• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.519-522
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• 2001

In this paper, I propose double parallel manipulator for machining work. And I derive an kinematics by combining the kinematics of the central axis and the kinematics of the link train of linear actuator. The Jacobian of the central axis and the Jacobian of the link train of the linear actuators are induced by a motor algebra and they are combined to an entire Jacobian matrix to transform the velocity of the end effector to those of linear actuators. And then this paper presents the development of control system and user interface program for machining work.

• Applied Microscopy
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• v.24 no.4
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• pp.115-122
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• 1994

A computer program has been developed to analyze easily the Kikuchi pattern which is useful in obtaining the crystallographic data of materials. This program can simulate the Kikuchi patterns for 14 Bravais lattice by using the matrix algebra. Convenient menu system was also added to enhance the applications of the program. That is, by varying the tilting angle, camera length (RADIUS) and $S_{max}$ in the menu, various Kikuchi patterns can be obtained. The simulated patterns, then, can be compared with the experimentally-obtained Kikuchi pattern to examine validity of simulation.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.19-22
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• 1987

A program is developed for generations the dynamic equations for robotic manipulators using the symbolic language muSIMP/MATH. The muSIMP/MATH is a LISP-based computer algebra package, devoted to the manipulation of algebraic expressions including number, variables, functions, and matrix. The muSIMP/MATH can operate on IBM-PC compatibles with MS-DOS. The program is developed, on the e formalism. This is program is applicable to the manipulators of any number of degrees of freedom, maximum six degree of freedom in this program. To control robotic manipulators by using dynamic equation is required a symbolic equations. The generated dynamic equation can be applied directly to the robotic manipulators, for the generated dynamic equation is a reduced form of symbolic expression.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.565-570
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• 1994

In this article we prove a version of the Perron-Frobenius Theorem in linear algebra using the Brouwer's Fixed Point Theorem in topology. We will mostly concentrate on he qualitative aspect of the Perron-Frobenius Theorem rather than quantitative formulas, which would be enough for theoretical investigations in ergodic theory. By the nature of the method of the proof, we do not expect to obtain a numerical estimate. But we may regard it worthwhile to see why a certain type of result should be true from a topological and geometrical viewpoint. However, a geometric argument alone would give us a sharp numerical bounds on the size of the eigenvalue as shown in Section 2. Eigenvectors of a matrix A will be fixed points of a certain mapping defined in terms of A. We shall modify an existing proof of Frobenius Theorem and that will do the trick for Perron-Frobenius Theorem.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.47
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• pp.219-232
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• 1998

A lot of difficulties exist in analyzing the structure of a system owing to the complex and organic relations in the systems we face in reality. Focuses have been put on the research of optimal solution in a defined structure, however, on the assumption that the structure of the system has been already defined. With the grasping of the structure as the most prior condition, ISM(Interpretive Structural Modeling) and FSM(Fuzzy Structural Modeling) are suggested as solutions in this paper. ISM uses the systematic application of some elementary notions of graph theory and boolean algebra, FSM uses Fuzzy conception for representing relationship between elements. In FSM, the entries in the relation matrix are taken to value on the interval [0,1] by virtue of a fuzzy binary relation. Numeric examples are used as the actual application as follows.

• Communications of Mathematical Education
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• v.22 no.4
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• pp.459-469
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• 2008

We give a mathematical approach using Linear Algebra, especially largest eigenvalue and eigenvector on decision making support system. We find a mathematical modeling on decision making problem which could be solved by AHP(Analytic Hierarchy Process) method. Especially, we give a new approach to change evaluation indicator weight on assessing research proposals.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.493-510
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• 2010

This paper presents effects of anisotropy and curvature on free vibration characteristics of cross-ply laminated composite cylindrical shallow shells. Shallow shells have been considered for different lamination thickness, radius of curvature and elasticity ratio. First, kinematic relations of strains and deformation have been showed. Then, using Hamilton's principle, governing differential equations have been obtained for a general curved shell. In the next step, stress-strain relation for laminated, cross-ply composite shells has been given. By using some simplifications and assuming Fourier series as a displacement field, differential equations are solved by matrix algebra for shallow shells. The results obtained by this solution have been given tables and graphs. The comparisons made with the literature and finite element program (ANSYS).

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1257-1272
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• 2019

This article concerns the structure of idempotents in reversible and pseudo-reversible rings in relation with various sorts of ring extensions. It is known that a ring R is reversible if and only if $ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba; and a ring R shall be said to be pseudoreversible if $0{\neq}ab{\in}I(R)$ for $a,b{\in}R$ implies ab = ba, where I(R) is the set of all idempotents in R. Pseudo-reversible is seated between reversible and quasi-reversible. It is proved that the reversibility, pseudoreversibility, and quasi-reversibility are equivalent in Dorroh extensions and direct products. Dorroh extensions are also used to construct several sorts of rings which are necessary in the process.

• Journal of the Korea Society of Computer and Information
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• v.16 no.12
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• pp.139-155
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• 2011

In recent years, parents of students and government have been taking a growing interest in education for the gifted students and there are many research reports about the gifted education. Most of the reports, however, focuses on the conceptional feature of the gifted education program such as organization, operation, management, evaluation, etc,. In other words, there are very few researches on instructional materials for gifted students even though the materials is a critical factor for successful education programs. So, this paper introduces a lecture notes used in a personal education for gifted students to contribute in developing education contents in computer science area. The instructional materials titled as "The Necessity and Application of Matrix in Computer Science" is based on linear equation to usher the students into creative problem recognition and groping for solutions. Also, the instructional materials is useful for students to understand the tight mathematics-computer science relationship and the basic concept of liner algebra.

• Communications of Mathematical Education
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• v.37 no.1
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• pp.65-84
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• 2023

The method of Lagrange multipliers, one of the most fundamental algorithms for solving equality constrained optimization problems, has been widely used in basic mathematics for artificial intelligence (AI), linear algebra, optimization theory, and control theory. This method is an important tool that connects calculus and linear algebra. It is actively used in artificial intelligence algorithms including principal component analysis (PCA). Therefore, it is desired that instructors motivate students who first encounter this method in college calculus. In this paper, we provide an integrated perspective for instructors to teach the method of Lagrange multipliers effectively. First, we provide visualization materials and Python-based code, helping to understand the principle of this method. Second, we give a full explanation on the relation between Lagrange multiplier and eigenvalues of a matrix. Third, we give the proof of the first-order optimality condition, which is a fundamental of the method of Lagrange multipliers, and briefly introduce the generalized version of it in optimization. Finally, we give an example of PCA analysis on a real data. These materials can be utilized in class for teaching of the method of Lagrange multipliers.