• 대한수학회논문집
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• 제32권1호
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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.

• 대한수학회보
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• 제61권2호
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• pp.317-333
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• 2024

For the classes of analytic functions f defined on the unit disk satisfying ${\frac{2zf'(z)}{f(z)-f(-z)}}{\prec}{\varphi}(z)$) and ${\frac{(2zf'(z))'}{(f(z)-f(-z))'}}{\prec}{\varphi}(z)$, denoted by S^*_s(𝜑) and C_s(𝜑), respectively, the sharp bound of the n^th Taylor coefficients are known for n = 2, 3 and 4. In this paper, we obtain the sharp bound of the fifth coefficient. Additionally, the sharp lower and upper estimates of the third order Hermitian Toeplitz determinant for the functions belonging to these classes are determined. The applications of our results lead to the establishment of certain new and previously known results.

• Journal of the Korean Association of Oral and Maxillofacial Surgeons
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• 제32권4호
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• pp.287-294
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• 2006

The secondary correction of cleft lip nasal deformity (CLND) presents difficult surgical problems. Characteristically, nostrils are asymmetric. The present study was aimed to examine and compare the effect of Straith's alar web Z-plasty, Millard's alar web Z-plasty, alar web excision, and lateral V-Y advancement of the alar base for augmentation of the nostril with or without lengthening the columella in CLND. The subjects were 28 patients with unilateral cleft lip, who had secondary nostril correction. The nostril correction methods were Straith's alar web Z-plasty, Millard's alar web Z-plasty, alar web excision, and lateral V-Y advancement of the alar base. Facial photographs were taken before and 20 days after the operation. By using Adobe photoshop, the columella length and the nostril width were measured from the facial frontal photograph and Worm's eye view. The degree of improvement was calculated and statistically analyzed. The degree of improvement of the columella length using Straith's alar web Z-plasty was 70.20%. And then Millard's alar web Z-plasty was 55.01%, alar web excision was 39.93%, and lateral V-Y advancement of the alar base was 16.38% in order. The degree of improvement of the nostril size using lateral V-Y advancement of the alar base was 55.26%. And then alar web excision was 52.72%, Millard's alar web Z-plasty was 34.86%, and Straith's alar web Z-plasty was 16.06% in order. Straith's alar web Z-plasty and Millard's alar web Z-plasty resulted in elongation of the columella, equalization of asymmetrical nostril, and enlargement of small nostrils. Alar web excision enlarged nostrils and restored symmetry. Lateral VY advancement of the alar base increased nostril width and enlarged nostrils. These results indicate that the correction of nostrils improve the shape and the symmetry of the nostrils in CLND.

• 대한수학회논문집
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• 제34권2호
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• pp.543-555
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• 2019

In this paper, we give some results on ${\frac{zf^{\prime}(z)}{f(z)}}$ for the certain classes of holomorphic functions in the unit disc $E=\{z:{\mid}z{\mid}<1\}$ and on ${\partial}E=\{z:{\mid}z{\mid}=1\}$. For the function $f(z)=z^2+c_3z^3+c_4z^4+{\cdots}$ defined in the unit disc E such that $f(z){\in}{\mathcal{A}}_{\alpha}$, we estimate a modulus of the angular derivative of ${\frac{zf^{\prime}(z)}{f(z)}}$ function at the boundary point b with ${\frac{bf^{\prime}(b)}{f(b)}}=1+{\alpha}$. Moreover, Schwarz lemma for class ${\mathcal{A}}_{\alpha}$ is given. The sharpness of these inequalities is also proved.

• Maxillofacial Plastic and Reconstructive Surgery
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• 제27권1호
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• pp.66-70
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• 2005

이차 구순비성형술을 받고자 본과에 내원한 편측성 완전 구순구개열을 가진 29세 남자 환자에서 상방으로 반전된 큐피드활과 적순부의 휘파람 변형을 교정하기 위해 중복 Z-성형술을 시행하였다. 수술 후에 반전된 큐피드활이 정상적인 형태로 재건되고 휘파람 변형이 없어졌으며 상순의 긴장도가 완화되었다. 중복 Z-성형술시 적순부 내에서만 피판을 형성하므로 피부에는 새로운 반흔이 생기지 않아 심미적으로 만족스러웠고 상순결절은 더욱 볼록해 졌다. 수술 4년경과 후 큐피드활은 부드러운 곡선으로 좌우 대칭을 이루고 매우 자연스럽게 보였으며 장기적인 추적관찰 결과 양호한 결과를 보였다. 중복 Z-성형술은 반전된 큐피드활의 교정시 다른 수술방법에 비해 술식이 간단하고 주위조직 손상이 적으며 휘파람 변형의 교정도 가능한 좋은 방법이라고 사료된다.

• 한국식품과학회지
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• 제31권2호
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• pp.322-328
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• 1999

동시증류추출장치를 사용하여 획득한 수박(Citrullus vulgaris S.)과 참외(Cucumis melo L.)의 휘발성 향기성분을 기체크로마토그래피로 분리하여 질량분석법으로 동정하였다. 수박에서 분리동정된 37종의 화합물로는 16종의 alcohol 류, 15종의 aldehyde 류, 2종의 ester류, 2종의 ketone 류와 기타 2종의 화합물이 확인되었다. 전체 상대적 농도의 68.66%를 차지한 alcohol 류가 수박의 주요 향기성분이었으며, 불포화 $C_{9}$ 화합물인 (Z)-3-nonen-1-ol, (Z,Z)-nonadien-1-ol, (E,Z)-2,6-nonadienal, (E)-2-nonenal이 특징적 향기성분으로 나타났다. 참외에서 분리동정된 55종의 화합물로는 26종의 ester 류, 16종의 alcohol 류, 10종의 aldehyde 류와 기타 3종의 화합물이 확인되었으며, 전체 상대적 농도의 63.8%를 차지한 ester류가 참외의 주요 향기 성분으로 나타났다. 이 중에서 (Z)-3-nonenyl acetate, (Z)-6-nonenyl acetate와 (Z,Z)-3,6-nonadienyl acetate, $C_{9}$-불포화 ester 류가 중요한 향기성분이었으며, 황함유 ester 류인 ethyl (methylthio)acetate, ethyl 3-(methylthio) propanoate 또한 참외의 향기에 중요한 역할을 하는 화합물이었다.

• 충청수학회지
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• 제20권3호
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• pp.333-342
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• 2007

Suppose that ${\mu}$ is a finite positive Borel measure on the unit ball $B{\subset}C^n$. The boundary of B is the unit sphere $S=\{z:{\mid}z{\mid}=1\}$. Let ${\sigma}$ be the rotation-invariant measure on S such that ${\sigma}(S)=1$. In this paper, we will show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$ where $P(z,{\zeta})$ is the Poission-Szeg$\ddot{o}$ kernel for B, then ${\mu}$ is a Carleson measure. We will also show that if $sup_{{\zeta}{\in}S}\;{\int}_{B}\;P(z,{\zeta})d{\mu}(z)$<${\infty}$, then the operator T such that T(f) = P[f] is compact as a mapping from $L^p(\sigma)$ into $L^p(B,d{\mu})$.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.889-906
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• 2020

In this article, we consider the uniqueness problem of the shift polynomials $f^n(z)(f^m(z)-1){\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$ and $f^n(z)(f(z)-1)^m{\prod\limits_{j=1}^{s}}f(z+c_j)^{{\mu}_j}$, where f(z) is a transcendental entire function of finite order, cj (j = 1, 2, …, s) are distinct finite complex numbers and n(≥ 1), m(≥ 1), s and µj (j = 1, 2, …, s) are integers. With the concept of weakly weighted sharing and relaxed weighted sharing we obtain some results which extend and generalize some results due to P. Sahoo [Commun. Math. Stat. 3 (2015), 227-238].

• Kyungpook Mathematical Journal
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• 제55권1호
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• pp.73-81
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• 2015

In this paper, we present the general solution of the functional equation $$rf(\frac{x+y+z+w}{s})+rf(\frac{x+y-z-w}{s})+rf(\frac{x-y+z-w}{s})+rf(\frac{x-y-z+w}{s})=tf(x)+tf(y)+tf(z)+tf(w)$$ and improve the Hyers-Ulam stability of the equation.

• Journal of the Korean Wood Science and Technology
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• 제15권2호
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• pp.79-89
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• 1987

This study was executed to examine helical structure and other feature, of Taxus cuspidata S. et Z. and Larix gmelinii var. principis-ruprechtii Pilger through photomicroscopic and scanning electron microscopic observation, and the obtained result, were summarized as follows: 1. Tracheid transition from springwood to summerwood was abrupt, mel slightly gradual in Taxus cuspidata S. et Z. and summerwood width of Larix gmelinii var. principis-ruprechtii Pilger was wider than that of Taxus cuspidata S. et Z. 2. Normal vertical and horizontal resin canals and surrounding thick epithelial cells were present in Larix gmelinii var. principis-ruprechtii Pilger but not present in Taxus cuspidata S. et Z. 3. Instead of helical thickening, helical chicks were observed only in summerwood trachieds of Larix gmelinii var. principis-ruprechtii Pilger. However, helical thickenings forming S, Z., and horizontal helix perpendicular to long axis of tracheid were observed in springood and summerwood tracheids of Taxus cuspidata S. et Z. and these helical thickenings were considered as analogous to the innermost layer of secondary wall. 4. Uniseriate and fusiform rays were appeared on tangential surface of Larix gmelinii var. principis-ruprechtii Pilger but oly uniserate ray was observed on tangential surface ot Taxus cuspidata S. et Z. The fusiform rays of Larix gmelinii var. principis-ruprechtii Pilger usually contained one horizontal resin canal bot occasionally two horizontal resin canals were contained in a fusiform ray. 5. Trabeculae and crassulae were observed in the tracheids of Larix gmelimii var. principis-ruprechtii Pilger but not observed in the tracheids of Taxus cuspidata S. et Z.