• 대한수학회지
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• 제45권3호
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• pp.757-769
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• 2008

This paper deals with the existence of optimal controls and maximal principles for semilinear evolution equations with the nonlinear term satisfying Lipschitz continuity. We also present the necessary conditions of optimality which are described by the adjoint state corresponding to the linear equations without a condition of differentiability for nonlinear term.

• 대한수학회보
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• 제54권1호
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• pp.17-28
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• 2017

In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

• Journal of the Korean Data and Information Science Society
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• 제22권3호
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• pp.575-587
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• 2011

We investigate some statistical properties of several dierence-based error variance estimators in nonparametric regression model. Most of existing dierence-based methods are developed under asymptotical properties. Our focus is on the exact form of mean and variance for the lag-k dierence-based estimator and the second-order dierence-based estimator in a nite sample size. Our approach can be extended to Tong's estimator (2005) and be helpful to obtain optimal k.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
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• pp.850-855
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• 1991

In this paper, neural network-based compliance control of telerobot is presented, This is a method to learn the compliance of human behavior and control telerobot using learned compliance. The consistency of human behavior is checked using Lipschitz's condition. The neural compliance model is composed of a multi-layered neural network which mimics the compliant notion of the human operator. The effectiveness of proposed scheme ie verified by a simulation study.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.447-455
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• 2003

For some sequnces of monotone nondecreasing convex $\Phi$-functions $\Phi$$_1$, $\Phi$$_2$ and $\Phi$$_3$and $textsc{k}$-functions $textsc{k}$$_1$, $textsc{k}$$_2$ and $textsc{k}$$_3$, we obtain the most general Holder type inequalities, and some special cases are considered for the functions of $textsc{k}$G$\Phi$-bounded variations.

• Journal of applied mathematics & informatics
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• 제30권1_2호
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• pp.173-181
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• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권4호
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• pp.279-282
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• 대한수학회보
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• 제45권3호
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• pp.563-571
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• 2008

We deduce the necessary conditions for the optimality of endpoint constrained optimal control problem. These conditions comprise the adjoint equation, the maximum principle and the transversality condition. We assume that the cost function is merely differentiable. Therefore the technique under Lipschitz continuity hypothesis is not directly applicable. We introduce Fermat's rule and value function technique to obtain the results.

• East Asian mathematical journal
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• 제23권2호
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• pp.257-260
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• 2007

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.339-342
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• 2009

In this paper, we investigate the existence and uniqueness of fuzzy solutions for semilinear fuzzy integrodifferential equations using integral contractor. The notion of 'bounded integral contractor', introduced by Altman[1], is weaker than Lipschitz condition.