• Journal of the Korean Institute of Navigation
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• v.16 no.1
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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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• v.45 no.3
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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

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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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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• v.23 no.2
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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.

• Korean journal of applied entomology
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• v.45 no.2 s.143
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• pp.161-167
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• 2006

The citrus leafminer (CLM), Phyllocnistis citrella Stainton, is an oligophagous pest of Rutaceae family, especially Citrus spp. occurring in most worldwide citrus-growing areas. This study was conducted to evaluate a sex pheromone chemical of CLM, (Z,Z)-7,11-hexadecadienal (7Z,11Z-16:Al) in monitoring CLM by trap types, the diel activity and the influence of some weather factors on trap catch. CLM was well attracted on a trap baited 7Z,11Z-16:Al 1mg. Sticky wing trap was more effective than bucket trap. Most caught CLM were attracted at 2$\sim$6 a.m. regardless of season, and activity time of CLM was affected by sunrise time as well as sunset time. The trap catch of CLM was more influenced by wind velocity than temperature for activity time of CLM. The number of caught CLM was fallen at below 13$^{\circ}C$, but there was little effect for trap catch at over that temperature. The average wind velocity at over 2.0 m/sec made the number of caught CLM drop down. The precipitation did not affect the number of caught CLM when the average wind velocity was lower than at 2.0 m/sec.

• Korean Journal of Plant Taxonomy
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• v.51 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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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.

• Journal of the Korean Mathematical Society
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• v.56 no.1
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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].

• Communications of the Korean Mathematical Society
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• v.31 no.3
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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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• v.7 no.1
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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 $Z_2{\times}Z_2{\times}Z_2{\times}Z_2$.