• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• Journal of Electrical Engineering and Technology
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• v.7 no.3
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• pp.420-428
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• 2012

In this paper, a novel intelligent digital redesign (IDR) technique is proposed for the nonlinear interconnected systems which can be represented by a Takagi-Sugeno (T-S) fuzzy model. The IDR technique is to convert a pre-designed analog controller into an equivalent digital one. To develop this method, the discretized models of the analog and digital closed-loop system with the decentralized controller are presented, respectively. Using these discretized models, the digital decentralized control gain is obtained to minimize the norm between the state variables of the analog and digital closed-loop systems and stabilize the digital closed-loop system. Its sufficient conditions are derived in terms of linear matrix inequalities (LMIs). Finally, a numerical example is provided to verify the effectiveness of the proposed technique.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.33 no.10
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• pp.410-422
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• 1984

This paper presents a new practical method for optimal active and reactive power control for the economic operation in electrical power system, and the programs are developed for digital computer solution. The major features and techniques of this paper are as follows: 1) The method is presented for finding the equivalent active power balance equation applying the sparse Jacobian matrix of power flow equation instead of using B constant as active power balance equation considering transmission loss, and thus for determining directly optimal active power allocation berween generator unitw satisfying the equality and inequality constraints. 2) The method is proposed for solving directly the optimum economim dispatch problem without using gradient method and penalty function for both active and reactive power control. As a result, the computing time are reduced and convergence characteristic is remarkably improved. 3) Unlike most of conventional methods which adopt the transmission loss as a objective function for reactive power control, the total fuel cost of themal power plant is adopted as objective function for both active and reactive power control. consequently, more reasonable and economic profit can be achieved.

• Proceedings of the KIEE Conference
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• 2005.07c
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• pp.2453-2455
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• 2005

We represent an efficient intelligent digital redesign method for a Takagi-Sugeno (T-S) fuzzy system Intelligent digital redesign means that an existing analog fuzzy-model-based controller converts to equivalent digital counter part in the sense of state-matching. The proposed method performs previous work, moreover, it allows re matching the states of the overall closed-loop T-S fuzzy system with the predesigned analog fuzzy-model-based controller. And the problem of stability represent convex optimization problem and cast into linear matrix inequality (LMI) framework. This method applies to the helicopter systems which are the nonlinear plant and determine the feasibility and effectiveness of the proposed method.

• Proceedings of the KIEE Conference
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• 2005.07b
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• pp.1811-1813
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• 2005

We represent an efficient intelligent digital redesign method for a Takagi-Sugeno(T-S) fuzzy system. Intelligent digital redesign means that an existing analog fuzzy-model-based controller converts to equivalent digital counter part in the sense of state-matching. The proposed method performs previous work, moreover, it allows to matching the states of the overall closed-loop T-S fuzzy system with the predesigned analog fuzzy-model-based controller. And the problem of stability represent convex optimization problem and cast into linear matrix inequality(LMI) framework. This method applies to the helicopter systems which are the nonlinear plant and determine the feasibility and effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.60 no.1
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• pp.33-69
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• 2023

Let α ∈ (0, ∞), p ∈ (0, ∞) and q(·) : ℝⁿ → [1, ∞) satisfy the globally log-Hölder continuity condition. We introduce the weak Herz-type Hardy spaces with variable exponents via the radial grand maximal operator and to give its maximal characterizations, we establish a version of the boundedness of the Hardy-Littlewood maximal operator M and the Fefferman-Stein vector-valued inequality on the weak Herz spaces with variable exponents. We also obtain the atomic and the molecular decompositions of the weak Herz-type Hardy spaces with variable exponents. As an application of the atomic decomposition we provide various equivalent characterizations of our spaces by means of the Lusin area function, the Littlewood-Paley g-function and the Littlewood-Paley $g^*_{\lambda}$-function.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.883-898
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• 2013

The purpose of this study is to examine that high school students recognize mathematical situation when they are requested for changing identical mathematics situations into different situations. The results of the study are followings. First, percentage of correct answers to the questions of turning equal mathematical situation into function is higher than the one of turning equal mathematical situation into equation and inequality. As a result of individual interview for comprehensibility of the students on these relations, it is found that if degree goes up and there is different expressions of questionaries although mathematical situation is identical, it affects comprehensibility of the subjects. Second, we found that they cannot understand identical mathematics situations because they have trouble in drawing graph or applying to get the answer while many students understand a point of intersection on the graph as a correct answer. Third, As a result of individual interview for comprehensibility of the students on relation between equation, inequality and function, we found that students manage to get correct answer even without perfect comprehensibility on this relation.

• Land and Housing Review
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• v.11 no.3
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• pp.11-19
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• 2020

This study aims to examine the relationship between the improvement of the income distribution index from the late 1980s to the 1990s and large-scale housing supply projects such as the 2 million housing construction project. Looking at Korea's economic development in terms of income growth and distribution, GDP has continuously increased since the establishment of the government, especially in the late 1980s. The Gini Index, a representative income inequality index, rapidly deteriorated in the early 1970s, and gradually improved from the late 1980s. The 2 million housing construction project, announced in 1988, supplied a third of the existing nationwide housing stock of 6.5 million units in three years. The project cost was 65 trillion won, equivalent to 50% of Korea's GDP at the time. This study questioned whether the ratio of the number of employed workers in the construction industry was a variable directly affecting the Gini Index. To verify this, the causal relationship between the proportion of employed workers in the construction and manufacturing industries and the Gini Index from 1979 to 2008 was statistically analyzed. For this, the ARIMA model was established for each variable, and the correlation of their residuals was verified. The 2 million housing construction project had the effect of improving income inequality in terms of rising wages for production workers and creating jobs for the low-educated and low-income class. During the project period, the number of middle-income earners increased sharply, and the income gap between the high-income and low-income earners greatly decreased. The expansion of the construction volume can be used as a powerful and direct policy tool for improving income distribution. However, the effect may be limited. When the proportion of workers exceeds the threshold, the effect is weakened.

• Korean Journal of Veterinary Research
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• v.48 no.3
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• pp.357-361
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• 2008

Although power analysis is of important tool of research, investigators in veterinary medicine are unaware of the concepts of the statistical power. Two types of error occur in classical hypothesis testing and, those errors should be avoided, if possible. Since power is highly dependent on the sample size, whenever declaring non-statistically significant result they should consider the potential for committing a Type II error in their studies, which refers to the probability of falsely stating that two treatments are equivalent despite true difference between them. Also, sample size determination is one of the most important tasks facing the researcher when planning a diagnostic study, and provides valuable information on the characteristics of a test performance. This type of analysis forms the basis for proper interpretation of test results. The aim of this article was to re-evaluate some selected studies on diagnostic test reported in the domestic veterinary publications to determine the power and necessary sample size for inequality testing to ensure the desired power. Power calculations were illustrated using real-life examples of comparison of a new test and a reference test for detecting antibodies of various animal diseases. Factors affecting to the power were also discussed.

• Journal of Institute of Control, Robotics and Systems
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• v.13 no.5
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• pp.487-492
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• 2007

This paper presents the development of digital robust fuzzy controller for uncertain nonlinear systems. The proposed approach is based on the intelligent digital redesign(IDR) method with considering the relaxed stability condition of fuzzy control system. The term IDR in the concerned system is to convert an existing analog robust control into an equivalent digital counterpart in the sense of the state-matching. We shows that the IDR problem can be reduced to find the digital fuzzy gains minimizing the norm distance between the closed-loop states of the analog and digital robust control systems. Its constructive conditions are expressed as the linear matrix inequalities(LMIs) and thereby easily tractable by the convex optimization techniques. Based on the nonquadratic Lyapunov function, the robust stabilization conditions are given for the sampled-data fuzzy system, and hence less conservative. A numerical example, chaotic Lorentz system, is demonstrated to visualize the feasibility of the proposed methodology.