• Title/Summary/Keyword: Denominator

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DEVELOPMENT OF A NON-STANDARD FINITE DIFFERENCE METHOD FOR SOLVING A FRACTIONAL DECAY MODEL

  • SAID AL KATHIRI;EIHAB BASHIER;NUR NADIAH ABD HAMID;NORSHAFIRA RAMLI
    • Journal of applied mathematics & informatics
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    • v.42 no.3
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    • pp.695-708
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    • 2024
  • In this paper we present a non-standard finite difference method for solving a fractional decay model. The proposed NSFDM is constructed by incorporating a non-standard denominator function, resulting in an explicit numerical scheme as easy as the conventional Euler method, but it provides very accurate solutions and has unconditional stability. Two examples from the literature are presented to demonstrate the performance of the proposed numerical scheme, which is compared to three methods from the literature. It is found that the method's estimated errors are extremely minimal, such as within the machine precision.

An Analysis on the Error According to Academic Achievement Level in the Fractional Computation Error of Elementary Sixth Graders (초등학교 6학년 학생이 분수 계산문제에서 보이는 오류의 학업성취수준별 분석)

  • Park, Miyeon;Park, Younghee
    • Journal of Elementary Mathematics Education in Korea
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    • v.21 no.1
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    • pp.23-47
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    • 2017
  • The purpose of this study is to analyze the types of errors that may occur in the four arithmetic operations of the fractions after classified according to the level of academic achievement for sixth-grade elementary school student who Learning of the four arithmetic operations of the fountain has been completed. The study was proceed to get the information how change teaching content and method in accordance with the level of academic achievement by looking at the types of errors that can occur in the four arithmetic operations of the fractions. The test paper for checking the type of errors caused by calculation of fractional was developed and gave it to students to test. And we saw the result by error rate and correct rate of fraction that is displayed in accordance with the level of academic achievement. We investigated the characteristics of the type of error in the calculation of the arithmetic operations of fractional that is displayed in accordance with the level of academic achievement. First, in the addition of the fractions, all levels of students showing the highest error rate in the calculation error. Specially, error rate in the calculation of different denominator was higher than the error rate in the calculation of same denominator Second, in the subtraction of the fractions, the high level of students have the highest rate in the calculation error and middle and low level of students have the highest rate in the conceptual error. Third, in the multiplication of the fractions, the high and middle level of students have the highest rate in the calculation error and low level of students have the highest rate in the a reciprocal error. Fourth, in the division of the fractions, all levels of students have the highest r rate in the calculation error.

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Reconsideration of Teaching Addition and Subtraction of Fractions with Different Denominators: Focused on Quantitative Reasoning with Unit and Recursive Partitioning (이분모분수의 덧셈과 뺄셈 교육 재고 - 단위 추론 및 재귀적 분할을 중심으로 -)

  • Lee, Jiyoung;Pang, JeongSuk
    • School Mathematics
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    • v.18 no.3
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    • pp.625-645
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    • 2016
  • This study clarified the big ideas related to teaching addition and subtraction of fractions with different denominators based on quantitative reasoning with unit and recursive partitioning. An analysis of this study urged us to re-consider the content related to the addition and subtraction of fraction. As such, this study analyzed textbooks and teachers' manuals developed from the fourth national mathematics curriculum to the most recent 2009 curriculum. In addition and subtraction of fractions with different denominators, it must be emphasized the followings: three-levels unit structure, fixed whole unit, necessity of common measure and recursive partitioning. An analysis of this study showed that textbooks and teachers' manuals dealt with the fact of maintaining a fixed whole unit only as being implicit. The textbooks described the reason why we need to create a common denominator in connection with the addition of similar fractions. The textbooks displayed a common denominator numerically rather than using a recursive partitioning method. Given this, it is difficult for students to connect the models and algorithms. Building on these results, this study is expected to suggest specific implications which may be taken into account in developing new instructional materials in process.

Estimation Method of Predicted Time Series Data Based on Absolute Maximum Value (최대 절대값 기반 시계열 데이터 예측 모델 평가 기법)

  • Shin, Ki-Hoon;Kim, Chul;Nam, Sang-Hun;Park, Sung-Jae;Yoo, Sung-Soo
    • Journal of Energy Engineering
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    • v.27 no.4
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    • pp.103-110
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    • 2018
  • In this paper, we introduce evaluation method of time series prediction model with new approach of Mean Absolute Percentage Error(hereafter MAPE) and Symmetric Mean Absolute Percentage Error(hereafter sMAPE). There are some problems using MAPE and sMAPE. First MAPE can't evaluate Zero observation of dataset. Moreover, when the observed value is very close to zero it evaluate heavier than other methods. Finally it evaluate different measure even same error between observations and predicted values. And sMAPE does different evaluations are made depending on whether the same error value is over-predicted or under-predicted. And it has different measurement according to the each sign, even if error is the same distance. These problems were solved by Maximum Mean Absolute Percentage Error(hereafter mMAPE). we used the absolute maximum of observed value as denominator instead of the observed value in MAPE, when the value is less than 1, removed denominator then solved the problem that the zero value is not defined. and were able to prevent heavier measurement problem. Also, if the absolute maximum of observed value is greater than 1, the evaluation values of mMAPE were compared with those of the other evaluations. With Beijing PM2.5 temperature data and our simulation data, we compared the evaluation values of mMAPE with other evaluations. And we proved that mMAPE can solve the problems that we mentioned.

A Study on the Environmental Evaluation in Use Stage of KTX and Samaul Train : the Development of Eco-efficiency Indicator (생태효율성(Eco-efficiency)지표 개발을 통한 KTX와 새마을호 열차의 사용단계 환경성 평가에 관한 연구)

  • Choi, Yong-Sin;Chun, Yoon-Young;Lee, Kun-Mo;Kim, Yong-Ki
    • Proceedings of the KSR Conference
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    • 2011.05a
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    • pp.1313-1320
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    • 2011
  • World Business Council for Sustainable Development(WBCSD) is effort to achieve sustainable development in economic growth, environmental preservation and social development. Being this way, it is essential for developing evaluation tool which quantify to fulfill sustainable development. Eco-efficiency is one of the quantitative tools to evaluate environmental impact and economic aspect. Eco-efficiency, in general term, means creating more value of product or services with less impact to environment. It indicates as environmental impact in denominator and value of product or services in numerator. Eco-efficiency shows how much economic value reveals to unit environmental impact caused by product or service as an indicator. This study aims at developing eco-efficiency indicator of railway industry considering use stage among the entire life cycle stage of KTX and Saemaul train and also, figure out eco-efficiency value through indicator. Therethrough, it is enables to evaluate created value per environmental aspects. Since rail vehicles demands a lot of energy to transport people during use stage, the environmental impact is more significant than other lkfe cycle stages. Therefore, it quantified environmental indicator as CO2 emission and economic indicator as transportation record per a year with an annual income. This study contributes to be used as a tool for quantifying indicator of comparison evaluation in respect of rail vehicle in use stage.

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Wide-Range Sensorless Control for SPMSM Using an Improved Full-Order Flux Observer

  • Lee, Kyoung-Gu;Lee, June-Seok;Lee, Kyo-Beum
    • Journal of Power Electronics
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    • v.15 no.3
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    • pp.721-729
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    • 2015
  • A sensorless control method was recently investigated in the robot and automation industry. This method can solve problems related to the rise of manufacturing costs and system volume. In a vector control method, the rotor position estimated in the sensorless control method is generally used. This study is based on a conventional full-order flux observer. The proposed full-order flux observer estimates both currents and fluxes. Estimated d- and q-axis currents and fluxes are used to estimate the rotor position. In selecting the gains, the proposed full-order flux observer substitutes gain k for the speed information in the denominator of the gain for fast convergence. Therefore, accurate speed control in a low-speed region can be obtained because gains do not influence the estimation of the rotor position. The stability of the proposed full-order flux observer is confirmed through a root-locus method, and the validity of the proposed observer is experimentally verified using a surface permanent-magnet synchronous motor.

Parameter Reduction in Digital Adaptive Flight Control System for Spaceplanes

  • Togasaki, Yoshihiro;Shimada, Yuzo;Uchiyama, Kenji
    • 제어로봇시스템학회:학술대회논문집
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    • 2004.08a
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    • pp.995-1000
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    • 2004
  • A digital adaptive flight control system is presented for a Japanese automatic landing flight experiment vehicle (ALFLEX). In previous adaptive control systems based on a linear-parameter-varying (LPV) form, the output behavior was excellent, while the behavior of the adjusted parameters was unsatisfactory. In the present study, to obtain a more appropriate parameter adjustment law, the relationship between the coefficient matrices in a continuous-time state equation and the coefficients of a pulse transfer function in a discrete system for conventional aircraft is investigated. As a result, it is revealed that the coefficients of the numerator can be treated as a linear function of dynamic pressure (linear-parameter-varying: LPV), while the coefficients of the denominator can be treated as constant (linear-time-invariant: LTI). From the above analysis, an improved parameter adjustment law is derived by reducing the number of the adjustment parameters. Simulation results also revealed both good output tracking and good parameter adjustment compared with the previous results.

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Robust Relay Design for Two-Way Multi-Antenna Relay Systems with Imperfect CSI

  • Wang, Chenyuan;Dong, Xiaodai;Shi, Yi
    • Journal of Communications and Networks
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    • v.16 no.1
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    • pp.45-55
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    • 2014
  • The paper investigates the problem of designing the multiple-antenna relay in a two-way relay network by taking into account the imperfect channel state information (CSI). The objective is to design the multiple-antenna relay based upon the CSI estimates, where the estimation errors are included to attain the robust design under the worst-case philosophy. In particular, the worst-case transmit power at the multiple-antenna relay is minimized while guaranteeing the worst-case quality of service requirements that the received signal-to-noise ratio (SNR) at both sources are above a prescribed threshold value. Since the worst-case received SNR expression is too complex for subsequent derivation and processing, its lower bound is explored instead by minimizing the numerator and maximizing the denominator of the worst-case SNR. The aforementioned problem is mathematically formulated and shown to be nonconvex. This motivates the pursuit of semidefinite relaxation coupled with a randomization technique to obtain computationally efficient high-quality approximate solutions. This paper has shown that the original optimization problem can be reformulated and then relaxed to a convex problem that can be solved by utilizing suitable randomization loop. Numerical results compare the proposed multiple-antenna relay with the existing nonrobust method, and therefore validate its robustness against the channel uncertainty. Finally, the feasibility of the proposed design and the associated influencing factors are discussed by means of extensive Monte Carlo simulations.

A Study on the architectural Idea of 'the natural Construction' of Frei Otto (프라이 오토의 '자연적 구조'의 건축적 이념에 관한 연구)

  • Lee, Ran-Pyo
    • Korean Institute of Interior Design Journal
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    • v.15 no.5 s.58
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    • pp.68-76
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    • 2006
  • Frei Otto, who is called to be the father of the ecological architecture, has shaped a peculiar architectural form style. In distance from the formalistic persistence to the modernist form canon and the postmodern tendencies to the self-representation of architects, Frei Otto has taken a more fundamentalistic position. Through the interdisciplinary researches on the self-organizing processes in the nature and the technical world Frei Otto could reason with architects, engineers, biologists, historians and philosophers the principle and structure of the natural construction that is applicable to the morphological research and the architectural construction research. In the middle of his architectural and scientific works is the idea of 'the natural construction' situated, and the basic principle and instrument of this 'Die Prinzip der Selbstbildung, The Principle of Self-making'. Founding himself on this principle, Frei Otto seeks after the new architectural form that is light, natural, flexible and variable by reasoning the typical formation process which refers to the common denominator of the self-making processes in the nature, the technique and the architecture. Despite his architecture is to be called to the anonymous, his architectural vision is headed toward the rationalistic form in accord with the natural laws. This study is purposed to elucidate the constellation to which his scientific attempts belong and the theoretical and methodological foundations of his architecture of 'the natural construction'.

A SUMMATION FORMULA FOR THE SERIES 3F2 DUE TO FOX AND ITS GENERALIZATIONS

  • Choi, Junesang;Rathie, Arjun K.
    • Communications of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.103-108
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    • 2015
  • Fox [2] presented an interesting identity for $_pF_q$ which is expressed in terms of a finite summation of $_pF_q$'s whose involved numerator and denominator parameters are different from those in the starting one. Moreover Fox [2] found a very interesting and general summation formula for $_3F_2(1/2)$ as a special case of his above-mentioned general identity with the help of Kummer's second summation theorem for $_2F_1(1/2)$. Here, in this paper, we show how two general summation formulas for $$_3F_2\[\array{\hspace{110}{\alpha},{\beta},{\gamma};\\{\alpha}-m,\;\frac{1}{2}({\beta}+{\gamma}+i+1);}\;{\frac{1}{2}}\]$$, m being a nonnegative integer and i any integer, can be easily established by suitably specializing the above-mentioned Fox's general identity with, here, the aid of generalizations of Kummer's second summation theorem for $_2F_1(1/2)$ obtained recently by Rakha and Rathie [7]. Several known results are also seen to be certain special cases of our main identities.