• Honam Mathematical Journal
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• v.22 no.1
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• pp.31-36
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• 2000

In this paper, we introduce the extremal length and examine its properties and consider the applications of extremal length to conformal mappings. We obtain the theorems in the connection with "the extremal length zero" and "the fundamental sequences".

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.47-54
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• 2007

In [6] some computation of spectral measures induced by normal operators $T^{*n}T^n$ was introduced. In this note we improve some computations by using spectral measures, which are related t o extremal vectors. Also, we discuss the extremal value properties and apply our spectral measure equations to moment sequences which are induced by weighted shifts.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.2
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• pp.147-156
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• 2007

We introduce the extremal length and examine its properties. And we consider the geometric applications of extremal length to the boundary behavior of analytic functions, conformal mappings. We derive the theorem in connection with the capacity. This theorem applies the extremal length to the analytic function defined on the domain with a number of holes. And we obtain the theorems in connection with the pure geometric problems.

• 제어로봇시스템학회:학술대회논문집
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• 1998.10a
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• pp.123-128
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• 1998

This paper presents time domain identification of an interval system. We conjectured that Markov parameters (Pulse Responses) from Kharitonov plants would envelope those of the whole interval system. The examination on interrelations between Markov parameters from Kharitonov plants of an interval system and those of the whole interval system determines the validity of the conjecture and is used to give some extremal properties of Markov parameters. The results of this paper are shown in simulations on MBC500 Magnetic Bearing System and a given interval system.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.33-36
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• 1972

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.8
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• pp.462-470
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• 2003

This paper presents an algorithm of identifying parametric uncertainty by way of an interval model. For a given set of frequency response data from an uncertain linear SISO system of which the upper and the lower bounds of both magnitude and phase responses are represented, the proposed algorithm consists of two main parts: first, the nominal model is identified by using Least Square Estimation (LSE), and then an interval model is constructed by expanding the extremal properties of interval systems, so that tightly enclose the given envelopes within those of interval model. Two numerical examples are given to demonstrate and verify the developed algorithm. The identified interval model can be used for evaluating the worst case performance and stability margins against parametric uncertainty by using some extremal properties on interval systems.

• 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].

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

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.339-358
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• 2021

Zagreb indices and their modified versions of a molecular graph are important descriptors which can be used to characterize the structural properties of organic molecules from different aspects. In this work, we investigate some properties of the modified second multiplicative Zagreb index of graphs with given connectivity. In particular, we obtain the maximum values of the modified second multiplicative Zagreb index with fixed number of cut edges, or cut vertices, or edge connectivity, or vertex connectivity of graphs. Furthermore, we characterize the corresponding extremal graphs.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.113-123
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• 2014

The term rank of a matrix A over a semiring $\mathcal{S}$ is the least number of lines (rows or columns) needed to include all the nonzero entries in A. In this paper, we characterize linear operators that preserve the sets of matrix ordered pairs which satisfy extremal properties with respect to term rank inequalities of matrices over nonbinary Boolean semirings.