• Title/Summary/Keyword: Simultaneous equation

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A Study of the Representation and Algorithms of Western Mathematics Reflected on the Algebra Domains of Chosun-Sanhak in the 18th Century (18세기 조선산학서의 대수 영역에 나타난 서양수학 표현 및 계산법 연구)

  • Choi, Eunah
    • Journal of the Korean School Mathematics Society
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    • v.23 no.1
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    • pp.25-44
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    • 2020
  • This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

Hydrolysis Mechanisms of Fish Oil by Lipolase-100T

  • HUR, BYUNG-KI;DONG-JIN WOO;CHONG-BO KIM
    • Journal of Microbiology and Biotechnology
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    • v.9 no.5
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    • pp.624-630
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    • 1999
  • In order to investigate the position of various fatty acids attached to glycerol and the specificity of Lipolase-100T, hydrolysis of fish oil was carried out with Lipolase-100T derived from Aspergillus oryzae. The amounts of free fatty acids produced from triglyceride, 1,2(2,3)-diglyceride, 1,3-diglyceride, and 2-monoglyceride and conversion rates of 1,2(2,3)-diglyceride to 1,3-diglyceride and 2-monoglyceride to 1(3)-monoglyceride were also calculated. The ratio of 1,2-diglyceride content to 1,3-diglyceride was higher than 70 in the early period of hydrolysis. The fatty acid content of the glyceride mixture after 72 h of hydrolysis was compared with that of fish oil, and it was found that polyunsaturated fatty acids such as C16:4, C20:4 n-3, C20:5 n-3, C21:5 n-3, C22:5 n-3 and C22:6 n-3 were located in the 2-position of glycerol. Material balance of each component in the hydrolysis system was written to obtain a set of simultaneous linear equations. The theoretical quantity of free fatty acids produced from triglyceride, 1,2-diglyceride, 1,3-diglyceride, and monoglyceride, respectively, were calculated by solving the linear equation system. The conversion rate of 1,2(2,3)-diglyceride to 1,3-diglyceride and that of 2-monoglyceride to 1(3)-monoglyceride were also obtained. The results showed that the migration rate of 1,2(2,3)-diglyceride to 1,3-diglyceride was higher than the hydrolysis rate of 1,2(2,3)-diglyceride to 2-monoglyceride and the conversion rate of 2-monoglyceride to 1(3)-monoglyceride was extremely low.

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Simulation of Two-Phase Fluid Flow in a Single Fracture Surrounding an Underground LPG Storage Cavern: II. Verification of Numerical Model and Field Application (지하 LPG 저아공동에 인접한 단일절리에서의 이상유체거동해석: II. 수치모형의 검증 및 적용)

  • Han, Il-Yeong;Seo, Il-Won
    • Journal of Korea Water Resources Association
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    • v.34 no.5
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    • pp.449-458
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    • 2001
  • In order to verify the numerical model, which was developed to simulate the behavior of the two-phase fluid flow in a single fracture, the characteristic equation of relative permeability was incorporated into the developed numerical model, and the computed results were compared with the experimental results of the model test. As results of the sensitivity analysis on the roughness and the aperture size of fracture, the gas velocity was inversely proportional to the fracture roughness, and not proportional to the square of aperture size which is usually observed in single phase flow in a single fracture. The numerical model was applied to the underground LPG storage terminal in order to check the field applicability. The simultaneous flow of water and gas in accordance with the operation pressures in a single fracture near cavern was simulated by the model. It was shown that the leaked gas was able to be controlled in a single fracture neither by the pressure of operation nor by that of groundwater in case the fracture became smoother in roughness and smaller in aperture size.

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An Analyzing the Cost-Saving Effect of R&D Investment: Focusing on the ICT Industry (연구개발투자에 따른 비용저감 효과 분석: ICT산업을 중심으로)

  • Pak, Cheolmin;Han, Jeongmin;Ku, Bonchul
    • Journal of Technology Innovation
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    • v.24 no.3
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    • pp.81-105
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    • 2016
  • The purpose of this study is to estimate the cost-saving effect of R&D investment in the ICT industry. As is well known, the R&D investment induces both the product innovation and the process innovation, in turn leads the effect of creating profit and cutting cost. However, it appears that studies concerned with the cost-saving effect of R&D investment have been unproductive, while most existing studies concentrate on the topic involved with the creating profit of R&D investment. Therefore, we extend the effect of R&D investment to a framework of the cost-saving focusing on the ICT industry. To empirically analyze the effect, we built a simultaneous three-equation model comprising a translog cost function and two cost share equations, and employed the SUR analysis. As a result, we found out that the cost-saving effect on the total cost is statistically significant. In addition, we examined relationships between the R&D investment and each cost of production elements. The results show that on the one hand, the R&D investment and the intermediate good cost have the substitution relationship. On the other hand, the complementary relationship is observed between the R&D investment and each labor or capital cost.

An Example of Internal Wave Detection in North Coastal Waters of Cheju Island Using a SAR Image (SAR를 이용한 제주도 북부해역에서의 내부파 관측예)

  • Kim, Tae-Rim;Won, Joong-Sun
    • The Sea:JOURNAL OF THE KOREAN SOCIETY OF OCEANOGRAPHY
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    • v.4 no.1
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    • pp.18-24
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    • 1999
  • The satellite image acquired by RADARSAT SAR on August 15, 1996 reveals internal waves in north coastal waters of Cheju Island. It is indicated from the image data, the tidal elevation data, and the bottom topography data, the internal waves seem to be generated by interaction between shallow bottom and tidal currents travelling in the stratified water in the summer time during the tidal changeovers from ebb to flood. The internal waves generated in such condition show patterns of trains of solitons. Probable amplitude of observed solitons is calculated using estimation of the soliton wave length from SAR image data and K-dV equation. Detection of the internal waves is very significant not only to military strategist for underwater maneuvers such as operation of submarines, but also to physical and biological oceanographers. Temporal and spatial variation of the internal waves are needed to be measured by simultaneous in-situ field study together with SAR to examine the nature of these internal waves.

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Formulation of Multivitamin Solutions for Infants (유아용 종합비타민 액제의 제제 설계)

  • Hong, Ji-Woong;Park, Eun-Seok;Chi, Sang-Cheol
    • YAKHAK HOEJI
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    • v.40 no.3
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    • pp.243-250
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    • 1996
  • In order to formulate aqueous multivitamin solutions containing both oil-soluble (A, D, E) and water-soluble vitmains ($B_1,\;B_2,\;B_6,\;B_{12}$, C and niacinamide) in 1ml-dose, the effects of various additives such as cosolvents (propylene glycol, polyethylene glycol, glycerin), a sweetener (sorbitol) and a surfactant (Cremophor$^{\circledR}$ RH40) on the solubility of oil-soluble vitamins in water were evaluated. Cremophor$^{\circledR}$ RH40 showed the excellent capacity on the solubilization of oil-soluble vitamins, and the simultaneous addition of cosolvents and surfactant resulted in synergetic effects on the solubilization of oil-soluble vitamins. The effects of the combination of the cosolvents and sweetener on the stability of multivitamin solutions were also evaluated by determining the amount of vitmain A and $B_1$ remained in the solutions after storing at $40^{\circ}C$ for 9 weeks. The formulation consisting of Cremophor$^{\circledR}$ RH40 15%, PG 20%, and sorbitol 20% resulted in the best stability of vitamin A and $B_1$. The stability of vitamin A and $B_1$ in this formulation was evaluated at 50, 60, and $70^{\circ}C$ up to 40 days. The shelf-lives of vitamin A and $B_1$ in the formulation, calculated using the Arrhenius equation, were 1,521 days and 475 days at $20^{\circ}C$, respectively.

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The Determinants of New Product Diffusion : A Simultaneous Equation Approach (신제품의 확산 결정요인 : 연립방정식 접근법)

  • Yoon, Choong Han;Lee, Jee Hoon
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.38 no.3
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    • pp.149-158
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    • 2015
  • The purpose of this paper is to investigate the determinants of new product diffusion. We seek to document and explain systematic features of product diffusion. In this essay, we examine the well-documented empirical regularity that the speed of diffusion has accelerated during the twentieth century. The empirical results show that the main source of acceleration are faster declines in prices. Faster price declines make the product affordable to more consumers within a given period of time. Based on theories of intertemporal price discrimination and learning-by-doing, the association between the speed of adoption and the speed of price decline was explained. Faster price declines are attributed to several product characteristics as well as changes in income distribution. Above all, the introduction of consumer electronic products in more recent years can be regarded as the most important factor in accelerating price declines. Consumer electronic products are technologically different from non-electronic goods, in that semiconductors are important components. As the price of semiconductors has dropped rapidly, the falling production costs can be rapidly incorporated to the price of consumer electronic goods. Furthermore, most of the recently introduced consumer electronic products have network externalities, and many products with network externalities require complementary products. A complementary product becomes more readily or cheaply available as more people have the main product. One major difference between previous studies and this study is that the former focuses only on the factors that operate directly on the speed of adoption, while this study incorporated factors that work through price changes as well as the factors that work directly on the speed of adoption.

Analysis of Effect of Learning to Solve Word Problems through a Structure-Representation Instruction. (문장제 해결에서 구조-표현을 강조한 학습의 교수학적 효과 분석)

  • 이종희;김부미
    • School Mathematics
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    • v.5 no.3
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    • pp.361-384
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    • 2003
  • The purpose of this study was to investigate students' problem solving process based on the model of IDEAL if they learn to solve word problems of simultaneous linear equations through structure-representation instruction. The problem solving model of IDEAL is followed by stages; identifying problems(I), defining problems(D), exploring alternative approaches(E), acting on a plan(A). 160 second-grade students of middle schools participated in a study was classified into those of (a) a control group receiving no explicit instruction of structure-representation in word problem solving, and (b) a group receiving structure-representation instruction followed by IDEAL. As a result of this study, a structure-representation instruction improved word-problem solving performance and the students taught by the structure-representation approach discriminate more sharply equivalent problem, isomorphic problem and similar problem than the students of a control group. Also, students of the group instructed by structure-representation approach have less errors in understanding contexts and using data, in transferring mathematical symbol from internal learning relation of word problem and in setting up an equation than the students of a control group. Especially, this study shows that the model of direct transformation and the model of structure-schema in students' problem solving process of I and D stages.

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An Analysis on the Effects of Economic Growth and Environmental Pollution by Openness (개방화가 한국의 경제성장과 환경오염에 미치는 영향 분석)

  • Cho, Sung Taek;Cho, Yongsung
    • International Area Studies Review
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    • v.13 no.3
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    • pp.269-286
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    • 2009
  • The aim of the paper is to study environmental impacts of openness and trade in korea, and analyze the relationships between trade, development and environment. This study established endogenous determinants such as inflow FDI, level of environmental pollution and economic growth, and assumed a proposition that each individual variables are in two-way relationships among the three key variables such as the openness, the environment and GDP. To estimate a system of equations, a simultaneous equation model is used because the simultaneity problems are formidable. The results show that the more openness and economic growth increase, the more level of environmental quality improve. This study also found that FDI and openness, and economic growth bring along the level of environmental quality.

A Study on the Influence of the Attributes of PPL Advertisement on the Consumer Preference, Psychological Repulsion, and Consumer Happiness: Focused on the Moderating Effect of PPL Expression Type

  • Jie, Guo Wen
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.4
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    • pp.83-90
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    • 2019
  • Is this paper, We propose to examined the relationship between advertising attributes and brand preference, consumer psychological repulsion, and consumer happiness. Due to the infinite competition between the companies, they are experiencing significant difficulties in operation. In this situation, effective advertising is obviously a very important means to overcome the difficulties of operation. Therefore, in order to maximize the advertising effect, sufficient awareness of the advertisement property and the production and exposure of the advertisement based on it can be very important. As such, the purpose of this study is to verify the effect of indirect advertising appearing on entertainment programs on consumers' preference for brands and their psychological resistance, and to verify the effect of consumers' preference for brands and psychological backlash on consumer happiness. In addition, the exposure pattern of indirect advertisement is intended to verify whether there is a control effect between the nature of the advertisement and the brand preference and psychological backlash. A total of 209 questionnaires were distributed to consumers who viewed program in order to achieve the purpose of this study. For empirical analysis, exploratory factor analysis, confirmatory factor analysis, frequency analysis, reliability analysis, structural equation model, and multimodal simultaneous comparison analysis were performed using SPSS V. 22.0 and AMOS V. 22.0. The results of the empirical analysis of this study are as follows. First, advertising attributes have a significant effect on brand preference. Second, the hypothesis that advertising attributes have a significant effect on psychological repulsiveness of consumers is partially adopted. Third, brand preference and psychological repulsion have a significant effect on consumer happiness. Fourth, we confirmed the moderating effect of PPL expression form in ad property, brand preference, and psychological repulsion. Based on these findings, we presented the implications, limitations and future research directions of the study.