• School Mathematics
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• v.7 no.4
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• pp.319-336
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• 2005

This study is to find the properties of Diffy activity and to investigate the problems and conjectures which could be posed in the Diffy activity. The Diffy is a simple subtracting activity. But, 1 think it is a field where the mathematical thinking can take place. I proposed some problems and conjectures which can be posed. I solved the problems using excel and the software I developed and proposed the related data. I think such problems and the data will be the good materials for elementary students and gifted to think mathematically with.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05a
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• pp.315-320
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• 1998

In this work, an automatic software verification method for Nuclear Power Plant (NPP) protection system is developed. This method utilizes Colored Petri net (CPN) for modeling and Prototype Verification system (PVS) for mathematical verification. In order to help flow-through from modeling by CPN to mathematical proof by PVS, a translator has been developed in this work. The combined method has been applied to a protection system function of Wolsong NPP SDS2(Steam Generator Low Level Trip)and found to be promising for further research and applications.

• Journal of the Korean Society for Railway
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• v.9 no.1 s.32
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• pp.50-56
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• 2006

This paper presents a mathematical model of the long-term track tamping scheduling problem in the Korean highspeed railway system. The presented model encompasses various operational field constraints, moreover improves a state-of-the-art model in extending the feasible space. We show the model is sized up to intractable scale, then propose another approximation model that is possible to handle with the present computer system and commercial optimization package, directly. The aggregated index, lot, is selected, considering the resolution of the planning horizon as well as scheduling purpose. Lastly, this paper presents two test results for the approximation model. The results expose the approximation model to quite promising in deploying it into an operational software program for the long-term track tamping scheduling problem.

• Steel and Composite Structures
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• v.18 no.2
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• pp.481-496
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• 2015

A Lead Extrusion Damper (LED) is experimentally studied under various frequencies and displacement amplitudes. Experimental results show that the force-displacement hysteresis loops of the LED are close to rectangular and the force-velocity hysteresis loops exhibit nonlinear hysteretic characteristic. Also, the LED can provide consistent energy dissipation without any stiffness degradation. Based on the experimental results, a mathematical model is then proposed to describe the effects of frequency and displacement on property of LED. It can be proved from the comparison between experimental and numerical results that the mathematical model can accurately describe the mechanical behavior of LED. Subsequently, the seismic responses of the Schwedler reticulated shell structure with LEDs are analyzed by ANSYS software, in which three different installation forms of LEDs are considered. It can be concluded that the LED can effectively reduce the displacement and acceleration responses of this type of structures.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.217-233
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• 2022

Although machine learning shows state-of-the-art performance in a variety of fields, it is short a theoretical understanding of how machine learning works. Recently, theoretical approaches are actively being studied, and there are results for one of them, margin and its distribution. In this paper, especially we focused on the role of margin in the perturbations of inputs and parameters. We show a generalization bound for two cases, a linear model for binary classification and neural networks for multi-classification, when the inputs have normal distributed random noises. The additional generalization term caused by random noises is related to margin and exponentially inversely proportional to the noise level for binary classification. And in neural networks, the additional generalization term depends on (input dimension) × (norms of input and weights). For these results, we used the PAC-Bayesian framework. This paper is considering random noises and margin together, and it will be helpful to a better understanding of model sensitivity and the construction of robust generalization.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1051-1066
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• 2013

By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.

• The Mathematical Education
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• v.38 no.2
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• pp.179-187
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• 1999

Math teachers are very short of computer tools and manipulatives to use in geometry classes of middle schools for the development of spatial abilities. At most they can ask student to make regular polyhedrons for helping the students to understand by concrete experience, but this experience is not enough to develop spatial abilities in spatial figures including the regular polyhedrons. This article is to introduce instructional materials for development of spatical ability in the regular polyhedrons using computer software, Geometer's Sketchpad. In this article, students can imagine the whole figure through the parts of a plane figure and think of the parts from the solid figure by free movement from 2 dimensions to 3 dimensions, or from 3 dimensions to 2 dimensions. Also, the instructional materials devised in this article will be good to enhance spatial abilities because the relation of 1-1 correspondence in the movement of the parts can be conserved and observed precisely, which is very hard to demonstrate and visualize by paper-and-pencil. It is recommended that this kind of materials should be developed in various ways for teachers to use them directly in their geometry classes.

• Smart Structures and Systems
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• v.11 no.1
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• pp.35-51
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• 2013

Over the last two decades Wavelet Transformation (WT) method has been widely utilized for the damage identification of structures. The main objective of this paper is to discuss and present some of common shortcomings and limitations of mathematical software, as well as other precautionary measures that need to be considered when using them for wavelet analysis applications. Due to popular usage of MATLABMATLAB(R) comparing to other mathematical tools among researchers for data processing of structural responses through WT analysis, this software was chosen for specific study. To the best of the authors' knowledge, these limitations and observations have not been previously identified or discussed in the literature. In this work, a square plate with a severe damage, in form of a crack, parallel to the left edge of the plate is selected for a pilot study. The steady state harmonic response is used for measuring the deflection shape across the line parallel to one edge and perpendicular to the damage. Several criteria and cases such as the smallest size damage that can be detected, correlation between the crack width and the number of sampling points, and the influence of the damage thickness on the accuracy of the result are investigated.

• Journal of Biosystems Engineering
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• v.43 no.4
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• pp.369-378
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• 2018

Purpose: The aim of this study was to construct a saponin content-predicting model using shortwave infrared imaging spectroscopy. Methods: The experiment used a shortwave imaging spectrometer and ENVI spectral acquisition software sampling a spectrum of 910 nm-2500 nm. The corresponding preprocessing and mathematical modeling analysis was performed by Unscrambler 9.7 software to establish a ginsenoside nondestructive spectral testing prediction model. Results: The optimal preprocessing method was determined to be a standard normal variable transformation combined with the second-order differential method. The coefficient of determination, $R^2$, of the mathematical model established by the partial least squares method was found to be 0.9999, while the root mean squared error of prediction, RMSEP, was found to be 0.0043, and root mean squared error of calibration, RMSEC, was 0.0041. The residuals of the majority of the samples used for the prediction were between ${\pm}1$. Conclusion: The experiment showed that the predicted model featured a high correlation with real values and a good prediction result, such that this technique can be appropriately applied for the nondestructive testing of ginseng quality.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.961-976
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• 2019

Let R be any commutative ring and S be any multiplicative closed set. We introduce an S-version of $\mathcal{F}$-Mittag-Leffler modules, called $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and define the projective dimension with respect to these modules. We give some characterizations of $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, investigate the relationships between $\mathcal{F}$-Mittag-Leffler modules and $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler modules, and use these relations to describe noetherian rings and coherent rings, such as R is noetherian if and only if $R_S$ is noetherian and every $\mathcal{F}_{\mathcal{S}}$-Mittag-Leffler module is $\mathcal{F}$-Mittag-Leffler. Besides, we also investigate the $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension of R, and prove that $R_S$ is noetherian if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is zero; $R_S$ is coherent if and only if its $\mathcal{M}^{\mathcal{F}_{\mathcal{S}}$-global dimension is at most one.