• Research in Mathematical Education
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• v.5 no.1
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• pp.1-12
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• 2001

Generating fractal images by graphing calculators such as TI_92 combines several important features, which convey the excitement of a living, changing mathematics appropriate to secondary or post-secondary students. The topic of fractal geometry can be illustrated using natural objects such as snowflakes, leaves and ferns. These complex and natural forms are often striking fantastic and beautiful. The examples highlight the fact that complex, natural behaviors can result from simple mathematical rules such as those embodied in iterated function systems(IFS). The visual splendor beauty of fractals, in concert with their ubiquity in nature, revels the intellectual beauty of nonlinear mathematics in a compelling way. The window is now open for students to experience and explore some of the wonder of fractal geometry.

• Research in Mathematical Education
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• v.15 no.2
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• pp.141-158
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• 2011

In recent years, an increasing number of viewpoints hold that students should be engaged in a learning environment where understanding and knowledge transfer take place. This study introduces Mathematics Created by You (MCY)-mentoring program, which allows students to construct artefacts that are required to learn. This program is online-based and so can be shared by several people and mathematics leaning takes place through interactions within this carefully designed environment. Also, MCY intends to provide students a series of sequential activities related to creative play, creative learning and creative inquiry based on a Constructive and interactive environment. Furthermore, a creative activity- constructing a creative product using building blocks- was presented as an example. Finally, we investigate the pedagogical implications and suggest directions for the further development.

• The Mathematical Education
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• v.43 no.4
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• pp.381-390
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• 2004

In this study, we conceptualized the ‘preformal proof’, which is a transitive level of proof from the experimental and inductive justification to the formalized mathematical proof. We investigated concrete features of the preformal proof in the historico-genetic and the didactical situations. The preformal proof can get the generality of the contents of proof, which makes a distinction from the experimental proof. And we can draw a distinction between the preformal and formal proof, in point that the preformal proof heads for the reality-oriented objects and does not use the formal language.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.187-198
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• 2021

This work presents an exposition of both the internal structure of derived category of an abelian category D^*(𝓐) and its contribution in solving problems, particularly in algebraic geometry. Calculation of some morphisms will be presented between objects in D^*(𝓐) as elements in appropriate cohomology groups along with their compositions with the help of Yoneda construction under the assumption that the homological dimension of D^*(𝓐) is greater than or equal to 2. These computational settings will then be considered under sheaf cohomological context with a particular case from projective geometry.

• Journal of Information Processing Systems
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• v.17 no.1
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• pp.1-13
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• 2021

In this research, we study the problem of font image skeletonization using an end-to-end deep adversarial network, in contrast with the state-of-the-art methods that use mathematical algorithms. Several studies have been concerned with skeletonization, but a few have utilized deep learning. Further, no study has considered generative models based on deep neural networks for font character skeletonization, which are more delicate than natural objects. In this work, we take a step closer to producing realistic synthesized skeletons of font characters. We consider using an end-to-end deep adversarial network, SkelGAN, for font-image skeletonization, in contrast with the state-of-the-art methods that use mathematical algorithms. The proposed skeleton generator is proved superior to all well-known mathematical skeletonization methods in terms of character structure, including delicate strokes, serifs, and even special styles. Experimental results also demonstrate the dominance of our method against the state-of-the-art supervised image-to-image translation method in font character skeletonization task.

• Journal of the Korean Mathematical Society
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• v.59 no.4
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• pp.733-756
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• 2022

In this paper, we introduce the notion of Gorenstein quasiresolving subcategories (denoted by 𝒢𝒬𝓡_𝒳 (𝓐)) in term of quasi-resolving subcategory 𝒳. We define a resolution dimension relative to the Gorenstein quasi-resolving categories 𝒢𝒬𝓡_𝒳 (𝓐). In addition, we study the stability of 𝒢𝒬𝓡_𝒳 (𝓐) and apply the obtained properties to special subcategories and in particular to modules categories. Finally, we use the restricted flat dimension of right B-module M to characterize the finitistic dimension of the endomorphism algebra B of a 𝒢𝒬_𝒳-projective A-module M.

• Communications of Mathematical Education
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• v.35 no.4
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• pp.413-423
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• 2021

This study investigated the empty set which is one of the mathematical objects. We inquired some misconceptions about empty set and the background of imposing empty set. Also we studied historical background of the introduction of empty set and the axiomatic system of Set theory. We investigated the nature of mathematical object through studying empty set, pure conceptual entity. In this study we study about the existence of empty set by investigating Alian Badiou's ontology known as based on the axiomatic set theory. we attempted to explain the relation between simultaneous equations and sets. Thus we pondered the meaning of the existence of empty set. Finally we commented about the thoughts of sets from a different standpoint and presented the meaning of axiomatic and philosophical aspect of mathematics.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.6
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• pp.1293-1299
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• 2012

In this paper, a real-time vehicle detection and tracking algorithms is proposed. The vehicle detection could be processed using GMM (Gaussian Mixture Model) algorithm and mathematical morphological processing with HD CCTV camera images. The vehicle tracking based on separated vehicle object was performed using Euclidean distance between detected object. In more detail, background could be estimated using GMM from CCTV input image signal and then object could be separated from difference image of the input image and background image. At the next stage, candidated objects were reformed by using mathematical morphological processing. Finally, vehicle object could be detected using vehicle size informations dependent on distance and vehicle type in tunnel. The vehicle tracking performed using Euclidean distance between the objects in the video frames. Through computer simulation using recoded real video signal in tunnel, it is shown that the proposed system works well.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.484-487
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• 1997

In this paper a simulation program for the powertrain control of a gasoline engine with automatic transmission is presented, The object-oriented programming approach has been pursued, and MATLAB/ SIMULINK was adopted for its environment. The purpose of the paper is to demonstrate the programmability of a control system in the object-oriented fashion so that the transferability of the objects is guaranteed. The program developed in the paper was applied to a gasoline engine and the mathematical models used in the paper were just adopted from the literature. It is shown that the simulation results and real experimental results coincide well. Therefore, it is expected that the program or objects made in the paper are useful for the automotive engineers when they design a new engine/transmission system or modify a part of existing system.

• The Pure and Applied Mathematics
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• v.9 no.1
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• pp.9-17
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• 2002

In this Paper, we will show that every basically disconnected space is a projective object in the category $Tych_{\sigma}$ of Tychonoff spaces and $_{\sigma}Z^{#}$ -irreducible maps and that if X is a space such that ${\Beta} {\Lambda} X={\Lambda} {\Beta} X$, then X has a projective cover in $Tych_{\sigma}$. Moreover, observing that for any weakly Linde1of space, ${\Lambda} X : {\Lambda} X\;{\longrightarrow}\;X$ is $_{\sigma}Z^{#}$-irreducible, we will show that the projective objects in $wLind_{\sigma}$/ of weakly Lindelof spaces and $_{\sigma}Z^{#}$-irreducible maps are precisely the basically disconnected spaces.