• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.893-913
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• 2020

Let 𝓢 be the collection of the operator matrices $\(\array{A&C\\Z&B}\)$ where the range of C is closed. In this paper, we study the properties of operator matrices in the class 𝓢. We first explore various local spectral relations, that is, the property (β), decomposable, and the property (C) between the operator matrices in the class 𝓢 and their component operators. Moreover, we investigate Weyl and Browder type spectra of operator matrices in the class 𝓢, and as some applications, we provide the conditions for such operator matrices to satisfy a-Weyl's theorem and a-Browder's theorem, respectively.

• Journal for History of Mathematics
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• v.26 no.1
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• pp.85-101
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• 2013

This study is to analyse the characteristics of Barrow's theorem on the historical standpoint of hermeneutics and to discuss the teaching-learning sequence for guiding students to reinvent the calculus according to historico-genetic principle. By the historical analysis on the Barrow's theorem, we show the geometric feature of the theorem, conjecture the Barrow's intention in dealing with it, and consider the epistemological obstacles undergone by Barrow. On a basis of this result, we suggest a purposeful and meaning-oriented teaching-learning way for students to realize the sameness of the 'integration' and 'anti-differentiation', and point out the shortcomings and supplement point in current School Mathematic Calculus.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Bulletin of the Korean Mathematical Society
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• v.54 no.6
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• pp.2081-2089
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• 2017

In this paper we generalize 3-dimensional Bour's Theorem to the case of 4-dimension. We proved that a helicoidal surface in $\mathbb{R}^4$ is isometric to a family of surfaces of revolution in $\mathbb{R}^4$ in such a way that helices on the helicoidal surface correspond to parallel circles on the surfaces of revolution. Moreover, if the surfaces are required further to have the same Gauss map, then they are hyperplanar and minimal. Parametrizations for such minimal surfaces are given explicitly.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.13-30
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• 2002

A generalization of Liouville's theorem on integration in finite terms, by enlarging the class of fields to an extension called Ei-Gamma extension is established. This extension includes the $\varepsilon$L-elementary extension of Singer, Saunders and Caviness and contains the Gamma function.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.853-869
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• 2018

We give a new characterization of Browder's theorem through equality between the pseudo B-Weyl spectrum and the generalized Drazin spectrum. Also, we will give conditions under which pseudo B-Fredholm and pseudo B-Weyl spectrum introduced in [9] and [25] become stable under commuting Riesz perturbations.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.1
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• pp.70-76
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• 2006

Some Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings was introduced and the existence of solutions to them under non-compact assumption was considered using the particular form of the generalized Ky Fan's section theorem due to Park [15]. As a corollary, Stampacchia type of generalized vector quasivariational-like inequalities for fuzzy mappings was studied under compact assumption using Ky Fan's section theorem [7].

• Communications of Mathematical Education
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• v.20 no.4 s.28
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• pp.587-594
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• 2006

In this paper we introduce a method of factorizing multi-variable polynomials using Viete's theorem and show some examples of factorizing multi-variable polynomials. We also discuss some aspects of this method.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.

• Korean Journal of Logic
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• v.15 no.3
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• pp.307-322
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• 2012

It is demonstrated that there is a simple, canonical way to show the independency of the Friedman-style miniaturization of Kruskal's theorem with respect to $(\prod_{2}^{1}-BI)_0$. This is done by a non-trivial combination of some well-known, non-trivial previous works concerning directly or indirectly the (proof-theoretic) strength of Kruskal's theorem.