• Korean Journal of Mathematics
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• v.23 no.1
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• pp.11-27
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• 2015

Nonlinear partial differential equations are more suitable to model many physical phenomena in science and engineering. In this paper, we consider three nonlinear partial differential equations such as Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation which serves as a model for the unidirectional propagation of the shallow water waves over a at bottom. The main objective in this paper is to apply the generalized Riccati equation mapping method for obtaining more exact traveling wave solutions of Novikov equation, an equation for surface water waves and the Geng-Xue coupled equation. More precisely, the obtained solutions are expressed in terms of the hyperbolic, the trigonometric and the rational functional form. Solutions obtained are potentially significant for the explanation of better insight of physical aspects of the considered nonlinear physical models.

• Journal of Communications and Networks
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• v.18 no.4
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• pp.658-669
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• 2016

The tremendous increase in mobile data traffic coupled with fierce competition in wireless industry brings about spectrum scarcity and bandwidth fragmentation. This inevitably results in asymmetric-valued long term evolution (LTE) spectrum allocation that stems from different timing for twice improvement in capacity between competing operators, given spectrum allocations today. This motivates us to study the economic effects of asymmetric-valued LTE spectrum allocation. In this paper, we formulate the interactions between operators and users as a hierarchical dynamic game framework, where two spiteful operators simultaneously make spectrum acquisition decisions in the upper-level first-price sealed-bid auction game, and dynamic pricing decisions in the lower-level differential game, taking into account user subscription dynamics. Using backward induction, we derive the equilibrium of the entire game under mild conditions. Through analytical and numerical results, we verify our studies by comparing the latest result of LTE spectrum auction in South Korea, which serves as the benchmark of asymmetric-valued LTE spectrum auction designs.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.753-765
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• 2020

Smoking is one of the main causes of health problems and continues to be one of the world's most significant health challenges. In this paper, we use the multi-step Adomian decomposition method (MSADM) to obtain approximate analytical solutions for a mathematical fractional model of the evolution of the smoking habit. The proposed MSADM scheme is only a simple modification of the Adomian decomposition method (ADM), in which ADM is treated algorithmically with a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding problems. A comparative study between the new algorithm and the classical Runge-Kutta method is presented in the case of integer-order derivatives. The solutions obtained are also presented graphically. The results reveal that the method is effective and convenient for solving linear and nonlinear differential equations of fractional order.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.2
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• pp.78.3-78.3
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• 2019

We develop a novel technique that can constrain the evolutionary track of the epoch of reionization (EoR) by applying the convolutional neural network (CNN) to the 21-cm differential brightness temperature. We use 21cmFAST, a fast semi-numerical cosmological 21-cm signal simulator, to produce mock 21-cm map between z=6-13. We design a CNN architecture that predicts the volume-averaged neutral hydrogen fraction from the given 21-cm map. The estimated neutral fraction has a good agreement with its truth value even after smoothing the 21-cm map with somewhat realistic choices of beam size and the frequency bandwidth of the Square Kilometre Array (SKA). Our technique could be further utilized to denoise the 21-cm map or constrain the properties of the radiation sources.

• Journal of the Korean Society of Safety
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• v.19 no.4 s.68
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• pp.1-7
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• 2004

This study investigated the effects of aging on the transformation behavior of $Ti-50.1at\%$ Ni alloy by means of differential scanning calorimetry. It was found that aging in the temperature range of $350^{\circ}C\~550^{\circ}C$ induced complex transformation behavior, involving the R-phase and multiple-stage martensitic transformation. Usually aged Ni-rich NiTi alloys undergo martensitic transformation on cooling from high temperatures in two step : B2 to R and then R to Bl9'(normal behavior). But under certain ageing conditions, the transformation can also occur in three or more step(unusual multiple step behavior). In the present study we use differential seaming calorimetry(DSC) for a systematic investigation of the evolution of transformation behavior with ageing temperature and time.

• Transactions of Materials Processing
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• v.30 no.4
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• pp.195-200
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• 2021

In this study, we investigated the dominant processing variables that would influence the microstructural development of AA6061 deformed by differential speed rolling (DSR) at ambient temperature. For this purpose, we carried out a series of DSR on the samples to investigate the effects of roll speed ratio, sample rotation, and number of operation under specific rotation. Among these, the condition with a height reduction of 75% at a speed ratio of 1:4 through rotation along rolling direction (RR) displayed the pronounced results of more homogenous matrix-structure and superior mechanical properties than the others tested in this study. This was mainly due to the cross shearing of macro-shear pattern in segment where dynamic recrystallization took place with ease throughout the sample. Thus, an average microhardness value of 101 Hv was obtained in the present sample deformed by 4-pass DSR with RR where macro cross-shearing was effectively applied.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.1053-1056
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• 2004

In this article we have applied Schweizer & Sklars t-norm based similarity measures to classification task. We will compare results to fuzzy similarity measure based classification and show that sometimes better results can be found by using these measures than fuzzy similarity measure. We will also show that classification results are not so sensitive to p values with Schweizer & Sklars measures than when fuzzy similarity is used. This is quite important when one does not have luxury of tuning these kind of parameters but needs good classification results fast.

• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.881-891
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• 2012

In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.393-404
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• 2003

In general, a differential operator can be used as a tool of treating the local properties of given function. However, when the given function is varied with high frequency and has irregular form with non-stationary evolution it may not act its role sufficiently as in case of nowhere differentiable curves. In this paper we introduce a multi-scale derivative as a form of weakened global derivative so that it may explain its semi global diffusion properties as well as local ones for the various irregular diffusion phenomena.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1817-1828
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• 2017

We give a simple and direct proof of the characterization of positivity preserving semi-flows for ordinary differential systems. The same method provides an abstract result on a class of evolution systems containing reaction-diffusion systems in a bounded domain of ${\mathbb{R}}^n$ with either Neumann or Dirichlet homogeneous boundary conditions. The conditions are exactly the same with or without diffusion. A similar approach gives the optimal result for invariant rectangles in the case of Neumann conditions.