• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.457-472
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• 2002

In this paper, we deal with the algebraic thinking from the perspective of ‘process’ and ‘object’ aspects. Generally, mathematical concepts have come from the concrete process. We consider the origin of algebra as the arithmetic calculations. Also, the concept of school arithmetic is beginning from actions or procedures. However, in order to develop the alge- braic thinking and to apply this thinking, we have to see the history of algebraic thinking, and find this duality. Next we investigate various researches relating to the ‘process-object duality’. Theses studies suppose that the concept formation and thinking process should be stared from the process-object duality. Finally, we reinterprete many difficulties in algebra - equals sign, variables, algebraic expressions, and linear equations, the principle of permanence of form- from the perspective of the process-object duality.

• The Transactions of the Korean Institute of Power Electronics
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• v.18 no.4
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• pp.342-348
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• 2013

In this paper, an improved non-isolated 3-level high step-up boost converter is proposed. By using the well known duality principle, the proposed converter is derived from two-phase buck converter. Compared with the traditional boost converter and 3-level boost converter, the proposed converter can obtain very high voltage conversion ratio and the voltage stress of switching devices and diodes is only 1/4 of the output voltage. A 1 kW prototype converter is built and tested to verify performances of the proposed converter.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.27-46
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• 1998

We are concerned with an optimal control problem governed by a Poisson equation in which body force acts like a control parameter. The cost functional to be optimized is taken to represent the error from the desired observation and the cost due to the control. We recast the problem into the mixed formulation to take advantage of the minimax principle for the duality method. The existence of a saddle point for the Lagrangian shall be shown and the optimality system will be derived therein. Finally, to attain an optimal control, we combine the optimality system with an operational technique. By achieving the gradient of the cost functional, a convergent algorithm based on the projected gradient method is established.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.97-103
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• 2013

As a suitable application of the well known generalized maximum principle of Omori-Yau, we obtain rigidity results concerning to a complete hypersurface immersed with bounded mean curvature in the $(n+1)$-dimensional hyperbolic space $\mathbb{H}^{n+1}$. In our approach, we explore the existence of a natural duality between $\mathbb{H}^{n+1}$ and the half $\mathcal{H}^{n+1}$ of the de Sitter space $\mathbb{S}_1^{n+1}$, which models the so-called steady state space.

• Journal of the Korean Mathematical Society
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• v.42 no.1
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• pp.17-35
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• 2005

Necessary conditions for a deterministic optimal control problem which involves states constraints are derived in the form of a maximum principle. The conditions are similar to those of F.H. Clarke, R.B. Vinter and G. Pappas who assume that the problem's data are Lipschitz. On the other hand, our data are not continuously differentiable but only differentiable. Fermat's rule and Rockafellar's duality theory of convex analysis are the basic techniques in this paper.

• Journal for History of Mathematics
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• v.10 no.2
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• pp.11-23
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• 1997

Category theory gives a convenient language for the study of mathematical structures besides its own study. In this paper, we investigate how the abstract structure theory emerged in 1930s affects the study in Topology and eventually becomes a rudiment for the category theory. Moreover, various extensions and universal mapping problems were put in their proper perspective as reflections by the category theory and by its duality principle, coreflections become an interesting subject in Topology, both of which give rise to a new discipline of the categorical topology.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.9
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• pp.1327-1335
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• 1990

In this paper, using the principle of duality between the spatial and spectral domain, we proposed a new microwave imaging technique of a coherent tomographic formulation in the spatial domain and reconstructed the image of dielectric cylinder through simulation and experiment. The numerical and experimental results for the variety o object size, relative dielectric constant have shown the limitation of Born approximation to be used and the effect of retrieved images for various signal bandwidth.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2001.10a
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• pp.199-202
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• 2001

This article deals with stochastic reliability systems that include a repair facility and unreliable machines: the main facility of working and an auxiliary facility of "super-reserve" machines. The number of super-reserve machines are random number with a arbitrarily distribution and working machines break down exponentially. Defective machines line up for repair, whose durations are arbitrarily distributed. Refurbished machines return to the main facility. If the main facility is restored to its original quantity, the repair facility leaves on routine maintenance until all of super-reserve machines are exhausted. Then, the busy period is regenerated. The whole system also falls into the category of closed queues, with more options than those of basic models. The techniques include two-variate Markov and semi-regenerative processes, and a duality principle, to find the probability distribution of the number of intact machines. Explicit formulas obtained demonstrate a relatively effortless use of functionals of the main stochastic characteristics (such as expenses due to repair, maintenance, waiting, and rewards for higher reliability) and optimization of their objective function. Applications include computer networking, human resources, and manufacturing processes.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.103-127
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• 2018

This paper is dedicated to studying some Hausdorff operators on the Heisenberg group ${\mathbb{H}}^n$. The sharp bounds on the strong-type weighted Lorentz spaces ${\Lambda}^p_u(w)$ and the weak-type weighted Lorentz spaces ${\Lambda}^{p,{\infty}}_u(w)$ are investigated. Especially, the results cover the classical power weighted space $L^{p,q}_{\alpha}$. The results are also extended to the product spaces ${\Lambda}^{p_1}_{u_1}(w_1){\times}{\Lambda}^{p_2}_{u_2}(w_2)$, especially for $L^{p_1,q_1}_{{\alpha}_1}{\times}L^{p_2,q_2}_{{\alpha}_2}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

• The Korean Journal of Ecology
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• v.13 no.4
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• pp.321-329
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• 1990

An investigation was performed to elucidate wave character of the timber line on the middle slope of the west side of Paektusan. The Betula ermanii forest, which composes the timber line on about 2, 060m elevation of sea level, is the pure community of B. ermanii. Diffraction pattern of wave distribution of B. eramnii due to boundary condition of alpine temperature gradient was found out on the timber line. Interference patterns of waves of B. ermanii communities produced by environment conditions such as soil layers, whids, snow and relief were shown on a specific area. These facts indicate that the B. ermanii individuals have wave and particle duality, the complementarity principle.