• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.35-43
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• 2015

Let q > 1 be an odd integer and c be a fixed integer with (c, q) = 1. For each integer a with $1{\leq}a{\leq}q-1$, it is clear that the exists one and only one b with $0{\leq}b{\leq}q-1$ such that $ab{\equiv}c$ (mod q). Let N(c, q) denote the number of all solutions of the congruence equation $ab{\equiv}c$ (mod q) for $1{\leq}a$, $b{\leq}q-1$ in which a and $\bar{b}$ are of opposite parity, where $\bar{b}$ is defined by the congruence equation $b\bar{b}{\equiv}1$ (modq). The main purpose of this paper is using the mean value theorem of Dirichlet L-functions to study the mean value properties of a summation involving $(N(c,q)-\frac{1}{2}{\phi}(q))$ and Kloosterman sums, and give a sharper asymptotic formula for it.

• Childhood Kidney Diseases
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• v.16 no.1
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• pp.46-50
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• 2012

C1q nephropathy is a distinct clinicopathologic entity, characterized by mesangial immunoglobulin and complement deposits, predominantly C1q, with no evidence for systemic lupus erythematosus. Clinically it may present as nephrotic syndrome and non-nephrotic proteinuria per se or associated with microscopic hematuria, gross hematuria, hypertension, or renal insufficiency. So far there is only one report about a familial case of C1q nephropathy (in two sisters). We present two cases of familial C1q nephropathy with nephrotic syndrome which was steroid resistant, but partially remitted with cyclosporine.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.915-937
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• 2021

In this paper we deal with the open problem posed by Lü, Li and Yang [10]. In fact, we prove the following result: Let f(z) be a transcendental meromorphic function of finite order having finitely many poles, c₁, c₂, …, c_n ∈ ℂ\{0} and k, n ∈ ℕ. Suppose fⁿ(z), f(z+c₁)f(z+c₂) ⋯ f(z+c_n) share 0 CM and fⁿ(z)-Q₁(z), (f(z+c₁)f(z+c₂) ⋯ f(z+c_n))^(k) - Q₂(z) share (0, 1), where Q₁(z) and Q₂(z) are non-zero polynomials. If n ≥ k+1, then $(f(z+c_1)f(z+c_2)\;{\cdots}\;f(z+c_n))^{(k)}\;{\equiv}\;{\frac{Q_2(z)}{Q_1(z)}}f^n(z)$. Furthermore, if Q₁(z) ≡ Q₂(z), then $f(z)=c\;e^{\frac{\lambda}{n}z}$, where c, λ ∈ ℂ \ {0} such that e^{λ(c₁+c₂+⋯+c_n)} = 1 and λ^k = 1. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Journal of Korean Society of Forest Science
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• v.111 no.3
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• pp.365-373
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• 2022

We compared carbon stocks in tree biomass and soils of Quercus acutissima, Q. mongolica, Q. serrata, and Q. variabilis stands. A total of 531 plots (Q. acutissima: 110 plots, Q. mongolica: 177 plots, Q. serrata: 96 plots, Q. variabilis: 148 plots) were examined between 2016 and 2021 to determine the tree biomass and soil carbon stocks throughout the country. The carbon stocks of tree biomass were significantly higher in Q. mongolica (mean stand age, 57 years, 144.9 Mg C ha^-1) than in Q. variabilis (mean stand age, 43 years, 123.7 Mg C ha^-1), Q. serrata (mean stand age, 43 years, 120.1 Mg C ha^-1), and Q. acutissima (mean stand age, 36 years, 113.2 Mg C ha^-1) stands. The soil carbon concentration was significantly higher in Q. mongolica (A: 43.1 mg C g-1) than in Q. serrata (31.0 mg C g-1), Q. variabilis (25.31 mg C g-1), and Q. acutissima (24.4 mg C g-1) stands. The soil carbon stocks were significantly higher in Q. mongolica (116.8 Mg C ha^-1) than in Q. acutissima (49.3 Mg C ha^-1) stands. Total carbon stocks of tree biomass and soil were highest in Q. mongolica (262 Mg C ha^-1), followed by Q. serrata (218 Mg C ha^-1), Q. variabilis (211 Mg C ha^-1), and Q. acutissima (163 Mg C ha^-1) stands. Multiple linear regressions were performed to estimate the total carbon stocks of the four Quercus spp., and results showed that total carbon stocks increased with increasing elevation, mean diameter at breast height, and basal areas. Basal area and elevation of Quercus spp. stands were important explanatory variables based on multiple linear regressions for estimating carbon stocks.

• Geophysics and Geophysical Exploration
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• v.14 no.3
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• pp.249-253
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• 2011

Based on intrinsic and scattering quality factor ($Q_i^{-1}$ and$Q_s^{-1}$) obtained from the seismic data of the southeastern Korean Peninsula, the expected coda quality factor (${Q_{Cexp}}^{-1}$) was theoretically calculated using multiple scattering model, and was compared with other quality factors such as $Q_i^{-1}$, $Q_s^{-1}$, and observed $Q_C^{-1}$ obtained by single scattering model. While the ${Q_{Cexp}}^{-1}$ values are typically comparable to the $Q_i^{-1}$ values, the $Q_C^{-1}$ values are different from the ${Q_{Cexp}}^{-1}$ values except for the higher frequency. Future works require to consider depth-dependent attenuation.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.733-746
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• 2009

For any integer k $\geq$ 2, let P(c, k + 1;q) be the number of all k+1-tuples with positive integer coordinates ($a_1,a_2,...,a_{k+1}$) such that $1{\leq}a_i{\leq}q$, ($a_i,q$) = 1, $a_1a_2...a_{k+1}{\equiv}$ c (mod q) and 2 $\nmid$ ($a_1+a_2+...+a_{k+1}$), and E(c, k+1; q) = P(c, k+1;q) - $\frac{{\phi}^k(q)}{2}$. The main purpose of this paper is using the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of the r-th hyper-Kloosterman sums Kl(h,k+1,r;q) and E(c,k+1;q), and give an interesting mean value formula.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.235-249
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• 2020

Let Q and R be the well-known matrices associated with Fibonacci and Lucas numbers, and k, m, and n be any integers. It is mainly established all solutions of the matrix equations c₁Qⁿ + c₂Q^m = Q^k, c₁Qⁿ + c₂Q^m = RQ^k, and c₁Qⁿ + c₂RQ^m = Q^k with unknowns c₁, c₂ ∈ ℂ*. Moreover, using the obtained results, it is presented many identities, some of them are available in the literature, and the others are new, related to the Fibonacci and Lucas numbers.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.12B
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• pp.1444-1451
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• 2009

This paper first proposes diverse C determining models in the Q algorithm which is proposed in the EPCglobal C1 Gen 2 standard and then compares and analyzes its performance. EPCglobal C1 Gen 2 standard proposes the slot-count (Q) selection algorithm for multiple tag identification environment, but there is no such definition for the C value which modifies the Q value depending on collision or no reply. During the tag anti-collision process, the Q algorithm adds C to the Q when there is a collision and reduces the Q by C when there is no reply. The modified Q value updates new slot-counts for tags which determines the tag identification speed, so the C value is an important factor. However, many researches only intend to increase the tag identification speed by proposing a new method or modifying the Q algorithm without any research about the C value. This paper suggests diverse C models which satisfies the EPCglobal C1 Gen 2 and analyzes their performance in the multi tag identification environment. The result of this paper can be used as an index for future researches on EPCglobal C1 Gen 2 C models and multiple tag identification performance.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.493-511
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• 2009

Let $q\;{\geq}\;3$ be an odd integer and a be an integer coprime to q. Denote by N(a, q) the number of pairs of integers b, c with $bc\;{\equiv}\;a$ (mod q), $1\;{\leq}\;b$, $c\;{\leq}\;{\frac{q-1}{2}}$ and with b, c having different parity. The main purpose of this paper is to study the sum ${\sum}^{'q}_{a=1}\;\(N(a,\;q)\;-\;\frac{{\phi}(q)}{8}\)^2$ and obtain a sharp asymptotic formula.

• Bulletin of the Korean Mathematical Society
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• v.53 no.2
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• pp.411-421
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• 2016

In this paper, we investigate the problem of transcendental entire functions that share two values with one of their derivative. Let f be a transcendental entire function, n and k be two positive integers. If $f^n-Q_1$ and $(f^n)^{(k)}-Q_2$ share 0 CM, and $n{\geq}k+1$, then $(f^n)^{(k)}{\equiv}{\frac{Q_2}{Q_1}}f^n$. Furthermore, if $Q_1=Q_2$, then $f=ce^{\frac{\lambda}{n}z}$, where $Q_1$, $Q_2$ are polynomials with $Q_1Q_2{\not\equiv}0$, and c, ${\lambda}$ are non-zero constants such that ${\lambda}^k=1$. This result shows that the Conjecture given by W. $L{\ddot{u}}$, Q. Li and C. Yang [On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51 (2014), no. 5, 1281-1289.] is true. Also we exhibit some examples to show that the conditions of our result are the best possible.