• 제목/요약/키워드: lemma

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초등 영재교육에 적용 가능한 이산수학 주제의 내용 구성에 관한 소고 -네트워크 문제를 중심으로- (A Study on Discrete Mathematics Subjects Focused on the Network Problem for the Mathematically Gifted Students in the Elementary School)

  • 최근배
    • 대한수학교육학회지:학교수학
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    • 제7권4호
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    • pp.353-373
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    • 2005
  • 최근의 급속한 정보화 사회로의 전환에 편승하여 이산수학에 대한 관심과 이에 따른 연구가 활발해지고 있으며, 제 7차 교육과정에서 이산수학을 선택과목으로 지정할 만큼 그 중요성이 인정되고 있다. 본 연구는 네트워크문제와 관련된 이중계수 문제, 한붓그리기, 그리고 도로망문제를 중심으로, 초등 수학영재학생을 위한 학습프로그램을 구성하는 문제와 관련된 교수학적 변환에 대하여 논의하였다.

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안정한 적응관측기법에 의한 제어계의 상태추정 (Stable adaptive observer for state Identification in control system)

  • 방시영;전상영;임화영
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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    • pp.898-901
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    • 1988
  • Up to now, using adaptive control method, Identification deals with system whose entire state variables and prameters are accessible for measurement. In practical situations, all the state variables cannot be measured and it is impossible to directly apply since the parameters of the system are unknown. Therefore, in this paper, using only input-output data, such a model of the system is not available since the parameters of the system are unknown. this leads to the concept of an adptive observer in which both the parameters and the state variable of the system are identified simultaniously. Lyapunov's direct method and Kalman-Yakubovich (K-Y) lemma are employed to ensure the stability of this schemes. The feature is that the signal and adaptive gain which is generated from filter is imposed upon feedback vector and then state variables and the unknown parameters can be identified. To show the usefulness of the proposed schemes, computer simulation result of unknown second-order system shows the effectiveness of the proposed schems.

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디스크립터 시스템을 위한 혼합 $H_{2}/H_{\infty}$제어기의 설계 (Mixed $H_{2}/H_{\infty}$ Controller Design for Descriptor Systems)

  • Choe, Yeon-Wook
    • 대한전기학회논문지:시스템및제어부문D
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    • 제53권7호
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    • pp.483-490
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    • 2004
  • The descriptor system model has a high ability in representing dynamical systems. It can preserve physical parameters in the coefficient matrices, and describe the dynamic part, static part, and even the improper part of the system in the same form. The design of mixed $H_{2}/H_{\infty}$ controllers for linear time-invariant descriptor systems is considered in this paper. Firstly, an $H_2$ and $H_{\infty}$ synthesis problems fur a descriptor system are presented separately in terms of linear matrix inequalities (LMIs) based on the bounded real lemma. Then, we show that the existence of a mixed $H_2/H_{\infty}$ controller by which the $H_2$ norm of the second channel is minimized while keeping the $H_2$ norm bound of the first channel less than ${\gamma}$, is reduced to the linear objective minimization problem. The class of desired controllers that are assumed to have the same structure as the plant is parameterized by using the linearizing change of variables.

Trajectory tracking control of underactuated USV based on modified backstepping approach

  • Dong, Zaopeng;Wan, Lei;Li, Yueming;Liu, Tao;Zhang, Guocheng
    • International Journal of Naval Architecture and Ocean Engineering
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    • 제7권5호
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    • pp.817-832
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    • 2015
  • This paper presents a state feedback based backstepping control algorithm to address the trajectory tracking problem of an underactuated Unmanned Surface Vessel (USV) in the horizontal plane. A nonlinear three Degree of Freedom (DOF) underactuated dynamic model for USV is considered, and trajectory tracking controller that can track both curve trajectory and straight line trajectory with high accuracy is designed as the well known Persistent Exciting (PE) conditions of yaw velocity is completely relaxed in our study. The proposed controller has further been enriched by incorporating an integral action additionally for enhancing the steady state performance and control precision of the USV trajectory tracking control system. Global stability of the overall system is proved by Lyapunov theory and Barbalat's Lemma, and then simulation experiments are carried out to demonstrate the effectiveness of the controller designed.

3상회로 직접해석에 의한 배편계통 1선지락사고 고장거리 계산 알고리즘 (A New fault Location Algorithm for a Line to Ground fault Using Direct 3-phase Circuit Analysis in Distribution Power Networks)

  • 최면송;이승재;이덕수;진보건;민병운
    • 대한전기학회논문지:전력기술부문A
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    • 제51권8호
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    • pp.409-416
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    • 2002
  • This paper presents a fault location algorithm using direct 3-phase circuit analysis for distribution power networks. The unbalanced feature of distribution networks due to single phase loads or asymmetric operation prohibits us from using the conventional symmetrical component transformation. Even though the symmetrical component transformation provides us with a very easy tool in three phase network analysis, it is limited to balanced systems in utilizing its strong point, which is not suitable for distribution networks. In this paper, a fault location algorithm using direct 3-phase circuit analysis is developed. The algorithm is derived and it Is shown that the proposed method if we use matrix inverse lemma, is not more difficult then the conventional methods using symmetrical component transformation. Since the symmetrical component transformation is not used in the suggested method, unbalanced networks also can be handled with the same difficulty as balanced networks. The case study results show the correctness and effectiveness of the proposed algorithm.

The Usage of an SNP-SNP Relationship Matrix for Best Linear Unbiased Prediction (BLUP) Analysis Using a Community-Based Cohort Study

  • Lee, Young-Sup;Kim, Hyeon-Jeong;Cho, Seoae;Kim, Heebal
    • Genomics & Informatics
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    • 제12권4호
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    • pp.254-260
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    • 2014
  • Best linear unbiased prediction (BLUP) has been used to estimate the fixed effects and random effects of complex traits. Traditionally, genomic relationship matrix-based (GRM) and random marker-based BLUP analyses are prevalent to estimate the genetic values of complex traits. We used three methods: GRM-based prediction (G-BLUP), random marker-based prediction using an identity matrix (so-called single-nucleotide polymorphism [SNP]-BLUP), and SNP-SNP variance-covariance matrix (so-called SNP-GBLUP). We used 35,675 SNPs and R package "rrBLUP" for the BLUP analysis. The SNP-SNP relationship matrix was calculated using the GRM and Sherman-Morrison-Woodbury lemma. The SNP-GBLUP result was very similar to G-BLUP in the prediction of genetic values. However, there were many discrepancies between SNP-BLUP and the other two BLUPs. SNP-GBLUP has the merit to be able to predict genetic values through SNP effects.

벼의 규소체 형태 (Opal Phytolith Morphology in Rice)

  • 김경식
    • Journal of Plant Biology
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    • 제37권1호
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    • pp.53-67
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    • 1994
  • 대표적인 규소축적 식물 중에 하나인 벼(Orzy sativa)의 규소체를 기관별로 광학현미경과 주사전자현미경 하에서 조사하였다. 또한 규소체의 명칭에 대하여 가능한 기원조직에 근거하여 정리하였다. 벼의 조사된 주요 기관 7개 부위, 즉 엽신, 엽초, 줄기, 뿌리, 포영, 호영, 그리고 내영에서 특징적인 규소체가 확인되었다. 각 기관에 형성된 규소체 중 특히 장세포 기원의 규소체, 단세포 기원의 규소체 그리고 표피부속체 기원의 규소체 등은 기관별로 그 형태가 다양하게 나타났다. 또한 엽신에서는 벼의 다른 기관에서 형성되는 대부분의 규소체가 형성되는 것으로 밝혀졌다.

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Asynchronous Cooperative Spectrum Sensing Scheme on Primary Users with Fast "On/Off" State Variations in Spectrum Sensing Windows

  • Jin, Jingying;Gu, Junrong;Kim, Jae Moung
    • 한국통신학회논문지
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    • 제38B권10호
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    • pp.832-842
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    • 2013
  • Cognitive Radio has attracted intensive interests of the researchers, recently. The data rate always increases in the emerging technologies. The increased data rate poses mainly two challenges for spectrum sensing. One is that the state of primary user (PU) is fast and alternatively varying between "on/off" in a spectrum sensing window. The other is that the asynchronicity among the reports in a cooperative spectrum sensing setting becomes more apparent. Both of them would deteriorate the spectrum sensing performance. Thus, we propose an asynchronous cooperative spectrum sensing method to cope with these two challenges. A likelihood ratio test based spectrum sensing is developed for a single cooperator. The likelihood ratio is obtained in the setting of fast varying PU state. The likelihood ratio test is uniformly powerful according to the Neyman-pearson lemma. Furthermore, the asynchronicity among the cooperators are studied. Two sets of fusion weights are discussed for the asynchronous time among cooperators. One is designed based on the condition probability of the PU state variation and the other one is designed based on the queueing theory. The simulation results are provided with different fusion methods. The performance improvements are demonstrated.

RBRLS 알고리즘의 탭 가중치 갱신에 따른 MSE 성능 분석 (MSE Convergence Characteristic over Tap Weight Updating of RBRLS Algorithm Filter)

  • 김원균;윤찬호;곽종서;나상동
    • 한국정보통신학회:학술대회논문집
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    • 한국해양정보통신학회 1999년도 추계종합학술대회
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    • pp.248-251
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    • 1999
  • We extend the sue of the method of least square to develop a recursive algorithm for the design of adaptive transversal filters such that, given the least-square estimate of this vector of the filter at iteration n-1, we may compute the updated estimate of this vector at i(oration n upon the arrival of new data. The RLS algorithm may be viewed as a special case of the Kalman filter. Indeed this special relationship between the RLS algorithm and the Kalman filter is considered. We begin the development of the RLS algorithm by reviewing some basic relations that pertain to the method of least squares. Then, by exploiting a relation in matrix algebra known as the matrix inversion lemma, we develop the RLS algorithm. An important feature of the RLS algorithm is that it utilizes information contained in the input data, extending back to the instant of time when the algorithm is initiated. The resulting rate of convergence is therefore typically an order of magnitude faster than the simple LMS algorithm. This improvement in performance, however, Is achieved at the expensive of a large increase in computational complexity.

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A Study on Synthetic OD Estimation Model based on Partial Traffic Volumes and User-Equilibrium Information

  • 조성길
    • 한국ITS학회 논문지
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    • 제7권5호
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    • pp.180-183
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    • 2008
  • 본 논문은 교통망에서 관측 링크 교통량, 미관측 링크의 이용자평형 정보를 이용하여 O-D행렬을 수학적으로 생성하는 모형을 제시하고 있다. 교통량이 관측되지 않은 링크로부터 이용자 평형 상태에서 추출 가능한 정보를 바탕으로 일련의 논리적 연산을 거쳐 실제교통량에 근접하는 서브알고리듬을 유추하여 O-D행렬 추정의 정확도와 연산의 일관성을 제고하였다. 이를 위해 이용자평형상태에서 새로운 정리(Theorem)와 보조정리(Lemma)를 유도하여 적용하였다. 모형의 시험은 3개의 초기 O-D 행렬과 3개의 미관측 링크 교통량 시나리오를 각각의 모형에 적용하여 그 결과를 비교하였다. 적용 결과 본 논문에서 제시된 모형은 기존의 이용자균형 접근방식의 모형emf에 비해 추정된 O-D값의 실제 값과의 차이(O-D Trip RMSE)가 현저히 감소되는 것을 확인하였다.

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