• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.361-366
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• 2009

In this paper we consider constructive function triples on the real numbers $\mathbb{R}$ and on (not necessarily commutative) integral domains D which permit the construction of a multitude of d-algebras via these constructive function triples. At the same time these constructions permit one to consider various conditions on these d-algebras for subsets of solutions of various equations, thereby producing geometric problems and interesting visualizations of some of these subsets of solutions. In particular, one may consider what notions such as "locally BCK" ought to mean, certainly in the setting provided below.

• Honam Mathematical Journal
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• v.34 no.3
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• pp.341-349
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• 2012

In this paper, we discuss a constructive approximation by Gaussian neural networks. We show that it is possible to construct Gaussian neural networks with integer weights that approximate arbitrarily well for functions in $C_c(\mathbb{R}^s)$. We demonstrate numerical experiments to support our theoretical results.

• Korean Journal of Mathematics
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• v.23 no.3
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• pp.327-336
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• 2015

In this paper, we study a constructive approximation by neural networks with positive integer weights. Like neural networks with real weights, we show that neural networks with positive integer weights can even approximate arbitrarily well for any continuous functions on compact subsets of $\mathbb{R}$. We give a numerical result to justify our theoretical result.

• 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.

• Honam Mathematical Journal
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• v.35 no.4
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• pp.729-738
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• 2013

In this paper, we investigate a localized approximation of a continuously differentiable function by neural networks. To do this, we first approximate a continuously differentiable function by B-spline functions and then approximate B-spline functions by neural networks. Our proofs are constructive and we give numerical results to support our theory.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.1
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• pp.46-51
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• 1987

Using the computer-generated Lyapunov functions due to Brayton-tong's constructive algorithm, we estimate the domains of attraction of dynamical systems of the second order, and analyze the asymptotic stability of large scale contincous-time and discrete-time systems by the decomposition and aggregation method. With this approach we get the less conservative stability results than the existing methods.

• Bulletin of the Korean Mathematical Society
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• v.46 no.4
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• pp.701-712
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• 2009

In this paper, we study the simultaneous approximation to functions in $C^m$[0, 1] by neural networks with a squashing function and the complexity related to the simultaneous approximation using a Bernstein polynomial and the modulus of continuity. Our proofs are constructive.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.3
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• pp.326-334
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• 2015

This paper describes the verification and the validation about the development of the integrated interoperability system for live, virtual, and constructive simulations on the aircraft weapon system. The proposed integrated interoperability system provides the framework and application softwares for implementing a synthetic environment emulating real-world environment among distributed simulation models, which are a mission model and an air combat model of a constructive level, an tactical simulator of a virtual level, and simulated ACMI of a live level. In this paper, we verify requested functions through an developmental test and evaluation, and validate operability and usability through conducing integrated LVC scenarios on the integrated interoperability system.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.568-572
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• 1998

This paper defines Fuzzy Logic Units(FLUs) which are piece wise finite elements in multidimension Euclidean space, and redefines triangular membership functions which are different from those defined in traditional literature. By analyzing FLUs, this paper gives a constructive method of fuzzy rules in fuzzy logic systems based on finite element method. The simulation results of single machine to infinite bus system show the effectiveness of the proposed method in this paper.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.679-686
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• 2017

The present paper is devoted to self-adjoint cyclically compact operators on Hilbert-Kaplansky module over a ring of bounded measurable functions. The spectral theorem for such a class of operators is given. We use more simple and constructive method, which allowed to apply this result to compact operators relative to von Neumann algebras. Namely, a general form of compact operators relative to a type I von Neumann algebra is given.