• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1641-1665
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• 2017

The paper considers p-valent functions in the open unit disk. We study the integral means along with the area integral problems for functions belonging to a family of p-valent functions.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1255-1266
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• 2007

We establish a weighted norm inequality for a class of rough parametric Marcinkiewicz integral operators $\mathcal{M}^{\rho}_{\Omega}$. As an application of this inequality, we obtain weighted $L^p$ inequalities for a class of parametric Marcinkiewicz integral operators $\mathcal{M}^{*,\rho}_{\Omega,\lambda}\;and\;\mathcal{M}^{\rho}_{\Omega,S}$ related to the Littlewood-Paley $g^*_{\lambda}-function$ and the area integral S, respectively.

• Kyungpook Mathematical Journal
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• v.46 no.1
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• pp.31-48
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• 2006

In this paper, we prove a weighted norm inequality for the Marcinkiewicz integral operator $\mathcal{M}_{{\Omega},h}$ when $h$ satisfies a mild regularity condition and ${\Omega}$ belongs to $L(log L)^{1l2}(S^{n-1})$, $n{\geq}2$. We also prove the weighted $L^p$ boundedness for a class of Marcinkiewicz integral operators $\mathcal{M}^*_{{\Omega},h,{\lambda}}$ and $\mathcal{M}_{{\Omega},h,S}$ related to the Littlewood-Paley $g^*_{\lambda}$-function and the area integral S, respectively.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.1
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• pp.31-37
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• 2009

This paper casts an application of an extended fuzzy integral on the selective extraction of color clusters characterized by a particular color hue from color document images. Despite of the negative role of fuzzy integral, the presented approach attains the detection of the seals through the neighborhood information via the center of area method. The conventional fuzzy integral evaluates the negative aspects of the importance about the items by min operator, which result in the discontinuous parts of seals. In an attempt to cope with the drawback our approach considers the integral aspects via the center of area method, which results in the robustness of the images. Finally, the framework is successfully tested on a data set formed by documents from a real application for the detection.

• The Mathematical Education
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• v.57 no.2
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• pp.157-177
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• 2018

The students in secondary schools have been taught calculus as an important subject in mathematics. The order of chapters-the limit of a sequence followed by limit of a function, and differentiation and integration- is because the limit of a function and the limit of a sequence are required as prerequisites of differentiation and integration. Specifically, the limit of a sequence is used to define definite integral as the limit of the Riemann Sum. However, many researchers identified that students had difficulty in understanding the concept of definite integral defined as the limit of the Riemann Sum. Consequently, they suggested alternative ways to introduce definite integral. Based on these researches, the definition of definite integral in the 2015-Revised Curriculum is not a concept of the limit of the Riemann Sum, which was the definition of definite integral in the previous curriculum, but "F(b)-F(a)" for an indefinite integral F(x) of a function f(x) and real numbers a and b. This change gives rise to differences among ways of introducing definite integral and explaining the relationship between definite integral and area in each textbook. As a result of this study, we have identified that there are a variety of ways of introducing definite integral in each textbook and that ways of explaining the relationship between definite integral and area are affected by ways of introducing definite integral. We expect that this change can reduce the difficulties students face when learning the concept of definite integral.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.297-308
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• 2002

• Korean Institute of Interior Design Journal
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• v.23 no.5
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• pp.104-111
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• 2014

This study puts its purpose on presenting an integral system of representative urban landscapes, public design and colors, in practicing urban design in the context of local identity. An integral design of public design that successfully plans and executes local identity, and changes recognition of integral management of urban design, is suggested as followings. Firstly, when the catchment area is divided in metropolitan area, it should be reset according to the natural environment condition regardless of administrative area system like city and county. It is the method to classify the metropolitan area by researching and analyzing geographical condition, weather condition, soil and vegetation in detail and subclassify it by the visual commonness of natural environment. Secondly, it is necessary to access the urban landscape, public design and urban color from the overall aspect emphasizing the plan for each field and local identity. They should be practiced by the role and category of each field on the basis of consistent design strategy and instruction but the cooperation system is required as a process to reinforce and specify the mutual limit. Thirdly, the artificial structure is constructed through artificial adjustment depending on the urban formation process and the development time point. Therefore, it is necessary to pay attention to the rapid urban development, the change speed and the landscape formation of each age. It is necessary to classify the type of artificial landscape by age and form similarity and separate the area that should be generalized and controlled by entire metropolitan area form the area that should be specialized by basic local government.

• Journal of Advanced Marine Engineering and Technology
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• v.33 no.4
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• pp.466-475
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• 2009

A numerical analysis of reactive flow in a liftoff flame is accomplished to elucidate the characteristics of flame propagation velocity and volume integral of reaction rate with the variation of fuel injection velocity at the fuel rich region, fuel lean region and diffusion flame region. The increase of fuel injection velocity enhances flame propagation velocity, but its effect on the flame propagation velocity is not much greater under 4%. The increase of fuel injection velocity affects directly and linearly on the flame surface area in the fuel rich region and so enhances volume integral of reaction rate to accommodate the increment of fuel.

• School Mathematics
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• v.11 no.2
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• pp.301-316
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• 2009

There are two distinct processes, definite integral and indefinite integral, in the integral calculus. And the term 'integral' has two meanings. Most students regard indefinite integrals as definite integrals with indefinite interval. One possible reason is that calculus textbooks do not concern the meaning in the relationship between definite integral and indefinite integral. In this paper we investigated the historical development of concepts of definite integral and indefinite integral, and the relationship between the two. We have drawn pedagogical implication from the result of analysis.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.77-94
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• 2011

This study aims to provide a teaching strategy accommodating the symbols of the definite integral and guiding students through the meaning of notations in area and volume calculations, based on characterization as to how students comprehend the symbols used in the Riemann sum formula and the definite integral, and their interrelationship. A survey was conducted on 70 high school students regarding the historical background of integral symbols and the textbook contents designated for the definite integral. In the following analysis, the comprehension was qualified by 5 levels; students in higher levels of comprehension demonstrated closer relation to the history of integral notations. A teaching strategy was developed accordingly, which suggested more desirable student understanding on the concept of definite integral symbols in area and volume calculations.