• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.1-5
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• 2018

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.

• 대한수학회논문집
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• 제33권2호
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• pp.561-569
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• 2018

In this paper, we introduce some notions of orthogonality in the setting of Finsler $C^*$-modules and investigate their relations with the Birkhoff-James orthogonality. Suppose that ($E,{\rho}$) and ($F,{\rho}^{\prime}$) are Finsler modules over $C^*$-algebras $\mathcal{A}$ and $\mathcal{B}$, respectively, and ${\varphi}:{\mathcal{A}}{\rightarrow}{\mathcal{B}}$ is a *-homomorphism. A map ${\Psi}:E{\rightarrow}F$ is said to be a ${\varphi}$-morphism of Finsler modules if ${\rho}^{\prime}({\Psi}(x))={\varphi}({\rho}(x))$ and ${\Psi}(ax)={\varphi}(a){\Psi}(x)$ for all $a{\in}{\mathcal{A}}$ and all $x{\in}E$. We show that each ${\varphi}$-morphism of Finsler $C^*$-modules preserves the Birkhoff-James orthogonality and conversely, each surjective linear map between Finsler $C^*$-modules preserving the Birkhoff-James orthogonality is a ${\varphi}$-morphism under certain conditions. In fact, we state a version of Wigner's theorem in the framework of Finsler $C^*$-modules.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.

• 천문학회보
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• 제35권2호
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• pp.38.1-38.1
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• 2010

We present the results of the survey for submillimeter galaxies in the MS0451 (04h 54m 10.8s, -03d 00m 57.0s) at z = 0.55 and PKS1138-262 (11h 40m 48.25s, -26d 29m 10.1s) at z = 2.16 with the 1.1mm bolometer array AzTEC at the James Clerk Maxwell Telescope. The samples were centered on a prominent large-scale structure overdensity. Submillimeter galaxies seem to be starburst galaxies at high redshift ($z\;\geq\;1$) with high starformation rates ($\sim1000M\odot\;yr^{-1}$) or active galactic nuclei (AGN). We have obtained AzTEC images using the AzTEC data reduction pipeline with the IDL language. Through a bayes' theorem, we determined the extragalaxy catalogue, containing the false-detection rate, completeness, flux deboosting correction, and the source positional uncertainty in this region. We compared the catalogue with HST, DSS, 2MASS observations.

• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.653-659
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• 2015

야구의 피타고라스 정리는 야구의 승률을 추정하는 방법으로 오랜 기간 동안 타당성이 입증되고 또 활용되고 있다. 본 연구에서는 2005년부터 2014년 사이의 한국프로야구 팀대 팀 전체기록을 이용하여 실제승률과 피타고라스 정리에 의해 추정된 기대승률의 차이가 발생하는 원인을 회귀모형을 이용하여 살펴보았다. 기대승률과 실제승률의 차이가 큰 경우는 득점과 실점의 분포가 특이하다는 가정아래에서 종속변수는 실제승률과 기대승률의 차이, 독립변수로는 게임당 득점 및 실점의 평균, 표준편차, 변동계수를 각각 이용하였다. 그 결과 실제승률과 기대승률의 차이에는 게임당 실점의 표준편차와 변동계수가 영향을 미치며 게임당 득점의 영향은 없는 것으로 나타났다.

• Restorative Dentistry and Endodontics
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• 제47권1호
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• pp.1.1-1.13
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• 2022

Objectives: This study assessed the shape and anatomical relationship of the mental foramen (MF) to mandibular posterior teeth in an Indian sub-population. Materials and Methods: In total, 475 existing cone-beam computed tomography records exhibiting 950 MFs and including the bilateral presence of mandibular premolars and first molars were assessed. Images were evaluated 3-dimensionally to ascertain the position, shape, and anatomical proximity of MFs to mandibular teeth. The position and shape of MFs were measured and calculated. The Pythagorean theorem was used to calculate the distance between the root apex of the mandibular teeth and the MF. Results: MFs exhibited a predominantly round shape (left: 67% and right: 65%) followed by oval (left: 30% and right: 31%) in both males and females and in different age groups. The root apices of mandibular second premolars (left: 71% and right: 62%) were closest to the MF, followed by distal to the first premolars and mesial to the second premolars. The mean vertical distance between the MF and the nearest tooth apex calculated on sagittal sections was 2.20 mm on the right side and 2.32 mm on the left side; no significant difference was found according to sex or age. The distance between the apices of the teeth and the MF was ≥ 4 mm (left; 4.09 ± 1.27 mm and right; 4.01 ± 1.15 mm). Conclusions: These findings highlight the need for clinicians to be aware of the location of the MF in treatment planning and while performing non-surgical and surgical endodontic procedures.