Nutrition and Health
• /
• v.29 no.7
• /
• pp.788-805
• /
• 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
• /
• v.56 no.2
• /
• pp.349-355
• /
• 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.

• Korean Journal of Materials Research
• /
• v.18 no.10
• /
• pp.558-563
• /
• 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
• /
• v.30 no.3_4
• /
• pp.455-462
• /
• 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
• /
• v.52 no.9
• /
• pp.2034-2040
• /
• 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
• /
• v.33 no.3
• /
• pp.257-263
• /
• 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).

• Journal of KIISE:Computer Systems and Theory
• /
• v.27 no.2
• /
• pp.209-215
• /
• 2000

In this paper we present polyline upward order preserving grid drawing algorithm for binary trees with n vertices that achieves 0(n) height, 0(log n) width and 0(nlog n) area, matching the previously known results, and that reduces the number of bends to 0(n/log n) from 0(n)