• Journal for History of Mathematics
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• v.25 no.1
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• pp.15-27
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• 2012

Thomas Harriot(1560-1621) introduced a simplified notation for algebra. His fundamental research on the theory of equations was far ahead of that time. He invented certain symbols which are used today. Harriot treated all answers to solve equations equally whether positive or negative, real or imaginary. He did outstanding work on the solution of equations, recognizing negative roots and complex roots in a way that makes his solutions look like a present day solution. Since he published no mathematical work in his lifetime, his achievements were not recognized in mathematical history and mathematics education. In this paper, by comparing his works with Viete and Descartes those are mathematicians in the same age, I show his achievements in mathematics.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.4
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• pp.577-584
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• 1986

본 연구에서는 측정자가 시간과 노력을 소비하면서 3차원 연쇄기구의 공간운 동을 유추적으로 측정한 현재까지의 실험측정을 지양하고, 국내에서 구입 가능하고 염 가인 Apple II와 같은 같은 마이크로 컴퓨터 또는 마이크로프로세서를 이용, 3차원 연 쇄기구의 공간운동을 신속하고 정확하게 측정분석하는 자동 실험장치를 설계 제작한 다음, 이 장치를 일반 3차원 연쇄기구 모델에 적용 측정된 결과를 기호방정식을 이용 한 일반 연쇄기구 운동식의 이론 결과와 비교 검토하였다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.102-109
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• 1986

Based on the Hartenberg-Denavit symbolic equation, which is one of equations for the kinematic analysis of three dimensional (3-D) linkage, a generalized kinematic motion equation is derived utilizing Euler angles and employing the coordinates transformation. The derived equation can feasibly be used for the motion analysis of any type of 3-D linkages as well as 2-D ones. In order to simulate the general motion of 3-D linkgages on digital computer, the generalized equation is programmed through the process of numerical analysis after converting the equation to the type of Newton-Raphson formula and denoting it in matrix form. The feasibility of theoretically derived equation is experimentally proved by comparing the results from the computer with those from experimental setup of three differrent but generally empolyed 3-D linkages.

• Journal for History of Mathematics
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• v.26 no.5_6
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• pp.355-370
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• 2013

Thomas Harriot has been introduced in middle school textbooks as a great mathematician who created the sign of inequality. This study is about Harriot's symbolism and the theory of equation. Harriot made symbols of mathematical concepts and operations and used the algebraic visual representation which were combinations of symbols. He also stated solving equations in numbers, canonical, and by reduction. His epoch-making inventions of algebraic equation using notation of operation and letters are similar to recent mathematical representation. This study which reveals Harriot's contribution to general and structural approach of mathematical solution shows many developments of algebra in 16th and 17th centuries from Viete to Harriot and from Harriot to Descartes.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.6
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• pp.145-151
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• 1995

The first-order Taylor series expansion can be evaluated analytically from the formulated symbolic nonlinear dynamic equations. A closed-form linear dynamic euation is derived about a nominal trajectory. The state space representation of the linearized dynamics can be derived easily from the closed-form linear dynamic equations. But manual symbolic expansion of dynamic equations and linearization is tedious, time-consuming and error-prone. So it is desirable to manipulate the procedures using a computer. In this paper, the analytic linearization is performed using the symbolic language MATHEMATICA. Two examples are given to illustrate the approach anbd to compare nonlinear model with linear model.

• Review of KIISC
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• v.2 no.2
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• pp.25-30
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• 1992

본 논제에서는 원시근과 이차 잉여규를 중심으로 관련되는 암호학에 이용을 언급하기로 한다. 이외에도 이산로그(discrete logarithm), 연분수(conti-nued fraction), 여러 부정방정식(diophantine equation)의 이론등이 암호학에서 빈번히 사용되는 알고리즘의 근간을 이루는 이론들로 알려져 있다. 또한, 유사임의 수열(pseudo-random number sequence)을 만들기 위한 생성자 (generator)들 중에는 정수론에 기초하고 있는 것들이 않이 있다. 제2절에서는 정수의 위수와 원시근에 대한 성질을 논하고, 제 3절에서는 2차 잉여류와 Legender 기호를 소개한 후, 제4절에서 이들이 주로 사용되는 암호학의 분야를 논하기로 한다.

• New Physics: Sae Mulli
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• v.68 no.12
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• pp.1364-1373
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• 2018

A recognizable form having meaning is called a sign in semiotics. The sign is transformed into a physical counter form in this work. Its internal structure is restricted on the linguistic concept structure. We borrow the concept of a mathematical function from the utility function of a rational personal in the economy. Universalizing the utility function by introducing the consistency of independency on the manner of construction, we construct the probability. We introduce a random variable for the probability and join it to a position variable. Thus, we propose a physical sign and its serial changes in the forms of stochastic equations. The equations estimate three patterns (jumping, drifting, diffusing) of possible solutions, and we find them in the one-day stock-price flow. The periods of jumping, drifting and diffusing were about 2, 3.5, and 6 minutes for the Kia stock on 11/05/2014. Also, the semiotic sign (icon, index, symbol) can be expected from the equations.

• The Proceedings of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.1 no.1
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• pp.67-74
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• 1987

백열등의 POWER 평형 방정식을 통한 동작중의 필라멘트 온도와 광속 그리고 수명을 예측할 수 있는 이론이 제시되었다. POWER 평형 방정식을 설정함으로써 백열등 시스템을 모형화 하고, 방정식을 풀므로써 예측할 수 있는 형식으로 예측이론은 구성되었다. 가정용 110V전구에 대해 실측치와 비교해 본 결과, 충분한 타당성이 있음이 입증되었다. 본 이론의 정확한 예측성은 백열등을 해석, 이해하는 데 열쇠가 되는 제특성치를 제공할 수 있었는데 아직 생산단계에 있지 않은 크립톤가스등의 특성치도 추정할 수 있었다. 또 하나의 유용성은 백열등 설계를 위한 제 매개변수간의 관계식을 본 이론으로부터 도출하여 기존의 경험에만 의존하는 설계법을 보완하고 새로운 설계시 최적설계치를 선정할 수 있다는 점에 있다.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.1
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• pp.35-43
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• 1996

A computer program for automatic deriving the symbolic equations of motion for robots using the programming language MATHEMATICA has been developed. The program, developed based on the Lagrange formalism, is applicable to the closed chain robots as well as the open chain robots. The closed chains are virtually cut open, and the kinematics and dynamics of the virtual open chain robot are analyzed. The constraints are applied to the virtually cut joints. As a result, the spatial closed chain robot can be considered as a tree structured open chain robot with kinematic constraints. The topology of tree structured open chain robot is described by a FATHER array. The FATHER array of a link indicates the link that is connected in the direction of base link. The constraints are represented by Lagrange multipliers. The parallel robot, DELTA, having three-dimensional closed chains is modeled and simulated to illustrate the approach.