• Korean Journal of Mathematics
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• v.16 no.3
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• pp.413-424
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• 2008

In [21], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\parallel}\frac{1}{n}\sum\limits_{i=1}^{n}x_i{\parallel}^2+\sum\limits_{i=1}^{n}{\parallel}x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j{\parallel}^2=\sum\limits_{i=1}^{n}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\dots},x_n{\in}V$. We consider the functional equation $$nf(\frac{1}{n}\sum\limits^n_{i=1}x_i)+\sum\limits_{i=1}^{n}f(x_i-\frac{1}{n}\sum\limits_{j=1}^{n}x_j)=\sum\limits_{i=1}^nf(x_i)$$ Using fixed point methods, we prove the generalized Hyers-Ulam stability of the functional equation $$(1)\;2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})=f(x)+f(y)$$.

• Journal of the Korea Computer Graphics Society
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• v.29 no.1
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• pp.1-11
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• 2023

Deep-learning-based image segmentation is one of the most widely employed lane detection approaches, and it requires a post-process for extracting the key points on the lanes. A general approach for key-point extraction is using a fixed threshold defined by a user. However, finding the best threshold is a manual process requiring much effort, and the best one can differ depending on the target data set (or an image). We propose a novel key-point extraction algorithm that automatically adapts to the target image without any manual threshold setting. In our adaptive key-point extraction algorithm, we propose a line-level normalization method to distinguish the lane region from the background clearly. Then, we extract a representative key point for each lane at a line (row of an image) using a kernel density estimation. To check the benefits of our approach, we applied our method to two lane-detection data sets, including TuSimple and CULane. As a result, our method achieved up to 1.80%p and 17.27% better results than using a fixed threshold in the perspectives of accuracy and distance error between the ground truth key-point and the predicted point.

• 한국연소학회:학술대회논문집
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• 2013.06a
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• pp.21-23
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• 2013

Various solid particle materials are treated in the industrial processes including fixed-beds or moving grate beds, and modeling approaches have been widely applied to the processes to predict and evaluate their performance. For this study, the modeling approach was applied to iron ore sintering process with various improvement measures. Based on the previous modeling approach, the changes and effects of the improvement measures were discussed at the point of controlling the combustion environment in the bed.

• The Pure and Applied Mathematics
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• v.16 no.1
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• pp.13-18
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• 2009

A semilocal convergence analysis is provided for Newton's method in a Banach space. The inverses of the operators involved are only locally $H{\ddot{o}}lderian$. We make use of a point-based approximation and center-$H{\ddot{o}}lderian$ hypotheses for the inverses of the operators involved. Such an approach can be used to approximate solutions of equations involving nonsmooth operators.

• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.111-120
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• 2008

A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.131-164
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• 2024

In this research, we study a modified relaxed Tseng method with a single projection approach for solving common solution to a fixed point problem involving finite family of τ-demimetric operators and a quasi-monotone variational inequalities in real Hilbert spaces with alternating inertial extrapolation steps and adaptive non-monotonic step sizes. Under some appropriate conditions that are imposed on the parameters, the weak and linear convergence results of the proposed iterative scheme are established. Furthermore, we present some numerical examples and application of our proposed methods in comparison with other existing iterative methods. In order to show the practical applicability of our method to real word problems, we show that our algorithm has better restoration efficiency than many well known methods in image restoration problem. Our proposed iterative method generalizes and extends many existing methods in the literature.

• Asia-Pacific Journal of Business
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• v.13 no.3
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• pp.361-373
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• 2022

Purpose - This paper analyzes the student determinants of college non-completion and estimates the effects of each determinant on college non-completion. Design/methodology/approach - We use student panel data from a large Korean university from 2011 to 2021. Our results are from estimation of fixed-effects logit model. Findings - The results show that grade point average, participation in extracurricular activities, the number of counseling sessions with teachers, and financial aid are the main determinants of college non-completion. Academic probation, which is defined as any person who has a cumulative grade point average below a one point seven five, increases the non-completion rate by 2.6 percentage points and an one-point rise in extracurricular activities index reduces the rate by 0.1 percentage points. The effects of each determinant are heterogeneous across student sub-groups which are separated by gender, nationality, and academic discipline. Research implications or Originality - Tailored support programs for academically discouraged students that incorporate student characteristics and backgrounds are necessary to increase college completion rates and degree attainment.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.04a
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• pp.389-392
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• 2008

This paper predicts the changes of natural frequencies due to the changes of mass at different point mass stations by using iterative calculation Transfer Matrices Method for different boundary conditions of a single beam structure (fixed-free and fixed-fixed beam). Firstly, the first three natural frequencies of an original beam are obtained using Transfer Matrices Method to verify the accuracy of the obtained results. The results are then compared with the exact solutions before purposely changing the parameter of mass. Both beams are modeled as discrete continuous systems with six-lumped-mass system. A single beam is broken down into a point mass and a massless beam which represent a single station and expressed in matrix form. The assembled matrices are used to determine the value of natural frequencies using numerical interpolation method corresponding to their mode number by manipulating some elements in the assembled matrix.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.1
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• pp.29-37
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• 2009

This paper proposes a curtailed-sequential probability ratio test (SPRT) control chart. For using the conventional SPRT control chart, the number of items inspected in a sampling point should have no restriction since items in a sampling point are inspected one by one until an SPRT Is terminated. The number of observations taken in a sampling point, however, has an upper bound since sampling and testing of an item is time-consuming or expensive. When the sample size reaches the upper bound without evidence of an in-control or out-of-control state of a process, the proposed chart makes a decision using the sample mean of all observations taken in a sampling point. The properties of the Proposed chart are obtained by a Markov chain approach and the performance of the chart is compared with fixed sample size (FSS) and variable sample size (VSS) control charts. A comparative study shows that the proposed chart performs better than VSS control charts as well as conventional FSS control charts.