• Honam Mathematical Journal
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• v.29 no.4
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• pp.543-554
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• 2007

In this paper, we prove the stability of a mixed type functional equation f( -x + y + z) + f(x - y + z) + f(x + y - z) = f(x - y) + f(y - z) + f(z - x) + f.(x) + f(y) + f(z).

• The Pure and Applied Mathematics
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• v.3 no.2
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• pp.103-111
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• 1996

Let $f(z)=z＋\alpha_2 z^2$＋…＋ \alpha_{n}z^n$＋… be regular and univalent in $\Delta$ = {z : │z│＜1}. In this paper, using the proper subordinate functions, we investigate the some relations between subordinations and conditions of functions belonging to subclasses of univalent functions.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.8C
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• pp.765-770
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• 2003

In this paper, the complete weight enumerator of the Delsarte-Goethals code over Z$_4$ is obtained. This code is divided into 3 cases and the complete weight enumerator of each case is calculated. During this weight enumeration, the blown distribution of exponential sums and binary weight distribution of the sub-codes are used. By combining this result and MacWilliams identity, the complete weight enumerator of the Goethals code over Z$_4$can be easily obtained. This result is also used for finding 3-designs from the Goethals and Delsarte-Goethals codes over Z$_4$.

• Bulletin of the Korean Chemical Society
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• v.23 no.10
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• pp.1435-1454
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• 2002

Bright yellow ${(Y_{1-x}Gd_x)}_{3-z}{(Al_{1-y}Ga_y)}_5O_{12}:Ce_z$ phosphors were synthesized. White LED was obtained by the combination of non-absorbed blue emission from a blue L ED itself and yellow emission from ${(Y_{1-x}Gd_x)}_{3-z}{(Al_{1-y}Ga_y)}_5O_{12}:Ce_z$ phosphors. The crystal structures and optical properties of ${(Y_{1-x}Gd_x)}_{3-z}{(Al_{1-y}Ga_y)}_5O_{12}:Ce_z$ phosphors were investigated.

• Journal of the Korea Fashion and Costume Design Association
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• v.22 no.3
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• pp.49-61
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• 2020

This study analyzed the social media accounts and performed a Big Data analysis of Z-generation fashion using Textom Text Mining Techniques program and Ucinet Big Data analysis program. The research results are as follows: First, as a result of keyword analysis on 67.646 Z-generation fashion social media posts over the last 5 years, 220,211 keywords were extracted. Among them, 67 major keywords were selected based on the frequency of co-occurrence being greater than more than 250 times. As the top keywords appearing over 1000 times, were the most influential as the number of nodes connected to 'Z generation' (29595 times) are overwhelmingly, and was followed by 'millennials'(18536 times), 'fashion'(17836 times), and 'generation'(13055 times), 'brand'(8325 times) and 'trend'(7310 times) Second, as a result of the analysis of Network Degree Centrality between the key keywords for the Z-generation, the number of nodes connected to the "Z-generation" (29595 times) is overwhelmingly large. Next, many 'millennial'(18536 times), 'fashion'(17836 times), 'generation'(13055 times), 'brand'(8325 times), 'trend'(7310 times), etc. appear. These texts are considered to be important factors in exploring the reaction of social media to the Z-generation. Third, through the analysis of CONCOR, text with the structural equivalence between major keywords for Gen Z fashion was rearranged and clustered. In addition, four clusters were derived by grouping through network semantic network visualization. Group 1 is 54 texts, 'Diverse Characteristics of Z-Generation Fashion Consumers', Group 2 is 7 Texts, 'Z-Generation's teenagers Fashion Powers', Group 3 is 8 Texts, 'Z-Generation's Celebrity Fashions' Interest and Fashion', Group 4 named 'Gucci', the most popular luxury fashion of the Z-generation as one text.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.935-951
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• 2020

The aim of the paper is to study some geometric properties of weakly Z-symmetric manifolds. Weakly Z-symmetric manifolds with Codazzi type and cyclic parallel Z tensor are studied. We consider Einstein weakly Z-symmetric manifolds and conformally flat weakly Z-symmetric manifolds. Next, it is shown that a totally umbilical hypersurface of a conformally flat weakly Z-symmetric manifolds is of quasi constant curvature. Also, decomposable weakly Z-symmetric manifolds are studied and some examples are constructed to support the existence of such manifolds.

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• Kyungpook Mathematical Journal
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• v.64 no.1
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• pp.57-68
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• 2024

Let V₃(z, f) and 𝜎⁽¹⁾₃(z, f) be the cubic polynomials representing, respectively, the 3rd de la Vallée Poussin mean and the 3rd Cesàro mean of order 1 of a power series f(z). If 𝒦 denotes the usual class of convex univalent functions in the open unit disk centered at the origin, we show that, in general, V₃(z, f) ⊀ 𝜎⁽¹⁾₃(z,f), for all f ∈ 𝒦. Making use of polylogarithms, we identify a transformation, Λ : 𝒦 → 𝒦, such that V₃(z, Λ(f)) ≺ 𝜎⁽¹⁾₃(z, Λ(f)) for all f ∈ 𝒦. Here '≺' stands for subordination between two analytic functions.

• Kyungpook Mathematical Journal
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• v.28 no.2
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• pp.129-139
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• 1988

Let $T^{\alpha}_{\lambda}$(p, A, B) denote the class of functions $$f(z)=z^p-{\sum\limits^{\infty}_{k=1}}{\mid}a_{p+k}{\mid}z^{p+k}$$ which are regular and p valent in the unit disc U = {z: |z| <1} and satisfying the condition $\left|{\frac{{e^{ia}}\{{\frac{f^{\prime}(z)}{z^{p-1}}-p}\}}{(A-B){\lambda}p{\cos}{\alpha}-Be^{i{\alpha}}\{\frac{f^{\prime}(z)}{z^{p-1}}-p\}}}\right|$<1, $z{\in}U$, where 0<${\lambda}{\leq}1$, $-\frac{\pi}{2}$<${\alpha}$<$\frac{\pi}{2}$, $-1{\leq}A$<$B{\leq}1$, 0<$B{\leq}1$ and $p{\in}N=\{1,2,3,{\cdots}\}$. In this paper, we obtain sharp results concerning coefficient estimates, distortion theorem and radius of convexity for the class $T^{\alpha}_{\lambda}$(p, A, B). It is further shown that the class $T^{\alpha}_{\lambda}$(p, A, B) is closed under "arithmetic mean" and "convex linear combinations". We also obtain class preserving integral operators of the form $F(z)=\frac{p+c}{z^c}{\int^z_0t^{c-1}}f(t)dt$, c>-p, for the class $T^{\alpha}_{\lambda}$(p, A, B). Conversely when $F(z){\in}T^{\alpha}_{\lambda}$(p, A, B), radius of p valence of f(z) has also determined.

• Proceedings of the KIPE Conference
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• 2007.11a
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• pp.90-93
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• 2007

본 연구에서는 전압품질에 민감한 설비를 위한 3상 하이브리드 Z-소스 동적 전압 보상기(Z-HDVR : Hybrid Z-Source Dynamic Voltage Restorer)을 제시하였다. 제안된 시스템은 수동필터와 Z-소스 토폴로지의 직렬형 능동필터로 구성된다. Z-HDVR의 ESS(Energy Storage System)로는 친환경적인 고분자 전해질 연료전지(PEMFC : Proton Exchange Membrane Fuel Cells)를 사용하였다. 고조파 검출 알고리즘은 동기좌표계의 $i_d-i_q$ 이론에 의하였으며, 부하전압 보상을 위하여 PI제어를 사용하였다. 전압swell 및 sag등 다양한 전원 조건하에서 제안된 시스템의 보상 성능을 검토하였다.