• East Asian mathematical journal
• /
• v.35 no.2
• /
• pp.239-257
• /
• 2019

The purpose of this study is to show that the topology is closely related to some subjects learned in school mathematics and then to give motivations for learning of the topology. To do this, it is showed that the topology is an abstracted device that deal with structure of limit and continuity introduced in school mathematics. This study took a literature study. The results of this study are as follows. First, the formal definition of general topology to structure open sets was examined. The nearness relation together with the closure operation was introduced and used to characterize for construction of general topology. Second, as definitions for continuity of function, we considered the intuitive definition, definition, structured definitions using open intervals and definition using open sets and then we investigated their roles. We also examined equivalent definition using the nearness relation which is helpful to understand continuity of function. Third, the sequence and its limit are treated in terms of continuous functions having the set of natural numbers and its extended set as domains. From these, it can be concluded that the convergence of sequence and the continuity of function are identified as functions that preserve the nearness relation and that the topology is a specialized tool for dealing with convergence and continuity.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2023.05a
• /
• pp.95-95
• /
• 2023

Common hydrological problems of developing countries include poor data management, insufficient measuring devices and ungauged watersheds, leading to small or unreliable data availability. This has greatly affected the adoption of artificial intelligence techniques for flood risk mitigation and damage control in several developing countries. While climate datasets have recorded resounding applications, but they exhibit more uncertainties than ground-based measurements. To encourage AI adoption in developing countries with small ground-based dataset, we propose data augmentation for regression tasks and compare performance evaluation of different AI models with and without data augmentation. More focus is placed on simple models that offer lesser computational cost and higher accuracy than deeper models that train longer and consume computer resources, which may be insufficient in developing countries. To implement this approach, we modelled and predicted streamflow data of the Asa River Watershed located in Ilorin, Kwara State Nigeria. Results revealed that adequate hyperparameter tuning and proper model selection improve streamflow prediction on small water dataset. This approach can be implemented in data-scarce regions to ensure timely flood intervention and early warning systems are adopted in developing countries.

• Journal of applied mathematics & informatics
• /
• v.19 no.1_2
• /
• pp.165-177
• /
• 2005

In this paper, an adaptive trust region method based on the conic model for unconstrained optimization problems is proposed and analyzed. We establish the global and super linear convergence results of the method. Numerical tests are reported that confirm the efficiency of the new method.

• The Pure and Applied Mathematics
• /
• v.16 no.1
• /
• pp.13-18
• /
• 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
• /
• v.15 no.2
• /
• pp.111-120
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.479-488
• /
• 2024

Convergence to a steady state in the long term limit is established for global weak solutions to a chemotaxis model with degenerate local sensing and consumption, when the motility function is C¹-smooth on [0, ∞), vanishes at zero, and is positive on (0, ∞). A condition excluding that the large time limit is spatially homogeneous is also provided. These results extend previous ones derived for motility functions vanishing algebraically at zero and rely on a completely different approach.

• Journal of Korea Multimedia Society
• /
• v.20 no.8
• /
• pp.1291-1298
• /
• 2017

Optical coherence tomography (OCT) is the most common medical imaging device with the ability to image the retina in eyes at micrometer resolution and to visualize the pathological indicators of many retinal diseases such as Age-Related Macular Degeneration (AMD) and diabetic retinopathy. Accordingly, there have been research activities to analyze and process OCT images to identify those indicators and make medical decisions based on the findings. In this paper, we use a deep convolutional neural network for analysis of OCT volume data to distinguish AMD from normal patients. We propose a novel approach where images in each OCT volume are grouped together into sub-volumes and the network is trained by those sub-volumes instead of individual images. We conducted an experiment using public data set to evaluate the performance of the proposed approach. The experiment confirmed performance improvement of our approach over the traditional image-by-image training approach.

• ETRI Journal
• /
• v.36 no.3
• /
• pp.439-449
• /
• 2014

In this paper, a novel vision-based nighttime vehicle detection approach is presented, combining state machines and downhill simplex optimization. In the proposed approach, vehicle detection is modeled as a sequential state transition problem; that is, vehicle arrival, moving, and departure at a chosen detection area. More specifically, the number of bright pixels and their differences, in a chosen area of interest, are calculated and fed into the proposed state machine to detect vehicles. After a vehicle is detected, the location of the headlights is determined using the downhill simplex method. In the proposed optimization process, various headlights were evaluated for possible headlight positions on the detected vehicles; allowing for an optimal headlight position to be located. Simulation results were provided to show the robustness of the proposed approach for nighttime vehicle and headlight detection.

• Journal of Korea Multimedia Society
• /
• v.19 no.3
• /
• pp.603-611
• /
• 2016

Educational games offer an opportunity to engage and inspire students to take an interest in every subject material in school. The "fun" obtain when playing games become a trigger for the use of games in learning. However, there are doubts whether the players actually learn while they are having fun. Vidyanusa is an Online Mathematics Education Game being developed by Crayonpedia Education Ecosystem in Indonesia. The learning goal of Vidyanusa is to engage junior high school students in learning mathematics. In this paper, we design the Vidyanusa game material Functions and Relations by using Balanced Design Approach. This approach has three models in succession; the Content Model outlines the purpose of the game, the Task Model maps out the mission, and the Evidence Model outlines student measurement. This paper will then discusses the quality of games produced in term of Usability factor for effective results and objective. The measurement of the game was carried out based on International Standard ISO/IEC 9126-1 FDIS about Software Quality Product.

• IEMEK Journal of Embedded Systems and Applications
• /
• v.16 no.4
• /
• pp.137-143
• /
• 2021

We propose an adaptive non-singular terminal sliding-mode control for the fast finite-time convergence (FANTSMC) in robot manipulator. The proposed FANTSMC approach is developed to be applied without singularity in robot manipulator, which has a new pole-placement control with the non-singular terminal sliding variable while generating the desirable control torque. Moreover, the switching gain is designed to suppress the time-delayed estimation error appropriately, which aims at providing the high robust tracking performance. Also, the proposed one employs one-sample delayed information to cancel out the system uncertainties and disturbances. For these reasons, it offers strong attraction within the finite time. It is shown that the tracking performance of the proposed FANTSMC approach is guaranteed to be uniformly ultimately bounded through the Lyapunov stability. The effectiveness of the proposed FANTSMC approach is illustrated in simulations, which is compared with that of the up-to-date control approach.