• East Asian mathematical journal
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• v.28 no.2
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• pp.159-172
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• 2012

In all Mathematics I Textbooks(Kim, S. H., 2010; Kim, H. K., 2010; Yang, S. K., 2010; Woo, M. H., 2010; Woo, J. H., 2010; You, H. C., 2010; Youn, J. H., 2010; Lee, K. S., 2010; Lee, D. W., 2010; Lee, M. K., 2010; Lee, J. Y., 2010; Jung, S. K., 2010; Choi, Y. J., 2010; Huang, S. K., 2010; Huang, S. W., 2010) in high schools in Korea these days, it is written and taught that for a positive real number $a$, $a^{\frac{m}{n}}$ is defined as $a^{\frac{m}{n}}={^n}\sqrt{a^m}$, where $m{\in}\mathbb{Z}$ and $n{\in}\mathbb{N}$ have common prime factors. For that situation, the author shows his opinion that the definition is not well-defined and $a^{\frac{m}{n}}$ must be defined as $a^{\frac{m}{n}}=({^n}\sqrt{a})^m$, whenever $^n\sqrt{a}$ is defined, based on the field axiom of the real number system including rational number system and natural number system. And he shows that the following laws of exponents for reals: $$\{a^{r+s}=a^r{\cdot}a^s\\(a^r)^s=a^{rs}\\(ab)^r=a^rb^r$$ for $a$, $b$>0 and $s{\in}\mathbb{R}$ hold by the completeness axiom of the real number system and the laws of exponents for natural numbers, integers, rational numbers and real numbers are logically equivalent.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1999.06a
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• pp.125-131
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• 1999

In this paper, we address practical methods for calculating camera lens distortion for real time applications. Although the lens distortion problem can be easily ignored for constant-parameter lenses, in the field of real-time camera calibrations, for zoom lenses a large number of calculations are needed to calculate the distortion. However, if the distortion can be calculated independently of the other camera parameter, we can easily calibrate a camera without the need for a large number of calculations. Based on Tsai's camera model, we propose two different methods for calculating lens distortion. These methods are so simple and require so few calculations that the lens distortion can be rapidly calculated even in real-time applications. The first method is to refer to the focal length - lens distortion Look Up Table(LUT), which is constructed in the initialization process. The second method is to use the relationship between the feature points found in the image. Experiments were carried out for both methods, results of which show that the proposed methods are favorably comparable in performance with non-real full optimization method.

• Korean Journal of Mathematics
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• v.8 no.2
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• pp.193-198
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• 2000

In [4], it is proved that the algebra ($S,k^{14}$) is not a $C_1$- construction if the field is the real number field. In this paper, we will introduce a different proof of the fact that the algebra ($S,k^{14}$) is not a $C_1$-construction.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1559-1568
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• 2015

The relative class number $H_d(f)$ of a real quadratic field $K=\mathbb{Q}(\sqrt{m})$ of discriminant d is the ratio of class numbers of $O_f$ and $O_K$, where $O_K$ denotes the ring of integers of K and $O_f$ is the order of conductor f given by $\mathbb{Z}+fO_K$. In a recent paper of A. Furness and E. A. Parker the relative class number of $\mathbb{Q}(\sqrt{m})$ has been investigated using continued fraction in the special case when $(\sqrt{m})$ has a diagonal form. Here, we extend their result and show that there exists a conductor f of relative class number 1 when the continued fraction of $(\sqrt{m})$ is non-diagonal of period 4 or 5. We also show that there exist infinitely many real quadratic fields with any power of 2 as relative class number if there are infinitely many Mersenne primes.

• Genomics & Informatics
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• v.17 no.4
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• pp.44.1-44.3
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• 2019

Artificial intelligence (AI), big data, and ubiquitous robotic companions -the three most notable technologies of the 4th Industrial Revolution-are receiving renewed attention each day. Technologies that can be experienced in daily life, such as autonomous navigation, real-time translators, and voice recognition services, are already being commercialized in the field of information technology. In the biosciences field in Korea, such technologies have become known to the local public with the introduction of the AI doctor Watson in large number of hospitals. Additionally, AlphaFold, a technology resembling the AI AlphaGo for the game Go, has surpassed the limit on protein folding predictions-the most challenging problems in the field of protein biology. This report discusses the significance of AI technology and big data on the bioscience field. The introduction of automated robots in this field is not just only for the purpose of convenience but a prerequisite for the real sense of AI and the consequent accumulation of basic scientific knowledge.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.2
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• pp.795-800
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• 2012

Recently, as communication is evolved by leaps and bounds through wired/wireless networks, variety of services are routinely made through communication networks. Accordingly, technology that is for protecting data and personal information is required essentially, and study of security technology is actively being make progress to solve these information protection problems. In this paper, to expand selection scope of the key of elliptic curve cryptography, arithmetic items of real number based elliptic curve algorithm among various cryptographic algorithms was studied. The result of an experiment, we could know that elliptic curve cryptography using the real number can choose more various keys than existing elliptic curve cryptography using integer and implement securer cryptographic system.

• Proceedings of the Korea Institute of Fire Science and Engineering Conference
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• 2008.11a
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• pp.363-370
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• 2008

The present study has been performed to investigate the effect of statistical number of droplets on the simulation of the sprinkler spray using fire field model. In order to simulate the sprinkler spray characteristics, the present study uses NIST Fire Dynamics Simulator version 5.2. A group of Lagrangian particle with similar droplet characteristics, such as diameter, velocity, temperature and so on, is represented by parcel concept to decrease the total number of droplets tracked in the simulation. The present study introduces a new parameter to represent the ratio between real number of droplets and computational parcels. The dependency of the number of parcels on the fire suppression characteristics and spray patterns is quantitatively examined for different ratio between the real number of droplets and computational parcels.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.53 no.5
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• pp.309-314
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• 2004

In the established virtual-reality system, although it is possible to transact a faculty of sensation and graphic in a single PC, virtual object forcibly treated with rigid body for the reason of the huge amount of calculation, and the number of polygon is restricted. Furthermore, there is some difficulty in the financial aspect and a program field, because the existing virtual-reality system needs at least two workstations or super computers. In this study, the new force-reflecting algorithm called as "Proxy" and a finite element method of Hyperion are applied to this system in order to transact in real-time. Consequently, though the number of polygon, which brings about an obstacle is increased in the real-time graphic transaction, this system makes it possible to transact in the real-time, not being influenced by the size of the virtual object.

• Bulletin of the Korean Chemical Society
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• v.35 no.2
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• pp.365-370
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• 2014

For real-time monitoring of colloidal nanoparticles (NPs) in aqueous media, a light sheet type dark-field microscopy system combined with a microfluidic concentration gradient generator (${\mu}FCGG$-LSDFM) was developed. Various concentrations of colloidal Au NPs were simultaneously generated with the iFCGG and characterized with the LSDFM setup. The number concentrations and hydrodynamic size distributions were measured via particle counting and tracking analysis (PCA and PTA, respectively) approaches. For the 30 nm Au NPs used in this study, the lower detection limit of the LSDFM setup was 3.6 ng/mL, which is about 400 times better than that of optical density measurements under the same ${\mu}FCGG$ system. Additionally, the hydrodynamic diameter distribution of Au NPs was estimated as $39.7{\pm}12.2nm$ with the PTA approach, which agrees well with DLS measurement as well as the manufacturer's specification. We propose this ${\mu}FCGG$-LSDFM setup with features of automatic generation of NP concentration gradient and real-time monitoring of their physicochemical characteristics (e.g., number concentration, and hydrodynamic size distribution) as an important component of future high-throughput screening or high-content analysis platforms of nanotoxicity.

• Wind and Structures
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• v.16 no.2
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• pp.137-156
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• 2013

A wind tunnel test of a scaled-down model and field measurement were effective methods for elucidating the aerodynamic behavior of a chimney under a wind load. Therefore, the relationship between the results of the wind tunnel test and the field measurement had to be determined. Accordingly, the set-up and testing method in the wind tunnel had to be modified from the field measurement to simulate the real behavior of a chimney under the wind flow with a larger Reynolds number. It enabled the results of the wind tunnel tests to be correlated with the field measurement. The model surface roughness and different turbulence intensity flows were added to the test. The simulated results of the wind tunnel test agreed with the full-scale measurements in the mean surface pressure distribution behavior.