• Journal of the Chungcheong Mathematical Society
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• v.35 no.3
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• pp.227-234
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• 2022

Let 𝔽_q be a finite field with odd q elements. In this article, we prove that if E ⊆ 𝔽^d_q, d ≥ 2, and |E| ≥ q, then there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d such that for all y ∈ Y, the number of distances between the point y and the set E is ~ q. As a corollary, we obtain that for each set E ⊆ 𝔽^d_q with |E| ≥ q, there exists a set Y ⊆ 𝔽^d_q with |Y| ~ q^d so that any set E ∪ {y} with y ∈ Y determines a positive proportion of all possible distances. The averaging argument and the pigeonhole principle play a crucial role in proving our results.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Journal of Ecology and Environment
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• v.41 no.3
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• pp.66-71
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• 2017

Background: The sprouts of oak species play an important role in maintaining the oak community in a disturbed environment. In this study, we cut 1-year-old oak in three times during the 3 years and measured the sprout responses to know sprouting ability of six deciduous oaks in Korea. Results: Oak sprouts have appeared in spring and fall, and some of the sprouts had lifespan as short as a month. As the number of cutting increases, sprout number of Quercus acutissima increased whereas the other oak species decreased or died. The average number of sprouts over the 3 years was from 1.4 (Quercus mongolica) to 2.2 (Q. acutissima) per individual. Quercus serrata died after the second cutting, and Quercus dentata died after the third cutting. So, the two species have the lowest sprouting ability among six oak species. The sprouts grew actively during fall and slowly in summer. The sprout length during the 3 years was in the following descending order: Q. acutissima, Quercus aliena, Q. dentata, and Q. mongolica. Sprout of Q. acutissima and Q. aliena generated steadily over the 3 years, and sprout of Quercus variabilis and Q. mongolica was changed by year. After the 3 years, the number of sprouts increased only in Q. acutissima but sprout number of the other five oak species decreased. The sprout length of Q. acutissima, Q. aliena, and Q. variabilis increased, but sprout length of the other three oak species decreased. The average survival rate of saplings over the 3 years was in the following descending order: Q. acutissima, Q. aliena, Q. variabilis, and Q. mongolica. Conclusions: As a result, the sprouting ability of Q. acutissima was the highest. Such level of sprouting ability may be the evidence of how Q. acutissima community exists as a dominant species in a disturbed environment in lowlands of Korea peninsula.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.37-42
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• 2005

We analyzed spectral attenuation of coda waves and estimated coda Q values in the crust of the Korean peninsula. 574 NS-component seismograms registered by the Korea Meteorological Administration (KMA) and Korea Institute of Geology, Mining and Materials (KIGAM) seismic networks with epicentral distances less than 100 km and sampling rate greater than 80 Hz were selected for this study. We estimated coda Q values using the single isotropic scattering model at center frequencies of 1.5, 3, 6, 9, 12, 15, and 18 Hz with 20 s time window starting from double of the S-wave arrival times. Estimated coda Q value at 1 Hz ($Q_0$) and n value range 50 to 250 and 0.5 to 1.0, respectively, and they are well correlated with the regional geology in the Korean peninsula. The $Q_0$ values in western Korea agree well with those of eastern China.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1483-1504
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• 2017

We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

• Korean Journal of Environmental Biology
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• v.27 no.1
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• pp.82-87
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• 2009

In order to characterize the ecological traits of Quercus acutissima, Q. variabilis and Q. mongolica, which dominated in Korean mountain, we treated the sapling of the three oak species under the major environment factors (light, soil moisture and nutrient) with four gradient levels, for 8 months in glass house. Then we measured and analyzed the growth difference among them. The growth of Q. acutissima and Q. variabilis were increased with higher light intensity, but there is no apparent trend in Q. mongolica for light gradients. Q. mongolica did not show high reduction of growth, even in the lowest light intensity. Q. variabilis and Q. mongolica had a constant growth state to soil moisture treatment, but only Q. acutissima grew well in higher soil moisture gradient condition. All the growth of three oak species decreased with higher nutrient gradient condition. The growth reduction was increased in order of Q. variabilis, Q. mongolica and Q. acutissima. with increased nutrient gradient level. These results means that Q. mongolica, Q. acutissima and Q. variabilis have adaptation ability to shade, high moisture and low nutrient condition, respectively.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.221-236
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• 2002

Using the p-adic q-integral due to T. Kim[4], we define a number B＊$_{n}$(q) and a polynomial B＊$_{n}$(q) which are p-adic q-analogue of the ordinary Bernoulli number and Bernoulli polynomial, respectively. We investigate some properties of these. Also, we give slightly different construction of Tsumura＇s p-adic function $\ell$$_{p}$(u, s, $\chi$) [14] using the p-adic q-integral in [4].n [4].

• 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.

• Journal of applied mathematics & informatics
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• v.30 no.1_2
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• pp.321-325
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• 2012

In this paper, we consider twisted $q$-Euler polynomials and define a $p$-adic $q$-transfer operator (see [6]). From this operator, we investigate the eigenvalues of the $p$-adic $q$-transfer operator on the space of twisted $q$-Euler polynomials.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.555-565
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• 2018

The main subject of this paper is to introduce the (p, q)-Euler polynomials and obtain several interesting symmetric properties of the modified (p, q)-Hurwitz Euler Zeta function with regard to (p, q) Euler polynomials. In order to get symmetric properties, we introduce the new (p, q)-analogue of Euler polynomials $E_{n,p,q}(x)$ and numbers $E_{n,p,q}$.