• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.183-203
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• 2014

We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.

• The Journal of the Korea institute of electronic communication sciences
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• v.12 no.6
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• pp.1181-1188
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• 2017

The unit and fundamental units of number fields are important to number field sieves testing primality of more than 400 digits integers and number field seive factoring the number in RSA cryptosystem, and multiplication of ideals and counting class number of the number field in imaginary quadratic cryptosystem. To minimize the time and space in H/W implementation of cryptosystems using fundamental units, in this paper, we introduce the Dirichlet's unit Theorem and propose our process of generating the fundamental units of the number field. And then we present the algorithm generating our fundamental units of the number field to minimize the time and space in H/W implementation and implementation results using the algorithm over the number field.

• Bulletin of the Korean Mathematical Society
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• v.58 no.5
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• pp.1149-1161
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• 2021

In this paper, we present new bounds on the fundamental units of real quadratic fields ${\mathbb{Q}}({\sqrt{d}})$ using the continued fraction expansion of the integral basis element of the field. Furthermore, we apply these bounds to Dirichlet's class number formula. Consequently, we provide computational advantages to estimate the class numbers of such fields. We also give some numerical examples.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.417-426
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• 2017

We explicitly determine fundamental units and regulators of an infinite family of cyclic quartic function fields $L_h$ of unit rank 3 with a parameter h in a polynomial ring $\mathbb{F}_q[t]$, where $\mathbb{F}_q$ is the finite field of order q with characteristic not equal to 2. This result resolves the second part of Lehmer's project for the function field case.

• Korean Journal of Optics and Photonics
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• v.30 no.4
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• pp.133-141
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• 2019

Revision of the International System of Units (SI) in terms of fundamental constants was achieved by the 26th General Conference on Weights and Measures (CGPM) in November 2018. Four base units (kilogram, ampere, kelvin, and mole) of SI were redefined by fixing the values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant $N_A$ respectively. In this paper the scientific principle for redefining the kilogram from the Planck constant with the Kibble balance is explained as an example. The revised SI takes effect on May 20, 2019.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.697-707
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• 2022

It is well known that the continued fraction expansion of ${\sqrt{d}}$ has the form $[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}]$ and ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1}$ is a palindromic sequence of positive integers. For a given positive integer l and a palindromic sequence of positive integers ${\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},$ we define the set $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})\;:=\;\{d{\in}{\mathbb{Z}}{\mid}d>0,\;{\sqrt{d}}=[{\alpha}_0,\;{\bar{{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1},\;2_{{\alpha}_0}}],\;where\;{\alpha}_0={\lfloor}{\sqrt{d}}{\rfloor}\}.$ In this paper, we completely determine when $S(l;{\alpha}_1,\;{\ldots},\;{\alpha}_{l-1})$ is not empty in the case that l is 4, 5, 6, or 7. We also give similar results for $(1+{\sqrt{d}})/2.$ For the case that l is 4, 5, or 6, we explicitly describe the fundamental units of the real quadratic field ${\mathbb{Q}}({\sqrt{d}}).$ Finally, we apply our results to the Mordell conjecture for the fundamental units of ${\mathbb{Q}}({\sqrt{d}}).$

• Proceedings of the KWS Conference
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• 2002.10a
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• pp.675-680
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• 2002

Cracking and bulging in welded and internally lined pressure vessels that work in thermal-mechanical cycling service have been well known problems in the petrochemical, power and nuclear industries. However, published literature and industry surveys show that similar problems have been occurring during the last 50 years. A better understanding of the causes of cracking and bulging causes is needed to improve the reliability of these pressure vessels. This study attempts to add information required for increasing the knowledge and fundamental understanding required. Typical examples of this problem are the coke drums in the delayed coking units refinery process. This case was selected for experimental work, field study and results comparison. Delayed coking units are among the refinery units that have higher economical yields. To shut down these units represents a high negative economical impact in refinery operations. Also, the maintenance costs associated with repairs are commonly very high. Cracking and bulging occurrences in the coke drums, most often at the weld areas, characterize the history of the operation of delayed coking units. To design and operate more robust coke drums with fewer problems, an improved metallurgical understanding of the cracking and bulging mechanisms is required. A methodology that is based field experience revision and metallurgical analyses for the screening of the most important variables, and subsequent finite element analyses to verify hypotheses and to rank the variables according to their impact on the coke drum lives has been developed. This indicated approach provides useful information for increasing coke drum reliability. The results of this work not only order the most important variables according to their impact in the life of the vessels, but also permit estimation of the life spans of coke drums. In conclusion, the current work shows that coke drums may fail as a combination of thermal fatigue and other degradation mechanisms such as: corrosion at high and low temperatures, detrimental metallurgical transformations and plastic deformation. It was also found that FEA is a very valuable tool for understanding cracking and bulging mechanisms in these services and for ranking the design, fabrication, operation and maintenance variables that affect coke drum reliability.

• Educational Technology International
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• v.19 no.2
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• pp.175-197
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• 2018

Flipped classroom (FC) has gained attention as an active learning approach. Designing effective out-of-class activities to help prepare students for in-class activities is fundamental for successful implementation of FC. This study investigated the effectiveness of Goal-Based Scenarios (GBS) for out-of-class learning in FC. Four out of twelve units in a medical humanities course for Year 2 medical students was redesigned into a FC format, where e-learning modules were designed using a GBS approach for out-of-class activities and classroom debates were implemented for in-class activities. The other eight units were delivered in a conventional classroom debate format, which included reading text materials as pre-class assignments. A formative evaluation study was conducted using questionnaires and interview methods and students' academic achievements were evaluated by comparing their pre- and post-test scores between FC and conventional units. Students had positive perceptions of the e-learning modules in GBS approach and preferred the structure of learning in the FC format. Students' pre-test scores were slightly higher in the FC units, yet their post-test scores were comparable with conventional units. This study illustrates students' perceptions that the learning was bettered structured in FC and that the out-of-class learning using the GBS approach helped them better prepared for in-class activities.

• International Journal of Advanced Culture Technology
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• v.12 no.1
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• pp.249-253
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• 2024

The ultimate purpose of this study is as follows: The current primary concern in the defense sector revolves around how to strategically utilize Fourth Industrial Revolution technologies in combat. The Fourth Industrial Revolution denotes a shift towards an environment where automation and connectivity are maximized, driven by technologies such as artificial intelligence. Coined by Klaus Schwab in the 2015 Davos Forum, this term highlights the significant role of machine learning and artificial intelligence. Particularly, the military application of Fourth Industrial Revolution technologies is expected to be actively researched and implemented. Combat involves military actions between units, typically conducted as part of a larger war, with units striving to achieve one or more objectives. The concept of combat refers to the fundamental ideas of how units should engage with the enemy, both presently and in future scenarios, to achieve assigned objectives.

• Proceedings of the KSRS Conference
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• 2003.11a
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• pp.1371-1373
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• 2003

The importance of Fundamental Geographical Information Framework for Digital City (FGFDC) is analysed, it provides all city agencies and units with uniform geographic references. Six kind of data are chosen as the core data sets of a FGDC, a web-based distributed mechanism is constructed to promote data sharing among different agencies. Elementary functional requirements of FGDC are analyzed, so that it can serve as a common distributed urban GIS. A practical FGFDC is developed for Yangzhou Development Administrative Region, and an 3D visualization system is developed within this framework.