• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.55-64
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• 2017

For -2 < ${\alpha}$ < ${\infty}$ and 0 < p < ${\infty}$, the $\mathcal{Q}_K$-type space is the space of all analytic functions on the open unit disk ${\mathbb{D}}$ satisfying $$_{{\sup} \atop a{\in}{\mathbb{D}}}{\large \int_{\mathbb{D}}}{{\mid}f^{\prime}(z){\mid}}^p(1-{{\mid}z{\mid}^2})^{\alpha}K(g(z,a))dA(z)<{\infty}$$, where $g(z,a)=log\frac{1}{{\mid}{\sigma}_a(z){\mid}}$ is the Green's function on ${\mathbb{D}}$ and K : [0, ${\infty}$) [0, ${\infty}$), is a right-continuous and non-decreasing function. For 0 < s < ${\infty}$, the space $\mathcal{Q}_s$ consists of all analytic functions on ${\mathbb{D}}$ for which $$_{sup \atop a{\in}{\mathbb{D}}}{\large \int_{\mathbb{D}}}{{\mid}f^{\prime}(z){\mid}}^2(g(z,a))^sdA(z)<{\infty}$$. Boundedness and compactness of composition operators $C_{\varphi}$ acting on $\mathcal{Q}_K$-type spaces and $\mathcal{Q}_s$ spaces is characterized in terms of the norms of ${\varphi}^n$. Thus the author announces a solution to the problem raised by Wulan, Zheng and Zhou.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1441-1462
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• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.757-771
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• 2010

We study Gauss sums on ${\mathbb{F}}_q[T]$ and get some functional equations for L-functions.

• The Plant Pathology Journal
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• v.34 no.3
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• pp.163-170
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• 2018

Strawberry Fusarium wilt disease, caused by Fusarium oxysporum f. sp. fragariae, is the most devastating disease in strawberry production. The pathogen produces chlamydospores which tolerate against harsh environment, fungicide and survive for decades in soil. Development of detection and quantification techniques are regarded significantly in many soilborne pathogens to prevent damage from diseases. In this study, we improved specific-quantitative primers for F. oxysporum f. sp. fragariae to reveal correlation between the pathogen density and the disease severity. Standard curve $r^2$ value of the specific-quantitative primers for qRT-PCR and meting curve were over 0.99 and $80.5^{\circ}C$, respectively. Over pathogen $10^5cfu/g$ of soil was required to cause the disease in both lab and field conditions. With the minimum density to develop the wilt disease, the pathogen affected near 60% in nursery plantation. A biological control microbe agent and soil solarization reduced the pathogen population 2-fold and 1.5-fold in soil, respectively. The developed F. oxysporum f. sp. fragariae specific qRT-PCR protocol may contribute to evaluating soil healthiness and appropriate decision making to control the disease.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.23 no.2
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• pp.49-67
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• 2020

This study was conducted to compare and analyze forest vegetation distributed in Geumosanseong-inside in Geumosan Provincial Park from 2017.10 to 2019.6. The vegetation structure was classified by the phytosociological method and TWINSPAN and the correlation between the community structure and the environmental factors was analyzed using DCCA ordination analydsis. The vegetation structures are Quercus mongolica, Fraxinus mandshurica, Q. acutissima, Larix leptolepis, Prunus padus and Morus alba community by the phytosociological method and 16 communities under TWINSPAN. The importance value of Q. mongolica(64.5) was the highest, and followed by F. mandshurica, L. leptolepis, Acer pseudosieboldianum, M. alba, P. padus, Q. acutissima, Sorbus alnifolia, P. serrulata var. pubescens, F. sieboldiana, Rhododendron schlippenbachii and Castanea crenata which is consistent with species having the dominance status by analysis of the vegetation structure. As the results of DBH analysis for taxon with high importance values, Q. mongolica and M. alba represented normal distribution, and thus, the dominance status of these species is likely to continue. L. leptolepis will maintain the dominance status due to high density of large individuals as compared with species above medium size. However, it will decrease because of high mortality after increase in age class. F. mandshurica and P. padus continue to show dominance status due to high density of young individuals as compared with species above medium size. Q. acutissima have high density of individuals above intermediate size and low density of young individuals, and thus, will maintain the dominance status. A. pseudosieboldianum, F. sieboldiana and R.schlippenbachii which are arborescent will present continuously high dominance status because of high density of young individuals. Soil analysis shows that whereas pH, Ca²⁺ and Mg²⁺ in the research area were lower than the average values of overall forest soil and O.M, T-N, C.E.C and P₂O₅ were higher. We expected that these results were due to agricultures until 50 years ago in Geumosanseong-inside. As a result of DCCA ordination analysis using eleven environmental factors and communities classified by the phytosociological method analysis showed that Q. mongolica was distributed in the environment with higher elevation and O.M and steep slope, and lower P₂O₅, Mg²⁺ and Ca²⁺. In contrast to F. mandshurica, Q. acutissima was distributed in higher K⁺ and lower pH. L. leptolepsis was distributed in various environment.

• 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).

• The Mathematical Education
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• v.12 no.2
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• pp.5-12
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• 1974

단위원을 가지는 하환환에 있어서의 Prime Spectrum에 관하여 다음 세가지 사실을 증명하였다. 1. X를 환 R의 prime spectrum, C(X)를 X에서 정의되는 실연적함수의 환, X를 C(X)의 maximal spectrum이라 하면 X는 C(X)의 prime spectrum의 부분공간으로서의 한 T-space로 된다. N을 환 R의 nilradical이라 하면, R/N이 regula 이면 X와 X는 위상동형이다. 2. f: R$\longrightarrow$R'을 ring homomorphism, P를 R의 한 Prime ideal, $R_{p}$, R'$_{p}$를 각각 S=R-P 및 f(S)에 관한 분수환(ring of fraction)이라 하고, k(P)를 local ring $R_{p}$의 residue' field라 할 때, R'의 prime spectrum의 부분공간인 $f^{*-1}$(P)는 k(P)(equation omitted)$_{R}$R'의 prime spectrum과 위상동형이다. 단 f*는 f*(Q)=$f^{-1}$(Q)로서 정의되는 함수 s*:Spec(R')$\longrightarrow$Spec(R)이다. 3. X를 환 S의 prime spectrum, N을 R의 nilradical이라 할 때, 다음 네가지 사실은 동치이다. (1) R/N 은 regular 이다. (2) X는 Zarski topology에 관하여 Hausdorff 공간이다. (3) X에서의 Zarski topology와 constructible topology와는 일치한다. (4) R의 임의의 원소 f에 대하여 f를 포함하지 않는 R의 prime ideal 전체의 집합 $X_{f}$는 Zarski topology에 관하여 개집합인 동시에 폐집합이다.폐집합이다....

• Journal of the Microelectronics and Packaging Society
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• v.10 no.2
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• pp.13-17
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• 2003

In this study, new LTCC materials of $ZnWO_4$-LiF system were developed for the application to RF Module fabrication. Pure $ZnWO_4$ must be sintered above $1050^{\circ}C$ in order to obtain up to 98% of full density. The measured dielectric constant ($\epsilon_r$)quality factor ($Q{\times}f0$), and temperature coefficient of resonant frequency ($\tau_f$ were 15.5, 74000 GHz, and $-70ppm^{\circ}C$, respectively. LiF addition resulted in a liquid phase formation at 81$0^{\circ}C$ due to interaction between ZnWO$_4$ and LiF. Therefore, ZnWO$_4$ with 0.5∼1.5 wt% LiF could be densified at $850^{\circ}C$. In the given LiF addition range, the sintering shrinkage increased with increasing LiF content. Addition of LiF slightly lowered the dielectric constant from 15.5 to 14.2∼15 due to lower dielectric constant of LiF. Qxfo value decreased with increasing LiF content. This can be explained in terms of the interaction between LiF and $ZnWO_4$, and inhomogeneity of grain structure.

• Proceedings of the Korean Geotechical Society Conference
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• 2005.03a
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• pp.1159-1166
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• 2005

In the present study, a series of laboratory tests with sands of different silt contents, are conducted and methods to assess non-linear behaviors based on in-situ test results are proposed. Modified hyperbolic stress-strain model is used to analyze non-linearity of silty sands in terms of non-linear degradation parameters f and g as a function of silt contents and relative density $D_R$. Stress-strain relationship results were obtained from a series of triaxial tests on sands containing different amounts of silt. Initial shear modulus which was applied to normalize modulus degradation of silty sands were determined based on the resonant column test results. From the laboratory test results, it was observed that, as the relative density increases, values of f decrease and those of g increase. Cone resistance $q_c$ for silty soil condition used in the triaxial tests were estimated based on the cavity expansion analysis. A suggestion to make an estimation of degradation parameters f and g as a function of fine contents is addressed in terms of cone resistance $q_c$ .

• Honam Mathematical Journal
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• v.34 no.3
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• pp.327-340
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• 2012

Gottlieb polynomials were introduced and investigated in 1938, and then have been cited in several articles. Very recently Khan and Akhlaq introduced and investigated Gottlieb polynomials in two and three variables to give their generating functions. Subsequently, Khan and Asif investigated the generating functions for the $q$-analogue of Gottlieb polynomials. Very recently, Choi defined a $q$-extension of the generalized two variable Gottlieb polynomials ${\varphi}^2_n({\cdot})$ and presented their several generating functions. Also, by modifying Khan and Akhlaq's method, Choi presented a generalization of the Gottlieb polynomials in m variables to give two generating functions of the generalized Gottlieb polynomials ${\varphi}^m_n({\cdot})$. Here, in the sequel of the above results for their possible general $q$-extensions in several variables, again, we aim at trying to define a $q$-extension of the generalized three variable Gottlieb polynomials ${\varphi}^3_n({\cdot})$ and present their several generating functions.