• Journal of the Korea Computer Graphics Society
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• v.16 no.4
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• pp.17-23
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• 2010

Effective visualizing is an important issue when one processing real number domain volume data such as distance fields, or volume texture. In this paper, we introduce a framework for inspecting, magnifying, cross-section viewing of real number domain volume data from an implementation of a simple interface. The interface can be freely implemented from any kind of existing algorithm, so that we can easily view the result and evaluate the algorithm.

• East Asian mathematical journal
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• v.37 no.5
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• pp.613-617
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• 2021

Abstract. For a positive square-free integer m, let K = ℚ($\sqrt{m}$) be a real quadratic field. The relative class number H_d(f) of K of discriminant d is the ratio of class numbers 𝒪_K and 𝒪_f, where 𝒪_K is the ring of integers of K and 𝒪_f is the order of conductor f given by ℤ + f𝒪_K. In 1856, Dirichlet showed that for certain m there exists an infinite number of f such that the relative class number H_d(f) is one. But it remained open as to whether there exists such an f for each m. In this paper, we give a result for existence of real quadratic field ℚ($\sqrt{m}$) with relative class number one where the period of continued fraction expansion of $\sqrt{m}$ is 6.

• Journal of Digital Contents Society
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• v.12 no.4
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• pp.585-592
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• 2011

Real Estate Auction Information System purposes on providing high quality information of auction customized to consumer's situation and preference. Especially, ever-changing real time information such as the number of hits and advanced analysis for expecting the winning bid are requiring of mobile information system based on context awareness. Therefore, this paper studies on Real Estate Auction Information System based on context awareness under a smart phone environment providing auction information such as consumer's current position, the number of hits to a specific real estate, and the number of bidder to anticipate the winning bid.

• Journal of Korea Multimedia Society
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• v.24 no.3
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• pp.468-480
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• 2021

Realistic real-time rain streaks rendering has been treated as a very difficult problem because of various natural phenomena. Also, in creating and managing a large number of particles, a large amount of computer resources had to be used. Therefore, in this paper, we propose a more efficient real-time rain streaks rendering algorithm by generating view-dependent rain particles and expressing a large amount of rain even with a small number. By creating a 'rain space' dependent on the field of view of the camera moving in real time, particles are rendered only in that space. Accordingly, even if a small number of particles are rendered, since the rendering is performed in a limited space, an effect of rendering a very large amount of particles can be obtained. This enables very efficient real-time rendering of rain streaks.

• Journal for History of Mathematics
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• v.13 no.2
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• pp.49-64
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• 2000

Every real number can be expressed as a simple continued fraction. In particular, a number is rational if and only if its simple continued fraction has a finite number of terms. Owing to this property, continued fractions have been a powerful tool which determines a real number to be rational or not. Continued fractions provide not only a series of best estimate for a real number, but also a useful method for finding near commensurabilities between events with different periods. In this paper, we investigate the history and some properties of continued fractions, and then consider their applications in several examples. Also we explain why the Fibonacci numbers and the Golden section appear in nature in terms of continued fractions, with some examples such as the arrangements of petals round a flower, leaves round branches and seeds on seed head.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.2
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• pp.428-431
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• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.

• Proceedings of the Korea Society for Simulation Conference
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• 1998.03a
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• pp.101-105
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• 1998

A large system predictor, which can perform prediction of sales trend in a huge number of distribution centers, is presented using neural predictive model. There are 20,000 number of distribution centers, and each distribution center need to forecast future demand in order to establish a reasonable inventory policy. Therefore, the number of forecasting models corresponds to the number of distribution centers, which is not possible to estimate that kind of huge number of accurate models in ERP (Enterprise Resource Planning)module. Multilayer neural net as universal approximation is employed for fitting the prediction model. In order to improve prediction accuracy, a sequential simulation procedure is performed to get appropriate network structure and also to improve forecasting accuracy. The proposed simulation procedure includes neural structure identification and virtual predictive model generation. The predictive model generation consists of generating virtual signals and estimating predictive model. The virtual predictive model plays a key role in tuning the real model by absorbing the real model errors. The complement approach, based on real and virtual model, could forecast the future demands of various distribution centers.

• Honam Mathematical Journal
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• v.45 no.3
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• pp.542-554
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• 2023

Given a real number α, the Lagrange number of α is the supremum of all real numbers L > 0 for which the inequality |α - p/q| < (Lq²)^-1 holds for infinitely many rational numbers p/q. All Lagrange numbers less than 3 can be arranged as a set {l_p/q : p/q ∈ ℚ ∩ [0, 1]} using the Farey index. The present paper considers a function C(α) devised from Sturmian words. We demonstrate that the function C(α) contains all information on Lagrange numbers less than 3. More precisely, we prove that for any real number α ∈ (0, 1], the value C(α) - C(0) is equal to the sum of all numbers 3 - l_p/q where the Farey index p/q is less than α.

• 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.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.4
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• pp.176-184
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• 2002

We provide a checkpointing framework reflecting both the timeliness and the dependability in order to make checkpointing applicable to dependable real-time systems. The predictability of real-time tasks with checkpointing is guaranteed by the worst case execution time (WCET) based on the allocated number of checkpoints and the permissible number of failures. The permissible number of failures is derived from fault tolerance requirements, thus guaranteeing the dependability of tasks. Using the WCET and the permissible number of failures of tasks, we develop an algorithm that determines the minimum number of checkpoints allocated to each task in order to guarantee the schedulability of a task set. Since the framework is based on the amount of time redundancy caused by checkpointing, it can be extended to other time redundancy techniques.