• Honam Mathematical Journal
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• v.32 no.1
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• pp.177-192
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• 2010

We study the concepts of congruent number problems and elliptic curves. We research the structure of the group of elliptic curves and find out a method of the computation of L($E_n$, 1) and L'($E_n$, 1) by using SAGE program. In this paper, we obtain the first few congruent numbers for n ${\leq}$ 2500.

• Honam Mathematical Journal
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• v.35 no.3
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• pp.351-372
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• 2013

In this paper, we study a distinction the two generating functions : ${\varphi}^k(q)=\sum_{n=0}^{\infty}r_k(n)q^n$ and ${\varphi}^{*,k}(q)={\varphi}^k(q)-{\varphi}^k(q^2)$ ($k$ = 2, 4, 6, 8, 10, 12, 16), where $r_k(n)$ is the number of representations of $n$ as the sum of $k$ squares. We also obtain some congruences of representation numbers and divisor function.

• Journal of Information Technology Applications and Management
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• v.18 no.1
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• pp.1-14
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• 2011

Mixed reality (MR) representation of accounting numbers is used as an alternative way of virtually engaging users of real three dimensional graphics of financialdata. An experiment was conducted to compare the usability and knowledge drawn from utilizing a table of numbers versus MR representations. The results showed that when MR was used, the participants' ratings of the firm's financial status and performance were more congruent with those of experts than when a table was employed. Also, MR was seen as providing less complex information with a shorter amount of time being spent and was perceived as being easy and useful.

• Journal for History of Mathematics
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• v.28 no.2
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• pp.85-102
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• 2015

Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.

• Korean Journal of Plant Taxonomy
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• v.52 no.4
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• pp.214-218
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• 2022

Eleocharis R. Br. (Cyperaceae) is characterized by unbranched culms, one terminal spikelet, bisexual flowers, and bristly perianths, occurring mainly in circumboreal marshes and wetlands. There are about 250 species worldwide, and 15 taxa in Korea have been recognized. Chromosomes in Cyperaceae are known to be holocentric, missing constricted centromeres during cell division. For the first time, we report the chromosome counts of Eleocharis from Korean populations of E. attenuata f. laeviseta (Nakai) H. Hara (2n = 20); E. parvula (Roem. & Schult.) Link ex Bluff, Nees & Schauer (2n = 10); E. ussuriensis Zinserl. (2n = 16); and E. valleculosa var. setosa Ohwi (2n = 16). The populations exhibit variations in their chromosome sizes from ca.1.7 ㎛ to ca. 6 ㎛, categorized as gradient and bimodal karyotypes. The karyotypes observed are congruent with previous phylogenetic groups proposed. To clarify the traditional and phylogenetic classification of Korean Eleocharis, further taxonomic and chromosomal investigations with additional taxon sampling efforts are required.

• Korean Journal of Adult Nursing
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• v.19 no.2
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• pp.329-337
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• 2007

Purpose: Increasing numbers of Koreans have immigrated to the United States since the late 1960s. The first generation of Korean immigrants or their parents become old and institutionalized in American nursing home setting. Although the Korean elders would experience many cultural differences in the nursing home, no study to date has investigated their everyday lives on how they live through their later lives within a different cultural environment from their own. Methods: Using ethnographic methodology, the purpose of this paper was to illustrate Korean residents' experiences and daily lives in a nursing home located in an east coastal city in the U.S. Participant observation, filed notes, semi-structured interviews were utilized by means of data collection. Eighteen Korean residents were observed, and five of them and two nurses participated in informal qualitative interviews. Results: The overriding theme from the findings is "thrown in a different world." Three sub-themes include "constant struggles in making themselves understood", "dealing with culturally inappropriate nursing care," and "maintaining their own ways of life". Conclusions: The discovered themes reflect culturally isolated lives of the participants and open a venue for designing a culturally congruent nursing care for Korean elders living in the U.S. nursing homes.

• Journal of the Korean School Mathematics Society
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• v.20 no.2
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• pp.119-139
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• 2017

The construction in the ancient Greek era had more meanings than a construction in the present education. Based on this fact, this study examines the meaning of the current textbook. In contrast, we have extracted the meaning of the constructions in Euclid Elements. In addition, we have been thinking about what benefits can come up if the meaning of the construction in Euclid Elements was reflected in current education, and suggested a way to exploit that advantage. As results, it was confirmed that the construction in the current textbook was merely a means for introducing and understanding the congruent conditions of the triangle. On the other hand, the construction had four meanings in Euclid Elements; Abstract activities that have been validated by the postulates, a mean of demonstrating the existence of figures and obtaining validity for the introduction of auxiliary lines, refraining from intervening in the argument except for the introduction of auxiliary lines, a mean of dealing with numbers and algebra. Finally we discussed the advantages of using the constructions as a means of ensuring the validity of the introduction of the auxiliary line to the argument. And we proposed a viewpoint of construction by intervention of virtual tools for auxiliary lines which can not be constructed with Euclid tool.

• Asia Marketing Journal
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• v.15 no.4
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• pp.161-186
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• 2014

There are many cases of rebranding and its numbers are growing. However, rebranding is still under research in the academic field, and there is no guideline on the effective way to change brand name. The objective of this paper is to integrate two inconsistent predictions from categorization theory and schema incongruity theory: a negative linear relationship (categorization theory) versus an inverted-U-shape relationship (schema incongruity theory) between brand name incongruity and consumer evaluation into one framework. Specifically, this study examines how the effect of incongruity between an existing brand name and a new brand name (hereafter called "brand name incongruity") on the new brand name attitude differs depending on a consumer's individual characteristics (need for cognition). The experiment demonstrates that consumers with a high need for cognition show a better attitude towards a new brand name when the brand name was rebranded moderately incongruent compared to congruent or extremely incongruent. Thus, the experiment demonstrates that there is an inversed U-shape relationship between brand name incongruity and new brand name evaluation for consumers with a high need for cognition. On the contrary, consumers with a low need for cognition show a better attitude towards a new brand name when the brand name is rebranded congruently compared to incongruent conditions (moderate incongruity and extreme incongruity). This result indicates that there is a negative linear relationship between brand name incongruity and new brand name evaluation. Key theoretical and managerial implications of the present study are as follows. This study integrates two alternative views of research on incongruity evaluation into one framework by demonstrating that need for cognition moderates the relationship between brand name incongruity and consumer evaluation. This present study provides a conceptual basis for understanding consumer evaluation towards a new brand name. Next, though rebranding is a very important decision making of brand management, there is no guideline on how to change a brand name. The findings of this research can suggest which degree of change is optimal when rebranding in order to utilize and strengthen existing brand equity. More specifically, when our target customer has high need for cognition, moderately incongruent rebranding can be optimal, whereas for those with low need for cognition, rebranding in accordance with existing brand name will be optimal.

• Korean Journal of Plant Taxonomy
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• v.41 no.4
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• pp.353-360
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• 2011

The sequence data of the plastid DNA (trnL-F IGS, trnL intron, and trnH-psbA) and nuclear DNA (RNApol2_i23) markers were utilized to study phylogenetic relationships among the taxa in the Polygonatum odoratum complex (Ruscaceae). European P. odoratum individuals form a clade with a high bootstrap value, which is a sister to the clade of Korean P. odoratum var. odoratum, P. odoratum var. pluriflorum and P. robustum. The formation of the clade with P. odoratum var. odoratum, P. robustum, and one accession of P. odoratum var. pluriflorum indicates geological speciation in isolated populations in the islands following dispersal events from the mainlands. All data sets form two major clades, which are congruent with the subgroups divided by the basic chromosome numbers (x = 9 and x = 10). Although it is not easy to test the hypothesis of the decrease in the basic chromosome number due to scatter taxon sampling in this study, the molecular data strongly suggested that aneuploidy plays an important role in lineage diversification in the genus Polygonatum. The cytological data was not strongly supported by the cpDNA sequences. Further investigations of the cytological, morphological, and geographical characteristics with comprehensive sampling are desired to understand the evolution and lineage diversification in the genus.