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  • Title/Summary/Keyword: matrix theory

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Uncertainty reaction force model of ship stern bearing based on random theory and improved transition matrix method

  • Zhang, Sheng dong;Liu, Zheng lin
    • Ocean Systems Engineering
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    • v.6 no.2
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    • pp.191-201
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    • 2016
  • Stern bearing is a key component of marine propulsion plant. Its environment is diverse, working condition changeable, and condition severe, so that stern bearing load is of strong time variability, which directly affects the safety and reliability of the system and the normal navigation of ships. In this paper, three affecting factors of the stern bearing load such as hull deformation, propeller hydrodynamic vertical force and bearing wear are calculated and characterized by random theory. The uncertainty mathematical model of stern bearing load is established to research the relationships between factors and uncertainty load of stern bearing. The validity of calculation mathematical model and results is verified by examples and experiment yet. Therefore, the research on the uncertainty load of stern bearing has important theoretical significance and engineering practical value.

Design of Unknown Input Observer for Linear Time-delay Systems

  • Fu, Yan-Ming;Duan, Guang-Ren;Song, Shen-Min
    • International Journal of Control, Automation, and Systems
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    • v.2 no.4
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    • pp.530-535
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    • 2004
  • This paper deals with the unknown input observer (UIO) design problem for a class of linear time-delay systems. A case in which the observer error can completely be decoupled from an unknown input is treated. Necessary and sufficient conditions for the existences of such observers are present. Based on Lyapunov stability theory, thedesign of the observer with internal delay is formulated in terms of linear matrix inequalities (LMI). The design of the observer without internal delay is turned into a stabilization problem in linear systems. Two design algorithms of UIO are proposed. The effect of the proposed approach is illustrated by two numerical examples.

ON COMPUTATION OF MATRIX LOGARITHM

  • Sherif, Nagwa;Morsy, Ehab
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.105-121
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    • 2009
  • In this paper we will be interested in characterizing and computing matrices XCn×n that satisfy eX = A, that is logarithms of A. The study in this work goes through two lines. The first is concerned with a theoretical study of the solution set, S(A), of eX = A. Along the second line computational approaches are considered to compute the principal logarithm of A, LogA.

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NOTE ON PURE-STRATEGY NASH EQUILIBRIA IN MATRIX GAMES

  • Ma, Weidong
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1251-1254
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    • 2012
  • Pure-strategy Nash Equilibrium (NE) is one of the most important concepts in game theory. Tae-Hwan Yoon and O-Hun Kwon gave a "sufficient condition" for the existence of pure-strategy NEs in matrix games [5]. They also claimed that the condition was necessary for the existence of pure-strategy NEs in undominated matrix games. In this short note, we show that these claims are not true by giving two examples.

Analysis of Graphs Using the Signal Flow Matrix (신호 흐름 행렬에 의한 그래프 해석)

  • 김정덕;이만형
    • 전기의세계
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    • v.22 no.4
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    • pp.25-29
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    • 1973
  • The computation of transmittances between arbitrary input and output nodes is of particular interest in the signal flow graph theory imput. The signal flow matrix [T] can be defined by [X]=-[T][X] where [X] and [Y] are input nose and output node matrices, respectively. In this paper, the followings are discussed; 1) Reduction of nodes by reforming the signal flow matrix., 2) Solution of input-output relationships by means of Gauss-Jordan reduction method, 3) Extension of the above method to the matrix signal flow graph.

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COMPUTATION OF HANKEL MATRICES IN TERMS OF CLASSICAL KERNEL FUNCTIONS IN POTENTIAL THEORY

  • Chung, Young-Bok
    • Journal of the Korean Mathematical Society
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    • v.57 no.4
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    • pp.973-986
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    • 2020
  • In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

GEOMETRIC APPLICATIONS AND KINEMATICS OF UMBRELLA MATRICES

  • Mert Carboga;Yusuf Yayli
    • Korean Journal of Mathematics
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    • v.31 no.3
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    • pp.295-303
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    • 2023
  • This paper introduces a novel method for obtaining umbrella matrices, which are defined as orthogonal matrices with row sums of one, using skew-symmetric matrices and Cayley's Formula. This method is presented for the first time in this paper. We also investigate the kinematic properties and applications of umbrella matrices, demonstrating their usefulness as a tool in geometry and kinematics. Our findings provide new insights into the connections between matrix theory and geometric applications.

Applications of Graph Theory for the Pipe Network Analysis (상수관망해석을 위한 도학의 적용)

  • Park, Jae-Hong;Han, Geon-Yeon
    • Journal of Korea Water Resources Association
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    • v.31 no.4
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    • pp.439-448
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    • 1998
  • There are many methods to calculate steady-state flowrate in a large water distribution system. Linear method which analyzes continuity equations and energy equations simultaneously is most widely used. Though it is theoretically simple, when it is applied to a practical water distribution system, it produces a very sparse coefficient matrix and most of its diagonal elements are to be zero. This sparsity characteristic of coefficient matrix makes it difficult to analyze pipe flow using the linear method. In this study, a graph theory is introduced to water distribution system analysis in order to prevent from producing ill-conditioned coefficient matrix and the technique is developed to produce positive-definite matrix. To test applicability of developed method, this method is applied to 22 pipes and 142 pipes system located nearby Taegu city. The results obtained from these applications show that the method can calculate flowrate effectively without failure in converage. Thus it is expected that the method can analyze steady state flowrate and pressure in pipe network systems efficiently. Keywords : pipe flow analysis, graph theory, linear method.

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An Algorithm for One-to-One Mapping Matrix-star Graph into Transposition Graph (행렬-스타 그래프를 전위 그래프에 일-대-일 사상하는 알고리즘)

  • Kim, Jong-Seok;Lee, Hyeong-Ok
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.18 no.5
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    • pp.1110-1115
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    • 2014
  • The matrix-star and the transposition graphs are considered as star graph variants that have various merits in graph theory such as node symmetry, fault tolerance, recursive scalability, etc. This paper describes an one-to-one mapping algorithm from a matrix-star graph to a transposition graph using adjacent properties in graph theory. The result show that a matrix-star graph MS2,n can be embedded in a transposition graph T2n with dilation n or less and average dilation 2 or less.

Group Average-consensus and Group Formation-consensus for First-order Multi-agent Systems (일차 다개체 시스템의 그룹 평균 상태일치와 그룹 대형 상태일치)

  • Kim, Jae Man;Park, Jin Bae;Choi, Yoon Ho
    • Journal of Institute of Control, Robotics and Systems
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    • v.20 no.12
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    • pp.1225-1230
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    • 2014
  • This paper investigates the group average-consensus and group formation-consensus problems for first-order multi-agent systems. The control protocol for group consensus is designed by considering the positive adjacency elements. Since each intra-group Laplacian matrix cannot be satisfied with the in-degree balance because of the positive adjacency elements between groups, we decompose the Laplacian matrix into an intra-group Laplacian matrix and an inter-group Laplacian matrix. Moreover, average matrices are used in the control protocol to analyze the stability of multi-agent systems with a fixed and undirected communication topology. Using the graph theory and the Lyapunov functional, stability analysis is performed for group average-consensus and group formation-consensus, respectively. Finally, some simulation results are presented to validate the effectiveness of the proposed control protocol for group consensus.