• Bulletin of the Korean Mathematical Society
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• v.41 no.2
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• pp.241-256
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• 2004

In this paper, we introduce and study a new class of variational inclusions, called the general variational inclusion. We prove the equivalence between the general variational inclusions, the general resolvent equations, and the fixed-point problems, using the resolvent operator technique. This equivalence is used to suggest and analyze a few iterative algorithms for solving the general variational inclusions and the general resolvent equations. Under certain conditions, the convergence analyses are also studied. The results presented in this paper generalize, improve and unify a number of recent results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.2
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• pp.533-543
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• 2018

Under the symbol ${\Omega}$ is a combination of ${\phi}_i$ ($i=1,2,3,{\ldots},n$) which has a suitable growth condition, for dimension n = 2 and $n{\geq}3$, when the initial data f belongs to homogeneous Sobolev space, we obtain the global $L^q$ estimate for maximal operators generated by operators family $\{S_{t,{\Omega}}\}_{t{\in}{\mathbb{R}}}$ associated with solution to dispersive equations, which extend some results in [27].

• Journal of the Korean Chemical Society
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• v.25 no.5
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• pp.291-299
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• 1981

A test particle kinetic theory for reaction dynamics in liquids is presented at the repeated ring collision level for the hard sphere model. A kinetic equation for the equilibrium time correlation function of the reactive test particle phase space density is derived and the rate kernel expression for the reversible chemical reaction of the type A +B ${\rightleftharpoons$ C + D in the presence of inert solvent S is obtained by the projection operator method.

• Bulletin of the Korean Chemical Society
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• v.35 no.11
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• pp.3294-3298
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• 2014

We theoretically investigated the coherent control of Autler-Townes splitting in photoelectron spectroscopy of K2 molecule within an ultrafast laser pulse by solving the time-dependent Schrodinger equation using a quantum wave packet method. It was theoretically shown that we can manipulate the splitting of photoelectron spectroscopy by altering the laser intensity. Furthermore, it was found that the percentages of each peak in photoelectron spectroscopy can be controlled by changing the envelope of the laser pulse.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.55 no.6
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• pp.259-264
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• 2006

This paper addresses the collusive bidding that functions as a potential obstacle to a fully competitive wholesale electricity market. Cooperative game is formulated and the equation of its Nash Equilibrium (NE) is derived on the basis of the supply function model. Gencos' willingness to selectively collude is expressed through a bargain theory. A Collusion Incentive Index(CII) for representing the willingness is defined through computing the Gencos' profits at NE. In order to keep the market non-cooperative, the market operator has to know the highest potentially collusive combination among the Gencos. Another index, which will be called the Collusion Monitoring Index(CMI), is suggested to detect the highest potential collusion and it is calculated using the marginal cost functions of the Gencos without any computation of NE. The effectiveness of CMI for detecting the highest potential collusion is verified through application on many test market cases.

• Proceedings of the KIEE Conference
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• 2001.05a
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• pp.270-272
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• 2001

This paper proposes an algorithm of analyzing the conductor temperature distribution of underground power cables buried ill ducts. This algorithm used an equation of the permissible current-carrying capability of power cables. The algorithm will be given to an operator an ability to operate the underground power system in comfort.

• Journal of applied mathematics & informatics
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• v.4 no.1
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• pp.83-108
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• 1997

Chebysheff-Halley methods are probably the best known cubically convergent iterative procedures for solving nonlinear equa-tions. These methods however require an evaluation of the second Frechet-derivative at each step which means a number of function eval-uations proportional to the cube of the dimension of the space. To re-duce the computational cost we replace the second Frechet derivative with a fixed bounded bilinear operator. Using the majorant method and Newton-Kantorovich type hypotheses we provide sufficient condi-tions for the convergence of our method to a locally unique solution of a nonlinear equation in Banach space. Our method is shown to be faster than Newton's method under the same computational cost. Finally we apply our results to solve nonlinear integral equations appearing in radiative transfer in connection with the problem of determination of the angular distribution of the radiant-flux emerging from a plane radiation field.

• 제어로봇시스템학회:학술대회논문집
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• 1990.10b
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.513-523
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• 2015

We present a local convergence analysis of some Newton-like methods of R-order at least three in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second $Fr{\acute{e}}chet$-derivative of the operator involved. These conditions are weaker that the corresponding ones given by Hernandez, Romero [10] and others [1], [4]-[9] requiring hypotheses up to the third $Fr{\acute{e}}chet$ derivative. Numerical examples are also provided in this study.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.