• Title/Summary/Keyword: mathematical discussions

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A Comparative Study on Early Algebra between Korea and USA Textbooks -focusing to operation sense in the elementary mathematics- (우리나라와 미국의 초기대수 비교 연구 -초등수학 교과서에 제시된 연산 감각을 중심으로-)

  • Kim, Sung Joon
    • East Asian mathematical journal
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    • v.29 no.4
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    • pp.355-392
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    • 2013
  • Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

The Consumer Rationality Assumption in Incentive Based Demand Response Program via Reduction Bidding

  • Babar, Muhammad;Imthias Ahamed, T.P.;Alammar, Essam A.
    • Journal of Electrical Engineering and Technology
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    • v.10 no.1
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    • pp.64-74
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    • 2015
  • Because of the burgeoning demand of the energy, the countries are finding sustainable solutions for these emerging challenges. Demand Side Management is playing a significant role in managing the demand with an aim to support the electrical grid during the peak hours. However, advancement in controls and communication technologies, the aggregators are appearing as a third party entity in implementing demand response program. In this paper, a detailed mathematical framework is discussed in which the aggregator acts as an energy service provider between the utility and the consumers, and facilitate the consumers to actively participate in demand side management by introducing the new concept of demand reduction bidding (DRB) under constrained direct load control. Paper also presented an algorithm for the proposed framework and demonstrated the efficacy of the algorithm by considering few case studies and concluded with simulation results and discussions.

RECTANGULAR DOMAIN DECOMPOSITION METHOD FOR PARABOLIC PROBLEMS

  • Jun, Youn-Bae;Mai, Tsun-Zee
    • The Pure and Applied Mathematics
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    • v.13 no.4 s.34
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    • pp.281-294
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    • 2006
  • Many partial differential equations defined on a rectangular domain can be solved numerically by using a domain decomposition method. The most commonly used decompositions are the domain being decomposed in stripwise and rectangular way. Theories for non-overlapping domain decomposition(in which two adjacent subdomains share an interface) were often focused on the stripwise decomposition and claimed that extensions could be made to the rectangular decomposition without further discussions. In this paper we focus on the comparisons of the two ways of decompositions. We consider the unconditionally stable scheme, the MIP algorithm, for solving parabolic partial differential equations. The SOR iterative method is used in the MIP algorithm. Even though the theories are the same but the performances are different. We found out that the stripwise decomposition has better performance.

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Application of Intra-particle Combustion Model for Iron Ore Sintering Bed (제철 소결공정에 대한 단입자 연소 모델의 응용)

  • Yang, Won;Choi, Sang-Min;Jin, Hong-Jong
    • 한국연소학회:학술대회논문집
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    • 2006.04a
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    • pp.181-188
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    • 2006
  • Operation parameters for large scale industrial facility such as iron making plant are carefully selected through elaborate tests and monitoring rather than through a mathematical modeling. One of the recent progresses for better energy utilization in iron ore sintering process is the distribution pattern of fuel inside a macro particle which is formed with fines of iron ore, coke and limestone. Results of model tests which have been used as a basis for the improved operation in the field are introduced and a theoretical modeling study is presented to supplement the experiment-based approach with fundamental arguments of physical modeling, which enables predictive computation beyond the limited region of tests and adjustment. A single fuel particle model along with one-dimensional bed combustion model of solid particles are utilized, and thermal processes of combustion and heat transfer are found to be dominant consideration in the discussions of productivity and energy utilization in the sintering process.

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Numerical Analysis of Solid Propellant Ignition ~Numerical Formulation Assessment~

  • Shimada, Toru;Novozhilov, Boris V.
    • Proceedings of the Korean Society of Propulsion Engineers Conference
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    • 2004.03a
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    • pp.528-531
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    • 2004
  • For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

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Neural Network Based Rudder-Roll Damping Control System for Ship

  • Nguyen, Phung-Hung;Jung, Yun-Chul
    • Journal of Navigation and Port Research
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    • v.31 no.4
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    • pp.289-293
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    • 2007
  • In this paper, new application of adaptive neural network to design a ship's Rudder-Roll Damping(RRD) control system is presented Firstly, the ANNAI neural network controller is presented. Secondly, new RRD control system using this neural network approach is developed. It uses two neural network controllers for heading control and roll damping control separately. Finally, Computer simulation of this RRD control system is carried out to compare with a linear quadratic optimal RRD control system; discussions and conclusions are provided. The simulation results show the feasibility of using ANNAI controller for RRD. Also, the necessity of mathematical ship model in designing RRD control system is removed by using NN control technique.

Theoretical Considerations on Combined Optical Distance Measurements Using a Femtosecond Pulse Laser

  • Joo, Ki-Nam;Kim, Seung-Woo
    • Journal of the Optical Society of Korea
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    • v.16 no.4
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    • pp.396-400
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    • 2012
  • We introduce a combined technique and the mathematical description for distance measurements using a femtosecond pulse laser in a long range and a fine resolution. For distance measurements, the maximum measurable range can be extended by combining measurement results from several different methods while requiring relationships between the different measurement uncertainties and unambiguity ranges. This paper briefly explains why the uncertainty of a rough measurement technique (RMT) should be, at least, smaller than the half unambiguity range of a fine measurement technique (FMT) in order to combine a FMT with a RMT. Further discussions about the total measurement range, resolution, and uncertainty for various optical measurement techniques are also discussed.

Diagrammatic Reasoning in Joseon Mathematics Book 'JuseoGwangyeon' (조선 산학서 《주서관견》의 도해적 추론)

  • CHANG Hyewon
    • Journal for History of Mathematics
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    • v.36 no.4
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    • pp.61-78
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    • 2023
  • By virtue of the characteristics inherent in diagrams, diagrammatic reasoning has potential and limitations that distinguish it from general thinking. It is natural that diagrams rarely appeared in Joseon mathematical books, which were heavily focused on computation and algebra in content, and preferred linguistic expressions in form. However, as the late Joseon Dynasty unfolded, there emerged a noticeable increase in the frequency of employing diagrams, due to the educational purposes to facilitate explanations and the influence of Western mathematics. Analyzing the role of diagrams included in Jo Taegu's 'JuseoGwangyeon', an exemplary book, this study includes discussions on the utilization of diagrams from the perspective of mathematics education, based on the findings of the analysis.

The Smart City: Trends and Evolution, Readiness and Adaptability in Africa

  • Bashir Aliyu Yauri;Ekpobodo Raymond Ovwigho
    • International Journal of Computer Science & Network Security
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    • v.24 no.4
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    • pp.119-126
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    • 2024
  • This paper reviewed and provides clarifications as to the meaning and concept of Smart Cities with particular reference to the Smart City Components. The paper also discusses Internet of Things and the Big Data in relation to the role they played in the development and evolution of smart cities. The paper further provides discussions on the 5G Wireless Networks and Industry 4.0 buttressing their significance in the smart cities concept. The paper as the name implies; discusses on the readiness and adaptability of this trending concept 'Smart City' in the African global space.

The Status of Scientiae Mediae in the History of Mathematics: Biancani's Case

  • Park, Woo-Suk
    • Korean Journal of Logic
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    • v.12 no.2
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    • pp.141-170
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    • 2009
  • We can witness the recent surge of interest in the controversy over the scientific status of mathematics among Jesuit Aristotelians around 1600. Following the lead of Wallace, Dear, and Mancosu, I propose to look into this controversy in more detail. For this purpose, I shall focus on Biancani's discussion of scientiae mediae in his dissertation on the nature of mathematics. From Dear's and Wallace's discussions, we can gather a relatively nice overview of the debate between those who championed the scientific status of mathematics and those who denied it. But it is one thing to fathom the general motivation of the disputation, quite another to appreciate the subtleties of dialectical strategies and tactics involved in it. It is exactly at this stage when we have to face some difficulties in understanding the point of Biancani's views on scientiae mediae. Though silent on the problem of scientiae mediae, Mancosu's discussions of the Jesuit Aristotelians' views on potissima demonstrations, mathematical explanations, and the problem of cause are of utmost importance in this regard, both historically and philosophically. I will carefully examine and criticize some of Mancosu's interpretations of Piccolomini's and Biancani's views in order to approach more closely what was really at stake in the controversy.

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