• East Asian mathematical journal
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• v.24 no.1
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• pp.111-123
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• 2008

In this paper, we introduce a new system of first-order impulsive fuzzy differential equations. By using Banach fixed point theorem, we obtain some new existence and uniqueness theorems of solutions for this system of first-order impulsive fuzzy differential equations in the metric space of normal fuzzy convex sets with distance given by maximum of the Hausdorff distance between level sets.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.441-452
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• 2009

In this paper, a fifth order numerical method is presented for solving singularly perturbed differential-difference equations with negative shift. In recent papers the term negative shift has been using for delay. Similar boundary value problems are associated with expected first exit time problem of the membrane, potential in models for neuron and in variational problems in control theory. In the numerical treatment for such type of boundary value problems, first we use Taylor approximation to tackle terms containing small shifts which converts it to a boundary value problem for singularly perturbed differential equation. The two point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a fifth order compact difference scheme is presented for the first order system and is solved using the boundary conditions. Several numerical examples are solved and compared with exact solution. It is observed that present method approximates the exact solution very well.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1669-1675
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• 2017

The group of automorphisms of the first Weyl algebra acts on commuting ordinary differential operators with polynomial coefficient. In this paper we prove that for fixed generic spectral curve of genus two the set of orbits is infinite.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Korean Journal of Mathematics
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• v.26 no.4
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• pp.675-681
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• 2018

In the paper, by virtue of techniques in combinatorial analysis, the authors simplify three families of nonlinear ordinary differential equations in terms of the Stirling numbers of the first kind and establish a new family of nonlinear ordinary differential equations in terms of the Stirling numbers of the second kind.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1171-1184
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• 2022

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1133-1143
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• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.299-315
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• 2015

In this paper, we study the first-order system least-squares (FOSLS) spectral method for parabolic partial differential equations. There were lots of least-squares approaches to solve elliptic partial differential equations using finite element approximation. Also, some approaches using spectral methods have been studied in recent. In order to solve the parabolic partial differential equations in parallel, we consider a parallel numerical method based on a hybrid method of the frequency-domain method and first-order system least-squares method. First, we transform the parabolic problem in the space-time domain to the elliptic problems in the space-frequency domain. Second, we solve each elliptic problem in parallel for some frequencies using the first-order system least-squares method. And then we take the discrete inverse Fourier transforms in order to obtain the approximate solution in the space-time domain. We will introduce such a hybrid method and then present a numerical experiment.

• 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 Society for Industrial and Applied Mathematics
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• v.11 no.1
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• pp.85-93
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• 2007

In this paper we prove the existence of mild solutions of a first order impulsive initial value problems for functional differential equations in Banach spaces. The results are obtained by using the Lerey-Schauder nonlinear alternative fixed point theorem.