• Communications of Mathematical Education
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• v.28 no.3
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• pp.339-352
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• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Journal of Communications and Networks
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• v.10 no.1
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• pp.44-54
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• 2008

In this paper, an iterative multiple symbol differential detection for turbo coded differential unitary space-time modulation using a posteriori probability (APP) demodulator is investigated. Two approaches of different complexity based on linear prediction are presented to utilize the temporal correlation of fading for the APP demodulator. The first approach intends to take account of all possible previous symbols for linear prediction, thus requiring an increase of the number of trellis states of the APP demodulator. In contrast, the second approach applies Viterbi algorithm to assist the APP demodulator in estimating the previous symbols, hence allowing much reduced decoding complexity. These two approaches are found to provide a trade-off between performance and complexity. It is shown through simulation that both approaches can offer significant BER performance improvement over the conventional differential detection under both correlated slow and fast Rayleigh flat-fading channels. In addition, when comparing the first approach to a modified bit-interleaved turbo coded differential space-time modulation counterpart of comparable decoding complexity, the proposed decoding structure can offer performance gain over 3 dB at BER of $10^{-5}$.

• Journal of the Korean Mathematical Society
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• v.47 no.6
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• pp.1183-1196
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• 2010

Some annulus oscillation criteria are established for the second order damped elliptic differential equation $$\sum\limits_{i,j=1}^N D_i[a_{ij}(x)D_jy]+\sum\limits_{i=1}^Nb_i(x)D_iy+C(x,y)=0$$ under quite general assumption that they are based on the information only on a sequence of annuluses of $\Omega(r_0)$ rather than on the whole exterior domain $\Omega(r_0)$. Our results are extensions of those due to Kong for ordinary differential equations. In particular, the results obtained here can be applied to the extreme case such as ${\int}_{\Omega(r0)}c(x)dx=-\infty$.

• Journal of Korean Society for Atmospheric Environment
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• v.23 no.6
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• pp.708-717
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• 2007

In the present study, one of the widely applied equations for gas-solid cyclones, Leith and Licht model, was evaluated based on the 3-D CFD technique. The initial and boundary values of radial position and tangential velocity obtain-ed from the CFD simulation enabled complete calculation of the nonlinear second differential equation. This approach showed about 30% errors between calculations with and without the second order differential term. The calculation by using the simple first order equation presented shorter times to migrate up to the inner wall of the cyclone than by the second order, which theoretically implies higher separation efficiency. Further comparison is now under evaluation in terms of the detailed grade efficiency.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.25 no.10B
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• pp.1832-1840
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• 2000

The error diffusion algorithm is good for reproducing continuous images to binary images. However the reproduction of edge characteristics is weak in power spectrum an analysis of display error. In this paper an edge enhanced error diffusion method is proposed to improve the edge characteristic enhancement. Spatial gradient information in original image is adapted for edge enhance in threshold modulation of error diffusion. First the horizontal and vertical second order differential values are obtained from the gradient of peripheral pixels(3x3) in original image. second weighting function is composed by function including absolute value and sign of second order differential values. The proposed method presents a good visual results which edge characteristics is enhanced. The performance of the proposed method is compared with that of the conventional edge enhanced error diffusion by measuring the edge correlation and the local average accordance over a range of viewing distances and the RAPSD of display error.

• Journal of The Korean Astronomical Society
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• v.28 no.2
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• pp.197-208
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• 1995

Real time CCD differential photometry was performed for BT Cnc in Praesepe cluster from February to March, 1994. New 885 differential V magnitudes were obtained for thirteen nights. From the frequency analysis, we have detected two distinct pulsational frequencies of $f_1$=9.7783c/d and $f_2$=7.0153c/d. The first frequency is nearly equal to the previous result(Breger 1980), but the second one is much different. Our reanalysis of the previous data obtained by Guerrero el al.(1979) indicates that the previous result of $f_s$=5.95c/d might be uncertain; it was not detected in the power spectrum. Also it turns out that our second frequency could not be fitted to the previous data and the reanalyzed frequency($f_2$=7.8813c/d) of the previous data was poor-fitted to our data. Therefore we suggest that the second frequency which might be newly excited in the nonradial mode, has been changed over the last eighteen years.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.39-53
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• 2014

In this paper, a non-asymptotic method is presented for solving singularly perturbed delay differential equations whose solution exhibits a boundary layer behavior. The second order singularly perturbed delay differential equation is replaced by an asymptotically equivalent first order neutral type delay differential equation. Then, Simpson's integration formula and linear interpolation are employed to get three term recurrence relation which is solved easily by Discrete Invariant Imbedding Algorithm. Some numerical examples are given to validate the computational efficiency of the proposed numerical scheme for various values of the delay and perturbation parameters.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• Structural Engineering and Mechanics
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• v.52 no.5
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• pp.971-995
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• 2014

The parts of semi-rigid connected and partially embedded piles in elastic soil, above the soil and embedded in the soil are called the first region and second region, respectively. The upper end of the pile in the first region is supported by linear-elastic rotational spring. The forth order differential equations of both region for critical buckling load of partially embedded and semi-rigid connected pile with shear deformation are established using small-displacement theory and Winkler hypothesis. These differential equations are solved by differential transform method (DTM) and analytical method and critical buckling loads of semirigid connected and partially embedded pile are obtained, results are given in tables and graphs are presented for investigating the effects of relative stiffness of the pile and flexibility of rotational spring.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.795-814
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• 2021

In this paper, we study the transcendental meromorphic solutions for the nonlinear differential equations: fⁿ + P(f) = R(z)e^α(z) and fⁿ + P_*(f) = p₁(z)e^α₁(z) + p₂(z)e^α₂(z) in the complex plane, where P(f) and P_*(f) are differential polynomials in f of degree n - 1 with coefficients being small functions and rational functions respectively, R is a non-vanishing small function of f, α is a nonconstant entire function, p₁, p₂ are non-vanishing rational functions, and α₁, α₂ are nonconstant polynomials. Particularly, we consider the solutions of the second equation when p₁, p₂ are nonzero constants, and deg α₁ = deg α₂ = 1. Our results are improvements and complements of Liao ([9]), and Rong-Xu ([11]), etc., which partially answer a question proposed by Li ([7]).