• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.487-497
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• 2020

In this paper, we establish a complex matrix representation of the Clifford algebra Cℓ_p,q. The size of our representation is significantly smaller than the size of the elements in L_p,q(ℝ). Additionally, we give detailed information about the spectrum of the constructed matrix representation.

• Journal of applied mathematics & informatics
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• v.26 no.3_4
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• pp.605-614
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• 2008

In this paper, we find the matrix representation of multi-degree reduction by $L_{\infty}$ of $B{\acute{e}}zier$ curves with constraints of endpoints continuity. Using the basis transformation between Chebyshev polynomials and Bernstein polynomials we can derive the matrix representation of multi-degree reduction of $B{\acute{e}}zier$ with respect to $L_{\infty}$ norm.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1119-1129
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• 2022

We formulate the matrix representation of a composition operator on the Hardy space of the unit disc with the symbol which is a Riemann map of the unit disc, with respect to a special orthonormal basis.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.103-110
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• 2005

This paper is aimed at studying a historical background of graph theory and we deal with the computer representation of graph through a simple example. Graph is represented by adjacency matrix, edge table, adjacency lists and we study the matrix representation by Euler circuit. The effect of the matrix representation by Euler circuit economize the storage capacity of computer. The economy of a storage capacity has meaning on a mobile system.

• Journal of the Korean Mathematical Society
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• v.44 no.2
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• pp.487-498
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• 2007

In this paper, we obtain important combinatorial identities of generalized harmonic numbers using symmetric polynomials. We also obtain the matrix representation for the generalized harmonic numbers whose inverse matrix can be computed recursively.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.212-217
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• 1992

In this paper, a two ports machine(TPM) model for discrete event dynamic systems(DEDS) is proposed. The proposed model is a finite state machine which has two inputs and two outputs. Inputs and outputs have two components, events and informations. TPM is different from other state machine models, since TPM has symmetric input and output. This symmetry enables the block diagram representation of the DEDS with TPM blocks, summing points, multiplying points, branch points, and connections. The graphical representation of DEDS is analogous to that of control system theory. TPM has a matrix representation of its transition and information map. This matrix representation simplifies the analysis of the DEDS.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.3
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• pp.135-142
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• 2011

Unlike using the sequence-based representation for a chromosome in previous genetic algorithms for Bayesian structure learning, we proposed a matrix representation-based genetic algorithm. Since a good chromosome representation helps us to develop efficient genetic operators that maintain a functional link between parents and their offspring, we represent a chromosome as a matrix that is a general and intuitive data structure for a directed acyclic graph(DAG), Bayesian network structure. This matrix-based genetic algorithm enables us to develop genetic operators more efficient for structuring Bayesian network: a probability matrix and a transpose-based mutation operator to inherit a structure with the correct edge direction and enhance the diversity of the offspring. To show the outstanding performance of the proposed method, we analyzed the performance between two well-known genetic algorithms and the proposed method using two Bayesian network scoring measures.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1133-1136
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• 1993

Fuzzy algorithm is essentially nondeterministic, but to guarantee the stable control the fuzzy control program should be deterministic in practice. Fuzzy controllers with matrix representation is very simple in construction and very fast in computation. The value of the matrix is not adequate at the first place, but can be modified by using the neural networks. We apply the simple heuristic techniques to modify the matrix successfully.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.380-392
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• 2000

This paper proposes a qualitative reasoning approach for the spatial configuration of mechanisms that could be applied in the early phase of the conceptual design. The spatial configuration problem addressed in this paper involves the relative direction and position between the input and output motion, and the orientation of the constituent primitive mechanisms of a mechanism. The knowledge of spatial configuration of a primitive mechanism is represented in a matrix form called spatial configuration matrix. This matrix provides a compact and convenient representation scheme for the spatial knowledge, and facilitates the manipulation of the relevant spatial knowledge. Using this spatial knowledge of the constituent primitive mechanisms, the overall configuration of a mechanism is described and identified by a spatial configuration state matrix. This matrix is obtained by using a qualitative reasoning method based on sign algebra and is used to represent the qualitative behavior of the mechanism. The matrix-based representation scheme allows handling the involved spatial knowledge simultaneously and the proposed reasoning method enables the designer to predict the spatial behavior of a mechanism without knowing specific dimension of the components of the mechanism.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.489-495
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• 2000

Stress and strain in continuum mechanics have a mathematical form of the second order tensor. it is well-known that the usefulness of tensor components could be explained in a relation with coordin ates system transformation and Mohr's circle could be easily used to make a coordinate system transformation of tensors. However, Mohr's circle is applied mainly to plane problems and its use to three dimensional cases is limitedly employed. In this paper, we propose a matrix and dyadic representation of stress and strain tensors which could equivalently replace the graphical representation of second order tensors. The use of the proposed representation might provide a valuable means for the educational respects as well as research view point.