• 한국인터넷방송통신학회논문지
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• 제14권5호
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• pp.87-93
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• 2014

n/m=qm+r에서 에서 m=7인 단순한 경우에도 주어진 수 n이 m의 배수 판정법은 간단하지가 않다. 만약, m이 두 자리 수 이상이 되면 더욱 복잡해진다. 일반적인 배수 판정법으로 둔켈스 (Dunkels)법이 있지만 n이 컴퓨터로 처리하지 못하는 매우 큰 자리수인 경우 이 방법도 처리할 수 없다. 본 논문은 n과 m의 자리수와 무관하게 n(modm)=0 여부로 n이 m의 배수인지 여부를 검증하는 간단하면서도 정확한 방법을 제안한다. 제안된 방법은 $n=n_1n_2n_3{\cdots}n_k$, $m=m_1m_2{\cdots}m_l$에 대해 $r_1=n_1n_2{\cdots}n_l(mod m)$으로 설정하고, $r_i=r_{i-1}{\times}10+n_i(mod m)$, $i=2,3,{\cdots},k-1+1$로 n의 자리수를 1자리씩 감소시키는 방법을 적용하였다. 제안된 방법을 다양한 n,m 데이터에 적용한 결과 쉽고, 빠르며 정확한 몫과 나머지 값을 구할 수 있음을 보였다.

• Archives of Pharmacal Research
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• 제17권6호
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• pp.420-423
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• 1994

Various N'-substituted anilino-N-methyl-N'-nitrosoureas(2a-n) were easily prepared from the reaction of substituted phenylhydraines $(3, 4-CH_3, {\;} 3-, {\;} 4-OCH_3, {\;} 3-, {\;} 4-F, {\;} 3, {\;} 4-Cl, {\;} 4-Br, {\;} 2-, {\;} 3-, {\;} 4-NO_2, 4-(NO_2)_2)$ with methyl isocyanate, followed by the nitrosation with 99% HCOOH and dry sodium lnitrite powder. Surprisingly, of these series of analogus, the anilino-nitrocosureas substituted with eletron-withdrawing nitro groups (2k-a) showed significantly low $ED_{30}$ values of $1.4-3.4 {\mu}g/ml.$ In addition, none of these copounds subtituted with electron-donating groups exhibited cytotoxicities.

• 약학회지
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• 제28권4호
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• pp.197-206
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• 1984

The derivatives of N-(alkylcarbamoyl) amino acid methyl ester, N-(2-chloroethylcarbamoyl)-glycine methyl ester (7a), -valine methyl ester (8a), -phenylalanine methyl ester (9a), N-(N'-methylcarbamoyl)-glycine methyl ester (7b), -valine methyl ester (8b), and-phenylalanine methyl ester (9b), were prepared by reacting the corresponding free amino acid methyl ester (glycine-, valine-, phenylalanine-methyl ester) with isocyanate (R-N=C=O${\cdot};R=Cl-CH_2-CH_2-or\; CH_3-)$. The prepared N-(alkylcarbamoyl) amino acid methyl esters (7,8,9) were treated with $NaNO_2$/98% HCOOH in order to obtain their nitrosoated products, N-(alkyl-N'-nitrosocarbmoyl)amino acid methyl ester. The compound (7,8,9) gave N-(2-chloroethyl-N'-nitrosocarbamoyl)-valine methyl ester (14a),-phenylalanine methyl ester (15a), N-(N'-alkyl-N'-nitrosocarbamoyl)-glycine methyl ester (13b),-valine methyl ester. (14b), and-phenylalanine methyl ester (15b) respectively under the nitrosoation. On the other hand, N-(2-chloroethylcarbamoyl) glycine methyl ester produced N-(2-chloroethylcarbamoyl)-N-nitrosoglycine methyl ester (13a). The inhibitory activity of the prepared N-(alkylcarbamoyl) amino acid methyl ester (7,8,9) and N-(alkyl-N'-nitrosocarbamoyl) amino acid methyl ester (13,14,15) towards the growth of L1210 murine leukemia cells were examined. Among them the compound (14a) and (15a) exhibit excellent activity having $ED_{50}\; to\;be\;1.5{\mu}g/ml\;and\;3.0{\mu}g/ml respectively.

• 호남수학학술지
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• 제44권4호
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• pp.521-534
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• 2022

In this paper, we introduce a new class 𝓡^k_λ(λ ≥ 1, k is any positive real number) of univalent complex functions, which consists of functions f of the form f(z) = z + Σ^∞_n=2 a_nzⁿ (|z| < 1) satisfying the subordination condition $$(1-{\lambda}){\frac{f(z)}{z}}+{\lambda}f^{\prime}(z){\prec}{\frac{1+r^2_kz^2}{1-k{\tau}_kz-{\tau}^2_kz^2}},\;{\tau}_k={\frac{k-{\sqrt{k^2+4}}}{2}$$, and investigate the Fekete-Szegö problem for the coefficients of f ∈ 𝓡^k_λ which are connected with k-Fibonacci numbers $F_{k,n}={\frac{(k-{\tau}_k)^n-{\tau}^n_k}{\sqrt{k^2+4}}}$ (n ∈ ℕ ∪ {0}). We obtain sharp upper bound for the Fekete-Szegö functional |a₃-𝜇a²₂| when 𝜇 ∈ ℝ. We also generalize our result for 𝜇 ∈ ℂ.

• 대한수학회보
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• 제52권5호
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• pp.1467-1480
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• 2015

Generalized Fibonacci and Lucas sequences ($U_n$) and ($V_n$) are defined by the recurrence relations $U_{n+1}=PU_n+QU_{n-1}$ and $V_{n+1}=PV_n+QV_{n-1}$, $n{\geq}1$, with initial conditions $U_0=0$, $U_1=1$ and $V_0=2$, $V_1=P$. This paper deals with Fibonacci and Lucas numbers of the form $U_n$(P, Q) and $V_n$(P, Q) with the special consideration that $P{\geq}3$ is odd and Q = -1. Under these consideration, we solve the equations $V_n=5kx^2$, $V_n=7kx^2$, $V_n=5kx^2{\pm}1$, and $V_n=7kx^2{\pm}1$ when $k{\mid}P$ with k > 1. Moreover, we solve the equations $V_n=5x^2{\pm}1$ and $V_n=7x^2{\pm}1$.

• 한국결정학회지
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• 제8권1호
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• pp.1-5
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• 1997

표제화합물의 결정구조는 4-N,N-dimethylamino-4'-N'-methyl-stilbazolium, $C_{16}H_{19}N_2$와 tosylate, $C_7H_7SO_3$의 불연속한 이분자체로 구성되어 있다. 4-N,N-dimethylamino-4'-N'-methyl-stilbazolium 분자는 중간에 있는 C=C double bond에서 trans conformation을 가지고 있으며 phenyl 및 pyridyl ring들간의 이면각은 $5.7(2)^{\circ}$을 이루어 전분자는 $0.138(8){\AA}$ 내에서 평면을 이루고 있다. Tosylate 분자들은 거리가 각각 2.855(9) and $2.899(8){\AA}$인 O-H...O 수소결합으로 연결된 이분자체를 나타내고 있다. 이 두 분자간의 가장 가까운 거리는 O(3)와 C(16) 원자간의 $3.10(1){\AA}$이다.

• 정보보호학회논문지
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• 제14권1호
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• pp.71-77
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• 2004

n개의 LFSR과 l 비트의 메모리를 이용하는 combiner에 대하여 [n(l+1)/2] 차 이하의 대수적 관계식이 존재하는 것이 이론적으로 밝혀졌다. 본 논문에서는 k 비트의 메모리를 사용하는 2$^{k}$ 개의 LFSR로 이루어진 summation Generator는 연속된 k+1개의 출력 값을 이용하여 초기 치에 관한 2$^{k}$ 차 이하의 대수적 관계식을 만들 수 있음을 보인다. 일반적으로 n개의 LFSR로 이루어진 summation Generator는 연속된 [lo $g_2$n]＋1개의 출력 값을 이용하여 초기 치에 관한 2$^{[lo[g_2]n}$ 차 이하의 대수적 관계식을 만들 수 있다.

• Kyungpook Mathematical Journal
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• 제46권2호
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• pp.255-260
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• 2006

Let $m$ and $k$ be any positive integers, let $\mathbb{Z}_k$ the ring of integers of modulo $k$, let $G_m(\mathbb{Z}_k)$ the group of all $m$ by $m$ nonsingular matrices over $\mathbb{Z}_k$ and let ${\phi}_m(k)$ the order of $G_m(\mathbb{Z}_k)$. In this paper, ${\phi}_m(k)$ can be computed by the following investigation: First, for any relatively prime positive integers $s$ and $t$, $G_m(\mathbb{Z}_{st})$ is isomorphic to $G_m(\mathbb{Z}_s){\times}G_m(\mathbb{Z}_t)$. Secondly, for any positive integer $n$ and any prime $p$, ${\phi}_m(p^n)=p^{m^2}{\cdot}{\phi}_m(p^{n-1})=p{^{2m}}^2{\cdot}{\phi}_m(p^{n-2})={\cdots}=p^{{(n-1)m}^2}{\cdot}{\phi}_m(p)$, and so ${\phi}_m(k)={\phi}_m(p_1^n1){\cdot}{\phi}_m(p_2^{n2}){\cdots}{\phi}_m(p_s^{ns})$ for the prime factorization of $k$, $k=p_1^{n1}{\cdot}p_2^{n2}{\cdots}p_s^{ns}$.

• 한국초전도ㆍ저온공학회논문지
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• 제17권3호
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• pp.9-12
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• 2015

NbN thin films were deposited on thermally oxidized Si substrate at room temperature by using reactive magnetron sputtering in an $Ar-N_2$ gas mixture. Total sputtering gas pressure was fixed while varying $N_2$ flow rate from 1.4 sccm to 2.9 sccm. X-ray diffraction pattern analysis revealed dominant NbN(200) orientation in the low $N_2$ flow rate but emerging of (111) orientation with diminishing (200) orientation at higher flow rate. The dependences of the superconducting properties on the $N_2$ gas flow rate were investigated. All the NbN thin films showed a small negative temperature coefficient of resistance with resistivity ratio between 300 K and 20 K in the range from 0.98 to 0.89 as the $N_2$ flow rate is increased. Transition temperature showed non-monotonic dependence on $N_2$ flow rate reaching as high as 11.12 K determined by the mid-point temperature of the transition with transition width of 0.3 K. On the other hand, the upper critical field showed roughly linear increase with $N_2$ flow rate up to 2.7 sccm. The highest upper critical field extrapolated to 0 K was 17.4 T with corresponding coherence length of 4.3 nm. Our results are discussed with the granular nature of NbN thin films.

• Journal of Plant Biology
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• 제39권1호
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• pp.15-22
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• 1996

Seventy-three chromosome counts are reported from populations in 70 species from Korea, of which 34 counts in 32 species belong to Apiaceae. New species counts are in Acanthopanax chiisanensis(2n=48), Hydrocotyle japonica(2n=ca.96), H. maritima (n=12), Libanotis coreana (2n=22), Lindera sericea (n=12), Quercus myrsinaefolia (n=12), Rhamnus yoshinoi (n=12), Salix hulteni (n=19), Symplocos chinensis for. pilosa (n=11) and Vaccinium oldhami (n=12). New chromosome level for Asperula odorata (n=11), Cryptotaenia japonica (2n=16) and Sium ninsi (2n=18) is also provided. The taxonomic implications of certain of these counts are discussed.