• Education of Primary School Mathematics
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• v.24 no.4
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• pp.247-264
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• 2021

The area of a trapezoid is an important concept to develop mathematical thinking and competency, but many students tend to understand the formula for the area of a trapezoid instrumentally. A clue to solving these problems could be found in Dienes' theory of learning mathematics and Watson and Mason' concept of example spaces. The purpose of this study is to obtain implications for the teaching and learning of the area of the trapezoid. This study analyzed the example spaces constructed by students in learning the area of a trapezoid based on Dienes' theory of learning mathematics. As a result of the analysis, the example spaces for each stage of math learning constructed by the students were a trapezoidal variation example spaces in the play stage, a common representation example spaces in the comparison-representation stage, and a trapezoidal area formula example spaces in the symbolization-formalization stage. The type, generation, extent, and relevance of examples constituting example spaces were analyzed, and the structure of the example spaces was presented as a map. This study also analyzed general examples, special examples, conventional examples of example spaces, and discussed how to utilize examples and example spaces in teaching and learning the area of a trapezoid. Through this study, it was found that it is appropriate to apply Dienes' theory of learning mathematics to learning the are of a trapezoid, and this study can be a model for learning the area of the trapezoid.

• Korean Journal of Childcare and Education
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• v.11 no.2
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• pp.151-175
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• 2015

This study configured an integrated math program in which young children can directly participate through storytelling, a teaching technique that has recently earned great popularity. The purpose of the study is to have a positive effect on their mathematical disposition and self-efficacy through the adoption of this program. The program consists of the following five themes: 'understanding of the basic concept of numbers and calculation', 'understanding of the basic concept of space and figure', 'basic measurement', 'understanding of rules' and 'basic data collection and result representation'. The specific activities for each theme planned and executed according to a detailed plan were designed for 20 classes including integrated activities such as story sharing, fine arts and games. The study's participants were 48 five-year old children. The result of the research was that the experimental group's mathematical disposition and self-efficacy score was significantly higher than the control group. The Storytelling-Integrated Math Program was effective in young children's cultivating mathematical disposition and improving self-efficacy. Considering the reality that there has been some confusion and difficulty in carrying out storytelling math and an integrated math program based on the NURI curriculum, it appears that this study could provide a specific and effective teaching-learning program to teachers who want to introduce a program like this.g

• Economic and Environmental Geology
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• v.36 no.3
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• pp.243-255
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• 2003

The mathematical models for GIS-based spatial data integration have been developed for geological applications such as mineral potential mapping or landslide susceptibility analysis. Among various models, the effectiveness of fuzzy logic based integration of multiple sets of geological data is investigated and discussed. Unlike a traditional target-driven fuzzy integration approach, we propose a data-driven approach that is derived from statistical relationships between the integration target and related spatial geological data. The proposed approach consists of four analytical steps; data representation, fuzzy combination, defuzzification and validation. For data representation, the fuzzy membership functions based on the likelihood ratio functions are proposed. To integrate them, the fuzzy inference network is designed that can combine a variety of different fuzzy operators. Defuzzification is carried out to effectively visualize the relative possibility levels from the integrated results. Finally, a validation approach based on the spatial partitioning of integration targets is proposed to quantitatively compare various fuzzy integration maps and obtain a meaningful interpretation with respect to future events. The effectiveness and some suggestions of the schemes proposed here are illustrated by describing a case study for landslide susceptibility analysis. The case study demonstrates that the proposed schemes can effectively identify areas that are susceptible to landslides and ${\gamma}$ operator shows the better prediction power than the results using max and min operators from the validation procedure.

• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.679-710
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• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• Journal of radiological science and technology
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• v.31 no.1
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• pp.41-47
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• 2008

In order to better understand the effects of absorbed radioiodine upon Korean reference adult male, a mathematical phantom representation was contrived based on composite data of the physiology of Korean reference adult male. Using this, S-values of radioiodine($^{131}I$) per each organ were calculated. The calculated S-values were compared to the existing data described in the TM-8381 report of ORNLcalculated on the basis of an ICRP-23 reference male. The results indicated that S-values were higher for the phantom based on Korean reference adult male. The results of this study illustrate that, while the bio-chemical constitution of each source and target organ of the torso are important, the relative location of the organs and characteristics of the radionuclides also exert important influences.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.10
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• pp.1773-1778
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• 2006

This paper propose the method of constructing the Digital Logic Systems based on the Improved Automatic Theorem Proving Techniques(IATP) over Finite Fields. The proposed method is as following. First, we discuss the background and the important mathematical properties for Finite Fields. Also, we discuss the concepts of the Automatic Theorem Proving Techniques(ATP) including the syntactic method and semantic method, and discuss the basic properties for the Alf. In this step, we define several definitions of the IAIP, Table Pseudo Function Tab and Equal. Next, we propose the T-gate as Building Block(BB) and describe the mathematical representation for the notation of T-gate. Then we discuss the important properties for the T-gate. Also, we propose the several relationships that are Identity relationship, Constant relationship, Tautology relationship and Mod R cyclic relationship. Then we propose Mod R negation gate and the manipulation of the don't care conditions. Finally, we propose the algorithm for the constructing the method of the digital logic systems over finite fields. The proposed method is more efficiency and regularity than my other earlier methods. Thet we prospect the future research and prospects.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.1045-1060
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• 1998

Recently, Chung and et al. ([11], 1991c) introduced a new concept of a manifold, denoted by ＊g-SE $X_{n}$ , in Einstein's n-dimensional ＊g-unified field theory. The manifold ＊g-SE $X_{n}$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor ＊ $g^{λν}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor ＊ $g^{λν}$. This paper is the first part of the following series of two papers: I. The SE-curvature tensor of ＊g-SE $X_{n}$ II. The contracted SE-curvature tensors of ＊g-SE $X_{n}$ In the present paper we investigate the properties of SE-curvature tensor of ＊g-SE $X_{n}$ , with main emphasis on the derivation of several useful generalized identities involving it. In our subsequent paper, we are concerned with contracted curvature tensors of ＊g-SE $X_{n}$ and several generalized identities involving them. In particular, we prove the first variation of the generalized Bianchi's identity in ＊g-SE $X_{n}$ , which has a great deal of useful physical applications.tions.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• Journal of Educational Research in Mathematics
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• v.22 no.2
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• pp.163-178
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• 2012

The efforts to represent the numbers based on the decimal system give us fundamental understanding to construct and teach the concept network on the related knowledge of elementary and secondary school mathematics. In the process to represent natural numbers, integers, rational numbers, real numbers as decimal system, we will classify the extended decimal system. Moreover we will obtain the view to classify real numbers. In this paper, we will study the didactical significance of mathematical knowledge, which arise from process to represent real numbers as decimal system, starting from decimal system representation of natural numbers, and provide the theoretical base about the classification of real numbers. This study help math teachers to understand school mathematics in critical inside-measurement and provide the theore tical background of related knowledge. Furthermore, this study provide a clue to construct coherent curriculum and internal connections of related mathematical knowledge.

• Journal of the Korea Society of Computer and Information
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• v.21 no.8
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• pp.57-64
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• 2016

Initial prevention activities and rapid propagation conditions is the most important to prevent diffusion of water pollution. If water pollutants flow into streams river or main stresm located in environmental conservation area or water intake facilities, we must predict immediately arrival time and the diffusion concentration to the proactive. National Institute of Environmental Research developed water pollution incident response prediction system linking dam and movable weir. the system is mathematical model which is updated daily. Therefore it can quickly predict the arrival time and the diffusion concentration when there are accident of oil spills and hazardous chemicals. Also we equipped with mathematical model and toxicity model of EFDC(Environmental Fluid Dynamics Code) to calculate the arrival time and the diffusion concentration. However these systems offer the services of an offline manner than real-time control services. we have ensured the reliability of data collection and have developed a real-time water quality measurement data transmission device by using the data linkage utilizing a mode bus communication and a commercial SCADA system, in particular, we implemented to be able to do real-time water quality prediction through information infrastructure of the water quality integrated management business created by utilizing the construction of the real-time prediction system that utilizes the data collected, the Open map, the visual representation using charts API and development of integrated management system development based on web maps.