• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• Journal of Computational Design and Engineering
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• v.3 no.2
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• pp.151-160
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• 2016

Cutter-workpiece engagement (CWE) is the instantaneous contact geometry between the cutter and the in-process workpiece during machining. It plays an important role in machining process simulation and directly affects the calculation of the predicted cutting forces and torques. The difficulty and challenge of CWE determination come from the complexity due to the changing geometry of in-process workpiece and the curved tool path of cutter movement, especially for multi-axis milling. This paper presents a new method to determine the CWE for general milling processes. To fulfill the requirement of generality, which means for any cutter type, any in-process workpiece shape, and any tool path even with self-intersections, all the associated geometries are to be modeled as triangle meshes. The involved triangle-to-triangle intersection calculations are carried out by an effective method in order to realize the multiple subtraction Boolean operations between the tool and the workpiece mesh models and to determine the CWE. The presented method has been validated by a series of case studies of increasing machining complexity to demonstrate its applicability to general milling processes.

• Imaging Science in Dentistry
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• v.51 no.2
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• pp.167-174
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• 2021

Purpose: Sex determination can be done by morphological analysis of different parts of the body. The mastoid region, with its anatomical location at the skull base, is ideal for sex identification. Statistical shape analysis provides a simultaneous comparison of geometric information on different shapes in terms of size and shape features. This study aimed to investigate the geometric morphometry of the inter-mastoid triangle as a tool for sex determination in the Iranian population. Materials and Methods: The coordinates of 5 landmarks on the mastoid process on the 80 cone-beam computed tomographic images(from individuals aged 17-70 years, 52.5% female) were registered and digitalized. The Cartesian x-y coordinates were acquired for all landmarks, and the shape information was extracted from the principal component scores of generalized Procrustes fit. The t-test was used to compare centroid size. Cross-validated discriminant analysis was used for sex determination. The significance level for all tests was set at 0.05. Results: There was a significant difference in the mastoid size and shape between males and females(P<0.05). The first 2 components of the Procrustes shape coordinates explained 91.3% of the shape variation between the sexes. The accuracy of the discriminant model for sex determination was 88.8%. Conclusion: The application of morphometric geometric techniques will significantly impact forensic studies by providing a comprehensive analysis of differences in biological forms. The results demonstrated that statistical shape analysis can be used as a powerful tool for sex determination based on a morphometric analysis of the inter-mastoid triangle.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.6 no.10
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• pp.2567-2586
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• 2012

Localization of sensor nodes is a key technology in Wireless Sensor Networks(WSNs). Trilateration is an important position determination strategy. To further improve the localization accuracy, a novel Trilateration based on Point In Triangle testing Localization (TPITL)algorithm is proposed in the paper. Unlike the traditional trilateration localization algorithm which randomly selects three neighbor anchors, the proposed TPITL algorithm selects three special neighbor anchors of the unknown node for trilateration. The three anchors construct the smallest anchor triangle which encloses the unknown node. To choose the optimized anchors, we propose Point In Triangle testing based on Distance(PITD) method, which applies the estimated distances for trilateration to reduce the PIT testing errors. Simulation results show that the PIT testing errors of PITD are much lower than Approximation PIT(APIT) method and the proposed TPITL algorithm significantly improves the localization accuracy.

• Geomechanics and Engineering
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• v.15 no.2
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• pp.745-754
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• 2018

In the analysis of the effects of rock tunnel blasting vibration on adjacent existing buildings, the model of simplified equivalent load produces higher calculation result of vibration, due to the lack of consideration of the millisecond delay effect. This paper, based on the static force equivalence principle of blasting load, proposes a new determination method of equivalent load of blasting vibration. The proposed method, based on the elastic-static force equivalence principle of stress wave, equals the blasting loads of several single blastholes in the same section of millisecond blasting to the triangle blasting load curve of the exploded equivalent elastic boundary surface. According to the attenuation law of stress wave, the attenuated equivalent triangle blasting load curve of the equivalent elastic boundary is applied on the tunnel excavation contour surface, obtaining the final applied equivalent load. Taking the millisecond delay time of different sections into account, the time-history curve of equivalent load of the whole section applied on the tunnel excavation contour surface can be obtained. Based on Sailing Tunnel with small spacing on Sanmenxia-Xichuan Expressway, an analysis on the blasting vibration response of the later and early stages of the tunnel construction is carried out through numerical simulation using the proposed equivalent load model considering millisecond delay effect and the simplified equivalent triangle load curve model respectively. The analysis of the numerical results comparing with the field monitoring ones shows that the calculation results obtained from the proposed equivalent load model are closer to the measured ones and more feasible.

• Magazine of the Korean Society of Agricultural Engineers
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• v.18 no.4
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• pp.4209-4217
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• 1976

The purpose of this thesis is to search for the determination method of pumping rates in the existing tube wells for irrigation. Pumping tests were carried out for the twelve test tube wells which were selected in the provinces of Kyounggi, Kangwon, Chungbuk and Chungnam. The depths, static water levels, pumping levels, drawdowns and yields of tube wells were measured in the pumping tests, and a centrifugal pump with 3 inches diameter, a 5 HP motor and a 90$^{\circ}$ V-notch were used in the pumping tests. The average coefficient of transmissibility calculated by Chow's and Jacob's methods is 0.0336 square meter per second, and the average pumping rate calculated by Thiem's, Smreker's, Brinkhaus' and Theis' formulae, is 919 cubic meter per day, Therefore, the ground water storage in the test areas is comparatively abundant. Correlation between pumping rates and depths of tube wells is not in existence. Also, correlation between pumping rates and the thickness of aquifer is not found in this experiment. This shows that the depths of some tube wells are deep and their thicknesses of aquifer are thick, but their ground water storages are poor, and that the depths of some tube wells are shallow and their thicknesses of aquifer are thin, but their ground water storages are abundant. It seems that the test tube wells are influenced by the peculiar characteristics that the ground water in the test areas is free ground water in alluvium layer closely related with surface water. As drawdown increases, pumping rate decreases, and as the coefficient of transmissibility increases, pumping rate also increases. Namely, there are negative correlation between pumping rate and drawdown, and positive correlation between pumping rate and the coefficient of transmissibility. Judging from the results of the pumping tests in these tests areas, the pumping rate calculated by the formula, {{{{ { Q}_{m } =Q { ( { { S}_{ m} } over { TRIANGLE S } )}^{ { 2} over {3 } } }}}} used traditionally, is likely to be higher than real pumping rates. The formula, {{{{ { Q}_{m } =Q { { H}^{ 2} } over { (2H- TRIANGLE S) TRIANGLE S} }}}} derived from Thiem's theory, is looked upon as the reasonable one to detemine pumping rates in the existing tube wells for irrigation.

• Fashion & Textile Research Journal
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• v.19 no.5
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• pp.635-645
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• 2017

The industry of character toys is increasing and new characters are constantly being developed. However, the development of 2D cover patterns for toys is time-consuming due to frequent pattern modifications made through trial and error. Studies are now underway to obtain 2D clothing patterns from 3D body data, however, little research has been done on 2D pattern of character toys. This study suggests efficient guidelines to develop 2D cover patterns with a reasonable accuracy and processing time. Two 3D models of a dog and rabbit were used to develop 2D cover patterns. Independent variables of this study are set as 3 levels of triangle area (small, medium, and large) that influence the efficacy of 3D and 2D pattern development. The determination of the appropriate triangular area was based on the area and shape change of the 2D pattern. A medium or large triangle area was shown to be suitable for a character dog with a smooth curved surface. However, the appropriate triangle area was small if the characteristics of the curved surface are complicated as in the case of rabbit. The head of a dog (a double-curved surface) and the curved forepaw of a rabbit (a triangular area) should be small when the characteristics of the curved surface (such as the hind leg of a rabbit having a large convex surface and a small surface area) are complicated. Grouping by 3D surface characteristics could be a suitable guideline for the triangle area selection.

• Korean Journal of Environmental Agriculture
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• v.26 no.3
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• pp.204-209
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• 2007

Agricultural area in the vicinity of the ${\triangle}{\triangle}$ smelting factory in Kyeongbuk province, the third largest zinc smelting factory in the world, was contaminated by high concentration of heavy metals. However, the heavy metals source was not yet directly traced and thus, resulted to a conflict between the factory and residents within its vicinity. In order to determine the level of heavy metal contamination in the arable lands located at the north eastern part of the factory, soils were sampled systematically. To find out the major reason for the occurrence of this problem, waters and aerosols were sampled with constant intervals to the upward and downward direction from the factory and were analyzed to find out the heavy metal concentrations. Cadmium (Cd) and zinc (Zn) of the heavy metals were highly accumulated more than the Korean warning criteria (Cd 1.5, Zn 300 mg $kg^{-1}$) with mean values 1.7 and 407 mg $kg^{-1}$, respectively, at the surface soils (0-20 cm), and heavy metal concentration significantly decreased with increasing soil depth In addition, the concentration of both metals slightly decreased with increasing distance from the factory to the surface soils. Cadmium and Zn were detected in the upward stream water with low concentration and concentrations increased significantly in the downstream after passing across the factory. Aerosol samples also showed traces of Cd and Zn which could be attributed to the contamination of the water system and the surface soils. Conclusively, Cd and Zn emitted from the ${\triangle}{\triangle}$ smelting factory moved with the aerosol in the atmosphere and thus, contaminated the agricultural areas and the water system within it vicinity.

• Biotechnology and Bioprocess Engineering:BBE
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• v.10 no.4
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• pp.341-345
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• 2005

Since it is troublesome to estimate adequate flow rates in four sections of SMB chromatography, a systematic determination of the flow rates has been suggested by using ketoprofen as a model chiral enantiomer. S-ketoprofen. less retained species, was separated from raffinate stream and the variation in its purity was dependent on the changes of the flow rate of section 4 ($Q_4$), the raffinate flow rate ($Q_{raf}$), and the feed flow rate ($Q_{feed}$) under a fixed switch­ing time t$^{\ast}$. When one parameter was changed at the given experimental condition, purities of product were changed and these phenomena has be well explained by the triangle theory.

• Journal of Environmental Science International
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• v.12 no.1
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• pp.87-92
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• 2003

Synchronous spectrofluorimetry was carried out for the simultaneous determination of various polycyclic aromatic hydrocarbons(PAHs) in aqueous solution by fluorescence spectrometry have been studied. The optimal wavelength interval(${\triangle}{\lambda}$) for synchronous spectra of acenaphthene, anthracene, benzo[a]anthracene, fluorene and pyrene were investigated in the presence of surfactants. The great enhancement of the fluorescence of these PAHs in Triton X-100 was obtained and optimal wavelength was 50 nm. The calibration curves in synthetic mixture solution of 5 PAHs were linear over the range from $1.0{\times}10^{-8}M$ to $1.0{\tiems}10^{-4}M$. Under the optimal experimental conditions, the detection limits were $4.9{\tiems}10^{-9}M$,\;7.0{\times}10^{-9}M,\;4.7{\tiems}10^{-9}M,\;1.6{\tiems}10^{-9}M$ and $3.2{\tiems}10^{-9}M$ for acenaphthene, anthracene, benzo[a]anthracene, fluorene and pyrene, respectively.