• 한국항해학회지
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• 제16권1호
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• pp.94-97
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• 1992

In this paper, the individual number of the future has depended not only upon the present individual number but upon the present individual age, considering the stochastic process model of individual number when the life span of each individual number and the individual age as a set, this becomes a Markovian. Therefore, in this paper the individual is treated as invariable, without depending upon the whole record of each individual since its birth. As a result, suppose {N(t), t>0} be a counting process and also suppose $Z_n$ denote the life span between the (n-1)st and the nth event of this process, (n{$geq}1$) : that is, when the first individual is established at n=1(time, 0), the Z$Z_n$ at time nth individual breaks, down. Random walk $Z_n$ is $Z_n=X_1+X_2+{\cdots}{\cdots}+X_A, Z_0=0$ So, fixed time t, the stochastic model is made up as follows ; A) Recurrence (Regeneration)number between(0.t) $N_t=max{n ; Z_n{\leq}t}$ B) Forwardrecurrence time(Excess life) $T^-I_t=Z_{Nt+1}-t$ C) Backward recurrence time(Current life) $T^-_t=t-Z_{Nt}$

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.395-404
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• 2005

Let α be a complex number with 𝕽α > 0. Let the functions f and g be analytic in the unit disc E = {z : |z| < 1} and normalized by the conditions f(0) = g(0) = 0, f'(0) = g'(0) = 1. In the present article, we study the differential subordinations of the forms $${\alpha}{\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}+{\frac{zf^{\prime}(z)}{f(z)}}{\prec}{\alpha}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}}+{\frac{zg^{\prime}(z)}{g(z)}},\;z{\in}E,$$ and $${\frac{z^2f^{{\prime}{\prime}}(z)}{f(z)}}{\prec}{\frac{z^2g^{{\prime}{\prime}}(z)}{g(z)}},\;z{\in}E.$$ As consequences, we obtain a number of sufficient conditions for star likeness of analytic maps in the unit disc. Here, the symbol ' ${\prec}$ ' stands for subordination

• 천문학회보
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• 제40권2호
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• pp.28.2-28.2
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• 2015

High redshift quasars (z > 5) hold keys to understanding the evolution of the universe in its early stage. Yet, the number of high redshift quasars uncovered from previous studies is relatively small (70 or so), and are concentrated mostly in a limited redshift range (z ~ 6). To understand the early mass growth of supermassive black holes and the final stage of the cosmic reionization, it is important to find a statistically meaningful sample of quasars with various physical properties. Here we present a survey for high redshift quasars at 5 < z < 7. Through color selection techniques using multi-wavelength data, we found quasar candidates and carried out imaging follow-up observations to reduce contaminants. After optical spectroscopy, we discovered eight new quasars. We obtained near-infrared spectra for 3 of these 8 quasars, measured their physical properties such as black hole masses and Eddington ratios, and found that the high redshift quasars we discovered are growing via accretion more vigorous than those of their lower redshift counterparts. We estimated the quasar number densities from our discoveries and compared them to those expected from the quasar luminosity functions in literature. In contrast to the observed number density of quasars at z ~ 5, which agrees with literature, the observed number density at z ~ 7 shows values lower than what is expected, even after considering an extrapolated number density evolution. We conclude that the quasar number density at z ~ 7 declines toward higher redshift, more steeply than the empirically expected evolution.

• Korean Journal of Mathematics
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• 제23권2호
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• 한국응용곤충학회지
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• 제45권2호
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• pp.161-167
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• 2006

귤굴나방, Phyllocnistis citrella Stainton은 운향과(Rutaceae) 특히 감귤류를 가해하는 해충으로 성페로몬 (Z,Z)-7,11-hexadecadienal (7Z,11Z-16:Al)에 대한 귤굴나방의 반응 특성을 조사하였다. 귤굴나방의 포획효율은 7Z,11Z-16:Al을 미끼로 한 끈끈이날개트랩을 이용했을 때 높았다. 귤굴나방이 유인되는 시간대는 일출과 일몰시간이 관여하고 있으며, 그 시간은 오전 2$\sim$6시로 일일 유인수의 93.1%를 차지하였다. 또한 이 시간대의 평균온도와 풍속, 강우가 귤굴나방 트랩 포획에 미치는 영향을 조사한 결과 풍속의 영향이 가장 높았다. 평균온도 13$^{\circ}C$이하에서는 유인수가 감소하였으나 그 이상의 온도에서는 별다른 영향이 없었다. 풍속은 2.0 m/sec 이상일 때에는 유인수가 급격히 줄어드는 경향이었으며, 강우는 별다른 영향이 없었다.

• 식물분류학회지
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• 제51권1호
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• pp.100-102
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• 2021

The chromosome number of myoga ginger (Zingiber mioga (Thunb.) Roscoe: Zingiberaceae) has been reported as 2n = 22 for Chinese plants and 2n = 55 for Japanese plants. We checked the chromosome number of Z. mioga in plants collected in Jeollabuk-do and Jeollanam-do, Korea, and counted 2n = 44, the first report of this number for the species. As the basic chromosome number of Z. mioga is thought to be x = 11, Z. mioga plants in China, Korea, and Japan appear to be diploids, tetraploids, and pentaploids, respectively. In finding the tetraploid race of Z. mioga in Korea, we can hypothesize that the pentaploid race in Japan is derived through the fertilization of reduced gametes of the diploid race and unreduced gametes of the tetraploid race.

• 대한수학회지
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• 제54권4호
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• 대한수학회지
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• 제56권1호
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• pp.67-80
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• 2019

For positive integers a, b, c, and an integer n, the number of integer solutions $(x,y,z){\in}{\mathbb{Z}}^3$ of $a{\frac{x(x-1)}{2}}+b{\frac{y(y-1)}{2}}+c{\frac{z(z-1)}{2}}=n$ is denoted by t(a, b, c; n). In this article, we prove some relations between t(a, b, c; n) and the numbers of representations of integers by some ternary quadratic forms. In particular, we prove various conjectures given by Z. H. Sun in [6].

• 대한수학회논문집
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• 제31권3호
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• pp.447-450
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• 2016

Let $F_n$ and $L_n$ be the nth Fibonacci number and Lucas number, respectively. The order of appearance of m in the Fibonacci sequence, denoted by z(m), is the smallest positive integer k such that m divides $F_k$. Marques obtained the formula of $z(L^k_n)$ in some cases. In this article, we obtain the formula of $z(L^k_n)$ for all $n,k{\geq}1$.

• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.115-124
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• 2000

For a finite group G, #Cent(G) denotes the number of cen-tralizers of its clements. A group G is called n-centralizer if #Cent( G) = n. and primitive n-centralizer if #Cent(G) = #Cent(${\frac}{G}{Z(G)$) = n. In this paper we compute the number of distinct centralizers of some finite groups and investigate the structure of finite groups with Qxactly SLX distinct centralizers. We prove that if G is a 6-centralizer group then ${\frac}{G}{Z(G)$${\cong}D_8$,$A_4$, $Z_2{\times}Z_2{\times}Z_2$ or $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.