• Communications of the Korean Mathematical Society
• /
• v.16 no.4
• /
• pp.679-690
• /
• 2001

Doubly stochastic matrices are n$\times$n nonnegative ma-trices whose row and column sums are all 1. Convex polytope $\Omega$$_{n}$ of doubly stochastic matrices and more generally (R,S), so called transportation polytopes, are important since they form the domains for the transportation problems. A theorem by Birkhoff classifies the extremal matrices of , $\Omega$$_{n}$ and extremal matrices of transporta-tion polytopes (R,S) were all classified combinatorially. In this article, we consider signed version of $\Omega$$_{n}$ and (R.S), obtain signed Birkhoff theorem; we define a new class of convex polytopes (R,S), calculate their dimensions, and classify their extremal matrices, Moreover, we suggest an algorithm to express a matrix in (R,S) as a convex combination of txtremal matrices. We also give an example that a polytope of signed matrices is used as a domain for a decision problem. In this context of finite reflection(Coxeter) group theory, our generalization may also be considered as a generalization from type $A_{*}$ n/ to type B$_{n}$ D$_{n}$. n/.

• The Korean Journal of Financial Management
• /
• v.23 no.1
• /
• pp.193-225
• /
• 2006

The purpose of this paper is to analyze contagion in Asian foreign exchange markets using Extreme Value Theory and Copula. Our application deals with asymptotic dependence of daily exchange rate return for a sample of eight countries over period 1997.1.1-2005.4.13. The empirical results are summarized as follows. Firstly, Gumbel Copula is a good model to our data according to the value of AIC. Secondly, the extremal dependence between East Asian crisis countries became lower in the post crisis period than the crisis period. Thirdly, It seemed that high extremal dependence exists between East Asian countries with Singapore. Fourthly, the tail dependence between Indonesia, Malaysia, Thailand, Philippine became higher in the crisis period than the total period and post crisis period. Fifthly, the fact that the extremal dependence between Korea and Indonesia, Malaysia, Thailand, Philippine did not increase during the Asian Financial Crisis showed that the contagion effect was not the reason of the Korea's Fiancial Crisis. Sixthly, the extremal dependence between Asian exchange markets was not very high while comparing with the European exchange markets.

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

• Journal of the Korean Mathematical Society
• /
• v.28 no.1
• /
• pp.45-56
• /
• 1991

• Journal of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.181-189
• /
• 1985

• Bulletin of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.71-72
• /
• 1976

• East Asian mathematical journal
• /
• v.11 no.2
• /
• pp.303-313
• /
• 1995

• The Pure and Applied Mathematics
• /
• v.27 no.4
• /
• pp.171-186
• /
• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.

• Smart Media Journal
• /
• v.6 no.4
• /
• pp.32-40
• /
• 2017

In this paper, a robust text detection method based on edge enhanced contrasting extremal region (CER) is proposed using stroke width transform (SWT) and tensor voting. First, the edge enhanced CER extracts a number of covariant regions, which is a stable connected component from input images. Next, SWT is created by the distance map, which is used to eliminate non-text regions. Then, these candidate text regions are verified based on tensor voting, which uses the input center point in the previous step to compute curve salience values. Finally, the connected component grouping is applied to a cluster closed to characters. The proposed method is evaluated with the ICDAR2003 and ICDAR2013 text detection competition datasets and the experiment results show high accuracy compared to previous methods.

• Journal of applied mathematics & informatics
• /
• v.31 no.3_4
• /
• pp.533-544
• /
• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.