• Korean Journal of Mathematics
• /
• v.7 no.1
• /
• pp.123-130
• /
• 1999

We characterize the compactness, weak precompactness and weak compactness in $L^P({\mu},X)$ and in more general space $P^c({\mu},X)$. Moreover, we present this characterization in terms of extremal structure in X.

• The Pure and Applied Mathematics
• /
• v.5 no.2
• /
• pp.95-100
• /
• 1998

In this note we consider some basic facts concerning abstract M spaces and investigate extremal structure of the unit ball of bounded linear functionals on $\sigma$-complete abstract M spaces.

• Journal of the Korean Mathematical Society
• /
• v.52 no.5
• /
• pp.1003-1021
• /
• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.609-619
• /
• 1999

IN this note we study more about the omitted are for the extremal functions and its {{{{ {π } over {4 } }}}}-property based upon Schiffer's variational method and zBrickman-Wilken's result. we give an example other than the Koebe function which is both a support point of S and the extreme point of HS. Furthermore, we discuss the relations between the support points and the L wner chain.

• Honam Mathematical Journal
• /
• v.18 no.1
• /
• pp.43-58
• /
• 1996

• The Pure and Applied Mathematics
• /
• v.4 no.1
• /
• pp.19-26
• /
• 1997

In this paper, we characterize the existence of fixed points of a multivalued function by the existence of complete preorder on the given domain. Also we investigate relations between the completeness of a given order and the fixed point property of some multivalued functions.

• Structural Engineering and Mechanics
• /
• v.68 no.3
• /
• pp.377-384
• /
• 2018

Bi-stable structure can be stable in both its extended and coiled forms. For the un-stressed thin cylindrical shell, the strain energy expressions are deduced by using a theoretical model in terms of only two parameters. Based on the principle of minimum potential energy, the bi-stable behaviors of the cylindrical shells are investigated. The results indicate that the isotropic cylindrical shell does not have the second stable configuration and laminated cylindrical shells with symmetric or antisymmetric layup of fibers have the second stable state under some confined conditions. In the case of antisymmetric laminated cylindrical shell, the analytical expressions of the stability are derived based on the extremal principle, and the shell can achieve a compact coiled configuration without twist deformation in its second stable state. In the case of symmetric laminated cylindrical shell, the explicit solutions for the stability conditions cannot be deduced. Numerical results show that stable configuration of symmetric shell is difficult to achieve and symmetric shell has twist deformation in its second stable form. In addition, the roll-up radii of the antisymmetric laminated cylindrical shells are calculated using the finite element package ABAQUS. The results show that the value of the roll-up radii is larger from FE simulation than from theoretical analysis. By and large, the predicted roll-up radii of the cylindrical shells using ABAQUS agree well with the theoretical results.

• Magazine of the Korean Society of Agricultural Engineers
• /
• v.27 no.2
• /
• pp.23-37
• /
• 1985

This studies were carried out to get characteristics of frequency distribution, probable flood flows according to the return periods, and the correlation between return periods and those length of records affect the Risk of failure in the annual maximum series of the main river systems in Korea. Especially, Risk analysis according to the levels were emphasized in relation to the design frequency factors for the different watersheds. Twelve watersheds along Han, Geum, Nak Dong, Yeong San and Seom Jin river basin were selected as studying basins. The results were analyzed and summarized as follows. 1. Type 1 extremal distribution was newly confirmed as a good fitted distribution at selected watersheds along Geum and Yeong San river basin. Three parameter lognormal Seom Jin river basin. Consequently, characteristics of frequency distribution for the extreme value series could be changed in connection with the watershed location even the same river system judging from the results so far obtained by author. 2. Evaluation of parameters for Type 1 extremal and three parameter lognormal distribution based on the method of moment by using an electronic computer. 3. Formulas for the probable flood flows were derived for the three parameter lognormal and Type 1 extremal distribution. 4. Equations for the risk to failure could be simplified as $\frac{n}{N+n}$ and $\frac{n}{T}$ under the condition of non-parametric method and the longer return period than the life of project, respectively. 5. Formulas for the return periods in relation to frequency factors were derived by the least square method for the three parameter lognormal and Type 1 extremal distribution. 6. The more the length of records, the lesser the risk of failure, and it was appeared that the risk of failure was increasing in propotion to the length of return periods even same length of records. 7. Empirical formulas for design frequency factors were derived from under the condition of the return periods identify with the life of Hydraulic structure in relation to the risk level. 8. Design frequency factor was appeared to be increased in propotion to the return periods while it is in inverse proportion to the levels of the risk of failure. 9. Derivation of design flood including the risk of failure could be accomplished by using of emprical formulas for the design frequency factor for each watershed.

• Bulletin of the Korean Mathematical Society
• /
• v.25 no.2
• /
• pp.179-183
• /
• 1988

In this paper we study a $C^{*}$-dynamical system (A, G, .alpha.) where A is a UHF-algebra, G is a finite abelian group and .alpha. is a *-automorphic action of product type of G on A. In [2], A. Kishimoto considered the case G= $Z_{n}$, the cyclic group of order n and investigated a condition in order that the fixed point algebra $A^{\alpha}$ of A under the action .alpha. is UHF. In later N.J. Munch studied extremal tracial states on $A^{\alpha}$ by employing the method of A. Kishimoto [3], where G is a finite abelian group. Generally speaking, when G is compact (not necessarily discrete and abelian), $A^{\alpha}$ is an AF-algebra and its ideal structure was well analysed by N. Riedel [4]. Here we obtain some conditions for $A^{\alpha}$ to be UHF, where G is a finite abelian group, which is an extension of the result of A. Kishimoto.oto.

• The Journal of the Korea Contents Association
• /
• v.14 no.3
• /
• pp.11-21
• /
• 2014

Multi-scale image segmentation is important in many applications such as image stylization and medical diagnosis. This paper proposes a novel segmentation algorithm based on MSER(maximally stable extremal region) which captures multi-scale structure and is stable and efficient. The algorithm collects MSERs and then partitions the image plane by redrawing MSERs in specific order. To denoise and smooth the region boundaries, hierarchical morphological operations are developed. To illustrate effectiveness of the algorithm's multi-scale structure, effects of various types of LOD control are shown for image stylization. The proposed technique achieves this without time-consuming multi-level Gaussian smoothing. The comparisons of segmentation quality and timing efficiency with mean shift-based Edison system are presented.