• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.169-178
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• 2019

Let $M^{2n+1}$, $n{\geq}1$, be a smooth manifold with a pseudoconvex integrable CR structure of hypersurface type. We consider a sequence of CR invariant subsets $M={\mathcal{S}}_0{\supset}{\mathcal{S}}_1{\supset}{\cdots}{\supset}{\mathcal{S}}_n$, where $S_q$ is the set of points where the Levi-form has nullity ${\geq}q$. We prove that ${\mathcal{S}}{_q}^{\prime}s$ are locally given as common zero sets of the coefficients $A_j$, $j=0,1,{\ldots},q-1$, of the characteristic polynomial of the Levi-form. Some sufficient conditions for local existence of complex submanifolds are presented in terms of the coefficients $A_j$.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.811-825
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• 2022

Given a compact subset P ⊂ (ℝ⁺)^d and a compact set K in ℂ^d. We concern with the Bernstein-Markov properties of the triple (P, K, 𝜇) where 𝜇 is a finite positive Borel measure with compact support K. Our approach uses (global) P-extremal functions which is inspired by the classical case (when P = Σ the unit simplex) in [7].

• Korean Institute of Interior Design Journal
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• v.21 no.1
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• pp.203-210
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• 2012

Since a private museums started in Europe 17C, many private museums established for high-class people like aristocrats to collect and to keep art works and to appreciate for limited members. After the French Revolution in 18C, the publicity became an important social issue through all European regions, and the museum gradually changed into public ones. Like that, as the concept of museum changed, its social role as well as its function was also changed. The concept of collection and display or preservation changed into the concept of exhibition and appreciation featuring the publicity. With the year-round exhibition, a classical concept, the planned-exhibition, a new active concept set as an important factor for a museum's projects. The latter concept embraces new social issues. Therefore as the space for planned-exhibitions reflecting social issues every season was needed, a museum sets its planned-exhibition space with the changeability, and gradually expands this kind of space in size. It is expected that planned-exhibition spaces characterized as the changeability may give some changes on the flow of a museum's overall space, and may have substantial influences on the flow. To recognize the changes in a planned-exhibition space's influence on the museum, this study selected some national, public museums having the planned-exhibition space, and investigated their influences on each museum's overall space structure through the analysis on space syntax. This study assumed the change of planned-exhibition space as the changes in the number of convex spaces, and measured it. And to understand the planned-exhibition's changes on a museum's overall spaces, such changed assumed as the numeric changes in convex spaces and measured them. In addition, the numeric changes's influence on the overall space structure was analyzed by measuring the overall space's average integration level. Through the above two factors, the 3 research methodologies and analyzed results were drawn out.

• Journal of the Korea Convergence Society
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• v.7 no.5
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• pp.213-219
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• 2016

This paper presents a branch-and-bound algorithm for solving the concave minimization problem with upper bounded variables whose single constraint is linear. The algorithm uses simplex as partition element. Because the convex envelope which most tightly underestimates the concave function on the simplex is uniquely determined by solving the related linear equations. Every branching process generates two subsimplices one lower dimensional than the candidate simplex by adding 0 and upper bound constraints. Subsequently the feasible points are partitioned into two sets. During the bounding process, the linear programming problems defined over subsimplices are minimized to calculate the lower bound and to update the incumbent. Consequently the simplices which do certainly not contain the global minimum are excluded from consideration. The major advantage of the algorithm is that the subproblems are defined on the one less dimensinal space. It means that the amount of work required for the subproblem decreases whenever the branching occurs. Our approach can be applied to solving the concave minimization problems under knapsack type constraints.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.2
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• pp.130-135
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• 2004

This paper presents a new design methods of the short-term load forecasting system (STLFS) using the data mining. The structure of the proposed STLFS is divided into two parts: the Takagi-Sugeno (T-S) fuzzy model-based classifier and predictor The proposed classifier is composed of the Gaussian fuzzy sets in the premise part and the linearized Bayesian classifier in the consequent part. The related parameters of the classifier are easily obtained from the statistic information of the training set. The proposed predictor takes form of the convex combination of the linear time series predictors for each inputs. The problem of estimating the consequent parameters is formulated by the convex optimization problem, which is to minimize the norm distance between the real load and the output of the linear time series estimator. The problem of estimating the premise parameters is to find the parameter value minimizing the error between the real load and the overall output. Finally, to show the feasibility of the proposed method, this paper provides the short-term load forecasting example.

• Journal of Korean Society for Geospatial Information Science
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• v.20 no.4
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• pp.117-125
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• 2012

Although many studies have been conducted to extract buildings from airborne lidar data, most of them assume that all the boundaries of a building are straight line segments. This makes it difficult to model building boundaries containing curved segments correctly. This paper aims to model buildings containing curved segments as combination of straight lines and arcs. First, two sets of boundary points are extracted by adaptive convex hull algorithm and local convex hull algorithm with a larger radius. Then, arc segments are determined by average spacing of boundary points and intersection ratio of perpendicular lines. Finally, building boundary is modeled through regularization of least squares line or circle fitting. The experimental results showed that the proposed method can model the curved building boundaries as arc segments correctly by completeness of 69% and correctness of 100%. The approach will be utilized effectively to create automatically digital map that meets the conditions of the Korean digital mapping.

• Journal of the Korea Society of Computer and Information
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• v.15 no.4
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• pp.11-18
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• 2010

Fuzzy c-means (FCM) is a simple but efficient clustering algorithm using the concept of a fuzzy set that has been proved to be useful in many areas. There are, however, several well known problems with FCM, such as sensitivity to initialization, sensitivity to outliers, and limitation to convex clusters. In this paper, global fuzzy c-means (G-FCM) and kernel fuzzy c-means (K-FCM) are combined to form a non-linear variant of G-FCM, called kernel global fuzzy c-means (KG-FCM). G-FCM is a variant of FCM that uses an incremental seed selection method and is effective in alleviating sensitivity to initialization. There are several approaches to reduce the influence of noise and accommodate non-convex clusters, and K-FCM is one of them. K-FCM is used in this paper because it can easily be extended with different kernels. By combining G-FCM and K-FCM, KG-FCM can resolve the shortcomings mentioned above. The usefulness of the proposed method is demonstrated by experiments using artificial and real world data sets.

• Structural Engineering and Mechanics
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• v.56 no.6
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• pp.959-982
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• 2015

In this study, a non-stationary random earthquake Clough-Penzien model is used to describe earthquake ground motion. Using stochastic direct integration in combination with an equivalent linear method, a solution is established to describe the non-stationary response of lead-rubber bearing (LRB) system to a stochastic earthquake. Two parameters are used to develop an optimization method for bearing design: the post-yielding stiffness and the normalized yield strength of the isolation bearing. Using the minimization of the maximum energy response level of the upper structure subjected to an earthquake as an objective function, and with the constraints that the bearing failure probability is no more than 5% and the second shape factor of the bearing is less than 5, a calculation method for the two optimal design parameters is presented. In this optimization process, the radial basis function (RBF) response surface was applied, instead of the implicit objective function and constraints, and a sequential quadratic programming (SQP) algorithm was used to solve the optimization problems. By considering the uncertainties of the structural parameters and seismic ground motion input parameters for the optimization of the bearing design, convex set models (such as the interval model and ellipsoidal model) are used to describe the uncertainty parameters. Subsequently, the optimal bearing design parameters were expanded at their median values into first-order Taylor series expansions, and then, the Lagrange multipliers method was used to determine the upper and lower boundaries of the parameters. Moreover, using a calculation example, the impacts of site soil parameters, such as input peak ground acceleration, bearing diameter and rubber shore hardness on the optimization parameters, are investigated.

• Journal of Korea Multimedia Society
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• v.10 no.5
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• pp.569-582
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• 2007

Digital watermarking technique for copyright protection and prevention of illegal copy and distribution can provide the reliable transaction to both buyer and seller in e-commerce through the cryptographic protocol such as 'Buyer-seller watermarking protocol'. Recently there has been researched about some cryptographic protocols for watermarking system but there has no yet mentioned about the implementation of practical watermarking technique in protocol. This paper presents the watermark embedding technique based on POCS in buyer-seller watermarking protocol. The proposed method designs the robust convex set based on EZW and the invisible convex set using PSNR and then projects into two sets until the convergence condition is satisfied. Experimental results verified that BER of watermark that is embedded by the proposed method has lower 0.02-0.10 than BER of the conventional method.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.755-758
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• 2001

In this paper. Ive propose a postprocessing technique based on the theory of projection on convex sets(POCS) to reduce the blocking artifacts in HDTV decoded images. In BDCT of HDTV. the image is divided into a grid of non-overlapped 8 ${\times}$ 8 blocks. and then each block is coded separately. A block which is located one pixel apart from the grid of BDCT will include the boundary of the original 8 ${\times}$ 8 block. If the blocking artifact is Introduced alone the block boundary. this block will have different frequency characteristic from that of the original block. Thus, a comparison of frequency characteristics of these two overlapping blocks can detect the undesired high-frequency components mainly caused by the blocking artifact. By eliminating these undesired high-frequency components adaptively, robust smoothing projection operator can be obtained. Simulation results with real image sequences indicate that the proposed method performs better than conventional algorithms.