• Journal of the Korea Society of Computer and Information
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• v.11 no.4 s.42
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• pp.181-188
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• 2006

In this paper, we propose a search algorithm for similar example-sentences in the computer-aided translation. The search for similar examples, which is a main part in the computer-aided translation, is to retrieve the most similar examples in the aspect of structural and semantical analogy for a given query from examples. The proposed algorithm is based on the Needleman-Wunsch algorithm, which is used to measure similarity between protein or nucleotide sequences in bioinformatics. If the original Needleman-Wunsch algorithm is applied to the search for similar sentences, it is likely to fail to find them since similarity is sensitive to word's inflectional components. Therefore, we use the lemma in addition to (typographical) surface information. In addition, we use the part-of-speech to capture the structural analogy. In other word, this paper proposes the similarity metric combining the surface, lemma, and part-of-speech information of a word. Finally, we present a search algorithm with the proposed metric and present pairs contributed to similarity between a query and a found example. Our algorithm shows good performance in the area of electricity and communication.

• Journal of Internet Computing and Services
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• v.25 no.2
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• pp.93-99
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• 2024

In this paper, we derive the Partial Differential Bond Price Equation (PDBPE) by using Ito's Lemma to determine the pricing of bond on term-structure of interest rate (TSIR) model with jump. From PDBPE, the Maclaurin series (MS) and the moment-generating function (MGF) for the exponential function are used to obtain a numerical solution (NS) of the bond prices. And an algorithm for determining bond prices using Monte Carlo Simulation (MCS) techniques is proposed, and the pricing of bond is determined through the simulation process. Comparing the results of the implementation of the above two pricing methods, the relative error (RE) is obtained, which means the ratio of NS and MCS. From the results, we can confirm that the RE is less than around 2.2%, which means that the pricing of bond can be predicted very accurately using the proposed algorithms as well as numerical analysis. Moreover, it was confirmed that the bond price obtained using the MS has a relatively smaller error than the pricing of bond obtained by using the MGF.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.143-151
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• 2005

This paper considers a robust decentralized $H_\infty$ control problem for uncertain large-scale interconnected systems. The uncertainties are assumed to be time-invariant, norm-bounded, and exist in subsystems. A design method based on the bounded real lemma is developed for a dynamic output feedback controller, which is reduced to a feasibility problem for a nonlinear matrix inequality (NMI). It is proposed to solve the NMI iteratively by the idea of homotopy, where some of the variables are fixed alternately on each iteration to reduce the NMI to a linear matrix inequality (LMI). A decentralized controller for the nominal system is computed first by imposing structural constraints on the coefficient matrices gradually. Then, the decentralized controller is modified again gradually to cope with the uncertainties. A given example shows the efficiency of this method.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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• pp.193-199
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• 1993

A hereditary $C^{*}$-subalgebra B of a $C^{*}$-algebra A is said to be full if B is not contained in any proper closed two-sided ideal in A, so each hereditary $C^{*}$-subalgebra of a simple $C^{*}$-algebra is always full. It is well known that every $C^{*}$-algebra is strong Morita equivalent to its full hereditary $C^{*}$-subalgebra, but the strong Morita equivalence of a $C^{*}$-algebra A and its hereditary $C^{*}$-subalgebra B does not imply the fullness of B, ingeneral. We present the following lemma for our computational convenience in the course of the proof of the main theorem. Note that $L_{B}$, $L_{B}$$^{*}$ and $L_{B}$ $L_{B}$$^{*}$ are all .alpha.-invariant whenever B is .alpha.-invariant under the action .alpha. of G.a. of G.a. of G.a. of G.f G.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.773-786
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• 2001

On the setting of the half-space of the Euclidean n-space, we consider harmonic Bergman spaces and we also study properties of the reproducing kernel. Using covering lemma, we find some equivalent quantities. We prove that if lim$ lim\limits_{i\rightarrow\infty}\frac{\mu(K_r(zi))}{V(K_r(Z_i))}$ then the inclusion function $I : b^p\rightarrow L^p(H_n, d\mu)$ is a compact operator. Moreover, we show that if f is a nonnegative continuous function in $L^\infty and lim\limits_{Z\rightarrow\infty}f(z) = 0, then T_f$ is compact if and only if f $\in$ $C_{o}$ (H$_{n}$ ).

• Journal of the Korean Mathematical Society
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• v.47 no.3
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• pp.547-572
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• 2010

We study existence of positive solutions of the classical nonlinear Schr$\ddot{o}$dinger equation $-{\Delta}u\;+\;V(x)u\;-\;f(x,\;u)\;-\;H(x)u^{2*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$. In fact, we consider the following more general quasi-linear Schr$\ddot{o}$odinger equation $-div(|{\nabla}u|^{m-2}{\nabla}u)\;+\;V(x)u^{m-1}$ $-f(x,\;u)\;-\;H(x)u^{m^*-1}\;=\;0$, u > 0 in $\mathbb{R}^n$ $u\;{\rightarrow}\;0\;as\;|x|\;{\rightarrow}\;{\infty}$, where m $\in$ (1, n) is a positive number and $m^*\;:=\;\frac{mn}{n-m}\;>\;0$, is the corresponding critical Sobolev embedding number in $\mathbb{R}^n$. Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.439-449
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• 2014

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.271-287
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• 2008

This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here, the Jamshidian equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.688-691
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• 1997

This paper presents an $H^{\infty}$ controller design method for linear time-invariant systems with delayed state and control. Using the second method of Lyapunov, the stability for delayed systems is discussed. For delayed systems, we derive a sufficient condition of the bounded real lemma(BRL) which is similar to BRL for nondelayed systems. And the sufficient conditions for the existence of an output feedback $H^{\infty}$ controller of any order are given in terms of three linear matrix inequalities(LMls). Futhermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give a simple example to illustrate the validity of the proposed design procedure.e.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.2
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• pp.109-114
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• 1997

In this paper, we present an output feedback $H^\infty$controller design method and derive the sufficient condition of the bounded real lemma for linear systems with multiple delays in states. For state delayed systems, sufficient conditions for the existence $\kappa$-th order $H^\infty$controllers are given in terms of three linear matrix inequalities(LMIs). Furthermore, we show how to construct such controllers from the positive definite solutions of their LMIs and given an example to illustrate the validitiy of the proosed design procedure.