• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.247-260
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• 2015

The special form of Schur complement is extended to have a Schur's formula to obtains the explicit formula of determinant, inverse, and eigenvector formula of the doubly Leslie matrix which is the generalized forms of the Leslie matrix. It is also a generalized form of the doubly companion matrix, and the companion matrix, respectively. The doubly Leslie matrix is a nonderogatory matrix.

• Korean Journal of Mathematics
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• 제22권3호
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• pp.443-454
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• 2014

In this paper, we give linearization of generalized Fi-bonacci sequences {$g_n$} and {$q_n$}, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {$g_n$} and {$q_n$}, respectively. Then we re-prove the Cassini's identity for {$g_n$} and {$q_n$}, respectively.

• 호남수학학술지
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• 제38권4호
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• pp.725-738
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• 2016

In this paper, the explicit determinants of the circulant and negacyclic matrix involving Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$ are expressed by using only Tetranacci sequence $M_n$ and Companion-Tetranacci sequence $K_n$. Also euclidean norms and spectral norms of circulant and negacyclic matrices have been obtained.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.845-858
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• 2021

We present new bounds for the numerical radius of bounded linear operators and 2 × 2 operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new estimations for the zeros of that polynomial. We also show with numerical examples that our new estimations improve on the existing estimations.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.505-513
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• 2019

In this paper, we study orthanogonal polynomials by looking at their comrade matrices and reachability matrices. First, we focus on the algebraic structure that is exhibited by comrade matrices. Then, we explain some properties of this algebraic structure which helps us to find a connection between comrade matrices and reachability matrices. In the last section, we use this connection to determine the determinant, eigenvalues, and eigenvectors of these matrices. Finally, we derive a factorization for det R(A, x), where R(A, x) is the reachability matrix for a comrade matrix A and x is a vector of indeterminates.

• 한국통신학회논문지
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• 제40권4호
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• pp.646-652
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• 2015

본 논문은 다중 사용자 MIMO 시스템에서 사용자 선택을 위해 필요한 precoding matrix index (PMI)/channel quality indication (CQI)의 보고 방식에 따른 성능을 분석한다. 이러한 분석을 통해 셀 내의 단말의 수, 선택되는 사용자의 수, 그리고 코드북(codebook)의 크기가 Best Companion Grouping (BCG)방식 스케쥴링의 성능에 복잡하게 영향을 미치는 것을 확인한다. 이에 따라 셀 내의 사용자 수와 코드북의 크기에 따라 동시에 스케쥴링 되는 사용자들의 그룹이 형성될 수 있는 확률이 달라지는 것을 확인할 수 있으며, 피드백 오버헤드가 주어졌을 때 이에 따라 피드백하는 PMI의 수와 사용하는 코드북의 크기를 적응적으로 선택함으로써 시스템의 평균 수율 성능을 최적화할 수 있음을 보였다.

• 디자인융복합연구
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• 제16권6호
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• pp.137-152
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• 2017

본 연구는 실버세대를 위한 컴패니언 로봇의 인터랙션 경험 디자인을 위해 사용자 태스크- 로봇 기능 적합도 매핑에 기반한 로봇 유형 분석과 멀티모달 대화 인터랙션에서의 로봇 감정표현 연구를 수행하였다. 노인의 니즈 분석을 위해 노인과 자원 봉사자를 대상으로 FGI, 에스노그래피를 진행하였으며 로봇 지원 기능과 엑추에이터 매칭을 통해 로봇 기능 조합 유형에 대한 분석을 하였다. 도출된 4가지 유형의 로봇 중 표정 기반 대화형 로봇 유형으로 프로토타이핑을 하였으며 에크만의 얼굴 움직임 부호화 시스템(Facial Action Coding System: FACS)을 기반으로 6가지 기본 감정에 대한 표정을 시각화하였다. 사용자 실험에서는 로봇이 전달하는 정보의 정서코드에 맞게 로봇의 표정이 변화할 때와 로봇이 인터랙션 사이클을 자발적으로 시작할 때 사용자의 인지와 정서에 미치는 영향을 이야기 회상 검사(Story Recall Test: STR)와 표정 감정 분석 소프트웨어 Emotion API로 검증하였다. 실험 결과, 정보의 정서코드에 맞는 로봇의 표정 변화 그룹이 회상 검사에서 상대적으로 높은 기억 회상률을 보였다. 한편 피험자의 표정 분석에서는 로봇의 감정 표현과 자발적인 인터랙션 시작이 피험자들에게 정서적으로 긍정적 영향을 주고 선호되는 것을 확인하였다.

• 대한전기학회논문지:전력기술부문A
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• 제54권2호
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• pp.67-72
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• 2005

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this paper, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition equations. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.

• KIEE International Transactions on Power Engineering
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• 제5A권4호
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• pp.344-349
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• 2005

In conventional small signal stability analysis, the system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of the state matrix. However, when a system contains switching elements such as FACTS equipments, it becomes a non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is performed by means of eigenvalue analysis of the system's periodic transition matrix based on the discrete system analysis method. In this paper, the RCF (Resistive Companion Form) method is used to analyze the small signal stability of a non-continuous system including switching elements. Applying the RCF method to the differential and integral equations of the power system, generator, controllers and FACTS equipments including switching devices should be modeled in the form of state transition equations. From this state transition matrix, eigenvalues that are mapped into unit circles can be computed precisely.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2004년도 하계학술대회 논문집 A
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• pp.342-344
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• 2004

In conventional small signal stability analysis, system is assumed to be invariant and the state space equations are used to calculate the eigenvalues of state matrix. However, when a system contains switching elements such as FACTS devices, it becomes non-continuous system. In this case, a mathematically rigorous approach to system small signal stability analysis is by means of eigenvalue analysis of the system periodic transition matrix based on discrete system analysis method. In this research, RCF(Resistive Companion Form) method is used to analyse small signal stability of a non-continuous system including switching elements'. Applying the RCF method to the differential and integral equations of power system, generator, controllers and FACTS devices including switching elements should be modeled in the form of state transition matrix. From this state transition matrix eigenvalues which are mapped to unit circle can be calculated.