• 대한수학회보
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• 제51권5호
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• pp.1369-1374
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• 2014

We show that the Diophantine equation $$aQ(x_1,x_2)+bQ(x_3,x_4)+cQ(x_5,x_6)=abc$$ has integral solutions for arbitrary positive integers a, b, c when Q(x, y) is a norm form for some imaginary quadratic fields.

• East Asian mathematical journal
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• 제31권3호
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• pp.321-335
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• 2015

The existence of at least one solution to a system of multipoint boundary value problems on an infinite interval is investigated by using the Alternative of Leray-Schauder.

• 대한수학회논문집
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• 제13권1호
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• pp.73-76
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• 1998

It is proved that the partial differential operator $D_x + ix^q D^2_y$ is not locally solvable in any open set which intersects the line x = 0, when $q = - \frac{2l-1}{2k-1}$ is not an integer.

• 한국수학교육학회지시리즈A:수학교육
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• 제55권2호
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• pp.209-232
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• 2016

This study analyzed the process of steps in a program introducing Renzulli's enrichment triad model and various levels of posing open-ended problems of those who participated in the program for mathematics-gifted elementary students. As results, participants showed their abilities of problem posing related to real life in a program introducing Renzulli's enrichment triad model. From eighteen mathematical responses, gifted students were generally outstanding in terms of producing problems that demonstrated high quality completion, communication, and solvability. Amongst these responses from fifteen open-ended problems, all of which showed that the level of students' ability to devise questions was varied in terms of the problems' openness (varied possible outcomes), complexity, and relevance. Meanwhile, some of them didn't show their ability of composing problem with concepts, principle and rules in complex level. In addition, there are high or very high correlations among factors of mathematical problems themselves as well as open-ended problems themselves, and between mathematical problems and open-ended problems. In particular, factors of mathematical problems such as completion, communication, and solvability showed very high correlation with relevance of the problems' openness perspectives.

• 제어로봇시스템학회논문지
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• 제6권1호
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• pp.25-34
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• 2000

In this paper, we design a H^\infty servo controller for gauge control of tandem cold mill. To improve the performance of the AGC(Aotomatic Gauge Control) system based on the Taylor linearized model of tandem cold mill, the H^\infty servo controller is designed to satisfy robust stability, disturbance attenuation and robust tracking properties. The H^\infty servo controller problem is modified as an usual H^\infty control problem, and the solvability condition of the H^\infty servo problem depends on the solvability of the modified H^\infty control problem. Since this modified problem does not satisfied standard assumptions for the H^\infty control problem, it is solved by an LMI(Linear Matrix Inequality) technique. Consequently, the comparison between the H^\infty servo controller and the existing PID/FF(FeedForward) controller shows the usefulness of this study.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.111-127
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• 2011

We prove the uniqueness solvability of the Tricomi problem for the elliptic - hyperbolical equation of the second type by using a new representation of the solution in the generalized class R.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1726-1729
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• 1997

In general, the solvability of linear robust output regulation problem are not preserved under time-sampling. Thus, it is found that the digital regulator implemented by itme-sampling of anlog output regulator designed based on the continuous-time linear system model is nothing but a 1st order approximation with respect to time-sampling. By the way, one can design an improved sampled-data regulator with respect to sampling time by utilizing the intrinsic structure of the system. In this paper, we study the system structures which it is possible to design an improved sampled-data regulator with respect to sampling time.

• International Journal of Control, Automation, and Systems
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• 제5권6호
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• pp.712-717
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• 2007

This paper is concerned with the problem of state feedback control of continuous-time nonlinear Markovian jump systems, which are represented by Takagi-Sugeno fuzzy models. A new method for designing state feedback stabilizing controllers is presented in terms of solvability of a set of linear matrix inequalities (LMIs), and it is shown that the new design method provides better or at least the same results of the existing method in the literature. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

• East Asian mathematical journal
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• 제28권5호
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• pp.561-567
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• 2012

The approximate solvability of a generalized system for relaxed cocoercive extended general variational inequalities is studied by using the project operator technique. The results presented in this paper are more general and include many previously known results as special cases.

• 대한수학회지
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• 제37권6호
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.