• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1431-1437
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• 2010

We use the (G'/G)-expansion method to seek the traveling wave solution of the Seventh-order Sawada-Kotera Equation. The solutions that we get are more general than the solutions given in literature. It is shown that the (G'/G)-expansion method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제3권2호
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• pp.99-112
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• 1999

In this paper, we represent the Piagetian reversible thinking by using the concept of fuzzy complements. In this case the turning point to the reversible thinking can be corre-sponded to the equilibrium points of a fuzzy set, which are shown through some examples. On the other hand, Piaget considered disequilibrium in the theory of equi-libration as a stimulus for students' cognitive structure, furthermore as the driving forces behind intellectual growth. But we suggest a di erent application o Piagetian equi-librium in another point of view as a tool understanding students' psychological stability in problem solving activity.

• 대한수학회지
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• 제56권1호
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• pp.127-147
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• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.487-503
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• 2019

In this study, the author provided a discussion on one dimensional Laplace and Fourier transforms with their applications. It is shown that the combined use of exponential operators and integral transforms provides a powerful tool to solve space fractional partial differential equation with non - constant coefficients. The object of the present article is to extend the application of the joint Fourier - Laplace transform to derive an analytical solution for a variety of time fractional non - homogeneous KdV. Numerous exercises and examples presented throughout the paper.

• 충청수학회지
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• 제23권4호
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• pp.893-902
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• 2010

In this article we study self-dual codes of length 6 over ${\mathbb{Z}}_m$. A classification of such codes for $m{\leq}24$ is given. Main tool for the classification is the new double cosets decomposition method given in the recent article of the author.

• 대한기계학회논문집A
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• 제24권4호
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• pp.937-945
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• 2000

The assessment of machined surface is difficult because the freeform surface must be evaluated by surface fairness as well as dimensional accuracy. In this study, the machined freeform surface is modeled by interpolating the data measured on the machine tool into the mathematical continuous surface, and then the surface model is improved with the parameterization to minimize surface fairness. The accuracy reliability of the measured data is confirmed through compensation of volumetric errors of the machine tool and of probing errors. Non-uniform B-spline surface interpolation method is adopted to guarantee the continuity of surface model. Surface fairness is evaluated with the consideration of normal curvature on the interpolated surface. The validity and usefulness of the proposed method is examined through computer simulation and experiment on the machine tool.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.1045-1049
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• 1995

This paper proposes the state-space model of the thermal behavior of the spindle system to establish dynamic mathematical model of thermal characteristics in machine tool spindle system. the model is derived form physical law of heat transfer and thermoelasticity and represents the thermal behavior induced by uneven thermal expansions whitin a bearing. The model, which is sucessfully validated for two typical configurations of high speed spindle assembles, provides a tool for understanding the basis mechanics of induced thermal expansion as a function of initial preload, spindle speed and housing cooling conditions.

• 산업경영시스템학회지
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• 제18권35호
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• pp.9-16
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• 1995

The degeneration of tool in material removal processing machinery can be characterized by wear, deflection, chattering and any failure in tool or in the material In be processed. In the previous studies, first three of them are analyzed as a preventive maintenance strategy in quality control area. The last of them, any failure, is analyzed as a preventive maintenance strategy in reliability area. In this research, we propose a simple integrated mathematical model which minimizes the cost of machinery failures and producing defects. We determine the optimal wear limit of tool by considering the percent defects. cost, the preventive maintenance cost, and the corrective maintenance cost.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제16권1호
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• pp.79-90
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• 2012

This research investigated if the embodied symbol using a turtle metaphor in a microworld environment works as a cognitive tool to mediate the learning of combinatorics. It was found that students were able to not only count the number of cases systematically by using the embodied symbols in a situated problem regarding Permutation and Combination, but also find the rules and infer a concept of Combination through the activities manipulating the symbols. Therefore, we concluded that the embodied symbol, as a bridge that connects learners' concrete experiences with abstract mathematical concepts, can be applied to introduction of various mathematical concepts as well as a combinatorics concept.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제18권4호
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• pp.289-305
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• 2014

The current mathematical education calls for a learning environment from the constructionism perspective that actively creates mathematical objects. This research first analyzes JavaMAL's expression 'move' that enables students to express the agent's behavior constructively before they learn vector as a formal concept. Since expression 'move' is based on a coordinate, it naturally corresponds with the expression of vectors used in school mathematics and lets students take an embodied approach to the concept of vector. Furthermore, as a design tool, expression 'move' can be used in various activities that include vector structure. This research studies the educational significance entailed in JavaMAL's expression 'move'.