• Journal of the Korean Institute of Landscape Architecture
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• v.35 no.5
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• pp.46-55
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• 2007

This study was carried out to analyze both the root structure and the fine root phytomass of the vertical and horizontal distribution of Zelkova serrata Makino. which was transplanted in the reclaimed land from the sea in Gwangyang, Jeonnam, South Korea. The base ground was reclaimed land from the sea. $Z_1$ of the planting ground was filled to a $100{\sim}150cm$ thickness with the improved soil instead of the reclaimed soil from the sea, $Z_2$ of the planting ground was covered to a $20{\sim}30cm$ thickness with the improved soil and $Z_3$ of the planting ground was mounded to 120cm thickness with the improved soil on the reclaimed land from the sea. In addition, $Z_4,\;Z_5\;and\;Z_6$ of the planting grounds were at the large-sized mound on the reclaimed land from the sea. $Z_4$ of the planting ground was located at the lowest level, $Z_5$ planting ground was located at the slope and $Z_6$ planting ground was located at the top of the large-sized mound. The large-sized mounds contain 3 layers, the base layer was reclaimed land from the sea and the second layer was mounded to a $200{\sim}300cm$ thickness with the desalinized soil from the sea on the base layers and the finally layers were mounded to a $80{\sim}120cm$ thickness with improved soil on the second layer. The planting grounds $Z_3,\;Z_4,\;Z_5\;and\;Z_6$ developed roots such as tap roots, lateral roots and heart roots. However, in $Z_1\;and\;Z_2$ roots development were inhibited. The fine-root phytomass of the 6 planting ground types was as follows: $113.5g\;DM/m^2$ for $Z_5$, $105.5g\;DM/m^2$ for $Z_4$, $88.3g\;DM/m^2$ for $Z_3$, $81.0g\;DM/m^2$ for $Z_6$, $73.0g\;DM/m^2$ for $Z_2$, $43.3g\;DM/m^2$ for $Z_1$. The vertical distribution of the fine root phytomass decreased from the upper to the deeper soil profiles in the 6 mound types. The fine root phytomass was $43.3{\sim}71.8%$ in a $0{\sim}20cm$ thickness of soil layer and it decreased according to the distance from the nearest trees. The root growth in the improved soil was better than in the reclaimed soil from the sea. However, root growth decreased more in the disturbed soils even though the planting grounds contained the improved soils. The retarded development of roots and the spatial distribution patterns of the fine root phytomass were closely connected to the reclaimed soil from the sea. In the disturbed soil, the soil hardness and alkalic cation($Na^+,\;K^+,\;Ca^{2+},\;Mg^{2+}$). were high and the soil water was lacking. We suggest that the construction of planting grounds and the improvement of bad soil are necessary for the proper and effective growth of landscaping plants.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.687-696
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• 2013

In this note, we completely characterize the reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on $A^2_{\alpha}(D^2)$ where ${\alpha}$ > -1 and N, M are positive integers with $N{\neq}M$, and show that the minimal reducing subspaces of $T_{{z^N_1}{z^M_2}}$ on the unweighted Bergman space and on the weighted Bergman space are different.

• Journal of Plant Biotechnology
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• v.30 no.1
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• pp.59-63
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• 2003

This experiment was conducted to propagate Zantedeschia spp. in vitro. The frequency of adventitious bud clusters (ABC) formation from shoot tips in Z. 'Best Gold' was high at more than 65% on media with 2.0∼5.0 mg/L BA or 0.1∼1.0 mg/L thidiazuron. The highest formation rate of ABC (75%) was obtained on medium containing 2.0 mg/L BA. Comparing to treatment of BA alone, combined one of BA and NAA did not stimulate the formation of ABC and the shoot regeneration from shoot tips. The proliferation of ABC from sections (0.7∼1.0 cm) of ABC occurred effective on medium with 2.0 mg/L BA. Shoots developed from the sections (0.7∼1.0 cm) of ABC grew and rooted favorably on media containing 1.0∼2,0 mg/L IBA. The shoots were multiplicated effectively on medium with 0.5 mg/L thidiazuron in Z. 'Childsiana', on medium with 3.0 mg/L BA in 2. 'Golden Affair', and on medium with 5.0∼10.0 mg/L BA in Z. 'Pacific Pink'.

• Journal of the Korean Mathematical Society
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• v.38 no.3
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• pp.595-611
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• 2001

Let Q(n,1) be the set of even unimodular positive definite integral quadratic forms in n-variables. Then n is divisible by 8. For A[X] in Q(n,1), the theta series $\theta$(sub)A(z) = ∑(sub)X∈Z(sup)n e(sup)$\pi$izA[X] (Z∈h (※Equations, See Full-text) the complex upper half plane) is a modular form of weight n/2 for the congruence group Γ$_1$(8) = {$\delta$∈SL$_2$(Z)│$\delta$≡()mod 8} (※Equation, See Full-text). If n$\geq$24 and A[X], B{X} are tow quadratic forms in Q(n,1), the quotient $\theta$(sub)A(z)/$\theta$(sub)B(z) is a modular function for Γ$_1$(8). Since we identify the field of modular functions for Γ$_1$(8) with the function field K(X$_1$(8)) of the modular curve X$_1$(8) = Γ$_1$(8)＼h(sup)* (h(sup)* the extended plane of h) with genus 0, we can express it as a rational function of j(sub) 1,8 over C which is a field generator of K(X$_1$(8)) and defined by j(sub)1,8(z) = $\theta$$_3$(2z)/$\theta$$_3$(4z). Here, $\theta$$_3$ is the classical Jacobi theta series.

• 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.

• Journal of Digital Contents Society
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• v.15 no.2
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• pp.167-172
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• 2014

As there are few documents about how to design and implement a sensor network with Z-Stack, developers can get information from developer's community on Internet. That takes longer time to develop the network. This paper presents how to design and implement a range measuring sensor network with Z-Stack's Generic application and ultrasonic sensors based on CC2530, and then show experimental results through the implemented network. This work will make less time for a developer to implement a sensor network with Z-Stack.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.439-449
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• 2014

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• Bulletin of the Korean Mathematical Society
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• v.49 no.2
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• pp.395-409
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• 2012

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let ${\pi}$ be a group and let M ${\rightarrow}$ N be a homomorphism between projective $\mathbb{Z}[{\pi}]$-modules such that $\mathbb{Z}_p\;{\otimes}_{\mathbb{Z}[{\pi}]}M{\rightarrow}\mathbb{Z}_p{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ is injective; for which other right $\mathbb{Z}[{\pi}]$-modules V is the induced map $V{\otimes}_{\mathbb{Z}[{\pi}]}\;M{\rightarrow}\;V{\otimes}_{\mathbb{Z}[{\pi}]}\;N$ also injective? Our main theorem gives a new criterion which combines and generalizes many previous results.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.689-707
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• 2017

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f(z) holomorphic in the unit disc and f(0) = 0, f'(0) = 1 such that ${\Re}f^{\prime}(z)$ > ${\frac{1-{\alpha}}{2}}$, -1 < ${\alpha}$ < 1, we estimate a modulus of the second non-tangential derivative of f(z) function at the boundary point $z_0$ with ${\Re}f^{\prime}(z_0)={\frac{1-{\alpha}}{2}}$, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ${\mid}f^{{\prime}{\prime}}(z_0){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these inequalities is also proved.

• Nonlinear Functional Analysis and Applications
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• v.26 no.2
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• pp.373-380
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• 2021

If $p(z)={\sum\limits_{{\nu}=0}^{n}}a_{\nu}z^{\nu}$ is a polynomial of degree n having all its zeros on |z| = k, k ≤ 1, then Govil [3] proved that $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{n}{k^n+k^{n-1}}}\;{\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. In this paper, by involving certain coefficients of p(z), we not only improve the above inequality but also improve a result proved by Dewan and Mir [2].