• Korean Journal of Mathematics
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• v.11 no.1
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• pp.1-7
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• 2003

In this paper, we introduce two types of algebraic operations on fuzzy numbers using piecewise linear functions and then show that the Zadeh implication is smaller than the Diense-Rescher implication, which is smaller than the Lukasiewicz implication. If ($f$, *) is an available pair, then $A*_mB{\leq}A*_pB{\leq}A*_jB$.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.6
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• pp.606-613
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• 1988

This paper presents an unified method of obtaining the inverse of a matrix whose elements are a linear combination of piecewise constant functions. We show that the inverse of such a matrix can be obtained by solving a set of linear algebraic equations.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.635-682
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• 2023

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the weak solutions and which is not only locally piecewise Hölder continuous but locally Hölder continuous. The gradient of the weak solutions can be estimated by this derived function and we also prove the local piecewise gradient Hölder continuity which was obtained by the previous results.

• Korean journal of applied entomology
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• v.26 no.1 s.70
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• pp.31-36
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• 1987

A piecewise linear regression model able to describe disease progress curves with simplicity and flexibility was developed in this study. The model divides whole epidemic into several pieces of simple linear regression based on changes in pattern of disease progress in the epidemic and then incorporates the pieces of linear regression into a single mathematical function using indicator variables. When twelve epidemic data obtained from the field experiments were fitted to the piecewise linear regression model, logistic model and Gompertz model to compare statistical fit, goodness of fit was greatly improved with piecewise linear regression compared to other two models. Simplicity, flexibility, accuracy and ease in parameter estimation of the piece-wise linear regression model were described with examples of real epidemic data. The result in this study suggests that piecewise linear regression model is an useful technique for modeling plant disease epidemic.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2003.05a
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• pp.1122-1127
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• 2003

Typical application of detecting piecewise-linear curves includes vectorizing of scanned drawings whirh is a vital step in installing any geographic information system. This paper considers the problem of optimally approximating a piecewise linear curve to a set of digital points while satisfying given intersection angles between each pair of neighboring lines. The criterion for optimality is to minimize the sum of squared deviations. The problem is formulated as an unconstrained nonlinear programming model. An algorithm which guarantees an optimal solution is then proposed and its validity is tested with both a synthetically generated image and a real image. The test results illustrate the excellent performance of the proposed algorithm.

• Journal of Mechanical Science and Technology
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• v.15 no.12
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• pp.1630-1638
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• 2001

Partial rotor rub occurs when an obstacle on the stator of a rotating machinery disturbs the free whirling motion of the rotor, which is more common than full annular rub among the cases of rubbing in rotating machinery. The intermittent contacts and friction during partial rotor rub makes the phenomenon complex. The several nonlinear phenomena of superharmonics, subharmonics, and jump phenomenon are demonstrated for the partial rub using an experimental apparatus in this study. The orbit patterns are also measured experimentally. In order to explain the phenomena of partial rotor rub, the analytical model for the contact between the rotor and stator should be chosen carefully. In this respect, a piecewise-linear model and a rebound model using the coefficient of restitution are investigated on the basis of the experimental observations. Also, Numerical simulations for the two models of contact are done for the various system parameters of clearance, contact stiffness, and friction coefficient. The results show that the piecewise-linear model for partial rotor rub is more plausible to explain the experimental observgations.

• Journal of the Korean Operations Research and Management Science Society
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• v.37 no.4
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• pp.19-35
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• 2012

The Semantic Web technology, purporting to share, to reuse and to process by machines data stored in the Web environment, incessantly evolves to help human decision making; in particular, decision making based on data, or quantitative decision making. This trend drives researchers to fill the gap with strenuous efforts between the current state of the technology and the terminus of this evolution. The Semantic Web Constraint Language (SWCL) together with SWRL is one of these endeavors to achieve the goal. This paper focuses particularly on how to express the piecewise linear form in the context of SWCL. The importance of this ingredient can be fortified by the fact that any nonlinear expression can be approximated in the piecewise linear form. This paper will also provide the information of how it will work in the decision making process through an example of the Internet shopping mall problem.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.40 no.4
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• pp.293-304
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• 2022

In this study, to analyze the effect of buildings on the image co-registration performance, co-registration results are compared according to the presence or absence of matching points extracted from buildings. To remove the matching points extracted from buildings, a building mask generated by extracting building objects from the digital topographic map was used. In addition, matching points extraction performance and image co-registration accuracy were analyzed according to the magnitude of the convergence angle. Image co-registration results were compared by applying the affine and piecewise linear transformation models, respectively. According to the experimental results, the affine transformation model showed an overall improvement in accuracy after removing the matching points extracted from buildings. On the other hand, the piecewise linear transformation model improved the accuracy at the checkpoints including the surrounding buildings, but the accuracy improvement was not significant at checkpoints in the flat area without the existence of buildings. In addition, when the piecewise linear transformation model was applied, stable accuracy of less than 2 pixels was derived from images with a convergence angle of 20° or less.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• Kyungpook Mathematical Journal
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• v.60 no.2
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• pp.401-413
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• 2020

In this article we consider the following system of piecewise linear difference equations: x_n+1 = |x_n| - y_n - 1 and y_n+1 = x_n + |y_n| - 1. We show that when the initial condition is an element of the closed second or fourth quadrant the solution to the system is either a prime period-3 solution or one of two prime period-4 solutions.