• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1341-1360
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• 2008

In this paper we investigate the projections of bouquet graph B with two cycles. A projection of B is said to be trivial if only trivial embeddings are obtained from the projection. It is shown that, to cover all nontrivial projections of B, at least three embeddings of B are needed. We also show that a nontrivial projection of B is covered by one of some two embeddings if the image of each cycle has at most one self-crossing.

• Journal of the Chungcheong Mathematical Society
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• v.12 no.1
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• pp.1-13
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• 1999

The purpose of this paper is to show that if the Fatou set F(f) of a CF-meromorphic function f has two completely invariant components, then they are the only components of F(f) and that the Julia set of the entire transcendental function $E_{\lambda}(z)={\lambda}e^z$ for 0 < ${\lambda}$ < $\frac{1}{e}$ contains a Cantor bouquet by employing the Devaney and Tangerman's theorem[10].

• Proceedings of the Korea Database Society Conference
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• 2000.11a
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• pp.116-118
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• 2000

본 논문은 만델브로트 집합의 쌍곡성분과 0＜λ＜1/e에서 초월 정함수 $E_{λ}$(z)의 Julia집합의 성질에 대한 연구이다. 만델브로트 집합의 쌍곡성분은 $P_{c}$ $^{n}$ (0)의 영점을 항상 포함하고 있고 역으로 $P_{c}$ $^{n}$ (0)의 각각의 영점은 만델브로트 집합의 한 쌍곡성분에 포함된다. 그리고 $E_{λ}$(z)의 Julia 집합이 Cantor bouquet를 포함하고 있다는 사실을 Devaney 와 Tangerman의 결과를 이용하여 설명하였다.여 설명하였다.하였다.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.225-234
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• 1998

We compute genus distributions for bouquets of dipoles by using the method concerning the cycle structure of permutations in the symmetric group. From this, we can deduce that every bouquet of dipoles is upper embeddable. We find a foumula for computing the embedding polynomials for bouquets of dipoles.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.215-225
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• 2016

We consider a sufficient condition for w(z), analytic in ${\mid}z{\mid}$ < 1, to be bounded in ${\mid}z{\mid}$ < 1, where $w(0)=w^{\prime}(0)=0$. We apply it to the meromorphic starlike functions. Also, a certain Briot-Bouquet differential subordination is considered. Moreover, we prove that if $p(z)+zp^{\prime}(z){\phi}(p(z)){\prec}h(z)$, then $p(z){\prec}h(z)$, where $h(z)=[(1+z)(1-z)]^{\alpha}$, under some additional assumptions on ${\phi}(z)$.

• FLOWER RESEARCH JOURNAL
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• v.18 no.4
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• pp.308-314
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• 2010

Importance of color in floral design has been emphasized for long time, but it is difficult to find out standardization of color for floral design and for educational system. Wedding bouquet is major and important part of floral design and it shows same problem. The research is concentrated on color image analysis of wedding bouquet designs which have been submitted for 'Interflora World Cup Competition' with the intention to utilize the study result as the basic information of floral design. Colors of wedding bouquets from 20 different countries were analyzed. All of designers chose high brightness and saturation more for designing the bouquets. Warm colors and cold colors have been taken in similar portion. Blue color has been rarely used and it is probably because of the rarity of blue flowers. This study shows each continent has different color preference. European designers used wide variety of colors while Asian designers preferred red color. From this study, we found that color image scales of wedding bouquets represent 8 images out of 12 representative images. Four exceptions are 'clean', 'elegant', 'gentle' and 'modern' images.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.503-514
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• 2017

For real parameters ${\alpha}$ and ${\beta}$ such that ${\alpha}$ < 1 < ${\beta}$, we denote by $\mathcal{P}({\alpha},{\beta})$ the class of analytic functions p, which satisfy p(0) = 1 and ${\alpha}$ < ${\Re}\{p(z)\}$ < ${\beta}$ in ${\mathbb{D}}$, where ${\mathbb{D}}$ denotes the open unit disk. Let ${\mathcal{A}}$ be the class of analytic functions in ${\mathbb{D}}$ such that f(0) = 0 = f'(0) - 1. For $f{\in}{\mathcal{A}}$, ${\mu}{\in}{\mathbb{C}}{\backslash}\{0\}$ and ${\nu}{\in}{\mathbb{C}}$, let $I_{{\mu},{\nu}:{\mathcal{A}}{\rightarrow}{\mathcal{A}}$ be an integral operator defined by $$I_{{\mu},{\nu}[f](z)}=\({\frac{{\mu}+{\nu}}{z^{\nu}}}{\int}^z_0f^{\mu}(t)t^{{\nu}-1}dt\)^{1/{\mu}}$$. In this paper, we find some sufficient conditions on functions to be in the class $\mathcal{P}({\alpha},{\beta})$. One of these results is applied to the integral operator $I_{{\mu},{\nu}}$ of two classes of starlike functions which are related to the class $\mathcal{P}({\alpha},{\beta})$.

• Korean Journal of Plant Resources
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• v.32 no.5
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• pp.486-498
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• 2019

This study was conducted to investigate the leaf growth and flowering characteristics of 85 Hosta cultivars. The 85 cultivars were grown in a pot in Useful Plant Resources Center in Yangpyeong, Korea. H. 'Abiqua Blue Crinkles', H. 'Abiqua Drinking Gourd', H. 'Dancing in the Rain', H. 'Elegance', H. 'Inniswood', and H. 'Venus' were classified as a large size group (> 50 cm), while 27 cultivars including H. 'Abby', H. 'Birchwood Parky's Gold', H. 'Blue Cadet', and H. 'Blue Edge' were classified as a small size group (< 20 cm). The others were classified as a medium size groups. 79% of Hosta cultivars had leaf variegation. Leaf variegation type was divided into 5 types (standard, marginata, mediovarigata, albomaculata, striata). Among them 31 cultivars including H. 'Abby', H. 'Abiqua Moonbeam', and H. 'Atlantis' has a variegation type of marginata in the leaf. 36 cultivars including H. 'Abby', H. 'Abiqua Drinking Gourd', and H.'Abiqua Moonbeam' bloomed in late May and 9 cultivars including H. 'Black Hills', H. 'Boeun', and H. 'Fragrant Bouquet' started to flower on late August. Most flowers were below 3.0 cm in length, while H. 'Avocado' was longest on 10.0 cm. Most flowers have a lavender color group (63.5%), and 14 cultivars of Hosta showed white color group (16.5%). 12 cultivars including H. 'Blue Mouse Ears', H. 'Captain Kirk', and H. 'Fragrant Bouquet' had the fragrance in their flowers. H. 'Cherry Berry' and H. 'Revolution' had a colorful stalk, red and yellow, respectively.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.705-717
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• 2018

We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.