• Proceedings of the Korean Biophysical Society Conference
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• 2003.06a
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• pp.78-78
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• 2003

The glycolysis is one of the most important metabolic reactions through which the glucose is broken and the released energy is stored in the form of ATP. Rhythmic oscillation of the intracellular ATP is observed as the amount of the influx glucose is small in the yeast. The oscillation is also observed in the population of the yeast cells, which implies that the glycolytic oscillation of the yeasts is synchronous. It is not clear how the synchronous oscillation could be organized among the yeast cells. Although detailed mathematical models are available that show synchronization of the glycolytic oscillation, the stability of the synchronous oscillation is not clear. We introduce a phase model analysis that reduces a higher dimensional mathematical model to a much simpler one dimensional phase model. Then, the stability of the synchronous oscillation is easily determined by the stability of the corresponding fixed solution in the phase model. The effect of perturbation on the oscillatory rhythm is also easily analyzed in the reduced phase model.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.229-246
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• 2024

We consider the delay differential equations $$b(z)w(z+1)+c(z)w(z-1)+a(z)\frac{w'(z)}{w^k(z)}=\frac{P(z, w(z))}{Q(z, w(z))}$$, where k ∈ {1, 2}, a(z), b(z) ≢ 0, c(z) ≢ 0 are rational functions, and P(z, w(z)) and Q(z, w(z)) are polynomials in w(z) with rational coefficients satisfying certain natural conditions regarding their roots. It is shown that if this equation has a non-rational meromorphic solution w with hyper-order ρ2(w) < 1, then either deg_w(P) = deg_w(Q) + 1 ≤ 3 or max{deg_w(P), deg_w(Q)} ≤ 1. In addition, it is shown that in the case max{deg_w(P), deg_w(Q)} = 0 the equations above can have such a solution, with an additional zero density requirement, only if the coefficients of the equation satisfy certain strict conditions.

• Journal of Korea Multimedia Society
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• v.12 no.6
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• pp.842-855
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• 2009

We present a physics-based blending method for the second order algebraic implicit surface. Unlike other traditional blending techniques, the proposed method avoids complex mathematical operations and unwanted artifacts like bulge, which have highly limited the application of the second order algebraic implicit surface as a modeling primitive in spite of lots of its excellent properties. Instead, the proposed method provides the designer with flexibility to control the shapes of the blending surface on interactive basis; the designer can check and design the shape of blending surfaces accurately by simply adjusting several physics parameter in real time, which was impossible in the traditional blending methods. In the later parts of this paper, several results are also presented.

• Journal of the Korean Physical Society
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• v.73 no.9
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• pp.1197-1210
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• 2018

Since the first detection of gravitational-wave (GW), GW150914, September 14th 2015, the multi-messenger astronomy added a new way of observing the Universe together with electromagnetic (EM) waves and neutrinos. After two years, GW together with its EM counterpart from binary neutron stars, GW170817 and GRB170817A, has been observed. The detection of GWs opened a new window of astronomy/astrophysics and will be an important messenger to understand the Universe. In this article, we briefly review the gravitational-wave and the astrophysical sources and introduce the basic principle of the laser interferometer as a gravitational-wave detector and its noise sources to understand how the gravitational-waves are detected in the laser interferometer. Finally, we summarize the search algorithms currently used in the gravitational-wave observatories and the detector characterization algorithms used to suppress noises and to monitor data quality in order to improve the reach of the astrophysical searches.

• Electronics and Telecommunications Trends
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• v.39 no.4
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• pp.42-53
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• 2024

Mathematical modeling is the process of representing physical phenomena using equations, and it often describes various scientific phenomena through differential equations. Numerical analysis, which is capable of approximating solutions to partial differential equations representing physical phenomena, is widely utilized. However, in high-dimensional or nonlinear systems, computational costs can substantially increase, leading to potential numerical instability or convergence issues. Recently, Physics-Informed Neural Networks (PINNs) have emerged as an alternative approach. A PINN leverages physical laws even with limited data to provide highly reliable predictive performance and can address the convergence issues and high computational costs associated with numerical analysis. This paper analyzes the weak signals, research trends, patent trends, and case studies of PINNs. On the basis of this analysis, it proposes directions for the development of PINN techniques in the agricultural field. In particular, the application of PINNs in agriculture is expected to be more effective than in other industries because of their ability to reflect real-time changes in biological processes. While the technology readiness level of PINNs remains low, the potential for model training with minimal data and real-time prediction capabilities suggests that PINNs could replace traditional numerical analysis models. It is anticipated that the research and industrial applications of PINN will develop at an increasing pace while focusing on addressing the complexity of mathematical models in agriculture, mathematical modeling and the application of various biological processes; securing key patents related to PINNs; and standardizing PINN technology in the field of agriculture.

• East Asian mathematical journal
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• v.25 no.3
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• pp.399-413
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• 2009

Whitehead's philosophy is evaluated as an applicable philosophy and an accurate, logical explanation system about the world through mathematics. Whitehead's ideological development can be divided into mathematical research, critical consciousness about sciences and philosophical exploration. Although it is presented as a whole unified conceptual framework to understand nature and human beings which is based on modern mathematics and physics in the 20th century, Whitehead's philosophy has not been sufficiently understood and evaluated about the full meaning and mathematics educational values. In this paper, we study relations of Whitehead's philosophy and the mathematical education. Moreover, we study implicity of mathematical education.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.65-78
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• 2006

The law of refraction, which is called Snell's law in physics, has a significant meaning in mathematics history. After Snell empirically discovered the refraction law $\frac{v_1}{sin{\theta}_1}=\frac{v_2}{sin{\theta}_2$ through countless observations, many mathematicians endeavored to deduce it from the least time principle, and the need to surmount these difficulties was one of the driving forces behind the early development of calculus by Leibniz. Fermat solved it far advance of others by inventing a method that eventually led to the differential calculus. Historically, mathematics has developed in close connection with physics. Physics needs mathematics as an auxiliary discipline, but physics can also belong to the lived-through reality from which mathematics is provided with subject matters and suggestions. The refraction law is a suggestive example of interrelations between mathematical and physical theories. Freudenthal said that a purpose of mathematics education is to learn how to apply mathematics as well as to learn ready-made mathematics. I think that the refraction law could be a relevant content for this purpose. It is pedagogically sound to start in high school with a quasi-empirical approach to refraction. In college, mathematics and physics majors can study diverse mathematical proof including Fermat's original method in the context of discussing the phenomenon of refraction of light. This would be a ideal environment for such pursuit.

• Publications of The Korean Astronomical Society
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• v.26 no.2
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• pp.71-87
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• 2011

Gravitational waves are predicted by the Einstein's theory of General Relativity. The direct detection of gravitational waves is one of the most challenging tasks in modern science and engineering due to the 'weak' nature of gravity. Recent development of the laser interferometer technology, however, makes it possible to build a detector on Earth that is sensitive up to 100-1000 Mpc for strong sources. It implies an expected detection rate of neutron star mergers, which are one of the most important targets for ground-based detectors, ranges between a few to a few hundred per year. Therefore, we expect that the gravitational-wave observation will be routine within several years. Strongest gravitational-wave sources include tight binaries composed of compact objects, supernova explosions, gamma-ray bursts, mergers of supermassive black holes, etc. Together with the electromagnetic waves, the gravitational wave observation will allow us to explore the most exotic nature of astrophysical objects as well as the very early evolution of the universe. This review provides a comprehensive overview of the theory of gravitational waves, principles of detections, gravitational-wave detectors, astrophysical sources of gravitational waves, and future prospects.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.475-482
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• 2007

In this paper, we study composition operators $C_{\varph}f=f^{\circ}{\varph}$, induced by a fixed analytic self-map of the of the upper half-plane, acting between Hardy and Bloch-type spaces of the upper half-plane.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.599-608
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• 2004

Let R be an associative ring with identity and J(R) be the Jacobson radical of R. In this paper we investigate the generalization of the Jacobson radical of R, J＊ (R) say. Also we study the rings that J＊(R) = J(R).