• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.779-787
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• 2019

In this paper, we study two functional equations with two unknown functions from an Abelian group into a commutative ring without zero divisors. The two equations are generalizations of Swiatak's functional equations with an involution. We determine the general solutions of the two functional equations and the properties of the general solutions of the two functional equations under three different hypotheses, respectively. For one of the functional equations, we establish the Hyers-Ulam stability in the case that the unknown functions are complex valued.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.375-393
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• 2023

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.2
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• pp.107-123
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• 2023

In this paper, we present some hyperstability results for a general quintic functional equation and a general septic functional equation.

• School Mathematics
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• v.13 no.4
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• pp.651-674
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• 2011

Functional thinking is a central topic in school mathematics and the purpose of teaching functional thinking is to develop student's functional thinking ability. Functional thinking which has to be taught in elementary school must be the thinking in terms of phenomenon which has attributes of 'connection'- assignment and dependence. The qualitative methods for evaluation of development of functional thinking can be based on students' activities which are related to functional thinking. With this purpose, teachers have to provide students with paradigm of the functional situation connected to the other subjects which have attributes of 'connection' and guide them by proper questions. Therefore, the aim of this study is to find teaching method for functional thinking by situation posing connected with other subject. We suggest the following ways for functional situation posing though the process of three steps : preparation, adaption and reflection of functional situation posing. At the first stage of preparation for functional situation, teacher should investigate student's environment, mathematical knowledge and level of functional thinking. With this purpose, teachers analyze various curriculum which can be used for teaching functional thinking, extract functional situation among them and investigate the utilization of functional situation as follows : ${\cdot}$ Using meta-plan, ${\cdot}$ Using mathematical journal, ${\cdot}$ Using problem posing ${\cdot}$ Designing teacher's questions which can activate students' functional thinking. For this, teachers should be experts on functional thinking. At the second stage of adaption, teacher may suggest the following steps : free exploration ${\longrightarrow}$ guided exploration ${\longrightarrow}$ expression of formalization ${\longrightarrow}$ application and feedback. Because we demand new teaching model which can apply the contents of other subjects to the mathematic class. At the third stage of reflection, teacher should prepare analysis framework of functional situation during and after students' products as follows : meta-plan, mathematical journal, problem solving. Also teacher should prepare the analysis framework analyzing student's respondence.

• The Korean Journal of Applied Statistics
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• v.19 no.3
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• pp.431-445
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• 2006

In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.

• Journal of the Korean Ceramic Society
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• v.46 no.5
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• pp.441-446
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• 2009

Dense crack-free yttria film with 10 $\mu m$ thickness was prepared on aluminum by aerosol deposition. X-ray diffraction pattern on the film showed that it contained the same crystalline phase as the raw powder. Transmission electron microscopy revealed a nanostructured yttria film with grains smaller than 100 nm. Tensile adhesion strength between the film and aluminum substrate was 57.8 $\pm$ 6.3MPa. According to the etching test with $CF_4-O_2$ plasma, the etching rate of the yttria film was 1/100 that of quartz, 1/10 that of sintered alumina and comparable to that of sintered yttria.

• Journal of the Korean School Mathematics Society
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• v.4 no.1
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• pp.103-114
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• 2001

The purpose of this study is to develop learning materials for functional concept on variable and to verify the effect of how well students could learn functional concept after they studied with those materials. To accomplish the purpose of this study, I developed learning materials and after teaching students with them. I have concluded the followings : First, there was little effect in teaching functional concept on variable between two experimental groups, whereas teaching functional concept had greater effect on forming functional concept in high level groups in those two experimental groups. Second, teaching functional concept on variable had little effect on students' understanding of functional concept and perfecting tables in Black box, graph, and mathematical problems, whereas there was much effect in students' understanding functional concept and solving relation formula, image, and range problems related to everyday life or general things. On the basis of the problems which appeared in the process of this study, the following can be suggested : First, we should develop learning materials fit for low level students so that they could understand functional concept. Second, we should continue to teach the basic problems like solving relation formula, image, and range, and understanding functional concept in graph until students are able to understand them exactly. Third, since the goals of Unit Function in a middle school textbook is to solve problems related to everyday life through functional thinking, there should be change in constructing systematic contents of Unit Function in a middle school textbook.

• Korean Institute of Interior Design Journal
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• v.21 no.4
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• pp.21-30
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• 2012

Interior space of modern society has a request for non-functional considerations as well as a need for function. French sociologist Jean Baudrillard defined this phenomenon as a dialectical relationship between the functional system and the non-functional system in his book "The System of Objects". The main goal of interior design is the pursuit of non-functional aspects which can satisfy emotional needs of human being without ignoring functional side. This means that designer should exceed the limitation of the functional system and overcome it by his own idea and method. Under this recognition, this paper tried to understand how Shiro Kuramata and Takashi Sugimoto accomplished the overcoming successfully. Sugimoto breaks through mechanical monotony introducing the non-functional objects into the functional system. His objects have power and form of the nature. They also shows traces of manufacture and labor. They works as media transferring old life and values. Sugimoto sometimes adopts the non-functional system such as collection, so it reveals time of collecting and arrangement of various objects. In contrast to Sugimoto, Kuramata erased the form of functional object and turned over the everydayness of the functional system. Instead, aesthetical phenomena substitutes form. Having doubts about the geometrical order of functional system, he opened a discourse for its meaning and limitation. However they have something in common which works as a blueprint for establishing subject's discourse. This discourse is comprised of their own memories of scenes. These subjects' discourse institute worlds through their design works based on each methodology. From the Heideggerian point of view, the worlds offer a foundation which allows the establishment of art in interior design.

• Journal of the Korean Dietetic Association
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• v.17 no.2
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• pp.190-205
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• 2011

The purpose of this study was to investigate the consumption of health functional foods according to age group. We surveyed 300 subjects with quota sampling aged 10 to 50 and over. The rate of consumption of health functional foods by users was substantial (52.7%). Consumers of health functional foods showed higher scores for interest in health (3.97 vs 3.49, P<0.001) and knowledge of health functional foods (3.79 vs 3.30, P<0.001) than non-consumers of health functional foods. Regarding consumers of health functional foods, the number (P<0.01) and types (P<0.05) of health functional foods, reasons for taking (P<0.05), motivations for buying (P<0.05), periods of taking (P<0.001), cost per month (P<0.01), observance of instruction (P<0.01), and effectiveness (P<0.01) were significantly different according to age group. For non-consumers of health functional foods, reasons for not-taking (P<0.01) and types of health functional foods to be planned (P<0.001) were different according to age group. For consumers and non-consumers, problems (P<0.01) andimprovements (P<0.001) for health functional foods showed significant differences according to age group. The majority of subjects (85.4%) answered that heath functional foods had no side-effects. Reported side effects were inappetence (6.6%), constipation (2.6%), and headache (2.0%). In conclusion, differentiated strategies and specialized education programs according to age group might be needed for promoting adequate consumption and preventing side-effects of health functional foods.