• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.797-812
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• 1997

For analytic functions we give an expression for the kernel $K_n$ of the remainder terms for the Gauss-Radau and the Gauss-Lobatto rules with end points of multiplicity r and prove the convergence of the kernel we obtained. The error bound are obtained for the type $$\mid$R_n(f)$\mid$ \leq \frac{1}{\pi}l(\Gamma) max_{z \in \Gamma} $\mid$K_n(z)$\mid$ max_{z \in \Gamma} $\mid$f(z)$\mid$$, where $l(\Gamma)$ denotes the length of contour $\Gamma$.

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.471-478
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• 2007

In this article we shall introduce several operators on the reproducing kernel spaces and investigate quadratic forms on the $\mathcal{l}^2$ space. Using these operators we shall obtain a particular solution of a system of quadratic equations(1.5). Finally we can find an approximate solution of(1.5) by optimization of a nonnegative biquadratic polynomial.

• Korean Journal of Mathematics
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• v.29 no.1
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• pp.65-73
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• 2021

In this paper, we investigate the growth properties of solutions of the non-homogeneous linear complex differential equation L(f) = b (z) f + c (z), where L(f) is a linear differential polynomial and b (z), c (z) are entire functions and give some of its applications on sharing value problems.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.575-581
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• 1995

The simple modules and the simple comodules of the quantum group $X)q(2)$ defined by M. L. Ge, N. H. Jing and Y. S. Wu, are classified.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.197-204
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• 2012

In this paper, we study the problem of normal families and deduce some results, which improve and generalize several related theorems obtained by Pang [7], Fang and Xu [3], L$\ddot{u}$, Xu, and Yi [6]. Mean-while, some examples are given to show the sharpness of our results.

• Journal of the Korean Mathematical Society
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• v.56 no.2
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• pp.559-578
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• 2019

We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.31 no.6_2
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• pp.577-583
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• 2013

Recently, massive archives of ground information imagery from new sensors have become available. To establish a functional relationship between the image and the ground space, sensor models are required. The rational functional model (RFM), which is used as an alternative to the rigorous sensor model, is an attractive option owing to its generality and simplicity. To determine the rational polynomial coefficients (RPC) in RFM, however, we encounter the problem of obtaining a stable solution. The design matrix for solutions is usually ill-conditioned in the experiments. To solve this unstable solution problem, regularization techniques are generally used. In this paper, we describe the effective determination of the optimal regularization parameter in the regularization technique during RPC derivation. A brief mathematical background of RFM is presented, followed by numerical approaches for effective determination of the optimal regularization parameter using the Euler Method. Experiments are performed assuming that a tilted aerial image is taken with a known rigorous sensor. To show the effectiveness, calculation time and RMSE between L-curve method and proposed method is compared.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.6
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• pp.904-912
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• 1987

The main mode of heat transfer of combustion gases at high temperature is thermal radiation of nonluminous gases, CO$_{2}$ and H$_{2}$O. Therefore the information of the emissivities of CO$_{2}$ and H$_{2}$O would be very important in the thermal performance analysis of furnace. In this study, an exponential model for the emissivities of CO$_{2}$ and H$_{2}$O was derived as function of P$_{g}$L and polynomial of reciprocal of temperature. Error analysis between the calculated values from present model and the valued of Hottel Chart was performed over temperature range of 1000-5000 R and a partial-pressure-length product range of 0.003 to 20 ft-atm. For CO$_{2}$ gray gas, the error percent between the calculated values and the values from Hottel Chart was distributed within 2.5% in case of using a polynomial in 1/T of degree 4. For H$_{2}$O gray gas, the model has an error range of 0 to 2.5% in case of using a polynomial in 1/T of degree 3.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.271-279
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• 2014

Let $T_l$ be a transformation on the interval [-1, 1] defined by Chebyshev polynomial of degree $l(l{\geq}2)$, i.e., $T_l(cos{\theta})=cos(l{\theta})$. In this paper, we consider $T_l$ as a measure preserving transformation on [-1, 1] with an invariant measure $\frac{1}{\sqrt[\pi]{1-x^2}}dx$. We show that If f(x) is a nonconstant step function with finite k-discontinuity points with k < l-1, then it satisfies the Central Limit Theorem. We also give an explicit method how to check whether it satisfies the Central Limit Theorem or not in the cases of general step functions with finite discontinuity points.