• 대한수학회지
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• 제56권5호
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• pp.1403-1418
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• 2019

Let R be a commutative ring with unity. If f(x) is a zero-divisor polynomial such that $f(x)=c_f f_1(x)$ with $c_f{\in}R$ and $f_1(x)$ is not zero-divisor, then $c_f$ is called an annihilating content for f(x). In this case $Ann(f)=Ann(c_f )$. We defined EM-rings to be rings with every zero-divisor polynomial having annihilating content. We showed that the class of EM-rings includes integral domains, principal ideal rings, and PP-rings, while it is included in Armendariz rings, and rings having a.c. condition. Some properties of EM-rings are studied and the zero-divisor graphs ${\Gamma}(R)$ and ${\Gamma}(R[x])$ are related if R was an EM-ring. Some properties of annihilating contents for polynomials are extended to formal power series rings.

• Maxillofacial Plastic and Reconstructive Surgery
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• 제41권
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• pp.31.1-31.7
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• 2019

Background: To test the hypothesis that in profile smiling view, for ideal aesthetics, a tangent to the labial face of the maxillary central incisor crowns should be approximately parallel to the true vertical line and thereby perpendicular to the true horizontal line. Methods: An idealized female image was created with computer software and manipulated using the same software to construct an "ideal" female profile image with proportions, and linear and angular soft tissue measurements, based on currently accepted criteria for idealized Caucasian profiles. The maxillary incisor labial face tangent was altered in 5° increments from 70 to 120°, creating a range of images, shown in random order to 70 observers (56 lay people and 14 clinicians), who ranked the images from the most to the least attractive. The main outcome was the preference ranks of image attractiveness given by the observers. Results: The most attractive inclination of a tangent to the labial face of the maxillary incisor crowns in profile view in relation to the true horizontal line was 85°, i.e. 5° retroclined from a perpendicular 90° inclination. The most attractive range appears to be between 80 and 90°. Excessive proclination appeared to be less desirable than retroclination. Beyond 105° most observers recommend treatment. Conclusion: In natural head position, the ideal inclination of the maxillary incisor crown labial face tangent in profile view will be approximately parallel to the true vertical line and thereby approximately perpendicular to the true horizontal line.

• 대한수학회논문집
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• 제27권1호
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• pp.69-76
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• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• 대한수학회논문집
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• 제39권2호
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• pp.373-397
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• 2024

Lambek introduced the concept of symmetric rings to expand the commutative ideal theory to noncommutative rings. In this study, we propose an extension of symmetric rings called strongly α-symmetric rings, which serves as both a generalization of strongly symmetric rings and an extension of symmetric rings. We define a ring R as strongly α-symmetric if the skew polynomial ring R[x; α] is symmetric. Consequently, we provide proofs for previously established outcomes regarding symmetric and strongly symmetric rings, directly derived from the results we have obtained. Furthermore, we explore various properties and extensions of strongly α-symmetric rings.

• Archives of Plastic Surgery
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• 제33권1호
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• pp.95-100
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• 2006

The challenge of accurately predicting eyelid height after blepharoptosis surgery is well-known problem even in complete hands. From May, 1988 to December, 2004, authors reviewed 182 cases(240 eyes) of blepharoptosis corrected by frontalis muscle transfer or levator resection and had experienced 10 cases(15 eyelids) of early reoperation around 1 week. The period from initial operation to reoperation are between six to eight days and mean period is seven days. Initial operative procedures were frontalis muscle transfer in 3 cases(4 eyelids) and levator resection in 7 cases(11 eyelids). Follow up period ranged from 6 months to 16 years. Early adjusting surgery was performed in accordance with the preoperative and postoperative degree of ptosis of patient and considering previous operative technique. The results are evaluated according to the criteria of an ideal correction by Souther and Jordan. Seven patients have good or satisfactory results(less than 1 mm asymmetry, good in 5 cases and satisfactory in 2 cases). Three patients(5 eyelids) recorded as poor results(more than 2 mm asymmetry). Even if early or late reoperation can be effective in correcting unsatisfactory results after correction of blepharoptosis, early reoperation is better than later reoperation because early reoperation can offer a reduction in time to final result, the ease with which it is performed, potential cost savings. The experience of surgeon is also important factor for the reatment of recurred blepharoptosis

• Archives of Plastic Surgery
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• 제33권1호
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• pp.80-86
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• 2006

The challenge of accurately predicting eyelid height after blepharoptosis surgery is well-known problem even in complete hands. From May 1988 to December 2004, authors reviewed 182 cases(240 eyes) of blepharoptosis corrected by frontalis muscle transfer or levator resection and had experienced 10 cases(15 eyelids) of early reoperation around the first week. The period from initial operation to reoperation are between six to eight days and mean period is seven days. Initial operative procedures were frontalis muscle transfer in 3 cases(4 eyelids) and levator resection in 7 cases(11 eyelids). Follow up period ranged from 6 months to 16 years. Early adjusting surgery was performed in accordance with the preoperative and postoperative degree of ptosis of patient and by previous operative technique. The results are evaluated according to the criteria of an ideal correction by Souther and Jordan. Seven patients have good or satisfactory results(less than 1 mm asymmetry, good in 5 cases and satisfactory in 2 cases). Three patients(5 eyelids) recorded as poor results(more than 2 mm asymmetry). Even if early or late reoperation can be effective in correcting unsatisfactory results after correction of blepharoptosis, early reoperation may lead to better results than late reoperation because early reoperation can offer a reduction in time to final result, the ease with which it is performed and potential cost savings. The experience of surgeon is also important factor for the treat ment of recurred blepharoptosis.

• Maxillofacial Plastic and Reconstructive Surgery
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• 제40권
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• pp.20.1-20.10
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• 2018

Background: In the absence of clear guidelines for facial aesthetic surgery, most surgeons rely on expert intuitive judgement when planning aesthetic and reconstructive surgery. One of the most famous theories regarding "ideal" facial proportions is that of the golden proportion. However, there are conflicting opinions as to whether it can be used to assess facial attractiveness. The aim of this investigation was to assess facial ratios of professional black models and to compare the ratios with the golden proportion. Methods: Forty photographs of male and female professional black models were collected. Observers were asked to assign a score from 1 to 10 (1 = not very attractive, 10 = very attractive). A total of 287 responses were analysed for grading behaviour according to various demographic factors by two groups of observers. The best graded photographs were compared with the least well-graded photographs to identify any differences in their facial ratios. The models' facial ratios were calculated and compared with the golden proportion. Results: Differences in grading behaviour were observed amongst the two assessment groups. Only one out of the 12 facial ratios was not significantly different from the golden proportion. Conclusions: Only one facial ratio was observed to be similar to the golden proportion in professional model facial photographs. No correlation was found between facial ratios in professional black models with the golden proportion. It is proposed that an individualistic treatment for each ratio is a rather better method to guide future practice.