• Title/Summary/Keyword: 이론수학

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A Study on Construction of Multiplication Knowledge with Low Reasoning Ability (추론 능력이 열등한 초등학교 2학년 학생의 곱셈 지식 구성 능력에 관한 연구)

  • Lee, So-Min;Kim, Jin-Ho
    • Journal of the Korean School Mathematics Society
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    • v.12 no.1
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    • pp.47-70
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    • 2009
  • The purpose of this research was to confirm one of constructivists' assumptions that even children 조o are with low reasoning ability can make reflective abstracting ability and cognitive structures by this ability can make generation ability of new knowledge by themselves. To investigate the assumption, learner-centered instruction were implemented to 2nd grade classroom located in Suseong Gu, DaeGu City and with lesson plans which initially were developed by Burns and corrected by the researchers. Recordings videoed using 2 video cameras, observations, instructions, children's activity worksheets, instruction journals were analyzed using multiple tests for qualitative analysis. Some conclusions are drawn from the results. First, even children with low reasoning ability can construct mathematical knowledge on multiplication in their own. ways, Thus, teachers should not compel them to learn a learning lesson's goals which is demanded in traditional instruction, with having belief they have reasoning ability. Second, teachers need to have the perspectives of respects out of each child in their classroom and provide some materials which can provoke children's cognitive conflict and promote thinking with the recognition of effectiveness of learner-centered instruction. Third, students try to develop their ability of reflective and therefore establish cognitive structures such as webs, not isolated and fragmental ones.

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Estimation of Shear Strength Along Concrete Construction Joints Considering the Variation of Concrete Cohesion and Coefficient of Friction (콘크리트 시공줄눈 면에서 점착력 및 마찰계수의 변화를 고려한 전단내력 평가)

  • Yang, Keun-Hyeok;Kwon, Hyuck-Jin;Park, Jong-Beom
    • Journal of the Korea institute for structural maintenance and inspection
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    • v.21 no.6
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    • pp.106-112
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    • 2017
  • This paper presents a mathematical model derived from the upper-bound theorem of concrete plasticity to rationally evaluate the shear friction strength of concrete interfaces with a construction joint. The upper limit of the shear friction strength was formulated from the limit state of concrete crushing failure on the strut-and-tie action along the construction joints to avoid overestimating the shear transfer capacity of a transverse reinforcement with a high clamping force. The present model approach proposed that the cohesion and coefficient of friction of concrete can be set to be $0.27(f_{ck})^{0.65}$ and 0.95, respectively, for rough construction joints and $0.11(f_{ck})^{0.65}$ and 0.64, respectively, for smooth ones, where $f_{ck}$ is the compressive strength of concrete. From the comparisons with 155 data compiled from the available literature, the proposed model gave lower values of standard deviation and coefficient of variation of the ratios between predictions and experiments than AASHTO and fib 2010 equations, indicating that the proposed model has consistent trends with test results, unlike the significant underestimation results of such code equations in evaluating the shear friction strength.

Vibration Analysis of Thick Hyperboloidal Shells of Revolution from a Three-Dimensional Analysis (두꺼운 축대칭 쌍곡형 쉘의 3차원 진동해석)

  • 심현주;강재훈
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.16 no.4
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    • pp.419-429
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    • 2003
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components u/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

The Analysis of Forest Successional Trend by Species Replacement Model in the Natural Forest (천연림의 수종 대치 작용 모델에 의한 산림천이 경향 분석)

  • 김지홍
    • Journal of Korea Foresty Energy
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    • v.22 no.3
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    • pp.1-10
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    • 2003
  • The successional status and potential natural vegetation were examined in the natural deciduous forest in Mt. Chombong area. The examination was based on the subsequent process of generation replacement by understory saplings for the dominant canopy trees within 106 20mx20m square sample plots. The transition matrix model, which was modified from mathematical theory of Markov chain, was employed to analyze the successional status of the study forest. The model suggests that study forest is still seral, and it is considered to be more than 500 years away from the steady state or climax in terms of species composition. The simulations predict a remarkable decrease in the proportion of species composition of the present dominant Quercus mongolica and Kalopanax pictus from current 42.6% and 8.1% to less than 13.3% and 0.5%, respectively, at the steady state. On the contrary, the proportions of Abies holophylla, Acer mono, Fraxinus mandshurica, Tilia amurensis, and Acer pseudo-sieboldianum will increase at the steady state. The change of predicted composition ratio was generally coincide with the result of tolerance index to be compared with the study model. The hypothesis and sensitivity of the model were also discussed to evaluate the applicability to the real situation. The overall results indicated that the present dynamics of the forest must reflect the seral state due to previous disturbance mainly by human related interference.

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Performance Analysis of Routing Protocols for WLAN Mesh Networks (WLAN Mesh 망을 위한 라우팅 기법의 성능 분석)

  • Park, Jae-Sung;Lim, Yu-Jin;Ahn, Sang-Hyun
    • The KIPS Transactions:PartC
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    • v.14C no.5
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    • pp.417-424
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    • 2007
  • Mesh networks using WLAN technology have been paid attention as a key wireless access technology. However, many technical issues still exist for its successful deployment. One of those issues is the routing problem that addresses the path setup through a WLAN mesh network for the data exchanges between a station and a wired network. Since the characteristics of a WLAN mesh network can be very dynamic, the use of single routing protocol would not fit for all environments whether it is reactive or proactive. Therefore, it is required to develop an adaptive routing protocol that modifies itself according to the changes in the network parameters. As a logical first step for the development, an analytical model considering all the dynamic features of a WLAN mesh network is required to evaluate the performance of a reactive and a proactive routing scheme. In this paper, we propose an analytical model that makes us scrutinize the impact of the network and station parameters on the performance of each routing protocol. Our model includes the size of a mesh network, the density of stations, mobility of stations. and the duration of network topology change. We applied our model to the AODV that is a representative reactive routing protocol and DSDV that is a representative proactive routing protocol to analyze the tradeoff between AODV and DSDV in dynamic network environments. Our model is expected to help developing an adaptive routing protocol for a WLAN mesh network.

A Comparative Study of Fuzzy Based Frequency Ratio and Cosine Amplitude Method for Landslide Susceptibility in Jinbu Area (빈도비와 Cosine Amplitude Method를 이용한 진부지역의 퍼지기반 산사태 취약성 예측기법 비교 연구)

  • Kim, Kang Min;Park, Hyuck Jin
    • Economic and Environmental Geology
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    • v.50 no.3
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    • pp.195-214
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    • 2017
  • Statistical landslide susceptibility analysis, which is widely used among various landslide susceptibility analysis approaches, predicts the unstable area by analyzing statistical relationship between landslide occurrence locations and landslide controlling factors. However, uncertainties are involved in the procedures of the susceptibility analysis and therefore, fuzzy approach has been used to deal properly with uncertainties. The fuzzy approach used fuzzy set theory and fuzzy membership function to quantify uncertainties involved in landslide controlling factors. Various fuzzy approaches were suggested in the procedure of the membership value determination and fuzzy operation in the previous researches. However, few studies were carried out to compare the analysis results obtained from various approaches for membership function determination and fuzzy operation. Therefore, in this study, the authors selected Jinbu area, which a large number of landslides were occurred at in 2006, to apply two most commonly used methods, the frequency ratio and the cosine amplitude method to derive membership values for each controlling factor. In addition, the integration of different thematic layers to produce landslide susceptibility map was performed by several fuzzy operators such as AND, OR, algebraic product, algebraic sum and Gamma operator. The results of the landslide susceptibility analysis using two different methods for the determination of fuzzy membership values and various fuzzy operators were compared on the basis of ROC graph to check the feasibility of the fuzzy based landslide susceptibility analysis.

Performance Analysis of Location-Aware System based on Active Tags (능동태그 기반 위치인식 시스템의 성능 분석)

  • So, Sun-Sup;Eun, Seong-Bae;Kim, Jin-Chun
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.11 no.2
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    • pp.422-429
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    • 2007
  • Location awareness is one of the key functionalities to build an U-city. Recently, many of works of the location-aware systems are emerging to commercially apply to on-going large-scale apartment complex based on U-city. As dwellers or cars being attached with active tags are moving in the U-city complex, the active tags periodically broadcast their own identifiers and receivers fixed along the street or in building use those information to calculate location of them. There are several issues to be considered for such an environment. The first is that the number of active tags operating in the same region are large as much as tens of thousands, and the second is that the active tags should be alive without change of batteries more than a year, hence low power consumption is very important. In this paper we propose i) a new architecture for location-aware system considering such issues, ii) technical issues to implement it using active tags, and iii) a mathematical analytic model to investigate overall performance and verify it by comparing with actual experimental results. Through the analysis we can show the theoretical boundary of the lowest packet loss rate and the maximum number of tags with acceptable performance for the systems based on active tags. The results can be applied to practical design of location-based systems of U-City projects.

Kinematic Approximation of Partial Derivative Seismogram with respect to Velocity and Density (편미분 파동장을 이용한 탄성파 주시 곡선의 평가)

  • Shin, Chang-Soo;Shin, Sung-Ryul
    • Geophysics and Geophysical Exploration
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    • v.1 no.1
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    • pp.8-18
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    • 1998
  • In exploration seismology, the Kirchhoff hyperbola has been successfully used to migrate reflection seismo-grams. The mathematical basis of Kirchhoff hyperbola has not been clearly defined and understood for the application of prestack or poststack migration. The travel time from the scatterer in the subsurface to the receivers (exploding reflector model) on the surface can be a kinematic approximation of Green's function when the source is excited at position of the scatterer. If we add the travel time from the source to the scatterer in the subsurface to the travel time of exploding reflector model, we can view this travel time as a kinematic approximation of the partial derivative wavefield with respect to the velocity or the density in the subsurface. The summation of reflection seismogram along the Kirchhoff hyperbola can be evaluated as an inner product between the partial derivative wavefield and the field reflection seismogram. In addition to this kinematic interpretation of Kirchhoff hyperbola, when we extend this concept to shallow refraction seismic data, the stacking of refraction data along the straight line can be interpreted as a measurement of an inner product between the first arrival waveform of the partial derivative wavefield and the field refraction data. We evaluated the Kirchhoff hyperbola and the straight line for stacking the refraction data in terms of the first arrival waveform of the partial derivative wavefield with respect to the velocity or the density in the subsurface. This evaluation provides a firm and solid basis for the conventional Kirchhoff migration and the straight line stacking of the refraction data.

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Analysis of influence of parameter error for extended EMF based sensorless control and flux based sensorless control of PM synchronous motor (영구자석 동기전동기의 확장 역기전력 기반 센서리스 제어와 자속기반 센서리스 제어의 파라미터 오차의 영향 분석)

  • Park, Wan-Seo;Cho, Kwan-Yuhl;Kim, Hag-Wone
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.20 no.3
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    • pp.8-15
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    • 2019
  • The PM synchronous motor drives with vector control have been applied to wide fields of industry applications due to its high efficiency. The rotor position information for vector control of a PM synchronous motor is detected from the rotor position sensors or rotor position estimators. The sensorless control based on the mathematical model of PM synchronous motor is generally used and it can be classified into back EMF -based sensorless control and magnet flux-based sensorless control. The rotor position estimating performance of the back EMF-based sensorless control is deteriorated at low speeds since the magnitude of back EMF is proportional to the motor speed. The magnitude of the magnet flux for estimating rotor position in the flux-based sensorless control is independent on the motor speed so that the estimating performance is excellent for wide speed ranges. However, the estimation performance of the model-based sensorless control may be influenced by the motor parameter variation since the rotor position estimator uses the mathematical model of the PM synchronous motor. In this paper, the rotor position estimation performance for the back EMF based- and flux-based sensorless controls is analyzed theoretically and is compared through the simulation and experiment when the motor parameters including stator resistance and inductance are varied.

Verification of Radiation and Beam-Steering Characteristics for Planar-Phased Array Radars Using Near-Field Beam Focusing (근전계 빔 집속 시험 기법을 활용한 평면위상배열레이다 시스템 복사 및 빔 조향 특성 검증)

  • Kim, Young-Wan;Lee, Jaemin;Jung, Chae-Hyun;Park, Jongkuk;Lee, Yuri;Kim, Jong-Phil;Kim, Sunju
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.30 no.2
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    • pp.160-168
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    • 2019
  • In this study, we propose a verification method for a planar-phased array radar system using a near-field beam focusing(NFBF) test method. We then confirmed the validity of the results. The proposed method can be used to verify a radar system in the near-field range of twice the antenna aperture size, and this is done in the same manner as the field system performance test conducted in a non-outdoor electromagnetic anechoic chamber. The test configuration and procedure for verifying the NFBF using near-field energies were reviewed. In addition, the phase compensation values of additional individual channels were quantified through mathematical verification of the beam-steered NFBF test. Based on a theoretical verification, the actual NFBF test was performed and the validity of the test method was confirmed through comparison with ideal analytical results.