• 대한수학회논문집
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• 제23권1호
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• pp.1-10
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• 2008

Conditions for an ideal to be irreducible are provided. The notion of an order system in a subtraction algebra is introduced, and related properties are investigated. Relations between ideals and order systems are given. The concept of a fixed map in a subtraction algebra is discussed, and related properties are investigated.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권3호
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• pp.221-236
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• 2023

In this paper, we define the notions of (3, 2)-fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.

• Investigative Magnetic Resonance Imaging
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• 제22권2호
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• pp.102-109
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• 2018

Purpose: The purpose of this study is to compare the performance of the T1 3D subtraction technique and the conventional 2D dynamic contrast enhancement (DCE) technique in diagnosing Cushing's disease. Materials and Methods: Twelve patients with clinically and biochemically proven Cushing's disease were included in the study. In addition, 23 patients with a Rathke's cleft cyst (RCC) diagnosed on an MRI with normal pituitary hormone levels were included as a control, to prevent non-blinded positive results. Postcontrast T1 3D fast spin echo (FSE) images were acquired after DCE images in 3T MRI and image subtraction of pre- and postcontrast T1 3D FSE images were performed. Inter-observer agreement, interpretation time, multiobserver receiver operating characteristic (ROC), and net benefit analyses were performed to compare 2D DCE and T1 3D subtraction techniques. Results: Inter-observer agreement for a visual scale of contrast enhancement was poor in DCE (${\kappa}=0.57$) and good in T1 3D subtraction images (${\kappa}=0.75$). The time taken for determining contrast-enhancement in pituitary lesions was significantly shorter in the T1 3D subtraction images compared to the DCE sequence (P < 0.05). ROC values demonstrated increased reader confidence range with T1 3D subtraction images (95% confidence interval [CI]: 0.94-1.00) compared with DCE (95% CI: 0.70-0.92) (P < 0.01). The net benefit effect of T1 3D subtraction images over DCE was 0.34 (95% CI: 0.12-0.56). For Cushing's disease, both reviewers misclassified one case as a nonenhancing lesion on the DCE images, while no cases were misclassified on T1 3D subtraction images. Conclusion: The T1 3D subtraction technique shows superior performance for determining the presence of enhancement on pituitary lesions compared with conventional DCE techniques, which may aid in diagnosing Cushing's disease.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제36권2호
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• pp.229-252
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• 2022

본 연구는 한국, 싱가포르, 미국, 일본의 초등학교 교과서에 제시된 모으기와 가르기, 덧셈 및 뺄셈의 도입 단원을 비교하고 분석한 것이다. 분석의 초점은 시각적 모델 및 제시된 문제 상황과의 연결성, 언어적 표현 및 시각적 모델과의 연결성, 관계적 이해 및 추가 활동이다. 분석 결과, 교과서에 따라 문제 상황, 시각적 모델, 언어적 표현이 다르게 구현됨에 따라 연결성도 다르게 나타났다. 각 교과서는 문제 상황의 제시 방법과 순서에서 차이가 있었고, 시각적 모델 측면에서도 하나의 모델을 지속적으로 사용하는 경우와 다양한 모델을 사용하는 경우가 있었다. 언어적 표현 측면에서는 각 교과서 마다 다른 특징이 있었으며, 관계적 이해 측면에서는 모든 교과서가 등호 양변의 값이 같다는 것을 강조하는 활동을 제시하였다. 이와 같은 연구 결과를 바탕으로 덧셈과 뺄셈 도입과 관련된 문제 상황, 시각적 모델의 활용, 언어적 표현 방안 등 후속 교과서의 단원 개발과 관련한 시사점을 논의하였다.

• Journal of Periodontal and Implant Science
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• 제25권1호
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• pp.67-75
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• 1995

The progress of periodontal disease and the wound healing process after treatment result in alveolar bone bone change. So, detection of it is very important in the diagnosis and the radiograph of periodontal disease. Various effects have been made to assess the subtle alveolar bone change and digital subtraction radiography (DSR) has been reported to be the best method in evaluating it qualitatively and quantitatively. The present study was performed to estimate the detectable alveolar bone change qualitatively with digital subtraction radiography. For the in vitro study, 10 intraoral standard radiographs were taken from porcine dry mandible which a rectangular cortical bone chip of 0.1mm to 1.0mm thickness with 0.1mm increment was attached on the buccal surface. The radiographs without and with bone plates were reviewed at the same time by 10 observers and requested to detect the presence of cortical bone plates. Digital Subtraction radiograph was reviewed subsequently by using the DSR system(digital converter-256 grey-levels,DT 2851,Data Translation Co., U.S.A;IBM 386 ; CCD camera, FOTOVIX, Tamrom Co., Japan). The detectable thickness of cortical bone plate was O.4mm on the intraoral radiograph and 0.2mm on the subtaction images. For the human study, radiographs were taken from patients by using intraoral film holding device and aluminum reference wedge before and 3 month after bone graft and 1 week after osteoplasty. The grey level change was estimated in the subtraction images and calculated to aluminum equivalent thickness. The grey level of the grafted site was higher that that of healthy controls. Average grey levels of change on healthy controls were O.48mm aluminum equivalent. However, the amount of changes in grafted sites were 1.87mm aluminum thickness equivalent and in the site of osteoplasty were -1.49mm aluminum thickness equivalent. In conclusion, digital subtraction radiography was more effective in detecting as subtle change of alveolar bone than intraoral standard radiography. With the aid of quantitative analysis of digital subtraction radiography, alveolar bone resorption of apposition can be estimated during diagnosis and treatment of periodontally diseased patients.

• Imaging Science in Dentistry
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• 제31권1호
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• pp.51-55
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• 2001

Purpose : This study was performed to compare the diagnostic ability of conventional intraoral radiographs with that of digital subtraction image and to assess the quantifying ability of digital subtraction image for simulated apical root resorption Materials and Methods : Conventional intraoral radiographs and digital images of ten sound maxillary central incisors and those with simulated apical root resorption were taken with varying horizontal and vertical angulations of the x-ray beam. The diagnostic accuracy to detect the lesion was evaluated on conventional intraoral radiographs and digital subtraction images by ROC analysis. The amount of simulated apical root resorption was also estimated on the reconstruction images by Emago/sup (R)/ and compared with actual amount of tooth loss using paired t-test. Results: The diagnostic accuracy of conventional intraoral radiographs to detect the apical root resorption was low (ROC area = 0.6446), and the sensitivity and the specificity of digital subtraction images were 100%, respectively. The calculated amounts of apical root resorption showed no statistically significant difference with the actual amounts of the lesion (p>0.05). Conclusion: Digital subtraction radiography is powerful tool to detect the small apical root resorption, and quantitative analysis of small amounts of the lesion can be evaluated by digital subtraction radiography.

• Journal of Periodontal and Implant Science
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• 제23권3호
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• pp.595-604
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• 1993

Since $Gr{\"{o}}nadhl$ et al introduced a digital subtraction radiography into periodontal dignosis in 1983, many reports using this system has aimed to assess the peroiodontal disease activity and the alveolar bone changes after periodontal treatment. The present study was performed to evaluate the usefulness of digital subtraction radiography for asessing an alveolar bone changes in 3 months after periodontal flap surgery. Serial intraral raiographs were taken from 5 normal subjects and 6 periodontally diseased patients using customized bite blocks attached to film holder in fxation device and digitized by image processing system(consisting of IBM 386, digital frame grabber, CCD camera, Image-pro II software). And the reference parameters were measured by pixel unit and compared with respective radiographs. The serial radiographs showed a little and statistically insignificant difference in reference paramenters. The conventional intraoral radiographs, the subtraction images and the clor enhanced subtraction images were reviewed by 4 examiners and the examiner's agreement rates were compared. The subtraction images and its color enhanced images showed higher examiner's agreement rate than the conventional radiographs. And the propotions of sites diagnosed with bone loss or gain after periodontal surgery were highter in the subtraction images and its color enhanced images than in the conventional radiographs. Especially, in color enhanced images, the unber of bone agin sites tended to increase according to post-surgery periods. These results indicate that projection geometry could be standardized with the divice used in this study, and the subtraction radiography may be useful to assess an alveolar bone changes after periodntal flap surgery.

• 충청수학회지
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• 제31권2호
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• pp.247-254
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• 2018

In this paper, we introduce the notion of symmetric bi-multiplier of subtraction algebra and investigate some related properties. Also, we prove that if D is a symmetric bi-multiplier of X, then D is an isotone symmetric bi-multiplier of X.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.427-436
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• 2008

The notion of vague deductive systems in subtraction algebras is introduced, and several properties are investigated. Conditions for a vague set to be a vague deductive system are provided. Characterizations of a vague deductive system are established.

• 호남수학학술지
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• 제31권1호
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• pp.63-73
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• 2009

In this paper, we give adjoint semigroups of subtraction algebras, and investigate some properties of adjoint semigroups, and show that the adjoint semigroups of subtraction algebras are residualed semigroups.