• 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.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.563-569
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• 2005

In [2], Jahangiri studied the harmonic starlike functions of order $\alpha$, and he defined the class T$_{H}$($\alpha$) consisting of functions J = h + $\bar{g}$ where hand g are the analytic and the co-analytic part of the function f, respectively. In this paper, we introduce the class T$_{H}$($\alpha$, $\beta$) of analytic functions and prove various coefficient inequalities, growth and distortion theorems, radius of convexity for the function h, if the function J belongs to the classes T$_{H}$($\alpha$) and T$_{H}$($\alpha$, $\beta$).

• Journal of the Korean Mathematical Society
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• v.57 no.5
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• pp.1299-1322
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• 2020

We consider closed, star-shaped, admissible hypersurfaces in ℝⁿ⁺¹ expanding along the flow Ẋ = |X|^α-1 F^-β, α ≤ 1, β > 0, and prove that for the case α ≤ 1, β > 0, α + β ≤ 2, this evolution exists for all the time and the evolving hypersurfaces converge smoothly to a round sphere after rescaling. Besides, for the case α ≤ 1, α + β > 2, if furthermore the initial closed hypersurface is strictly convex, then the strict convexity is preserved during the evolution process and the flow blows up at finite time.

• The korean journal of orthodontics
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• v.14 no.1
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• pp.103-113
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• 1984

This work was undertaken to evaluate the integumental response in lower face to hard tissue changes, and to grope the prediction equation for expected integumental profile changes. Cephalometric headplates of 25 persons consisted of 8 Angle's class 1 maxillary protrusive and 17 Angle's class II division 1 patients whose mean age was 15.2 years were traced, diagramatized, and statistically analyzed. The results were as follows; 1. Upper incisor and lips were retracted and convexity of integumental profile decreased concurrently with decrease of hard tissue procumbency, however soft tissue point A', B', and Pog' did not undergo significant changes after orthodontic treatment. 2. Remarkable increment of upper lip thickness and upper lip height was shown and this was related to upper incisor retraction. The ratio between the amount of upper incisor retraction and the increment o f upper lip thickness was approximately 1.16:1. 3. Moderate correlation of upper lip retraction to upper incisor retraction, and of lower lip retraction to lower incisor movement were arranged, and yet comparatively wide variability from subject to subject was shown. 4. It was possible to predict statistically for horizontal alteration of lip position and change of upper lip angulation ground in orthodontic treatment.

• Journal of Korea Multimedia Society
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• v.3 no.3
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• pp.298-308
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• 2000

We present an efficient algorithm for finding the sequence of extreme vortices of a moving regular convex polyhedron of with respect to a fixed plane H.. The algorithm utilizes the spherical Voronoi diagram that results from the outward unit normal vectors nF$_{i}$ 's of faces of P. It is well-known that the Voronoi diagram of n sites in the plane can be computed in 0(nlogn) time, and this bound is optimal. However. exploiting the convexity of P, we are able to construct the spherical Voronoi diagram of nF$_{i}$ ,'s in O(n) time. Using the spherical Voronoi diagram, we show that an extreme vertex problem can be transformed to a spherical point location problem. The extreme vertex problem can be solved in O(logn) time after O(n) time and space preprocessing. Moreover, the sequence of extreme vertices of a moving regular convex polyhedron with respect to H can be found in (equation omitted) time, where m$^{j}$ $_{k}$ (1$\leq$j$\leq$s) is the number of edges of a spherical Voronoi region sreg(equation omitted) such that (equation omitted) gives one or more extreme vertices.

• Journal of Chest Surgery
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• v.39 no.8 s.265
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• pp.573-578
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• 2006

Background: Generally hernia is diagnosed with simple chest or gastrointestinal x-ray. Sometimes CT or MRI can give lots of information for the diagnosis. However, there was no study for the differentiation with using CT findings between Morgagni hernia and pleuropericardial fat. The aim of this study was to evaluate the useful CT findings for differentiating Morgagni hernia from pleuropericardial fat. Material and Method: We retrospectively analyzed CT scans of eight patients with Morgagni hernia and 20 patients with abundant pleuropericardial fat without peridiaphragmatic lesions. All CT scans were performed with coverage of the whole diaphragm in the inspiration state. We evaluated 1) the presence of the defect of the anterior diaphragm, 2) the interface between the lung and fat, 3) the angle between the chest wall and fat, 4) the continuity between the extrapleural fat and fat, 5) the presence of the vessels within fat, and 6) the presence of a thin line surrounding fat. Result: In all cases with Morgagni hernia, the defect of the anterior diaphragm was seen. The interface was well-defined, smooth, and convex to the lung. The angle with the chest wall was acute. The continuity with the extrapleural fat was not seen. In the cases with abundant pleuropericardial fat, the defect of the anterior diaphragm was seen in three (15%). The interface was usually irregular (n=10) and flat (n=17). The angle with the chest wall was variable. The continuity with the extrapleural fat, that was markedly increased in amount, was usually seen (n=16). The thin line surrounding fat was seen in four cases with Morgagni hernia, however, not seen in all cases with pleuropericardial fat. All of the above findings were statistically significant, however, vessels within fat was not significant to differentiate Morgagni hernia (n=8/8) from pleuropericardial fat (n=14/20). Conclusion: The useful CT findings of Morgagni hernia were fatty mass with sharp margin, convexity toward lung, acute angle with chest wall, and thin line surrounding hernia. Branching structure within fatty mass representing omental vessels that has been known as a characteristic finding of Morgagni hernia was not useful for differentiating Morgagni hernia from pleuropericardial fat.