• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.733-746
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• 2023

Let (X, d) be a semimetric space. A permutation Φ of the set X is a combinatorial self similarity of (X, d) if there is a bijective function f : d(X × X) → d(X × X) such that d(x, y) = f(d(Φ(x), Φ(y))) for all x, y ∈ X. We describe the set of all semimetrics ρ on an arbitrary nonempty set Y for which every permutation of Y is a combinatorial self similarity of (Y, ρ).

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.591-601
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• 2011

In this paper, we deal with the discrete p-Laplacian operators with a potential term having the smallest nonnegative eigenvalue. Such operators are classified as its smallest eigenvalue is positive or zero. We discuss differences between them such as an existence of solutions of p-Laplacian equations on networks and properties of the energy functional. Also, we give some examples of Poisson equations which suggest a difference between linear types and nonlinear types. Finally, we study characteristics of the set of a potential those involving operator has the smallest positive eigenvalue.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.605-616
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• 2000

Three primary interests frequently raised by mortgage companies are introduced and the corresponding statistical approaches for the default probability in mortgage companies are examined. Statistical models considered in this paper are time series, logistic regression, decision tree, neural network, and discrete time models. Usage of the models is illustrated using an artificially modified data set and the corresponding models are evaluated in appropriate manners.

• Bulletin of the Korean Mathematical Society
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• v.35 no.4
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• pp.689-700
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• 1998

We consider an infinite dimensional dynamical system what is called Lattice Dynamical System given by a discrete nonlinear diffusion equation. By assuming the nonlinearity to be a general nonlinear function with mild restrictions, we show that as the diffusion parameter changes the stationery state of the given system undergoes bifurcations from the zero state to a bounded invariant set or a 3- or 4-periodic state in the global phase space of the given system according to the values of the coefficients of the linear part of the given nonlinearity.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.2
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• pp.152-161
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• 1988

In this paper, a direct method for obtaining the trajectory set points is investigated in discrete-time, which is different from the other conventional schemes. We consider the tracking of a straight line path, where the trajectory set points for manipulator control are determined exactly on the straight line path. For the purpose of the munimum-time operation of manipulators, the problem is formulated as a maximization of the Cartesian distance between two consecutive servo time instants. The maximization is subject to the smoothness and torque constraints. Several algorithms are developed and utilized to maximize the Cartesian distance. The proposed approach has been simulated on a VAX-11/780 computer to verify its performance.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.1134-1139
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• 2003

Tracking is a fundamental technique which is able to be applied to gesture recognition, visual surveillance, tangible agent and so forth. Especially, multiple object tracking has been extensively studied in recent years in order to perform many and more complicated tasks. In this paper, we propose a new approach of multiple object tracking which is based on discrete event. We call this system the DEMOT (Discrete Event based Multiple Object Tracking). This approach is based on the fact that a multiple object tracking can have just four situations - initiation, continuation, termination, and overlapping. Here, initiation, continuation, termination, and overlapping constitute a primary event set and this is based on the change of the number of extracted objects between a previous frame and a current frame. This system reduces computational costs and holds down the identity of all targets. We make experiments for this system with respect to the number of targets, each event, and processing period. We describe experimental results that show the successful multiple object tracking by using our approach.

• Journal of the Korea Society for Simulation
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• v.13 no.4
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• pp.1-16
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• 2004

The modelling and simulation of the activation process for the heart system is meaningful to understand special excitatory and conductive system in the heart and to study cardiac functions because the heart activation conducts through this system. This thesis proposes two dimensional cellular automaton(CA) model for the activation process of the myocardium and conducted simulation by means of discrete time and discrete event algorithm. In the model, cells are classified into anatomically similar characteristic parts of the heart and each of cells has a set of cells with preassigned properties. Each cell in this model has state variables to represent the state of the cell and has some state transition rules to change values of state variables executed by state transition function. The state transition rule is simple as follows. First, the myocardium cell at rest stay in passive state. Second, if any one of neighborhood cell in the myocardium cell is active state then the state is change from passive to active state. Third, if cell's state is an active then automatically go to the refractory state after activation phase. Four, if cell's state is refractory then automatically go to the passive state after refractory phase. These state transition is processed repeatedly in all cells through the termination of simulation.

• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.37-53
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• 2021

In this paper we define scaled visual curvature and visual Frenet frame that can be visually accepted for discrete space curves. Scaled visual curvature is relatively simple compared to multi-scale visual curvature and easy to control the influence of noise. We adopt scaled minimizing directions of height functions on each neighborhood. Minimizing direction at a point of a curve is a direction that makes the point a local minimum. Minimizing direction can be given by a small noise around the point. To reduce this kind of influence of noise we exmine the direction whether it makes the point minimum in a neighborhood of some size. If this happens we call the direction scaled minimizing direction of C at p ∈ C in a neighborhood Br(p). Normal vector of a space curve is a second derivative of the curve but we characterize the normal vector of a curve by an integration of minimizing directions. Since integration is more robust to noise, we can find more robust definition of discrete normal vector, visual normal vector. On the other hand, the set of minimizing directions span the normal plane in the case of smooth curve. So we can find the tangent vector from minimizing directions. This lead to the definition of visual tangent vector which is orthogonal to the visual normal vector. By the cross product of visual tangent vector and visual normal vector, we can define visual binormal vector and form a Frenet frame. We examine these concepts to some discrete curve with noise and can see that the scaled visual curvature and visual Frenet frame approximate the original geometric invariants.

• Proceedings of the KOSOMBE Conference
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• v.1997 no.05
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• pp.145-149
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• 1997

This paper describes a methodology for the development of models of discrete event system. The methodology is based on transformation of continuous state space into discrete one to homomorphically represent dynamics of continuous processes in discrete events. This paper proposes a formal structure which can coupled discrete event system models within a framework. The structure employs the discrete event specification formalism for the discrete event system models. The proposed formal structure has been applied to develop a discrete event specification model for the complex spectral density analysis of strip for urin analyzer system. For this, spectral density data of strip is partitioned into a set of Phases based on events identified through urine spectrophotometry. For each phase, a continuous system of the continuous model for the urine spectral density analysis has been simulated by programmed C++. To validate this model, first develop the discrets event specification model, then simulate the model in the DEVSIM++ environment. It has the similar simulation results for the data obtained from the continuous system simulation. The comparison shows that the discrete event specification model represents dynamics of the urine spectral density at each phase.

• Kyungpook Mathematical Journal
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• v.50 no.4
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• pp.537-543
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• 2010

Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.