• 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.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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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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• v.32 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.34 no.2
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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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• v.27 no.1
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• pp.66-70
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• 2005

Cupid's bow, upper lip, columella, and ala of nose are esthetically important, in which their symmetrical plasties determine success or failure of the surgery in cleft lip and palate patients. Z-palsty and its modifications are simple and effective. The double Z-plasty is economical in surgical time and esthetics in reconstructing the cupid's bow compared with other methods. We report a 29-year-old male patient who represented reversed cupid's bow and whistle deformity after the primary repair of the cleft lip. He was corrected the cupid's bow using a double Z-plasty. The reversed cupid's bow was corrected to a normal shape and the whistle deformity disappeared. The tightness of the upper lip was relieved after the operation. The double Z-plasty was esthetically successful because the procedure was limited in the vermilion and did not produce a new scar on the skin. Furthermore, the lip tubercle became protuberant. The cupid's bow was symmetrically smoothly curved at 4 years after the operation. These results indicate that the double Z-plasty is simple, less traumatic to the surrounding tissues, and suitable for the correction of whistle deformity.

• Korean Journal of Food Science and Technology
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• v.31 no.2
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• pp.322-328
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• 1999

Volatile flavor components of watermelon (Citrullus vulgaris S.) and oriental melon (Cucumis melo L.) obtained by simultaneous steam distillation and extraction apparatus were separated by gas chromatography (GC) and gas chromatography-mass spectrometry (GC/MS). Thirty seven and fifty five volatile flavor components were identified in watermelon and oriental melon, respectively. (Z)-3-Nonen-1-ol, (Z,Z)-3,6-nonadien-1-ol, (E,Z)-2,6-nonadienal and (E)-2-nonenal containing unsaturated nine carbon atoms were the characteristic flavor components of watermelon. $C_{9}-Unsaturated$ esters including (Z)-3-nonenyl acetate, (Z)-6-nonenyl acetate, (Z,Z)-3,6-nonadienyl acetate and thioester were important components in the flavor profile of oriental melon.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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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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• v.28 no.4
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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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• v.55 no.1
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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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• v.15 no.2
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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.