• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.337-344
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• 2018

We extend Bowen's decomposition theorem to topologically Anosov homeomorphisms on first countable, locally compact, paracompact, Hausdorff spaces which are not necessarily metrizable and not necessarily compact.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.331-336
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• 1994

Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

• Interdisciplinary Bio Central
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• v.5 no.4
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• pp.8.1-8.3
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• 2013

Unlike the traditional view, it is not mysterious about how G. Mendel chose the seven characters of the pea, Pisum sativum, that he studied. He first chose the pea that met three conditions he set up and repeated experiments for two years. Apparently, he knew that those characters were controlled by countable elements. Then, he derived the prediction on the basis of his idea about the elements, and selected the seven characters that satisfied the prediction. He knew "no prediction no science". In population genetics the Hardy-Weinberg principle is well known and cited in many papers and books. However, Mendel already derived the same principle in his paper, because he was acquainted also with physics and mathematics. Actually, the principle was trivial when they derived, but not at all when Mendel did. It is also well known that Mendel's laws were forgotten and rediscovered at the term of the 19th century. That may not be true either. His laws were internationally well known before the rediscovery. In fact, the 1881-year version of the Encyclopedia Britannica contains his laws.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.47-63
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• 2019

For $y{\in}{\mathbb{R}}$, a sequence $x=(x_n){\in}{\ell}^{\infty}$, and a non-negative regular matrix A, Bartoszewicz et. al., in 2015, defined the notion of the A-density ${\delta}_A(y)$ of the indices of those $x_n$ that are close to y. Their main result states that if the set of limit points of ($x_n$) is countable and density ${\delta}_A(y)$ exists for any $y{\in}\mathbb{R}$ where A is a non-negative regular matrix, then ${\lim}_{n{\rightarrow}{\infty}}(Ax)_n={\sum}_{y{\in}{\mathbb{R}}}{\delta}_A(y){\cdot}y$. In this note we first show that the result can be extended to a more general class of matrices and then consider a conjecture which naturally arises from our investigations.

• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.217-227
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• 2024

Let G be an infinite countable group and A be a finite set. If Σ ⊆ A^G is a strongly irreducible subshift of finite type and 𝓖 is the local conjugacy equivalence relation on Σ. We construct a decreasing sequence 𝓡 of unital C^*-subalgebras of C(Σ) and a sequence of faithful conditional expectations E defined on C(Σ), and obtain a Toeplitz algebra 𝓣 (𝓡, 𝓔) and a C^*-algebra C^*(𝓡, 𝓔) for the pair (𝓡, 𝓔). We show that C^*(𝓡, 𝓔) is *-isomorphic to the reduced groupoid C^*-algebra C^*_r(𝓖).

• Communications of Mathematical Education
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• v.22 no.4
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• pp.471-487
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• 2008

Inventive mathematical thinking, original mathematical problem solving ability, mathematical invention and so on are core concepts, which must be emphasized in all branches of mathematical education. In particular, Polya(1981) insisted that inventive thinking must be emphasized in a suitable level of university mathematical courses. In this paper, the author considered two cases of inventive problem solving ability shown by his many students via real analysis courses. The first case is about the proof of the problem "what is the derived set of the integers Z?" Nearly all books on mathematical analysis sent the question without the proof but some books said that the answer is "empty". Only one book written by Noh, Y. S.(2006) showed the proof by using the definition of accumulation points. But the proof process has some mistakes. But our student Kang, D. S. showed the perfect proof by using The Completeness Axiom, which is very useful in mathematical analysis. The second case is to show the infinite countability of NxN, which is shown by informal proof in many mathematical analysis books with formal proofs. Some students who argued the informal proof as an unreasonable proof were asked to join with us in finding the one-to-one correspondences between NxN and N. Many students worked hard and find two singled-valued mappings and one set-valued mapping covering eight diagrams in the paper. The problems are not easy and the proofs are a little complicated. All the proofs shown in this paper are original and right, so the proofs are deserving of inventive mathematical thoughts, original mathematical problem solving abilities and mathematical inventions. From the inventive proofs of his students, the author confirmed that any students can develope their mathematical abilities by their professors' encouragements.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1481-1501
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• 2015

MR-TLCD (Magneto-Rheological Tuned Liquid Column Damper) is a new developed vibration control device, which combines the traditional passive control property with active controllability advantage. Based on traditional TLCD governing equation, this study further considers MR-fluid viscosity in the equation and by transforming the non-linear damping term into an equivalent linear damping, a solution can be obtained. In order to find a countable set of parameters for the design of the MR-TLCD system and also to realize its applicability to structures, a series of experimental test were designed and carried out. The testing programs include the basic material properties of the MR-fluid, the damping ratio of a MR-TLCD and the dynamic responses for a frame structure equipped with the MR-TLCD system subjected to strong ground excitations. In both the analytical and experimental results of this study, it is found that the accurately tuned MR-TLCD system could effectively reduce the dynamic response of a structural system.

• Journal of Communications and Networks
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• v.1 no.2
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• pp.89-98
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• 1999

In a synchronization (sync) $network^1$containing N nodes, it is shown (Theorem 1c) that an arbitrarily connected sync network & is the union of a countable set of isolated connecting sync networks${&_i,i= 1,2,.., L}, I.E., & = \bigcup_{I=1}^L&_i$ It is shown(Theorem 2e) that aconnecting sync network is the union of a set of disjoint irreducible subnetworks having one or more nodes. It is further shown(Theorem 3a) that there exists at least one closed irreducible subnetwork in $&_i$. It is further demonstrated that a con-necting sync network is the union of both a master group and a slave group of nodes. The master group is the union of closed irreducible subnetworks in $&_i$. The slave group is the union of non-colsed irre-ducible subnetworks in $&_i$. The relationships between master-slave(MS), mutual synchronous (MUS) and hierarchical MS/MUS ent-works are clearly manifested [1]. Additionally, Theorem 5 shows that each node in the slave group is accessible by at least on node in the master group. This allows one to conclude that the synchro-nization information avilable in the master group can be reliably transported to each node in the slave group. Counting and combinatorial arguments are used to develop a recursive algorithm which counts the number $A_N$ of arbitrarily connected sync network architectures in an N-nodal sync network and the number $C_N$ of isolated connecting sync network in &. EXamples for N=2,3,4,5 and 6 are provided. Finally, network examples are presented which illustrate the results offered by the theorems. The notation used and symbol definitions are listed in Appendix A.

• Journal of Distribution Science
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• v.14 no.10
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• pp.109-116
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• 2016

Purpose - This study investigates the purchase pattern relating to soybean products in Korea. Specifically, the effect of branding based on a regional name was analyzed in terms of consumer purchase frequencies. The primary purpose of this study is to understand why family characteristics affect product selection for a regional brand in the soybean food category. Research design, data, and methodology - We used data collected by the Rural Development Administration (RDA) of Korea. The RDA has monitored agricultural food consumers for years in order to obtain purchase records. Panel participants live in regions near the capital city of Seoul, Korea. Examining data from January 2010 to May 2016, 667 families were selected for analysis. The final data set was 1,335,402. Each purchase item by each individual family was aggregated to a countable weekly observation. To analyze the data set quantitatively, zero-inflation regression was adopted, which was appropriate to avoid biases from overly dispersed observations. Results - We hypothesized the effects of regional branding from the viewpoint of the family characteristics. The first hypothesis was that the number of children would be positively associated with the purchase of a regional brand of soybean products. The result strongly supported this hypothesis. The second hypothesis was that the number of family members would be negatively associated with the purchase of the soybean products of a regional brand. Based on empirical analysis, we concluded that this hypothesis was partially supported. The third hypothesis was the presence of an interaction effect between the number of children and the family size, which was supported by the results. As a supplementary analysis, we also tested mean-variance differences in terms of categories and regional branding with corporate branding. Conclusion - The results of this study provide insights for regional branding strategies in agricultural food management. This study appears to be one of the seminal studies trying to analyze purchase patterns from longitudinal observations. In addition, this study adopted variables characterizing family lifestyle. This study confirmed that children and family size should be considered when soybean product brands are introduced.