• Honam Mathematical Journal
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• v.41 no.3
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• pp.581-593
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• 2019

The notions of (${\in}$, ${\in}{\vee}q$)-permeable S-value and (${\in}$, ${\in}{\vee}q$)-permeable I-value are introduced, and related properties are investigated. Relations among (${\in}$, ${\in}{\vee}q$)-fuzzy subalgebra, (${\in}$, ${\in}{\vee}q$)-fuzzy ideal, (strong) lower and (strong) upper level sets, (${\in}$, ${\in}{\vee}q$)-permeable S-value, (${\in}$, ${\in}{\vee}q$)-permeable I-value, S-energetic set, I-energetic set, right stable set and right vanished set are discussed.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.29-38
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• 2016

For a transcendental entire function f(z) with zero order, the purpose of this article is to study the value distributions of q-difference polynomial $f(qz)-a(f(z))^n$ and $f(q_1z)f(q_2z){\cdots}f(q_mz)-a(f(z))^n$. The property of entire solution of a certain q-difference equation is also considered.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.571-590
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• 2015

Let a, b, q be integers with q > 0. The homogeneous Dedekind sum is dened by $$\Large S(a,b,q)={\sum_{r=1}^{q}}\(\({\frac{ar}{q}}\)\)\(\({\frac{br}{q}}\)\)$$, where $$\Large ((x))=\{x-[x]-{\frac{1}{2}},\text{ if x is not an integer},\\0,\hspace{75}\text{ if x is an integer.}$$ In this paper we study the mean value of S(a, b, q) by using mean value theorems of Dirichlet L-functions, and give some asymptotic formula.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1157-1171
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• 2013

In this paper, by using the $q$-difference analogue of lemma on the logarithmic derivative lemma to re-establish some estimates of Nevanlinna characteristics of $f(qz)$, we deal with the value distribution and uniqueness of certain types of $q$-difference polynomials.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.1
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• pp.9-16
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• 2014

Let $\mathbb{A}=\mathbb{F}_q[T]$ be a polynomial ring over $\mathbb{F}_q$. In this paper we determine an asymptotic mean value of quadratic Dirich-let L-functions L(s, ${\chi}_{{\gamma}D}$) at the central point s=$\frac{1}{2}$, where D runs over all monic square-free polynomials of even degree in $\mathbb{A}$ and ${\gamma}$ is a generator of $\mathbb{F}_q^*$.

• Journal of the Korean earth science society
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• v.28 no.6
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• pp.720-732
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• 2007

For the Seoul metropolitan area and the eastern Kyeongsang Basin, we simultaneously calculated $Q_P^{-1}$ and $Q_S^{-1}$ by applying the extended coda-normalization method for 98 seismograms of local Earthquakes. As frequency increases from 1.5 Hz to 24 Hz, the result decreased from $(4.0{\pm}9.2){\times}10^{-3}$ to $(4.1{\pm}4.2){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.5{\pm}5.6){\times}10^{-3}$ to $(3.4{\pm}1.3){\times}10^{-4}$ for $Q_S^{-1}$ in Seoul Metropolitan Area. The result of eastern Kyeongsang basin also decreased from $(5.4{\pm}8.8){\times}10^{-3}$ to $(3.7{\pm}3.4){\times}10^{-4}$ for $Q_P^{-1}$ and $(5.7{\pm}4.2){\times}10^{-3}$ to $(3.5{\pm}1.6){\times}10^{-4}$ for $Q_S^{-1}$. If we fit a frequency-dependent power law to the data, the best fits of $Q_P^{-1}$ and $Q_S^{-1}$ are $0.005f^{-0.89}$ and $0.004f^{-0.88}$ in Seoul metropolitan Area, respectively. The value of $Q_P^{-1}$ and $Q_S^{-1}$ in the eastern Kyeongsang basin are $0.007f^{-1.02}$ and $0.006f^{-0.99}$, respectively. The $Q_S^{-1}$ value of the eastern Kyeongsang basin is almost similar to Seoul metropolitan area. But the $Q_P^{-1}$ value of the eastern Kyeongsang basin is a little higher than that of Seoul metropolitan area. This may be that the crustal characteristics of the eastern Kyeongsang basin is seismologically more heterogeneous. However, these $Q_P^{-1}$ values in Korea belong to the range of seismically stable regions all over the world.

• Korean Journal of Food Science and Technology
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• v.37 no.4
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• pp.597-602
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• 2005

Quality factors of emulsified ginseng drink were determined during storage at various temperatures, and its shelf-life was predicted based on changes in emulsion stability, acidify, viscosity, and yellowness. Viscosity was highly dependent on storage temperature. Emulsion stability changed rapidly during early storage period (1st step), then slowly thereafter (2nd step). $Q_{10}$ values of emulsion stability were 2.50 and 1.38 for 1st and 2nd steps, respectively. Viscosity, acidity, and yellowness showed $Q_{10}$ values of 3.45, 1.77, and 1.99, respectively. Although $Q_{10}$ value of 2 has been generally used to predict shelf stability of food materials, our results suggest adopting same $Q_{10}$ value to predict shelf stability of emulsified ginseng drink is not appropriate.

• Geomechanics and Engineering
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• v.30 no.5
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• pp.449-460
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• 2022

Safe underground construction in a rock mass requires adequate ground investigation and effective determination of rock conditions. The estimation of rock mass behavior is difficult, because rock masses are innately anisotropic and heterogeneous at different scales and are affected by various environmental factors. Quantitative rock mass classification systems, such as the Q-system and rock mass rating, are widely used for characterization and engineering design. The measurement of rock classification parameters is subjective and can vary among observers, resulting in questionable accuracy. Geophysical investigation methods, such as seismic surveys, have also been used for ground characterization. Torsional shear wave propagation characteristics in cylindrical rods are equal to that in an infinite media. A probabilistic quantitative relationship between the Q-value and shear wave velocity is thus investigated considering long-wavelength wave propagation in equivalent continuum jointed rock masses. Individual Q-system parameters are correlated with stress-dependent shear wave velocities in jointed rocks using experimental and numerical methods. The relationship between the Q-value and the shear wave velocity is normalized using a defined reference condition. This relationship is further improved using probabilistic analysis to remove unrealistic data and to suggest a range of Q-values for a given wave velocity. The proposed probabilistic Q-value estimation is then compared with field measurements and cross-hole seismic test data to verify its applicability.