• Proceedings of the IEEK Conference
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• 2002.06b
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• pp.345-348
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• 2002

This paper presents new fast scalar multiplier of elliptic curve cryptosystem that is regarded as next generation public-key crypto processor. For fast operation of scalar multiplication a finite field multiplier is designed with LFSR type of bit serial structure and a finite field inversion operator uses extended binary euclidean algorithm for reducing one multiplying operation on point operation. Also the use of the window non-adjacent form (WNAF) method can reduce addition operation of each other different points.

• Bulletin of the Korean Mathematical Society
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• v.29 no.2
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• pp.295-300
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• 1992

In [5] it was shown that if T .mem. L(X) is regular on a Banach space X, with finite dimensional intersection T$^{-1}$ (0).cap.T(X) and if S .mem. L(X) is invertible, commute with T and has sufficiently small norm then T - S in upper semi-Fredholm, and hence essentially one-one, in the sense that the null space of T - S is finite dimensional ([4] Theorem 2; [5] Theorem 2). In this note we extend this result to incomplete normed space.

• Bulletin of the Korean Mathematical Society
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• v.34 no.1
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• pp.19-28
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• 1997

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$ T^*h \right\$\mid$ \leq \left\$\mid$ Th \right\$\mid$$ for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

• Bulletin of the Korean Mathematical Society
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• v.48 no.1
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• pp.183-195
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• 2011

In this paper we show that Helton class preserves the nilpotent and finite ascent properties. Also, we show some relations on non-transitivity and decomposability between operators and their Helton classes. Finally, we give some applications in the Helton class of weighted shifts.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.503-508
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• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.471-479
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• 2010

For a complex regular Borel measure ${\mu}$ on ${\Omega}$ which is a subset of ${\mathbb{C}}^k$, where k is a positive integer we define the Toeplitz operator $T_{\mu}$ on a reproducing analytic space which comtains polynomials. Using every symmetric polynomial is a polynomial of elementary polynomials, we show that if $T_{\mu}$ has finite rank then ${\mu}$ is a finite linear combination of point masses.

• Journal of Information Processing Systems
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• v.14 no.3
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• pp.590-599
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• 2018

Multivariate finite mixture model is becoming more and more popular in image processing. Performing image denoising from image patches to the whole image has been widely studied and applied. However, there remains a problem that the structure information is always ignored when transforming the patch into the vector form. In this paper, we study the operator which extracts patches from image and then transforms them to the vector form. Then, we find that some pixels which should be continuous in the image patches are discontinuous in the vector. Due to the poor anti-noise and the loss of structure information, we propose a new operator which may keep more information when extracting image patches. We compare the new operator with the old one by performing image denoising in Expected Patch Log Likelihood (EPLL) method, and we obtain better results in both visual effect and the value of PSNR.

• Communications of the Korean Mathematical Society
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• v.24 no.3
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• pp.381-393
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• 2009

Strong convergence theorems on viscosity approximation methods for finding a common zero of a finite family accretive operators are established in a reflexive and strictly Banach space having a uniformly G$\hat{a}$teaux differentiable norm. The main theorems supplement the recent corresponding results of Wong et al. [29] and Zegeye and Shahzad [32] to the viscosity method together with different control conditions. Our results also improve the corresponding results of [9, 16, 18, 19, 25] for finite nonexpansive mappings to the case of finite pseudocontractive mappings.

• Journal of the Korean Society of Combustion
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• v.6 no.2
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• pp.15-22
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• 2001

A pressure-based, unstructured finite volume method has been applied to couple the chemical kinetics and fluid dynamics and to capture effectively and accurately the steep gradient flame field. The pressure-velocity coupling is handled by two methodologies including the pressure-correction algorithm and the projection scheme. A stiff, operator-split projection scheme for the detailed nonequilibrium chemistry has been employed to treat the stiff reaction source terms. The conservative form of the governing equations are integrated over a cell-centered control volume with collocated storage for all transport variables. Computations using detailed chemistry and variable transport properties were performed for two laminar reacting flows: a counterflow hydrogen-air diffusion flame and a lifted methane-air triple flame. Numerical results favorably agree with measurements in terms of the detailed flame structure.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.807-819
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• 2008

We prove that for any continuous function f on the s-harmonic (1{\infty})$ boundary of a complete Riemannian manifold M, there exists a solution, which is a limit of a sequence of bounded energy finite solutions in the sense of supremum norm, for a certain elliptic operator A on M whose boundary value at each s-harmonic boundary point coincides with that of f. If $E_1,\;E_2,...,E_{\iota}$ are s-nonparabolic ends of M, then we also prove that there is a one to one correspondence between the set of bounded energy finite solutions for A on M and the Cartesian product of the sets of bounded energy finite solutions for A on $E_i$ which vanish at the boundary ${\partial}E_{\iota}\;for\;{\iota}=1,2,...,{\iota}$