• Title/Summary/Keyword: mathematical structure

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An Analysis on Teaching Methods of Patterns in Elementary Mathematics Textbooks (초등학교 수학 교과서에 제시된 패턴 지도방안에 대한 분석)

  • Pang, JeongSuk;Sunwoo, Jin
    • Education of Primary School Mathematics
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    • v.19 no.1
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    • pp.1-18
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    • 2016
  • Patterns are of great significance to develop algebraic thinking of elementary students. This study analyzed teaching methods of patterns in current elementary mathematics textbook series in terms of three main activities related to pattern generalization (i.e., analyzing the structure of patterns, investigating the relationship between two variables, and reasoning and representing the generalized rules). The results of this study showed that such activities to analyze the structure of patterns are not explicitly considered in the textbooks, whereas those to explore the relationship between two variables in a pattern are emphasized throughout all grade levels using function table. The activities to reason and represent the generalized rules of patterns are dealt in a way both for lower grade students to use informal representations and for upper grade students to employ formal representations with expressions or symbols. The results of this study also illustrated that patterns in the textbooks are treated rather as a separate strand than as something connected to other content strands. This paper closes with several implications to teach patterns in a way to foster early algebraic thinking of elementary school students.

The Critical Pigment Volume Concentration Concept for Paper Coatings: II. Later-Bound Clay; Ground Calcium Carbonate, and Clay- carbonate Pigment Coatings

  • Lee, Do-Ik
    • Journal of Korea Technical Association of The Pulp and Paper Industry
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    • v.34 no.5
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    • pp.18-38
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    • 2002
  • A previous study on the model coatings based on latex-bound plastic pigment coatings (1) has been extended to latex-bound No. 1 clay, ultra-fine ground calcium carbonate (UFGCC), and clay-carbonate pigment mixture coatings, which are being widely used in the paper industry. The latex binder used was a good film-forming, monodisperse S/B latex or 0.15$\mu\textrm{m}$. No. 1 clay was representative of plate-like pigment particles, whereas UFGCC was of somewhat rounded rhombohedral pigment particlel. Both of them had negatively skewed triangular particle size distributions having the mean particle suet of 0.7${\mu}{\textrm}{m}$ and 0.6$\mu\textrm{m}$, respectively. Their packing volumes were found to be 62.5% and 657%, respectively. while their critical pigment volume concentrations (CPVC's) were determined to be 52.7% and 50.5% ( average of 45% caused by the incompatibility and 55.9% extrapolated) by coating porosity, respectively. Each pigment/latex coating system has shown its unique relationship between coating properties and pigment concentrations, especially above its CPVC. Notably, the clay/latex coating system hat shown higher coating porosity than the UFGCC/latex system at high pigment concentrations above their respective CPVC's. It was also found that their coating porosity and gloss were inter-related to each other above the CPVC's, as predicted by the theory. More interestingly, the blends of these two pigments have shown unique rheological and coating properties which may explain why such pigment blends are widely used in the industry. These findings have suggested that the unique structure of clay coatings and the unique high-shear rheology of ground calcium carbonate coatings can be judiciously combined to achieve superior coatings. Importantly, the low-shear viscosity of the blends was indicative of their unique packing and coating structure, whereas their high-shear rheology was represented by a common mixing rule, i.e., a viscosity-averaging. Transmission and scanning electron and atomic force microscopes were used to probe the state of pigment / latex dispersions, coating surfaces, freeze fractured coating cross-sections, and coating surface topography. These microscopic studies complemented the above observations. In addition, the ratio, R, of CPVC/(Pigment Packing Volume) has been proposed as a measure of the binder efficiency for a given pigment or pigment mixtures or as a measure of binder-pigment interactions. Also, a mathematical model has been proposed to estimate the packing volumes of clay and ground calcium carbonate pigments with their respective particle size distributions. As well known in the particle packing, the narrower the particle size distributions, the lower the packing volumes and the greater the coating porosity, regardless of particle shapes.

A Study on Descriptive Assessment of Mathematics in Russia's Unified State Examination (러시아의 국가통합시험에서 수학교과의 서술형 평가 연구)

  • Han, Inki;Shin, Vladimir
    • Journal of Science Education
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    • v.46 no.1
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    • pp.121-149
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    • 2022
  • Descriptive assessment is a meaningful assessment method in relation to problem solving ability, reasoning ability, and communication ability as emphasized in mathematics curriculum. In Korea, as performance assessment has been emphasized since the 7th mathematics curriculum, descriptive assessment is being conducted as a method of performance assessment in schools. However, descriptive assessment has not been introduced in the university scholastic ability test for various reasons. Considering that descriptive assessment is emphasized in the mathematics classroom and has sufficient educational value, a serious discussion on the implementation of descriptive assessment in the university scholastic ability test will be necessary. In this study, we analyzed the descriptive assessment of Russia's unified state examination (USE) in the mathematics, which corresponds to Korea's university scholastic ability test. Through a literature review, we investigated how mathematics examination problems were structured in the USE and which mathematical abilities were required for the examination. In particular, the outer structure of the problems was analyzed focusing on the mathematics problems of the USE 2021, and the scoring method of the descriptive problems was also analyzed. The results of this study are expected to provide a variety of information on the possibility of introducing descriptive assessment in the Korean university scholastic ability tests.

An Analysis of Pattern Activities of a Finding Rules Unit in Government-Authorized Mathematics Curricular Materials for Fourth Graders (4학년 수학 검정 교과용 도서의 규칙 찾기 단원에 제시된 패턴 활동의 지도 방안 분석)

  • Pang, JeongSuk;Lee, Soojin
    • Education of Primary School Mathematics
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    • v.26 no.1
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    • pp.45-63
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    • 2023
  • The activity of finding rules is useful for enhancing the algebraic thinking of elementary school students. This study analyzed the pattern activities of a finding rules unit in 10 different government-authorized mathematics curricular materials for fourth graders aligned to the 2015 revised national mathematics curriculum. The analytic elements included three main activities: (a) activities of analyzing the structure of patterns, (b) activities of finding a specific term by finding a rule, and (c) activities of representing the rule. The three activities were mainly presented regarding growing numeric patterns, growing geometric patterns, and computational patterns. The activities of analyzing the structure of patterns were presented when dealing mainly with growing geometric patterns and focused on finding the number of models constituting the pattern. The activities of finding a specific term by finding a rule were evenly presented across the three patterns and the specific term tended to be close to the terms presented in the given task. The activities of representing the rule usually encouraged students to talk about or write down the rule using their own words. Based on the results of these analyses, this study provides specific implications on how to develop subsequent mathematics curricular materials regarding pattern activities to enhance elementary school students' algebraic thinking.

A Study on Pose Control for Inverted Pendulum System using PID Algorithm (PID 알고리즘을 이용한 역 진자 시스템의 자세 제어에 관한 연구)

  • Jin-Gu Kang
    • The Journal of Korea Institute of Information, Electronics, and Communication Technology
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    • v.16 no.6
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    • pp.400-405
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    • 2023
  • Currently, inverted pendulums are being studied in many fields, including posture control of missiles, rockets, etc, and bipedal robots. In this study, the vertical posture control of the pendulum was studied by constructing a rotary inverted pendulum using a 256-pulse rotary encoder and a DC motor. In the case of nonlinear systems, complex algorithms and controllers are required, but a control method using the classic and relatively simple PID(Proportional Integral Derivation) algorithm was applied to the rotating inverted pendulum system, and a simple but desired method was studied. The rotating inverted pendulum system used in this study is a nonlinear and unstable system, and a PID controller using Microchip's dsPIC30F4013 embedded processor was designed and implemented in linear modeling. Usually, PID controllers are designed by combining one or two or more types, and have the advantage of having a simple structure compared to excellent control performance and that control gain adjustment is relatively easy compared to other controllers. In this study, the physical structure of the system was analyzed using mathematical methods and control for vertical balance of a rotating inverted pendulum was realized through modeling. In addition, the feasibility of controlling with a PID controller using a rotating inverted pendulum was verified through simulation and experiment.

The Impact of the Internet Channel Introduction Depending on the Ownership of the Internet Channel (도입주체에 따른 인터넷경로의 도입효과)

  • Yoo, Weon-Sang
    • Journal of Global Scholars of Marketing Science
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    • v.19 no.1
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    • pp.37-46
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    • 2009
  • The Census Bureau of the Department of Commerce announced in May 2008 that U.S. retail e-commerce sales for 2006 reached $ 107 billion, up from $ 87 billion in 2005 - an increase of 22 percent. From 2001 to 2006, retail e-sales increased at an average annual growth rate of 25.4 percent. The explosive growth of E-Commerce has caused profound changes in marketing channel relationships and structures in many industries. Despite the great potential implications for both academicians and practitioners, there still exists a great deal of uncertainty about the impact of the Internet channel introduction on distribution channel management. The purpose of this study is to investigate how the ownership of the new Internet channel affects the existing channel members and consumers. To explore the above research questions, this study conducts well-controlled mathematical experiments to isolate the impact of the Internet channel by comparing before and after the Internet channel entry. The model consists of a monopolist manufacturer selling its product through a channel system including one independent physical store before the entry of an Internet store. The addition of the Internet store to this channel system results in a mixed channel comprised of two different types of channels. The new Internet store can be launched by the independent physical store such as Bestbuy. In this case, the physical retailer coordinates the two types of stores to maximize the joint profits from the two stores. The Internet store also can be introduced by an independent Internet retailer such as Amazon. In this case, a retail level competition occurs between the two types of stores. Although the manufacturer sells only one product, consumers view each product-outlet pair as a unique offering. Thus, the introduction of the Internet channel provides two product offerings for consumers. The channel structures analyzed in this study are illustrated in Fig.1. It is assumed that the manufacturer plays as a Stackelberg leader maximizing its own profits with the foresight of the independent retailer's optimal responses as typically assumed in previous analytical channel studies. As a Stackelberg follower, the independent physical retailer or independent Internet retailer maximizes its own profits, conditional on the manufacturer's wholesale price. The price competition between two the independent retailers is assumed to be a Bertrand Nash game. For simplicity, the marginal cost is set at zero, as typically assumed in this type of study. In order to explore the research questions above, this study develops a game theoretic model that possesses the following three key characteristics. First, the model explicitly captures the fact that an Internet channel and a physical store exist in two independent dimensions (one in physical space and the other in cyber space). This enables this model to demonstrate that the effect of adding an Internet store is different from that of adding another physical store. Second, the model reflects the fact that consumers are heterogeneous in their preferences for using a physical store and for using an Internet channel. Third, the model captures the vertical strategic interactions between an upstream manufacturer and a downstream retailer, making it possible to analyze the channel structure issues discussed in this paper. Although numerous previous models capture this vertical dimension of marketing channels, none simultaneously incorporates the three characteristics reflected in this model. The analysis results are summarized in Table 1. When the new Internet channel is introduced by the existing physical retailer and the retailer coordinates both types of stores to maximize the joint profits from the both stores, retail prices increase due to a combination of the coordination of the retail prices and the wider market coverage. The quantity sold does not significantly increase despite the wider market coverage, because the excessively high retail prices alleviate the market coverage effect to a degree. Interestingly, the coordinated total retail profits are lower than the combined retail profits of two competing independent retailers. This implies that when a physical retailer opens an Internet channel, the retailers could be better off managing the two channels separately rather than coordinating them, unless they have the foresight of the manufacturer's pricing behavior. It is also found that the introduction of an Internet channel affects the power balance of the channel. The retail competition is strong when an independent Internet store joins a channel with an independent physical retailer. This implies that each retailer in this structure has weak channel power. Due to intense retail competition, the manufacturer uses its channel power to increase its wholesale price to extract more profits from the total channel profit. However, the retailers cannot increase retail prices accordingly because of the intense retail level competition, leading to lower channel power. In this case, consumer welfare increases due to the wider market coverage and lower retail prices caused by the retail competition. The model employed for this study is not designed to capture all the characteristics of the Internet channel. The theoretical model in this study can also be applied for any stores that are not geographically constrained such as TV home shopping or catalog sales via mail. The reasons the model in this study is names as "Internet" are as follows: first, the most representative example of the stores that are not geographically constrained is the Internet. Second, catalog sales usually determine the target markets using the pre-specified mailing lists. In this aspect, the model used in this study is closer to the Internet than catalog sales. However, it would be a desirable future research direction to mathematically and theoretically distinguish the core differences among the stores that are not geographically constrained. The model is simplified by a set of assumptions to obtain mathematical traceability. First, this study assumes the price is the only strategic tool for competition. In the real world, however, various marketing variables can be used for competition. Therefore, a more realistic model can be designed if a model incorporates other various marketing variables such as service levels or operation costs. Second, this study assumes the market with one monopoly manufacturer. Therefore, the results from this study should be carefully interpreted considering this limitation. Future research could extend this limitation by introducing manufacturer level competition. Finally, some of the results are drawn from the assumption that the monopoly manufacturer is the Stackelberg leader. Although this is a standard assumption among game theoretic studies of this kind, we could gain deeper understanding and generalize our findings beyond this assumption if the model is analyzed by different game rules.

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Comparative Study of Design Methods for Sliding of Perforated-wall Caisson Breakwater (유공케이슨 방파제의 활동에 대한 설계법 비교 연구)

  • Kim, Nam-Hoon;Suh, Kyung-Duck
    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.26 no.5
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    • pp.267-277
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    • 2014
  • The conventional performance-based design method for the solid-wall caisson breakwater has been extended and applied to the perforated-wall caisson. The mathematical model to calculate the sliding distance of a perforated-wall caisson is verified against hydraulic experimental data. The developed performance-based design method is then compared with the conventional deterministic method in different water depths. Both the expected sliding distance and the exceedance percentage of total sliding distance during the structure lifetime decrease with decreasing water depth outside the surf zone, but they increase with decreasing water depth inside the surf zone. The performance-based design method is either more economical or less economical than the deterministic method depending on which design criterion is used. If the criterion for the ultimate limit state is used, the former method is less economical than the latter outside the surf zone, whereas the two methods are equally economical inside the surf zone. However, if the breakwater is designed to satisfy the criterion for the repairable limit state, the former method is more economical than the latter in all water depths.

Stability of Saturation Controllers for the Active Vibration Control of Linear Structures (선형 구조물의 능동 진동 제어를 위한 포화 제어기의 안정성)

  • Moon, Seok-Jun;Lim, Chae-Wook;Huh, Young-Chul
    • Journal of the Earthquake Engineering Society of Korea
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    • v.10 no.6 s.52
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    • pp.93-102
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    • 2006
  • Control input's saturation of active control devices for large structures under large external disturbances are often occurred. It is more difficult to obtain the exact values of mass and stiffness as structures are higher. The modelling errors between mathematical models and real structures must be also included as parameter uncertainties. Therefore, in active vibration control of civil engineering structures like buildings and bridges, the robust saturation controller design method considering both control input's saturation and parameter uncertainties of system is needed. In this paper, stabilities of linear optimal controller LQR, modified bang-bang controller, saturated sliding mode controller, and robust saturation controller among various controllers which have been studied and applied to active vibration control of buildings are investigated. Especially, unstable phenomena of the LQR, the modified bang-bang controller and the saturated sliding mode controller when the control input is saturated or parameter uncertainties exist are presented to show the necessity of the robust saturation controller. The robust stability of the robust saturation controller are shown through a numerical example of a 2DOF linear vibrating system and an experimental test of the two-story structure with an active mass damper (AMD).

An Analysis on Suitability of Words and Sentences in Mathematics Textbooks for Elementary First Grade (초등학교 1학년 수학 교과서의 어휘 및 문장 적합성 분석)

  • Chang, Hyewon;Lim, Miin
    • Journal of Educational Research in Mathematics
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    • v.26 no.2
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    • pp.247-267
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    • 2016
  • It has been pointed out that the mathematics textbooks according to 2009 revised national curriculum cause difficulty not by mathematical knowledge but concomitantly by words and sentences for the first graders who just started learning Korean alphabets. This study focused on the suitability of words and sentences in mathematics textbooks for elementary first grade. We analyzed the degree of difficulty and familiarity in terms of words and the structure, length, and expression in terms of sentences. The results show some causes that lead the first graders to the difficulty. In more detail, we found 108 difficult words and 6 unfamiliar words for the first graders. And it is noticed that the textbooks contain 37 compound sentences, 727 complex sentences, and 38 compound-complex sentences. They also contain 237 long sentences that are composed of 9 words or more, 168 sentences that assign two activities or more, and 52 sentences that contain three nouns or adjectives or more successively. Based on these results and discussions, we suggested several implications for writing mathematics textbooks for the lower grades in elementary school.

An Option Pricing Model for the Natural Resource Development Projects (해외자원개발사업 평가를 위한 옵션가격 결정모형 연구)

  • Lee, In-Suk;Heo, Eunnyeong
    • Environmental and Resource Economics Review
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    • v.13 no.4
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    • pp.735-761
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    • 2004
  • As a possible alternative to Traditional Discounted Cash Flow Method, "Option Pricing Model" has drawn academic attentions for the last a few decades. However, it has failed to replace traditional DCF method practically due to its mathematical complexity. This paper introduces an option pricing valuation model specifically adjusted for the natural resource development projects. We add market information and industry-specific features into the model so that the model remains objective as well as realistic after the adjustment. The following two features of natural resource development projects take central parts in model construction; product price is a unique source of cash flow's uncertainty, and the projects have cost structure from capital-intense industry, in which initial capital cost takes most part of total cost during the projects. To improve the adaptability of Option Pricing Model specifically to the natural resource development projects, we use Two-Factor Model and Long-term Asset Model for the analysis. Although the model introduced in this paper is still simple and reflects limited reality, we expect an improvement in applicability of option pricing method for the evaluation of natural resource development projects can be made through the process taken in this paper.

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