• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Kyungpook Mathematical Journal
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• v.53 no.1
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• pp.13-23
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• 2013

In this present work, the authors obtain Fekete-Szeg$\ddot{o}$ inequality for certain normalized analytic function $f(z)$ defined on the open unit disk for which $$\frac{{\lambda}{\beta}z^3(L(a,c)f(z))^{{\prime}{\prime}{\prime}}+(2{\lambda}{\beta}+{\lambda}-{\beta})z^2(L(a,c)f(z))^{{\prime}{\prime}}+z(L(a,c)f(z))^{{\prime}}}{{\lambda}{\beta}z^2(L(a,c)f(z))^{{\prime}{\prime}}+({\lambda}-{\beta})z(L(a,c)f(z))^{\prime}+(1-{\lambda}+{\beta})(L(a,c)f(z))}\;(0{\leq}{\beta}{\leq}{\lambda}{\leq}1)$$ lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Also certain applications of the main result for a class of functions defined by Hadamard product (or convolution) are given. As a special case of this result, Fekete-Szeg$\ddot{o}$ inequality for a class of functions defined through fractional derivatives are obtained.

• Proceedings of the KIEE Conference
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• 2004.11a
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• pp.209-211
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• 2004

In the Langmuir-Boldgett(LB) technique, a monolayer on the water surface is transferred on to a substrate, which is raised and dipped through the surface, and one can obtain multilayers in which constituent molecules periodically are arranged in layer. The LB technique has attracted considerable interest in the fabrication of electrical and electronic device, e.g.. Many researchers have investigated the electrical properties of monolayer and multiplayer films. Dendrimers represent a new class of synthetic macromolecules sharacterized by a regularly branched treelike structure. Multiple branching yields a large number of chain ends, which distinguishes dendrimers from conventional starlike polymers and microgels. Azobenzene dendrimer is one of the dendritic macromolecules that includes the azo-group which exhibits a photochromic character. Due to the presence of the charge transfer part, the azo-group, and having a rod-shaped structure, these compounds are expected to have the potential interest in electronics and ptoelectronics, especially in nonlinear optics. In the present paper, we give a pressure stimulation into organic thin films and detect the induced displacement current.

• The Journal of Korean Association of Computer Education
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• v.18 no.3
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• pp.1-14
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• 2015

The aim of this paper is to explore and understand the gifted student's characteristics such as NetLogo programming patterns, attitudes, his/her interest in problems solving. Based on transcripts and coding video frames, we explored the meaningful scenes to come up with thinking patterns, NetLogo programming patterns, attitudes, behaviors on tasks such as drawing regular starlike shapes. This case study contrasts with two other students revealing their unique characteristics both in computational thinking patterns and coding activities. The participant reveals his own ways of finding a clue and elaborating it further for coming up with concise NetLogo coding. This paper provides cross-case discussion and future research direction on how to improve gifted education in terms of problem solving in creative ways.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.135-145
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• 2022

This paper aims to investigate characterizations on parameters k₁, k₂, k₃, k₄, k₅, l₁, l₂, l₃, and l₄ to find relation between the class of 𝓗(k, l, m, n, o) hypergeometric functions defined by $$5_F_4\[{\array{k_1,\;k_2,\;k_3,\;k_4,\;k_5\\l_1,\;l_2,\;l_3,\;l_4}}\;:\;z\]=\sum\limits_{n=2}^{\infty}\frac{(k_1)_n(k_2)_n(k_3)_n(k_4)_n(k_5)_n}{(l_1)_n(l_2)_n(l_3)_n(l_4)_n(1)_n}z^n$$. We need to find k, l, m and n that lead to the necessary and sufficient condition for the function zF([W]), G = z(2 - F([W])) and $H_1[W]=z^2{\frac{d}{dz}}(ln(z)-h(z))$ to be in 𝓢^*(2^-r), r is a positive integer in the open unit disc 𝒟 = {z : |z| < 1, z ∈ ℂ} with $$h(z)=\sum\limits_{n=0}^{\infty}\frac{(k)_n(l)_n(m)_n(n)_n(1+\frac{k}{2})_n}{(\frac{k}{2})_n(1+k-l)_n(1+k-m)_n(1+k-n)_nn(1)_n}z^n$$ and $$[W]=\[{\array{k,\;1+{\frac{k}{2}},\;l,\;m,\;n\\{\frac{k}{2}},\;1+k-l,\;1+k-m,\;1+k-n}}\;:\;z\]$$.

• The Korean Journal of Soil Zoology
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• v.5 no.2
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• pp.101-112
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• 2000

Spiders usually have poor vision but not the jumping spiders. Their eight eyes are located on its distinctive box-shaped head and relatively well developed. The Spiders were fixated with 3% glutaraldehyde and thin section was performed with ultra-microtome. The specimens were observed with light microscopy, transmission and scanning electron microscopy. Eye area of jumping spider is competed of three rows. The first eye row comprise four eyes. Among them, two anterior median eyes are the largest and two anterior lateral eyes are relatively small. The former are main-eyes and have excellent vision. The second row, which has the two smallest eyes, is located about midway between the first and third rows. The third row is about half-way back on the thorax and eyed of which are middle size. To investigate ultrastructure of salticid spiders'eye, Menemerus fulvus was chosen. All of Menemerus fuvus's eyes are composed of cornea, lens, vitreous body and retina in histologically. Cornea layer, linked to exocuticle of exoskeleton. is regular layer structure without any cell tripe. Lenses are biconvex type. Retinas comprise well developed microvilli-shape rhabdomeres, unpigmented supporting cells, and pigmented cell. Retinas of anterior median eyes are surrounded by circular cylinder-shaped vitreous body, photoreceptor, i.e. rhabdomeres, of it is irregularly arranged compared to the other eyes.