• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.521-533
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• 2019

In this paper, we define a mean of two positive numbers called the k-golden mean and study some properties of it. Especially, we show that the 2-golden mean refines the harmonic and the geometric means. As an application, we define the k-golden ratio and give some properties of it as an generalization of the golden ratio. Furthermore, we define the matrix k-golden mean of two positive-definite matrices and give some properties of it. This is an improvement of Lim's results [2] for which the matrix golden mean.

• Honam Mathematical Journal
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• v.44 no.1
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• pp.1-16
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• 2022

In this paper, we define and study warped product skew semi-invariant submanifolds of a locally golden Riemannian manifold. We investigate a necessary and sufficient condition for a skew semi-invariant submanifold of a locally golden Riemannian manifold to be a locally warped product. An equality between warping function and the squared normed second fundamental form of such submanifolds is established. We also construct an example of warped product skew semi-invariant submanifolds.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.52 no.6
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• pp.709-718
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• 2019

Cephalopods, such as the Japanese flying squid Todarodes pacificus and golden cuttlefish Sepia esculenta, are an important food source for all toothed whales, particularly bottlenose dolphins in costal and offshore waters around the Korean Peninsula. A controlled laboratory experiment was conducted to investigate the broadband acoustic backscattering from live individuals of these two cephalopod species using linear chirp signals (100-200 kHz). The backscattered echo signal was measured at about 1° intervals from -45° (head down) to +45° (head up) in the dorsal plane. The species-specific, frequency-dependent scattering characteristics were investigated by comparing the relationship between the wavelength-normalized backscattering cross-section (σ/λ²) and the wavelength-normalized fish length L/λ for each species. The estimated σ/λ² value for Japanese flying squid was 9.51 at an L/λ range of 12.79-30.27 (mean, 21.26). This was approximately 7% of the σ/λ² value (136.1) for golden cuttlefish at an L/λ range of 9.07-25.49 (mean, 15.77).

• Archives of Plastic Surgery
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• v.35 no.5
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• pp.514-520
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• 2008

Purpose: Many attempts have been made to describe ideal facial proportions for over two thousands year and constantly lasted till now. Dr. Marquardt has derived supposedly ideal facial proportions from the facial golden mask using golden ratio of 1 : 1.618. On the other hand, facial reducing surgeries such as mandible angle reduction are popularized in Asia because the width of mid and lower face of Korean is recognized to be wider. The purpose is to analyze characters of Korean university students' faces in horizontal plane and establish the objective data for facial width distributions and clinical applications. Methods: We applied the facial golden mask to the photographs in 1000 cases, compared the width of mid and lower face between the facial golden mask and Korean university students' faces. And we first calculated the horizontal ratio(HR) of middle and lower face each for using comparative scale of width, facial golden mask. We divided 1,000 cases into 3 groups by degrees of HR and analyzed data of HR on each groups. Using calculated horizontal ratio, we newly invented the cumulative frequency of distribution graphs in Korean university students' faces. Results: Mean data of HR were over 1.0 in all groups, which means that Korean university students' faces are typically wider than facial golden mask in horizontal planes. And this study was statistically significant(p- value < 0.05). Clinically using the cumulative frequency distributions of Korean university students' face width, we can easily explain changes of facial width to patient after facial reducing surgery and describe the changes into objective data. Conclusion: This study concludes thatKorean university students' faces are wider than facial golden mask is significantly true and the cumulative frequency of distribution graphs are expected to be widely used for comparison of results in facial reducing surgery.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.105-120
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• 2000

In this study, it is certified that the golden ratio exists in the plants, the animals and human bodies(appearance), and is considered how much the ratio of positive and negative is in the psychological, political, social and cultural aspects. The result of this study shows that the golden sections or golden rectangles of the plants(N=58), the insects(N=44), the animals(N=21) and human bodies(N=260) are equal to $0.620{\pm}0.117$, $0.632{\pm}0.203$, $0.625{\pm}0.138$ and $0.60{\pm}0.169$, respectively. The slope in the regression analysis is equal to 0.627(R-square=0.925, p-value=0.0001). Whereas, for the public opinion poll, the ratios($mean{\pm}st.dev.$) of positive and negative of the public mental phenomena are equal to $0.508{\pm}0.179$, $0.808{\pm}0.216$ and $0.711{\pm}0.128$ in the political, economical, and sociocultural aspects, respectively. The slope in the regression is equal to 0.674(R-square=0.764, p-value=0.016). As results, we show that the golden ratio exists in the plants, the animals and human bodies in nature. This shows that the public mental phenomena has some more negative aspects than positive aspects and explains the shrinkage of the public mental phenomena in the economical field.

• Archives of Plastic Surgery
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• v.36 no.4
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• pp.469-474
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• 2009

Purpose: A lower facial contouring surgery has become a commonly performed procedure in Asia. Currently, mandibular angle sagittal ostectomy and botulinum toxin type A treatment are main procedures for aesthetic correction of a broad lower face. There are a few date to show the differences in the mandibular contouring changes between mandibular angle splitting ostectomy and botulinum toxin type A treatment. Facial golden mask is easy to apply, inexpensive, and relatively objective for evaluation of facial contour analysis. This study was designed specifically to compare the changes in lower face width after two different forms of lower facial contouring procedure using facial golden mask. Methods: Seventeen patients, aged 18 to 55 years (mean, 28.6 years), 15 women and 2 men, consented to the study and receive a contouring procedure of lower face. The patients were classified in to 2 groups. In group A, the sample consisted of 10 patients with a prominent squared mandibular angle and mandibular angle splitting ostectomy was performed. In group B, the sample consisted of 7 patients with masseteric hypertrophy and botulinum toxin type A treatment was performed. Photographs of the face were taken to record the facial change at preoperative and postoperative. The postoperative photographs were taken to considered maximal effect at 2 years after surgery in group A and 4.8 months after treatment in group B. The authors applied the facial golden mask to preoperative and postoperative photographs and horizontal ratio, which compares facial width with golden mask width, were calculated. We made an analysis of the result of horizontal ratio using SPSS. Results: Overall average horizontal ratio of pre- and postoperative photos of group A were 1.24 and 1.11, whereas overall average horizontal ratio of pre- and postoperative photos of group B were 1.19 and 1.12. The horizontal ratio decreased 10.24% in group A and 5.93% in group B. There was a statistically significant change in before and after treatment, but there was no significant change in comparing the group A and group B. Conclusions: The result from this study suggest that mandibular angle sagittal ostectomy and botulinum toxin type A treatment showed relatively satisfactory clinical effects on lower facial contouring treatment. There was no statistical significant difference within two lower facial contouring treatment. Facial golden mask is easy to apply, inexpensive, and relatively objective, so we think that facial golden mask is a good method for evaluation of lower facial contouring treatment.

• Fisheries and Aquatic Sciences
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• v.19 no.2
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• pp.8.1-8.11
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• 2016

To quantitatively estimate the influence of cuttlebone on the target strength (TS) of golden cuttlefish, the cuttlebone was carefully extracted from 19 live cuttlefish caught using traps in the inshore waters around Geojedo, Korea, in early May 2010 and the TS was measured using split-beam echosounders (Simrad ES60 and EY500). The TS-length relationships for the cuttlefish (before the extraction of cuttlebone, Fish Aquat Sci. 17:361-7, 2014) and the corresponding cuttlebone were compared. The cuttlebone length ($L_b$) ranged from 151 to 195 mm (mean $L_b$ = 168.3 mm) and the mass ($W_b$) ranged from 29.3 to 53.2 g (mean $W_b$ = 38.8 g). The mean TS values at 70 and 120 kHz were -33.60 dB (std = 1.12 dB) and -32.24 dB (std = 1.87 dB), respectively. The mean TS values of cuttlebone were 0.19 dB and 0.04 dB lower than those of cuttlefish at 70 and 120 kHz, respectively. For 70 and 120 kHz combined, the mean TS value of cuttlebone was -32.87 dB, 0.11 dB lower than that of cuttlefish (-32.76 dB). On the other hand, the mean TS value of cuttlebone predicted by the regression ($TS_b$ = 24.86 $log_{10}$ $L_b$ - 4.86 $log_{10}$ ${\lambda}$ - 22.58, $r^2$ = 0.85, N = 38, P < 0.01) was -33.10 dB, 0.04 dB lower than that of cuttlefish predicted by the regression ($TS_c$ = 24.62 $log_{10}$ $L_c$ - 4.62 $log_{10}$ ${\lambda}$ - 22.64, $r^2$ = 0.85, N = 38, P < 0.01). That is, the contribution of cuttlebone to the cuttlefish TS determined by the measured results was slightly greater than that by the predicted results. These results suggest that cuttlebone is responsible for the TS of cuttlefish, and the contribution is estimated to be at least 99 % of the total echo strength.

• Journal of the Korean Society of Costume
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• v.27
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• pp.27-40
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• 1996

1.It was recorded at "Dong Gook Tong Gam" of King "Jang Soo" that "Sim-Eui" in Korea was first introduced from China at the reign of King, "Moon Ja"(491,A.D), Go Goo Ryo. 2."Sim-Eui" was worn as a mourning dress during the period of "Go Ryo" and as a concanical robe of Confucian, a ceremonial dress at home and for the rules of etiquettes during Cho Sun Dunasty. 3.Several theories about the construction and the using services of "Sim-Eui" are obseved and summerized. 4.Mr. Kyu-soo Park gives a definition to "Sim-Eui" as a Fortune of Heaven & Earth, the Constellation of the Cosmic Dual Forces, the Revolution of the Four Seasons, a dignified mien & the Way of a Man of Virtue and Virtue of the golden Mean. 5.I observed the concrete measurements of the each parts of "Sim-Eui" by the construction method of Kyu-Soo Park. 6.The Symbolic Meaning following the Idea of Mr. Chung, Hyun. describes well the line of thinking in our nation, and Idea of Loyalty & Filial Piety, a Man of Virtue and the Virtue of the Golden Mean. 7.As described above, I dare insist of the fact that the Construction Theory of "Sim-Eui" by Kyu-Soo Park during the letter period of Chosun Dynasty is full of our national manners and cus-toms with symbolizing meaning, construction's exquisiteness, clothes' materials and it's size most suitable to our people, to the exclusion of the defects in "Sim-Eui" of China and Japan.

• Korean Journal of Oriental Medicine
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• v.2 no.1
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• pp.307-313
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• 1996

In order to study for the principle of the Dan-Jeon respiration and Seon meditation to be ascetic exercises for the sake of experience of Oriental medicine as practical science, they were investigated the theory of the Jeong-Gi-Shin. The results obtained were as fallows ; 1. The Dan-Jeon respiration was Mahayana of ascetic exercises to act demension of Gi to be observed two sides of material and spirit. 2. The Seon meditation was Mahayanea of exercises to experience demension of Shin to be the subject of life directly. 3. Even though Dan-Jeon respiration takes the golden mean of Shin, it belongs to the category of Jeon-Gi to correspond to appearance of material dimension. Seon meditation utilizes the Jeong-Gi in the stage of the golden mean of Shin. As results, Dan-Jeon respiration does not get out of the world of appearance centering around the Gi. But Seon meditation gets out of the world of appearance and utilizers the relativity in the free absoluteness.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.155-159
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• 2009

Using the Binet's formula, we show that the quotient related ratio $l_{1(x)}\;\neq\;0$ for the eventually periodic continued fraction x. Using this ratio, we also show that the derivative of the Minkowski question mark function at the simple periodic continued fraction is infinite or 0. In particular, $l_1({[\bar{1}]})$ = 2 log $\gamma$ where $\gamma$ is the golden mean $(1+\sqrt{5})/2$ and the derivative of the Minkowski question mark function at the simple periodic continued fraction $[\bar{1}]$ is infinite.