• Honam Mathematical Journal
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• v.36 no.3
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• pp.695-706
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• 2014

Various properties of digital covering spaces have been substantially used in studying digital homotopic properties of digital images. In particular, these are so related to the study of a digital fundamental group, a classification of digital images, an automorphism group of a digital covering space and so forth. The goal of the present paper, as a survey article, to speak out utility of digital covering theory. Besides, the present paper recalls that the papers [1, 4, 30] took their own approaches into the study of a digital fundamental group. For instance, they consider the digital fundamental group of the special digital image (X, 4), where X := $SC^{2,8}_4$ which is a simple closed 4-curve with eight elements in $Z^2$, as a group which is isomorphic to an infinite cyclic group such as (Z, +). In spite of this approach, they could not propose any digital topological tools to get the result. Namely, the papers [4, 30] consider a simple closed 4 or 8-curve to be a kind of simple closed curve from the viewpoint of a Hausdorff topological structure, i.e. a continuous analogue induced by an algebraic topological approach. However, in digital topology we need to develop a digital topological tool to calculate a digital fundamental group of a given digital space. Finally, the paper [9] firstly developed the notion of a digital covering space and further, the advanced and simplified version was proposed in [21]. Thus the present paper refers the history and the process of calculating a digital fundamental group by using various tools and some utilities of digital covering spaces. Furthermore, we deal with some parts of the preprint [11] which were not published in a journal (see Theorems 4.3 and 4.4). Finally, the paper suggests an efficient process of the calculation of digital fundamental groups of digital images.

• Research in Mathematical Education
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• v.24 no.1
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• pp.1-27
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• 2021

For elementary school children, learning the standard multiplication algorithm with accuracy, clarity, consistency, and efficiency is a daunting task. Nonetheless, what should be our expectation in procedural fluency, for example, in finding the product of 25 and 37 among fifth grade students? Collectively, has the mathematics education community emphasized the value of conceptual understanding to the detriment of procedural fluency? In addition to examining these questions, we survey multiplication algorithms throughout history and in textbooks and reconceptualize the standard multiplication algorithm by using a new tool called the Multiplication Aid Template.

• School Mathematics
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• v.9 no.4
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• pp.523-533
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• 2007

This article focused the meaning of Pythagoras' and Euclid's proof about the Pythagorean theorem in a historical and mathematical perspective. Pythagoras' proof using similarity is based on the arithmetic assumption about commensurability. However, Euclid proved the Pythagorean theorem again only using the concept of dissection-rearrangement that is purely geometric so that it does not need commensurability. Pythagoras' and Euclid's different approaches to geometry have to do with Birkhoff's axiom system and Hilbert's axiom system in the school geometry Birkhoff proposed the new axioms for plane geometry accepting real number that is strictly defined. Thus Birkhoff's metrical approach can be defined as a Pythagorean approach that developed geometry based on number. On the other hand, Hilbert succeeded Euclid who had pursued pure geometry that did not depend on number. The difference between the proof using similarity and dissection-rearrangement is related to the unsolved problem in the geometry curriculum that is conflict of Euclid's conventional synthetical approach and modern mathematical approach to geometry.

• Journal of The Korean Association For Science Education
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• v.32 no.3
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• pp.486-501
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• 2012

The aims of this study are to investigate two main problems for the hypothetico-deduction method and to develop a scientific inquiry model to resolve these problems. The structure of this scientific inquiry model consists of accounts of the context of discovery and justification that the hypothetico-deduction holds as two main problems : 1) the heuristic flaw in the hypothetico-deduction method is that there is no limit to creating hypotheses to explain natural phenomena; 2) Logically, this brings into question affirming the consequent and modus tollens. The features of the model are as follows: first, the generation of hypotheses using an analogical abduction and the selection of hypotheses using consilience and simplicity; second, the expansion phase as resolution for the fallacy of affirming the consequent and the recycle phase as resolution for modus tollens involving auxiliary hypotheses. Finally, we examine the establishment process of Copernicus's Heliocentric Hypothesis and the main role of the history of science for the historical invalidity of this scientific inquiry model based on three examples of If/and/then type of explanation testing suggested by Lawson (International journal of science and Mathematics Education, 2005a, 3(1): 1-5) We claim that this hypotheticho-deduction process involving abduction approach produced favorable in scientific literacy rising for science teacher as well as students.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.531-541
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• 2016

Cerebral atrophy affects the brain and is a common feature of patients with mild cognitive impairment or Alzheimer's diseases. It is evaluated by the radiologist or reader based on patient's history, age and the space between the brain and the skull as indicated by magnetic resonance (MR) images. A total of 70 patients were scanned in the supine and prone positions before three radiologist assessed their atrophy level. This study examined the radiologist's assessment of the cerebral atrophy level using a graded response model of item response theory (IRT). A graded response model (GRM) is fitted to our data and then item-fit and person-fit statistics are evaluated to assess the fitted model. Our analysis found that the cerebral atrophy level is better discriminated by readers in the prone position because all item slopes were greater than 2 at this position, versus the supine position where all the slope parameters were less than 1. However, the thresholds are very similar for the first reader and are quite different for the second and third readers because the scanning position affects readers differently as the category threshold estimates vary considerably between the readers..

• Journal of architectural history
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• v.15 no.1 s.45
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• pp.29-40
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• 2006

This paper is focused on Damheonseo(湛軒書), an anthology written by Hong Daeyong, and I deal with Chinese Architectural views which he had experienced in his itinerary to Beijing, and the vivid pictures of Joseonkwan (called the Koryo or Joseon Embassy) located in Beijing at that time. He was a scholar of great erudition over astronomy, mathematics, military science, politics, and so on. He was interested in practical sciences at early time, and criticized secular scholars full of vanity who had presented purposeless articles. In his age of 35, Qianlong(乾隆) 30 (1764, Youngjo 41), he, a military escort, accompanied by Hong Uk, Joseon envoy and his uncle. Before his itinerary, he self-studied Chinese. Also, during a long journey he got new experiences and information around each area, deviating his group whenever he had some times. He could get more variant experiences than others because of his character full of curiosity, and his observations from the vivid lives of the time helped us get various views between Chinese and Korean architecture. Likewise, although he denounced Qing(淸) scathingly as a barbarian, he mentioned several points about the characteristics of Chinese architecture at that time. First of all, totally Chinese architecture had strong rational and practical points. Secondly, based on bountiful products, buildings along streets shown in Chinese city had sophisticated compositions, and luxurious and magnificent appearances. Thirdly, using the brick from walls to houses was so universal. Fourthly, the layouts of building with three- or four-closed courtyard had very orderly shapes, and the structure of street was also so arranged. Finally, because of stand-up lives, the scales and appearances of interior space were even more extended, and storages were less developed than those of Joseon. As another points, I found that Joseonkwan was moved next to Shushangguan(庶常館)from Huidongnanguan(會同南館) around Hanlimyuan(翰林院), and had been remodeled into a house with Korean custom in using the inner spaces, although it was followed by a closed courtyard style. Likewise, I recognized that Ondols were sure to be established in all temporary houses during the journey to Qing, and felt their strong traditional residential custom in such mentions. Now that the past pictures have disappeared and ways of life and our values have been largely changed, this study has very important meaning in comparing the ancient Chinese and Korean architecture.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.44 no.4
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• pp.113-127
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• 2021

Topic modeling has been receiving much attention in academic disciplines in recent years. Topic modeling is one of the applications in machine learning and natural language processing. It is a statistical modeling procedure to discover topics in the collection of documents. Recently, there have been many attempts to find out topics in diverse fields of academic research. Although the first Department of Industrial Engineering (I.E.) was established in Hanyang university in 1958, Korean Institute of Industrial Engineers (KIIE) which is truly the most academic society was first founded to contribute to research for I.E. and promote industrial techniques in 1974. Korean Society of Industrial and Systems Engineering (KSIE) was established four years later. However, the research topics for KSIE journal have not been deeply examined up until now. Using topic modeling algorithms, we cautiously aim to detect the research topics of KSIE journal for the first half of the society history, from 1978 to 1999. We made use of titles and abstracts in research papers to find out topics in KSIE journal by conducting four algorithms, LSA, HDP, LDA, and LDA Mallet. Topic analysis results obtained by the algorithms were compared. We tried to show the whole procedure of topic analysis in detail for further practical use in future. We employed visualization techniques by using analysis result obtained from LDA. As a result of thorough analysis of topic modeling, eight major research topics were discovered including Production/Logistics/Inventory, Reliability, Quality, Probability/Statistics, Management Engineering/Industry, Engineering Economy, Human Factor/Safety/Computer/Information Technology, and Heuristics/Optimization.

• Communications of Mathematical Education
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• v.29 no.4
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• pp.699-722
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• 2015

Based on Lagrange's general theory of algebraic equations, by applying the solution of the equation using the relationship between roots and coefficients to the high school 1st grade class, the purpose of this study is to recognize the significance of symmetry associated with the solution of the equation. Symmetry is the core idea of Lagrange's general theory of algebraic equations, and the relationship between roots and coefficients is an important means in the solution. Through the lesson, students recognized the significance of learning about the relationship between roots and coefficients, and understanded the idea of symmetry and were interested in new solutions. These studies gives not only the local experience of solutions of the equations dealing in school mathematics, but the systematics experience of general theory of algebraic equations by the didactical organization, and should be understood the connections between knowledges related to the solutions of the equation in a viewpoint of the mathematical history.

• Fisheries and Aquatic Sciences
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• v.25 no.11
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• pp.549-558
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• 2022

The Indonesian Archipelago has a very complex geological history, along with equatorial warm sea temperature, resulting in diverse types of coral reefs and high diversity of coral reef fish. Many livelihoods of the coastal community are dependent on coral reef fisheries. The present study aimed to determine which region and location in the Indonesian Archipelago has the most diverse and abundant coral reef fish. The archipelago was divided into four regions: the Indian Ocean, Sunda Shelf, Wallacea, and the Pacific Ocean. Data were obtained from a national coral reef monitoring program of the Indonesian Research Center for Oceanography (RCO)-the National Board for Research and Innovation (BRIN). The reef fish data were collected using the underwater visual census method, from 321 belt transects on 24 locations (districts) across the archipelago. The results show that coral reef fish diversity of the Pacific region was the highest across the archipelago for all three trophic levels, i.e., corallivore, herbivore, and carnivore fish. The Pacific Ocean region also had the highest fish abundance for the three trophic levels. Comparison among locations revealed that the best ten locations in reef fish diversity and abundance were Sabang, Mentawai, Makassar, Selayar, Buton, Luwuk, Ternate, Raja Ampat, Biak, and Wakatobi. Wakatobi reefs showed their supremacy in carnivore fish diversity and abundance, while Biak reefs were the best in herbivore fish. The abundance of corallivore fish was also considerably high in Sabang reefs, but it is still lower than in Raja Ampat, Biak, and Wakatobi reefs. These results provide empirical evidence that the coral reefs of Wakatobi and Biak are the hottest hotspots of coral reef fish diversity and abundance in the Indonesian Archipelago.

• Asian Pacific Journal of Cancer Prevention
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• v.15 no.17
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• pp.7021-7027
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• 2014

Background: The problem of cancer, especially lung cancer, is very acute in Bangladesh. The present study was conducted to evaluate the risk of lung cancer among Bangladeshi people based on hereditary, socio-economic and demographic factors. Materials and Methods: This study was carried out in 208 people (patients-104, controls-104) from January 2012 to September 2013 using a structured questionnaire containing details of lung cancer risk factors including smoking, secondhand smoke, tobacco leaf intake, age, gender, family history, chronic lung diseases, radiotherapy in the chest area, diet, obesity, physical activity, alcohol consumption, occupation, education, and income. Descriptive statistics and testing of hypotheses were used for the analysis using SPSS software (version 20). Results: According to this study, lung cancer was more prevalent in males than females. Smoking was the highest risk factor (OR=9.707; RR=3.924; sensitivity=0.8872 and P<0.0001) followed by previous lung disease (asthma, tuberculosis etc.) (OR=7.095; RR=1.508; sensitivity=0.316 and P<0.0001)) for male patients. Highly cooked food (OR=2.485; RR=1.126; sensitivity=0.418 and P=0.004)) and also genetic inheritance (OR=1.93; RR=1.335; sensitivity=0.163 and P=0.138) demonstrated significant correlation with lung cancer as risk factors after these two and alcohol consumption was not prevalent. On the other hand, for female patients, tobacco leaf intake represented the highest risk (OR=2.00; RR=1.429; sensitivity= 0.667 and P=0.5603) while genetic inheritance and highly cooked food also correlate with lung cancer but not so significantly. Socioeconomic status and education level also play important roles in causing lung cancer. Some 78.5% male and 83.3% of female cancer patients were rural residents, while 58.2% lived at the margin or below the poverty line. Most male (39.8%) and female (50.0%) patients had completed only primary level education, and 27.6% male and 33.3% female patients were illiterate. Smoking was found to be more prevalent among the less educated persons. Conclusions: The results obtained in this study indicate the importance of creating awareness about lung cancer risk factors among Bangladeshi people and making appropriate access to health services for the illiterate, poor, rural people.