• East Asian mathematical journal
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• v.39 no.2
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• pp.119-139
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• 2023

Most of calculus and real analysis are concerned with the study on continuous functions. Because of self-sustaining concept caused by everyday language, continuity has difficulties. This kind of viewpoint is strengthened with that teacher explains continuity by graph drawn ceaselessly and so finally confused with mathematics concept which is continuity and connection. Thus such a concept image of continuity becomes to include components which create conflicts. Therefore, we try to analyze understanding of continuity on university students by using the concept image as an analytic tool. We survey centering on problems which create conflicts with concept definition and image. And we investigate that difference of definition in continuous function which handles in calculus and analysis exists and so try to present various results on university students' understanding of continuity concept.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.445-452
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• 2004

In [8], Rosenfeld's digital ($k_0,\;k_1$)-continuity was introduced and another was also established in terms of the preservation of ${k_i}-connectedness,\;i\;{\in}\;\{0,\;1\}$ [2, 3]. In this paper a new version of digital ($k_0,\;k_1$)-continuity for images in $Z^n$ is referred, which is proved to be an extended version of the formers [2, 3, 8]. The current digital ($k_0,\;k_1$)-continuity is derived from the notion of n kinds of digital neighborhoods with some radius without any difficulties on the dimension and adjacency of an image in $Z^n$. The aim of this paper is to compare among Rosenfeld's digital continuity, the current digital continuity and Boxer's digital ($k_0,\;k_1$)-continuity.

• Archives of design research
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• v.16 no.4
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• pp.233-242
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• 2003

The illustrations of picture book for children transmit not only one image but also the summary and contents of the picture book by connecting images harmoniously. The images of picture book give children a variety of emotion and impression depending upon the location of image at various factors such as blank and form, texture and colors, and space feeling, etc. Therefore, the picture book for children has the continuity transmitting the flow of images by not only the contents of natural story but also uniform and rhythmical factors. The continuity of images can transmit images by visual ideas that are produced depending upon the connections of pictures between writings and picture, between images, and inside images. In such a way, children can understand the contents of story. The paper examines the continuity of the images of the picture book for children and describes correct expressions on harmonious connections of the images made based on children's individuality and ingenuity.

• Journal of the Korean School Mathematics Society
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• v.15 no.3
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• pp.453-465
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• 2012

In this paper, we first analysis definition of continuity of functions in high school textbooks, the mathematics high school curriculum and university mathematics textbooks. We surveyed what was causing the students to struggle in their concept image of continuity of functions. We arrived at that students' concept for errors in images of continuity of function were caused by definition of continuity of functions in high school textbooks.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.137-149
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• 2018

In this paper, under the assumption of the symmetry point spread function, antireflective boundary conditions(AR-BCs) are considered in connection with the fast truncated Lagrange(FTL) method. The FTL method is proposed as an image restoration method for large-scale ill-conditioned BTTB(block Toeplitz with Toeplitz block) and BTHHTB(block Toeplitz-plus-Hankel matrix with Toeplitz-plus-Hankel blocks) linear systems([13, 17]). The implementation and efficiency of the FTL method in the AR-BCs are further illustrated. Especially, by employing the AR-BCs, both the continuity of the image and the continuity of its normal derivative are preserved at the boundary. A reconstructed image with less artifacts at the boundary is obtained as a result.

• The Journal of the Korea Contents Association
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• v.15 no.8
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• pp.258-270
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• 2015

The study aims at verifying the effect of the image, trust and responsiveness to social welfare organizations on continuing the sponsorship of private donors, the mediating effect of the organizational identification and the moderating effect of their financial status. As a result of causal analysis of the variables by structural equation models, regardless of donors' financial status, social welfare organizations' image, trust and responsiveness has no direct effect on continuing the sponsorship. Among the donors in relatively good financial status, social welfare organizations' image, trust and responsiveness positively have direct effects on organizational identification, which has a direct effect on continuing the sponsorship. That is, the image, trust and responsiveness influence the continuity of the sponsorship through the full mediating effect of organizational identification. On the other hand, among relatively poor donors, only the organizations' image and trust positively influence the organizational identification, The direct and indirect effects on the continuity of the sponsorship are different according to the private donors' financial status, which means that the moderating effect of the donors' financial status is proved. The result of latent mean analysis regarding 5 main latent variables according to the private donors' financial status, shows the significant difference in the continuity of sponsorship only(Mean= .197, Cohen's D=.779). By emphasizing that Organizational identification is a critical factor in terms of enhancing the continuity of sponsorship, some practical implications are discussed based on the study's findings.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.1
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• pp.217-228
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• 2020

The selection factors of service companies have changed in accordance with intensifying competition in the marine transportation service market and environment changes of transportation services. To explore the important factors of customer choice to marine transportation service, this study empirically examines the influence of these selection factors; service provision area, price competitiveness, corporate image, service expertise, and sales support, on transaction continuity through customers' perceived service value and satisfaction. Based on an online survey with those in the Korean marine transportation industry, this study conducted statistical analyses using structural equation modeling. Based on relevant previous studies, the current study constructed a total of 55 survey questions. Finally, 213 questionnaires were collected. Among the five selection factors, corporate image did not affect perceived service value, and price competitiveness was still the most important factor. However, service expertise and sales support were found to be more important factors than regional factors. In order to maintain transaction continuity, shipping companies should also strive to improve their service quality to their customers. In particular, service quality strategies focused on time and regional factors should develop to strategies with the key factors for the changed business environment.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.153-162
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• 2003

Recently, the generalized digital $(k_{0},\;k_{1})$-continuity and its properties are investigated. Furthermore, the k-type digital fundamental group for digital image has been studies with the generalized k-adjacencies. The main goal of this paper is to find some properties of the k-type digital fundamental group of Boxer and to investigate some properties of minimal simple closed k-curves with relation to their embedding into some spaces in ${\mathbb{Z}}^n(2{\leq}n{\leq}3)$.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.85-98
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• 2022

The purpose of this paper is to introduce the notion of Fermatean fuzzy topological space by motivating from the notion of intuitionistic fuzzy topological space, and define Fermatean fuzzy continuity of a function defined between Fermatean fuzzy topological spaces. For this purpose, we define the notions of image and the pre-image of a Fermatean fuzzy subset with respect to a function and we investigate some basic properties of these notions. We also construct the coarsest Fermatean fuzzy topology on a non-empty set X which makes a given function f from X into Y a Fermatean fuzzy continuous where Y is a Fermatean fuzzy topological space. Finally, we introduce the concept of Fermatean fuzzy points and study some types of separation axioms in Fermatean fuzzy topological space.

• Bulletin of the Korean Mathematical Society
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• v.22 no.2
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• pp.89-93
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• 1985

One of the most important problems in automatic continuity theory is to solve the question of continuity of an algebra homomorphism from a Banach algebra into a semisimple Banach algebra with dense range. Many results on this subject are obtained imposing some conditions on the domains or the ranges of homomorphisms. For most recent results and references in automatic continuity theory one may refer to [1], [4] and [5]. In this note we study some properties of homomorphisms from $C^{*}$-algebras into Banach algebras. It is shown that the range of an isomorphism from a $C^{*}$-algebra into a Banach algebra contains no non zero element of the radical of B. Using this result we show that the same holds for a continuous homomorphism, hence a Banach algebra which is the image of a $C^{*}$-algebra under a continuous homomorphism is necessarily semisimple. Thus if there is a homomorphism from a $C^{*}$-algebra onto a non-semisimple Banach algebra it must be discontinuous. Also it follows that every non zero homomorphism from a $C^{*}$-algebra into a radical algebra is discontinuous. Then we make a brief observation on the behavior of quasinilpotent element of noncommutative $C^{*}$-algebras in relation with continuous homomorphisms.momorphisms.