• The Pure and Applied Mathematics
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• v.2 no.2
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• pp.149-156
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• 1995

In stability theory of polysystems two concepts that playa very important role are the limit set and the prolongational limit set. For the above two concepts, A.Bacciotti and N.Kalouptsidis studied their properties in a locally compact metric space [2]. In this paper we investigate their results in c-first countable space which is more a general space than a metric space.(omitted)

• 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.

• 한국해양학회지
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• v.16 no.2
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• pp.99-107
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• 1981

A partial differential equation for the adjusted sea level, obtained from the long wave equations in shallow water, is reduced to a simpler one by the use of physically reasonable approximations based on the observations. The similar equation for the stream function indicates that shelf waves are generated by the longshore wind stress. This indication is in good agreement with the high correlation between the adjusted sea levels and the longshore wind stress. From the dispersion relationship and the boundary conditions, there exist a countable infinite number of modes which satisfy a first-order wave equations. The adjusted sea level for a given wind stress can easily be calculated by utilizing the convolution and the Fourier transformation. Some detailed solutions are presented here for sinusoidal and exponential wind stress.

• 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.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.273-285
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• 1997

The aim of this paper is to present theorems on the exitence of zeros for mappings defined on convex subsets of topological vector spaces with values in a vector space. In addition to natural assumptions of continuity, convexity, and compactness, the mappings are subject to some geometric conditions. In the first theorem, the mapping satisfies a "Darboux-type" property expressed in terms of an auxiliary numerical function. Typically, this functions is, in this case, related to an order structure on the target space. We derive an existence theorem for "obtuse" quasiconvex mappings with values in an ordered vector space. In the second theorem, we prove the existence of a "common zero" for an arbitrary (not necessarily countable) family of mappings satisfying a general "inwardness" condition againg expressed in terms of numerical functions (these numerical functions could be duality pairings (more generally, bilinear forms)). Our inwardness condition encompasses classical inwardness conditions of Leray-Schauder, Altman, or Bergman-Halpern types.

• East Asian mathematical journal
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• v.32 no.3
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• pp.365-375
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• 2016

In this paper, we study some classes of spaces determined by closure-like operators $[{\cdot}]_s$, $[{\cdot}]_c$ and $[{\cdot}]_k$ etc. which are wider than the class of $Fr{\acute{e}}chet-Urysohn$ spaces or the class of sequential spaces and related spaces. We first introduce a WADS space which is a generalization of a sequential space. We show that X is a WADS and k-space iff X is sequential and every WADS space is C-closed and obtained that every WADS and countably compact space is sequential as a corollary. We also show that every WAP and countably compact space is countably sequential and obtain that every WACP and countably compact space is sequential as a corollary. And we show that every WAP and weakly k-space is countably sequential and obtain that X is a WACP and weakly k-space iff X is sequential as a corollary.

• 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.

• Journal of the Korean Data and Information Science Society
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• v.21 no.4
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• pp.699-708
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• 2010

Korean universities have selected candidates through admission officer system since 2009. However, the universities now have to settle several problems that they faced at the first stage of the system. Therefore, this research, taking the admission screening data of J University as examples, aims to discuss how differently the weight of the screening factors appears depending on the subjects related to college entrance, such as parents, teachers, and admission officers. The research indicates that the subjects have different perspectives about entrance screening requisites. Parents and teachers more value the student record that is a countable indicator than the letter of self-recommendation that is a uncountable indicator. However, it also indicates that admission officers take attitude against parents and teachers.

• 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.