• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.1967-1973
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• 1994

The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.1141-1144
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• 2002

The research on computer graphics(CG) has been actively studied and developed. Namely, many surface/solid models have been proposed in the field of computer aided geometric design as well as the one of CG. Since it is difficult to visualize the complex shape exactly, an approximation by generating a set of meshes is usually used. Therefore it is important to guarantee the quality of the approximation in consideration of the computational cost. In this paper, a mesh generation algorithm will be proposed for a surface defined by Lie algebra. The proposed algorithm considers the quality in the meaning of validation of invariants obtained by the mesh, using automatic differentiation.

• Research in Mathematical Education
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• v.13 no.1
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• pp.1-4
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• 2009

We are considering the discovery and the promotion of the talent from the viewpoint of education of talented children. The education that develops the talent is from "Individual needs for all children." Computer Algebra System (CAS) can be used as a new possibility in the education that develops the talent. We will need to take advantage of the research results from cognitive science. In order to fully utilize CASs in education, teaching methods that are based on cognitive science will be needed, and these are clearly different from those used in paper and pencil teaching.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1103-1106
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• 2000

Recently, the research on computer graphics (CG) has been actively studied and developed. Namely, many surface/solid models have been proposed in the field of computer aided geometric design as well as the one of CG. Since it is difficult to visualize the complex shape exactly, an approximation by generating a set of meshes is usually used. Therefore it is important to guarantee the quality of the approximation in consideration of the computational cost. In this paper, a mesh generation algorithm will be proposed for a surface defined by linear tie algebra The proposed algorithm which considers the quality in the meaning of validation of invariants obtained by the mesh.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2006.05a
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• pp.85-90
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• 2006

• The Mathematical Education
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• v.45 no.2 s.113
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• pp.165-176
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• 2006

In this paper, we consider changes of algebra strands around the world. And we suggest needs of designing new computer environment where we make and manipulate geometric recursive patterns. For this purpose, we first consider relations among symbols, meanings and patterns. And we also consider Logo environment and characterize algebraic features. Then we introduce L-system which is considered as action letters and subgroup of turtle group. There are needs to be improved since there exists some ambiguity between sign and action. Based on needs of improving the previous L-system, we suggest new commands in JavaMAL microworld. So we design a microworld for recursive patterns and consider meanings of letters in new environments. Finally, we consider the method to integrate L-system and other existing microworlds, such as Logo and DGS. Specially, combining Logo and DGS, we consider the movement of such tiles and folding nets by L-system commands. And we discuss possible benefits in this environment.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.468-470
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• 1998

We have studied system identification model reduction method, optimal control by orthogonal functions. This paper presents the easy method that solves algebra equations instead of differential equations using Walsh, Haar, Block pulse function of orthogonal functions in state equation. The proposed algorithm is verified through some examples.

• Steel and Composite Structures
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• v.12 no.4
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• pp.303-324
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• 2012

This paper presents the mode-shape analysis of the cross-ply laminated composite cylindrical shallow shells. First, the kinematic relations of strains and deformation are given. Then, using Hamilton's principle, governing differential equations are developed for a general curved shell. Finally, the stress-strain relation for the laminated, cross-ply composite shells are obtained. By using some simplifications and assuming Fourier series as a displacement field, the governed differential equations are solved by the matrix algebra for shallow shells. Employing the computer algebra system called MATHEMATICA; a computer program has been prepared for the solution. The results obtained by this solution are compared with the results obtained by (ANSYS and SAP2000) programs, in order to verify the accuracy and reliability of the solution presented.

• East Asian mathematical journal
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• v.21 no.2
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• pp.249-260
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• 2005

Experimentation using computer plays an important part in education and research in graph theory. The purpose of this paper is to develop the CAS techniques for the hands-on approach in graph theory specifically on the topic of constructing the spanning tree. This paper discusses the advantages of CAS as the software system for doing graph theory and introduces the software solutions integrating multimedia user interface developed by the author, which extend the functionality of the existing CAS-based graph theory software package.

• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.16 no.1
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• pp.33-40
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• 2023

With the development of supercomputing technology and hardware technology, numerical computation methods are also being advanced. Accordingly, improved weather prediction becomes possible. In this paper, we propose to apply the LAPACK(Linear Algebra PACKage) BLAS(Basic Linear Algebra Subprograms) library to the linear algebraic numerical computation part within the source code to improve the performance of the cumulative parametric code, Unicon(A Unified Convection Scheme), which is included in SCAM(Single-Columns Atmospheric Model, simplified version of CESM(Community Earth System Model)) and performs standby operations. In order to analyze this, an overall execution structure diagram of SCAM was presented and a test was conducted in the relevant execution environment. Compared to the existing source code, the SCOPY function achieved 0.4053% performance improvement, the DSCAL function 0.7812%, and the DDOT function 0.0469%, and all of them showed a 0.8537% performance improvement. This means that the LAPACK BLAS application method, a library for high-density linear algebra operations proposed in this paper, can improve performance without additional hardware intervention in the same CPU environment.