• 대한수학회지
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• 제46권2호
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• pp.225-236
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• 2009

The equicontinuity and scattering properties of continuous semi-flows are studied on a compact metric space. The main results are obtained as follows: first, the complexity function defined by the spanning set is bounded if and only if the system is equicontinuous; secondly, if a continuous semi-flow is topologically weak mixing, then it is pointwise scattering; thirdly, several equivalent conditions for the time-one map of a continuous semi-flow to be scattering are presented; Finally, for a minimal continuous map it is shown that the "non-dense" requirement is unnecessary in the definition of scattering by using open covers.

• Journal of Microbiology and Biotechnology
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• 제16권11호
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• pp.1720-1727
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• 2006

To set up a kinetic model that can provide a theoretical basis for developing a new mathematical model of the Cr(VI) biosorption column using brown seaweed Ecklonia biomass, a differential reactor system was used in this study. Based on the fact that the removal process followed a redox reaction between Cr(VI) and the biomass, with no dispersion effect in the differential reactor, a new mathematical model was proposed to describe the removal of Cr(VI) from a liquid stream passing through the differential reactor. The reduction model of Cr(VI) by the differential reactor was zero order with respect to influent Cr(IlI) concentration, and first order with respect to both the biomass and influent Cr(VI) concentrations. The developed model described well the dynamics of Cr(VI) in the effluent. In conclusion, the developed model may be used for the design and performance prediction of the biosorption column process for Cr(VI) detoxification.

• 영재교육연구
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• 제16권1호
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• pp.81-100
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• 2006

본 논문에서는 초등정보과학영재의 선발을 위한 평가문항을 개발하고 학교 현장에 적용한 결과를 분석하여 개발 문항의 타당도를 검증하였다. 이를 위하여 다음과 같은 단계를 통하여 연구를 진행하였다. 첫째, 다양한 측면에서 정보과학영재에 대한 특성을 분석한 후 정보과학영재를 정의하였다. 둘째, 제7차 초등수학교육과정 속의 이산수학적 요소를 분석하여 초등정보과학영재의 선발을 위한 평가문항을 개발하였다. 셋째, 개발한 평가문항을 학교현장에 투입하여 다양한 관점의 결과를 분석하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제49권2호
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• pp.175-198
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• 2010

To understand natural or social phenomena, we need various information, knowledge, and thought skills. In this context, mathematics and sciences provide us with excellent tools for that purpose. This explains the reasons why there is always significant emphasis on mathematics and sciences in school education; some of the general goals in school education today are to illustrate physical phenomena with mathematical tools based on scientific consideration, to encourage students understand the mathematical concepts implied in the phenomena, and provide them with ability to apply what they learned to the real world problems. For the mentioned goals, we extract six fundamental principles for the integrated mathematics and science education (IMSE) from literature review and suggest a instructional design model. This model forms a fundamental of a case study we performed to which the IMSE was applied and tested to collect insights for design and practice. The case study was done for 10 students (2 female students, 8 male ones) at a coeducational high school in Seoul, the first semester 2009. Educational tools including graphic calculator(Voyage200) and motion detector (CBR) were utilized in the class. The analysis result for the class show that the students have successfully developed various mathematical concepts including the rate of change, the instantaneous rate of change, and derivatives based on the physical concepts like velocity, accelerate, etc. In the class, they described the physical phenomena with mathematical expressions and understood the motion of objects based on the idea of derivatives. From this result, we conclude that the IMSE builds integrated knowledge for the students in a positive way.

• Journal of the Korean Physical Society
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• 제73권9호
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• pp.1197-1210
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• 2018

Since the first detection of gravitational-wave (GW), GW150914, September 14th 2015, the multi-messenger astronomy added a new way of observing the Universe together with electromagnetic (EM) waves and neutrinos. After two years, GW together with its EM counterpart from binary neutron stars, GW170817 and GRB170817A, has been observed. The detection of GWs opened a new window of astronomy/astrophysics and will be an important messenger to understand the Universe. In this article, we briefly review the gravitational-wave and the astrophysical sources and introduce the basic principle of the laser interferometer as a gravitational-wave detector and its noise sources to understand how the gravitational-waves are detected in the laser interferometer. Finally, we summarize the search algorithms currently used in the gravitational-wave observatories and the detector characterization algorithms used to suppress noises and to monitor data quality in order to improve the reach of the astrophysical searches.

• Journal of applied mathematics & informatics
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• 제42권3호
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• pp.663-680
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• 2024

The zero divisor graph is the most basic way of representing an algebraic structure as a graph. For any commutative ring R, each element is a vertex on the zero divisor graph and two vertices are defined as adjacent if and only if the product of those vertices equals zero. In this research, we determine some topological indices such as the Wiener index, the edge-Wiener index, the hyper-Wiener index, the Harary index, the first Zagreb index, the second Zagreb index, and the Gutman index of zero divisor graph of integers modulo prime power and its direct product.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제7권2호
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• pp.75-84
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• 2003

The purpose of this study is to suggest the direction for development of function materials integrating mathematics and science. First, we must investigate curricular scope and sequence of mathematics and science. Second, the science contexts selected need to support the mathematics concepts, not overwhelm them. The mathematics can easily get lost if science becomes too complicated. We may be tempted, which can result in misconceptions that are hard to correct later. Third, Many different examples of mathematics-science integration exist, therefore, it is important to find rich science contexts to connect with mathematics.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.57-69
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• 2014

We obtain a formula for the conditional Wiener integral of the first variation of functionals and establish several integration by parts formulas of conditional Wiener integrals of functionals on a function space. We then apply these results to obtain various integration by parts formulas involving conditional integral transforms and conditional convolution products on the function space.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.1-18
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• 2012

We study various relationships that exist among generalized conditional integral transform, generalized conditional convolution and generalized first variation for a class of functionals defined on K[0, T], the space of complex-valued continuous functions on [0, T] which vanish at zero.

• 대한수학회지
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• 제54권3호
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.