• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1325-1337
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• 2014

In this paper we study the sequences defined by the last and the last non-zero digits of $n^n$ in base b. For the sequence given by the last digits of $n^n$ in base b, we prove its periodicity using different techniques than those used by W. Sierpinski and R. Hampel. In the case of the sequence given by the last non-zero digits of $n^n$ in base b (which had been studied only for b = 10) we show the non-periodicity of the sequence when b is an odd prime power and when it is even and square-free. We also show that if $b=2^2{^s}$ the sequence is periodic and conjecture that this is the only such case.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.513-520
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• 2014

We study numerical methods to obtain the stationary probabilities of continuous-time Markov chains whose embedded chains are periodic. The power method is applied to the balance equations of the periodic embedded Markov chains. The power method can have the convergence speed of exponential rate that is ambiguous in its application to original continuous-time Markov chains since the embedded chains are discrete-time processes. An illustrative example is presented to investigate the numerical iteration of this paper. A numerical study shows that a rapid and stable solution for stationary probabilities can be achieved regardless of periodicity and initial conditions.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.7 s.172
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• pp.170-176
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• 2005

Analysis of structures which are composed of numerous repeated unit structures can be simplified by using homogenized properties. If the unit structure is repeated in one direction, the whole structure may be regarded as a beam. Once the effective stiffness is obtained from the analysis of the unit structure in a proper way, the effort for the detail modeling of the global structure is not required, and the real structure can be replaced simply with a beam. This study proposes a kinematical periodicity constraint to be imposed on the FE model of the unit structure, which improves the accuracy of the effective stiffness. The method is employed to a one dimensionally arrayed 3D structure containing periodically repeated un-symmetric holes. It is demonstrated that the deformation behavior of the homogenized beam agrees well with that of the real structure.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.3
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• pp.387-398
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• 1996

In this study the cell arrival processes from pre-buffer into multiplexer for MPEG(Motion Picture Experts Group) coding video sources are analyzed with consideration of the traffic periodicity in frame level. The analysis is performed by introducing the two arrival models, that is, periodic on/off source model and periodic uniform arrival model. Modulated $N^*D$/D/1 queueing system is utilized in periodic on/off source model, while ${\Sigma}{N_i}^*D_i$/D/1 queueing system is used in periodic uniform arrival model. The presented models are validated by comparing with computer simulations. Numerical results for periodic uniform arrival model are shown to be very accurate, but those of periodic on/off source model are shown to be inaccurate as the number of sources are increased.

• Journal of Korea Multimedia Society
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• v.21 no.12
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• pp.1504-1512
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• 2018

The purpose of this study is to design and apply a simple game that can visually experience basic concepts of game mathematics in order to teach game mathematics effectively. To do this, simple games linked with game mathematical theory are to be developed by utilizing the functions provided by Unity so that students could actively learn game mathematics. To demonstrate the plausibility of this approach, "Bouncing Ball Game" was developed to understand the concept of periodicity of trigonometric functions. As a result, students were able to effectively learn how mathematical concepts related to ball movements applied to the game.

• Biomolecules & Therapeutics
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• v.29 no.1
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• pp.31-40
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• 2021

All living beings on earth have an important mechanism of 24-h periodicity, which controls their physiology, metabolism, and behavior. In humans, 24-h periodicity is regulated by the superchiasmatic nucleus (SCN) through external and environmental cues. Peripheral organs demonstrate circadian rhythms and circadian clock functions, and these are also observed in cultured cell lines. Every cell contains a CLOCK: BMAL1 loop for the generation of circadian rhythms. In this review, we focused on cell autonomous circadian rhythms in immune cells, the inflammatory diseases caused by disruption of circadian rhythms in hormones, and the role of clock genes in inflammatory diseases.

• Journal of IKEEE
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• v.25 no.1
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• pp.32-36
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• 2021

This paper presents a novel collided tag signals's periodic characteristic based radio frequency identification (RFID) tag collision detection method for the ultra high frequency (UHF) RFID. The proposed method utilizes that periodicity of tag signals is maintained even under tag collision. In the proposed method, the correlation between received signal and reference edge signal is used. Simulation result shows that the detection performance using the proposed method is about 10 dB better than that of existing method. In addition, the detection performances with different magnitude difference, phase difference, delay, number of tags are analyzed.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.667-680
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• 2020

Our paper deals with the following neutral nonlinear Levin-Nohel integro-differential with variable delay $${\frac{d}{dt}x(t)}+{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{t-r(t)}}^t}a(t,s)x(s)ds+{\frac{d}{dt}}g(t,x(t-{\tau}(t)))=0.$$ By using Krasnoselskii's fixed point theorem we obtain the existence of periodic and positive periodic solutions and by contraction mapping principle we obtain the existence of a unique periodic solution. An example is given to illustrate this work.

• Proceedings of the Korea Institute of Fire Science and Engineering Conference
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• 2002.05a
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• pp.95-101
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• 2002

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.417-427
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• 1994

Let C be a nonempty closed bounded convex subset of a real Banach space X.