• Journal of the Korean Society for Precision Engineering
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• v.6 no.2
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• pp.40-46
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• 1989

Recently, the researches on cutting the new material have been done for development of aerospace industrial engineering. Especially, titanium ally is well known as heat resisting, antiwear, anticorrosion and difficult-to-machine materials. Many studies on the analysis of shear angle have been done for improving productivity in cutting these materials. In case of titanium alloy, the saw-toothed type of chip which has wave surface of a triangular form, an eccentric from of a continuous type of chip that is produced in the cutting process, was checked. Nakayama supposed that a maximum shear strewss plane and the shear crack in the free surface made an angle of $45^{\circ}$ .deg. , but it's usually much larger than that. In this paper, the author analyzed the shear conditions of the cutting process in the quick-stopping device with the help SEM-photographs, and measured the hypotenuse angle directly in the photographs of the chips. In conclusion, the author tried to find the shear angle in the cutting process with the saw-toothed chip and compared it with the shear angles which can be calculated from the theories established by others. The results obtained are as follows. 1. In case of the saw-toothed chips, the equivalent cutting ratio can be calculated by using the chip thickness to two-thirds of ramp height. 2. The theory of Ernst-Merchant is not applicable to the titanium and its alloys which does not fractured in accordance with the theory of maximum shear stress. 3. When we cut the titanium alloys which produced the saw-toothed chips, the shear angle can be found with the theories of Rowe-Spick, P.K. Wright and the measurement of hypotenuse angle.

• Journal for History of Mathematics
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• v.32 no.4
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• pp.159-173
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• 2019

In this paper, we examine the brief history of the ring of four almonds regarding Mesopotamian mathematics, and present reasons why the Omar Khayyam's triangle, a special right triangle in a ring of four almonds, was essential for artisans due to its unique pattern. We presume that the ring of four almonds originated from a point symmetry figure given two concentric squares used in the proto-Sumerian Jemdet Nasr period (approximately 3000 B.C.) and a square halfway between two given concentric squares used during the time of the Old Akkadian period (2340-2200 B.C.) and the Old Babylonian age (2000-1600 B.C.). Artisans tried to create a new intricate pattern as almonds and 6-pointed stars by subdividing right triangles in the pattern of the popular altered Old Akkadian square band at the time. Therefore, artisans needed the Omar Khayyam's triangle, whose hypotenuse equals the sum of the short side and the perpendicular to the hypotenuse. We presume that artisans asked mathematicians how to construct the Omar Khayyam's triangle at a meeting between artisans and mathematicians in Isfahan. The construction of Omar Khayyam's triangle requires solving an irreducible cubic polynomial. Omar Khayyam was the first to classify equations of integer polynomials of degree up to three and then proceeded to solve all types of cubic equations by means of intersections of conic sections. Omar Khayyam's triangle gave practical meaning to the type of cubic equation $x^3+bx=cx^2+a$. The work of Omar Khayyam was completed by Descartes in the 17th century.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.211-224
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• 2020

Sensitivity and specificity are popular measures described by the receiver operating characteristic (ROC) curve. There are also two other measures such as the positive predictive value (PPV) and negative predictive value (NPV); however, the PPV and NPV cannot be represented by the ROC curve. Based on the total operating characteristic (TOC) curve suggested by Pontius and Si (International Journal of Geographical Information Science, 97, 570-583, 2014), explanatory methods are proposed to geometrically describe the PPV and NPV by the TOC curve. It is found that the PPV can be regarded as the slope of the right-angled triangle connecting the origin to a certain point on the TOC curve, while 1 - NPV can be represented as the slope of the right-angled triangle connecting a certain point to the top right corner of the TOC curve. When the neutral zone exists, the PPV and 1-NPV can be described as the slopes of two other right-angled triangles of the TOC curve. Therefore, both the PPV and NPV can be estimated using the TOC curve, whether or not the neutral zone is present.

• Asian Pacific Journal of Cancer Prevention
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• v.16 no.7
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• pp.2889-2894
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• 2015

Background: To investigate the impact of the breast size, shape, maximum heart depth (MDH), and chest wall hypotenuse (the distance connecting middle point of the sternum and the length of lung draw on the selected transverse CT slice) on the volumetric dose to heart with whole breast irradiation (WBI) of left-sided breast cancer patients. Materials and Methods: Fifty-three patients with left-sided breast cancer undergoing adjuvant intensity-modulated radiotherapy (IMRT) were enrolled in the study. The primary breast size and shape, MHD and DCWH (chest wall hypotenuse) were contoured on radiotherapy (RT) planning CT slices. The dose data of hearts were obtained from the dose-volume histograms (DVHs). Data were analyzed by one-way analysis of variance (ANOVA), Student's t-test and linear regression analysis. Results: Breast size was independent of heart dose, whereas breast shape, MHD and DCWH were correlated with heart dose. The shapes of breasts were divided into four types, as the flap type, hemisphere type, cone type and pendulous type with heart mean dose being $491.8{\pm}234.6cGy$, $752.7{\pm}219.0cGy$, $620.2{\pm}275.7cGy$, and $666.1{\pm}238.0cGy$, respectively. The flap type of breasts shows a strong statistically reduction in heart dose, compared to others (p=0.008 for V30 of heart). DCWH and MHD were found to be the most important parameters correlating with heart dose in WBI. Conclusions: More attention should be paid to the heart dose of non-flap type patients. The MHD was found to be the most important parameter to correlate with heart dose in tangential WBI, closely followed by the DCWH, which could help radiation oncologists and physicsts evaluate heart dose and design RT plan in advance.

• Magazine of the Korean Society of Agricultural Engineers
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• v.6 no.2
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• pp.816-825
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• 1964

1. Outline: The flow of the siphon spillway is very intricate and affected by vacuous condition. It is an intresting problem to make vacuum rapidly in_siphon, i.e, to provoke the perfect siphonaoge with the lowest water-level of overflow. The hydraulic experiments of siphon spillway have practiced at the Masan Lake, Haenam, the province of Junnam and gained rational and economical results which cannot be odtained by calculation. 2. Experiment: The model scale was a half of that of the prototype. 3. Results and discussion: In the experiments of 14 runs, washing, overflow water level, outlet, water level of cushion, phenomenon of water flying and water pressure of every part, etc. were studied. a) The relation of overflow water-level at siphon inlet and deflector When the elevation of the deflector is 10. 65m and the form of deflector O.4m long is the hypotenuse of an $45^{\circ}$ isosceles triangle, the over flow water-level is the minimum, i. e. the siphonage was excellent. There is no effect by the rising of overflow water-Ievel between 11.95m to 1O.65m of deflector elevation (in the first plan, it is 11.05m). But the overflow water-level rises remarkably in the outside region of the above limits. b) The relation of overflow water-level, the length of cushion and standard height of the base. The reduction of the length of cushion brings the rising of overflow waterlevel, and the rising of the standard height of the base brings the rising of overflow water level. For the long cushion length and low standard height of the base, it cannot be expeted to have the falling of overflow water-level. The most satisfactory data were obtained at 5.20m of the base standard height and 6.1m of the length of cushion. The first vah,le planned was 5.70 m and 4.30m.

• Journal of Fashion Business
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• v.15 no.3
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• pp.22-31
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• 2011

In this study, to develop a bodice pattern for women aged 18~24 years, statistical analysis was conducted using the body measurements from 2004 Size Korea and wearing test was conducted. As a result, ease of the bust level to set a horizontal line was decided to be 4cm, that of front interscye line 0cm, and that of back interscye line 0.7~1cm. And the line which divides the horizontal baseline into halves set as the side line. The conversion formula for decision of the scye depth line in the pattern is B/6 + 3.3(cm) + ease (2.5cm), and if bust circumference is 91 or more, it should be 21cm, and if bust circumference is 76 or less, it should be 18.5cm. The back neck line width is 7cm, front neck line width 6.5cm(back neck line width -0.5cm), and front neck depth 8cm(back neck line width +1cm). The shoulder slope was set as a slope of the hypotenuse of a right-angled triangle, which went out 15cm out of the shoulder point and went down 6cm, with tan$21.7^{\circ}$. To develop a final research pattern, wearing test was performed on the primary research pattern for 21 women aged 18~24 years. As a result, the research pattern was evaluated to be significantly higher.

• Journal of the Korean Society for Precision Engineering
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• v.4 no.3
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• pp.44-51
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• 1987

In metal cutting various types of chips are produced in consequence of cutting conditions. Flow-type chips have been studied in most cases because they are easier to be analyzed, but the actual surfaces of chips are not smooth, but crushed. This paper deals with saw-toothed chips, special types of flow-type chips, which have deep concaves and high convexes and sharp angles on the free surface. I tried to establish the theory of saw-toothed chip mechanism through experimental observation, that is, the mathmatical model of the cutting energy and cutting mechanism through the geometrical observation of the chips by using a microscope. The results obtained are as follows: 1. The mechanism of saw-toothed chips is diffenent from that of general flow-chips. 2. In the case of saw-toothed chips, the shear angle must be measured by the hypotenuse angle and the rake angle, and the shear angle is more affected by the rake angle than by the hypotenbuse angle. 3. The friction angle is represented by .beta. = . pi. /4+ .alpha./ sub n/- .phi. which is different from Merchant's equation. 4. The pitch and the slip are greatly influenced by depth of cut, but the influence of the rake angle on it is small. 5. The normal stress and the shear stress on the shear plane decrease with the increase of the cutting depth, and they are almost independent on the variation of a rake angle. 6. The unit friction energy on the tool face, the unit shear energy on the shear plane, and the total cutting energy per unit volume decrease with the increase of rake angle and cutting depth.

• Journal of Energy Engineering
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• v.24 no.1
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• pp.114-122
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• 2015

In the high convective gas flow condition, irregular shaped water waves from which droplet entrainment occurs are generated under horizontally stratified two-phase flow condition. KAERI proposed a new mechanistic droplet entrainment model based on the momentum balance equation consisting of the shear stress, surface tension, and gravity forces. However, this model requires correlation or experimental data of several physical parameters related to the wave characteristics. In the present study, we tried to measure the physical parameters such as wave slope, wave hypotenuse length, wave velocity, wave frequency, and wavelength experimentally. For this, an experiment was conducted in the horizontal rectangular channel of which width, height, and length are, respectively, 40 mm, 50 mm, and 4.2 m. In the present test, the working fluids are chosen as air and water. The PIV technique was applied not only to obtain images for phase interface waves but also to measure the velocity field of the water flow. Additionally, we developed the parallel wire conductance probe for the confirmation of wave height from PIV image. Finally, we measured the physical parameters to be used in the validation of new droplet entrainment model.