• 호남수학학술지
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• 제30권3호
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• pp.425-433
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• 2008

In this paper, we introduce the concept of p-preconvex sets on preconvexity spaces. We study some properties for p-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of pc-convex function, $p^*c$-convex function, pI-convex function and $p^*I$-convex function.

• 대한수학회보
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• 제60권4호
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• 한국인터넷방송통신학회논문지
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• 제15권6호
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• pp.257-266
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• 2015

비 볼록 발전비용함수에 대한 최적화 문제는 다항시간으로 해를 구하는 알고리즘이 알려져 있지 않아 전기분야에서는 부득이 2차 함수만을 사용하고 있다. 본 논문은 비 볼록 발전비용함수의 경제급전 최적화 문제에 대한 밸브지점 최적화 알고리즘을 제안하였다. 제안된 알고리즘은 초기 치로 최대 발전량 $P_i{\leftarrow}P_i^{max}$로 설정하고, 평균 발전단가가 $_{max}\bar{c}_i$인 발전기 i의 발전량을 밸브지점 $P_{ik}$로 감소시키는 방법을 적용하였다. 제안된 알고리즘을 13과 40-발전기 데이터에 적용한 결과 기존의 휴리스틱 알고리즘보다 좋은 성능을 보였다. 따라서 비 볼록 발전비용함수의 경제급전문제 최적 해는 각 발전기의 밸브지점 발전량으로 수렴함을 보였다.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• 한국인터넷방송통신학회논문지
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• 제15권5호
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• pp.155-162
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• 2015

본 논문은 운전금지영역을 가진 이차 볼록 발전비용 함수를 적용하는 경제급전의 최적화 문제에 대한 결정론적 최적화 알고리즘을 제안하였다. 제안된 알고리즘은 운전금지구역을 가진 발전기는 운전금지구역을 벗어나도록 분할하고, 초기치 $P_i{\leftarrow}P_i^{max}$에 대해 발전단가가 큰 순서대로 발전량을 감소시키고, $_{max}\{F(P_i)-F(P_i-{\beta})\}$ > $_{min}\{F(P_j+{\beta})-F(P_j)\}$, $i{\neq}j$, ${\beta}=1.0,0.1,0.01,0.001$에 대해 $P_i{\leftarrow}P_i-{\beta}$, $P_j{\leftarrow}P_j+{\beta}$의 교환 최적화 과정을 수행하였다. 제안된 방법을 15-발전기의 3가지 사례에 적용한 결과 간단하면서도 항상 동일한 결과로 휴리스틱 알고리즘들에 비해 최적의 결과를 나타내었다.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.359-366
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• 2008

Let A(p) be the class of functions $f\;:\;z^p\;+\;\sum\limits_{j=1}^{\infty}a_jz^{p+j}$ analytic in the open unit disc E. Let, for any integer n > -p, $f_{n+p-1}(z)\;=\;z^p+\sum\limits_{j=1}^{\infty}(p+j)^{n+p-1}z^{p+j}$. We define $f_{n+p-1}^{(-1)}(z)$ by using convolution * as $f_{n+p-1}\;*\;f_{n+p-1}^{-1}=\frac{z^p}{(1-z)^{n+p}$. A function p, analytic in E with p(0) = 1, is in the class $P_k(\rho)$ if ${\int}_0^{2\pi}\|\frac{Re\;p(z)-\rho}{p-\rho}\|\;d\theta\;\leq\;k{\pi}$, where $z=re^{i\theta}$, $k\;\geq\;2$ and $0\;{\leq}\;\rho\;{\leq}\;p$. We use the class $P_k(\rho)$ to introduce a new class of multivalent analytic functions and define an integral operator $L_{n+p-1}(f)\;\;=\;f_{n+p-1}^{-1}\;*\;f$ for f(z) belonging to this class. We derive some interesting properties of this generalized integral operator which include inclusion results and radius problems.

• 대한치과기공학회지
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• 제24권1호
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• pp.107-126
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• 2002

The first function of occlusion is mastication. Therefore the functional restoration of occlusal surface is very important. The restoration of occlusal surface is three method as wax bite technique, F.G.P. technique, cone technique. Many dental technician is using compound method. I am using compound method of wax bite technique and cone technique. I have knew common point on each teeth during I have waxing up wax pattern. So I studied on the design waxup technique for mandible molar occlusion. The results of the study were as follows; 1. The dam wax up method can restore axial contour of teeth very easy and make short working time of wax pattern. 2. The height of dam must be same with cusp of adjacent teeth. 3. Automatically the contour of tooth is appeared if the contour of dam is relationship with cuspid line of adjacent teeth. 4. The height of contour of buccal, lingual surface is formed natural curve to add fluid wax by gravitation. 5. The development groove of mandible first premolar is appeared V form. 6. The development groove of mandible second premolar is appeared Y form. 7, The development groove of mandible first molar is appeared M form. 8. The development groove of mandible second molar is W form. 9. The embrasure is formed to carve around contact point area as round convex. It affects to axial form of tooth. 10. The buccal, lingual groove of molar is formed parallel with direction of teeth arrangement.

• 대한치과기공학회지
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• 제21권1호
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• pp.97-114
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• 1999

The first function of occlusion is mastication. Therefore the functional restoration of occlusal surface is very important. The restoration of occlusal surface is three method as wax bite technique, F.G.P. technique, cone technique. Many dental technician is using compound method. I have knew common point on each teeth during I have waxing up wax pattern. So I studied on the design waxup technique for maxillary molar occlusion. The results of the study were as follows ; 1. The dam wax up method can restore axial contour of teeth very easy and make short working time of wax pattern. 2. The height of dam must be same with cusp of adjacent teeth. 3. Automatically the contour of tooth is appeared if the contour of dam is relationship with cuspid line of adjacent teeth. 4. The height of contour of buccal, lingual surface is formed natural curve to add fluid wax by gravitation. 5. The development groove of Maxillary premolar is appeared V form. 6. The development groove of Maxillary molar is appeared W form. 7. The embrasure is formed to carve around contact point area as round convex. It affects to axial form of tooth. 8. I was knew that the lingual groove and stuart's groove of molar runs parallel with oblique ridge. 9. The buccal groove of molar is formed parallel with direction of teeth arrangement.