• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.7
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• pp.569-573
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• 2001

An approximate representation of discrete functions {f$_{i,j}\mid$｜i, j=-1, 0, 1, …, N+1}in two variables by a fuzzy system is described. We use the cubic B-splines as fuzzy sets for the input fuzzification and spike functions as the output fuzzy sets. The ordinal number of f$_{i,j}$ in the sorted list is taken to be the out put fuzzy set number in the (i, j) th entry of the fuzzy rule table. We show that the fuzzy system is an exact representation of the cubic spline function s(x, y)=$\sum_{N+1}^{{i,j}=-1}f_{i,j}B_i(x)B_j(y)$ and that the approximation error S(x, y)-f(x, y) is surprisingly O($h^2$) when f(x, y) is three times continuously differentiable. We prove that when f(x, y) is a gray scale image, then the fuzzy system is a smoothed representation of the image and the original image can be recovered exactly from its fuzzy system representation when it is a digitized image.e.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.475-491
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• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.06a
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• pp.793-794
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• 2007

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.633-634
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• 2006

Recently we started a development of the digital meister expert system for the product design supporting in manufacturing industry. Knowledge representation is of major importance in digital moister expert system. This rule-based expert system-knowledges are designed for a certain type of knowledge representation such as rules or logic. The way in which a rule-based expert system represents knowledge affects the development, efficiency, speed, and maintenance. Eventually, this digital moister system is used to the engineer in manufacturing industry for the process control, production management and system management. In this paper, we propose the digital moister system knowledge representation method for product design supporting in manufacturing industry and we present introduction and contents of rule-based knowledge representation supporting tool.

• Bulletin of the Korean Mathematical Society
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• v.29 no.1
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• pp.41-55
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• 1992

The characteristic free representation theory of the general linear group is one of the powerful tools in the study of invariant theory, algebraic geometry, and commutative algebra. Recently the study of such representations became a popular theme. In this paper we study the representation-theoretic structures of the symmetric algebra and the exterior algebra over a commutative ring with unity 1.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.4
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• pp.43-52
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• 1996

This paper describes interactive computer procedures for design the forming sequences in cold forging. This system is implemented on the personal computer and its environment is a commercial AutoCAD system. The programming language. AutoLISP, was used for the configuration of the system. Since the process of metal forming can be considered as a transformation of geometry, treatment of the geometry of the part is a key in process planning. To recognize the part section geometry, the section entity representation, the section coordinate-redius representation and the section primitive geometru were adopted. This system includes six major modules such as input module, forging design module, forming sequence design module, die design module, FEM verification module and output module which are used independently or in all. The sequence drawing wigh all dimensions, which includes the dimensional tolerances and the proper sequence of operations, can generate under the environment of AutoCAD. The acceptable forming sequences can be verified further, using the FE simulation.

• Korean Journal of Computational Design and Engineering
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• v.11 no.4
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• pp.235-245
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• 2006

This paper proposes a CSG-based representation scheme for heterogeneous objects including multi-material objects and Functionally Graded Materials (FGMs). In particular, this scheme focuses on the construction of complicated heterogeneous objects guaranteeing desired material continuities at all the interfaces. In order to create various types of heterogeneous primitives, we first describe methods for specifying material composition functions such as geometry-independent, geometry-dependent functions. Constructive Material Composition (CMC) and corresponding heterogeneous Boolean Operators (e.g. material union, difference, intersection. and partition) are then proposed to illustrate how material continuities are dealt with. Finally, we describe the model hierarchy and data structure for computer representation. Even though the proposed scheme alone is sufficient for modeling all sorts of heterogeneous objects, the proposed scheme adopts a hybrid representation between CSG and decomposition. That is because hybrid representation can avoid the unnecessary growth of binary trees.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.233-236
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• 1989

This paper deals with the expert system using network configuration and input information composed of protective relays and tripped circuit breakers. This system has knowlegebase independent on network dimension because network representation consists of the type of the matrix. Therefore, the knowlege of network representation is simplified, the space of knowlege is reduced, the addition of facts to the knowlege is easy and the expansion of facts is possible. In this paper, the network representation is defined to system matrix. This expert system based on the system matrix diagnoses normal, abnormal operations of protective devices as well as possible fault sections. The brach and bound search technique is used: breadth first technique mixed with depth first technique of primitive PROLOG search technique. This system will be used for real time operations. This expert system obtaines the solution using the pattern matching in working memory without no listing approach for rule control. This paper is written in PROLOG, the A.I. language.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2010.11a
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• pp.185-186
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• 2010

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.8
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• pp.727-732
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• 2008

In this paper, the state-space representation of generalized complimentary filter is proposed. Complementary filter has the suitable structure to merge information from sensors whose frequency regions are complementary. First, the basic concept and structure of complementary filter is introduced. And then the structure of the generalized filter and its state-space representation are proposed. The state-space representation of complementary filter is able to design the complementary filter by applying modern filtering techniques like Kalman filter and $H_{\infty}$ filter. To show the usability of the proposed state-space representation, the design of Inertial Navigation System(INS) vertical channel damping loop using Global Positioning System(GPS) is described. The proposed GPS/INS damping loop lends the structure of Baro/INS(Barometer/INS) vertical channel damping loop that is an application of complementary filter. GPS altitude error has the non-stationary statistics although GPS offers navigation information which is insensitive to time and place. Therefore, $H_{\infty}$ filtering technique is selected for adding robustness to the loop. First, the state-space representation of GPS/INS damping loop is acquired. And next the weighted $H_{\infty}$ norm proposed in order to suitably consider characteristics of sensor errors is used for getting filter gains. Simulation results show that the proposed filter provides better performance than the conventional vertical channel loop design schemes even when error statistics are unknown.