• Title, Summary, Keyword: represented matrix

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THE UNITS AND INEMPOTENTS IN THE GROUP RING OF A FINITE CYCLIC GROUP

  • Park, Won-Sun
    • Communications of the Korean Mathematical Society
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    • v.12 no.4
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    • pp.855-864
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    • 1997
  • Let K be a algebraically closed field of characteristic 0 and G a cyclic group of order n. We find the units and idempotent elements of the group ring KG by using the basic group table matrix of G.

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On the Aeroelastic Characterisrics for the Flight Vehicle of Wing-Body Combination (익동체(翼胴體)의 공력탄성학적특성(空力彈性學的特性)에 관한 연구(硏究))

  • Hae-Kyong,Lee
    • Bulletin of the Society of Naval Architects of Korea
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    • v.10 no.1
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    • pp.27-32
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    • 1973
  • This paper shows the method for obtaining the body flutter velocity and frequency for flight body which consists of low aspect ratio wing and body combination by assuming slender body of cylinderical shell structure. The stiffness matrix of the cylinderical shell is represented from Donnel eq. by the finite difference method, and also unsteady aerodynamic influence matrix is represented by the Doublet Lattice Method of Albano & Rodden. The flutter matrix can be obtained from those matrices.

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THE UNITS AND IDEMPOTENTS IN THE GROUP RING K($Z_m$ $\times$ $Z_n$)

  • Park, Won-Sun
    • Communications of the Korean Mathematical Society
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    • v.15 no.4
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    • pp.597-603
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    • 2000
  • Let K be an algebraically closed filed of characteristic 0 and let G = Z(sub)m x Z(sub)n. We find the conditions under which the elements of the group ring KG are units and idempotents respectively by using the represented matrix. We can see that if $\alpha$ = ∑r(g)g $\in$ KG is an idempotent then r(1) = 0, 1/mn, 2/mn, …, (mn-1)/mn or 1.

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An Efficient Computing Method of the Orthogonal Projection Matrix for the Balanced Factorial Design

  • Kim, Byung-Chun;Park, Jong-Tae
    • Journal of the Korean Statistical Society
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    • v.22 no.2
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    • pp.249-258
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    • 1993
  • It is well known that design matrix X for any factorial design can be represented by a product $X = TX_o$ where T is replication matrix and $X_o$ is the corresponding balanced design matrix. Since $X_o$ consists of regular arrangement of 0's and 1's, we can easily find the spectral decomposition of $X_o',X_o$. Also using this we propose an efficient algorithm for computing the orthogonal projection matrix for a balanced factorial design.

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A Study on Development of an Algorithm for Vertex Creation to Define Ship Hull Forms (선체형상 정의를 위한 버텍스 산출 알고리즘 개발에 관한 연구)

  • Hyun-Kyoung Shin;Sang-Sung Shin;Kyu-Won Park
    • Journal of the Society of Naval Architects of Korea
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    • v.31 no.3
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    • pp.31-37
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    • 1994
  • When a lot of input data are not distributed uniformly n a chord-span direction or when the given shape is complicated, it is very difficult to obtain an inverse matrix which represents the smooth Bi-cubic B-spline surface of the initial shape. To overcome this problem, we suggest image Surface Expansion Method(ISE Method) which is suggested for vertex creation of B-spline curves and surfaces. Its basic concept, convergency and verification are shown. Also B-spline curves and Surfaces represented by ISE Method were compared with those represented by the existing method which is based on the inverse matrix method, the pseudoinverse matrix method and the chord length approximation method for vertex yielding. Ship Hull Forms which have Knuckle, Bulbous Bow, Transom and Stern frame were represented by the ISE Method.

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Matrix Game with Z-numbers

  • Bandyopadhyay, Sibasis;Raha, Swapan;Nayak, Prasun Kumar
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.15 no.1
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    • pp.60-71
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    • 2015
  • In this paper, a matrix game is considered in which the elements are represented as Z-numbers. The objective is to formalize the human capability for solving decision-making problems in uncertain situations. A ranking method of Z-numbers is proposed and used to define pure and mixed strategies. These strategies are then applied to find the optimal solution to the game problem with an induced pay off matrix using a min max, max min algorithm and the multi-section technique. Numerical examples are given in support of the proposed method.

Vector algorithm for layered reinforced concrete shell element stiffness matrix

  • Min, Chang Shik;Gupta, Ajaya Kumar
    • Structural Engineering and Mechanics
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    • v.3 no.2
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    • pp.173-183
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    • 1995
  • A new vector algorithm is presented for computing the stiffness matrices of layered reinforced concrete shell elements. Each element stiffness matrix is represented in terms of three vector arrays of lengths 78, 96 and 36, respectively. One element stiffness matrix is calculated at a time without interruption in the vector calculations for the uncracked or cracked elements. It is shown that the present algorithm is 1.1 to 7.3 times more efficient then a previous algorithm developed by us on a Cray Y-MP supercomputer.

The New Integral Operational Matrix of Block Pulse Function using Interpolation Method (보간법을 이용한 블록펄스 함수에 대한 새로운 적분 연산행렬의 유도)

  • Jo, Yeong-Ho;Sin, Seung-Gwon;Lee, Han-Seok;An, Du-Su
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.48 no.6
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    • pp.753-759
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    • 1999
  • BPF(block pulse function) has been used widely in the system analysis and controller design. The integral operational matrix of BPF converts the system represented in the form of the differential equation into the algebraic problem. Therefore, it is important to reduce the error caused by the integral operational matrix. In this paper, a new integral operational matrix is derived from the approximating function using Lagrange's interpolation formula. Comparing the proposed integral operational matrix with another, the result by proposed matrix is closer to the real value than that by the conventional matrix. The usefulness of th proposed method is also verified by numerical examples.

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