• 대한전기학회논문지
• /
• 제40권3호
• /
• pp.299-307
• /
• 1991

This paper deals with the determination of a firing sequence of transitions in the reachability problem of Safe Petri Net. The determination problem of a firing sequence is very important from the point of practical view, especially in the control of the discrete systems modelled by Safe Petri Net. The determination method of a firing sequence of transitions by means of the matrix equation for the discrete systems modelled by Safe Petri Net is proposed. First, a construction method of the indicence matrix and the firing rule for Safe Petri Net with self-loop are presented by defining the permissive arc in place of self-loop. Next, we develop a method that can find the enable transitions of Safe Petri Net by means of the matrix equation of Safe Petri Net. Finally, by using this method, we propose an algorithm that determines the firing sequence of transitions of Safe Petri Net.

• 한국자동차공학회논문집
• /
• 제5권1호
• /
• pp.154-161
• /
• 1997

This paper presents the method to eliminate the constraint reaction in the Lagrange multiplier form equation of motion by using a generalized coordinate driveder from the velocity constraint equation. This method introduces a matrix method by considering the m dimensional space spanned by the rows of the constraint jacobian matrix. The orthogonal vectors defining the constraint manifold are projected to null vectors by the tangential vectors defined on the constraint manifold. Therefore the orthogonal projection matrix is defined by the tangential vectors. For correcting the generalized position coordinate, the optimization problem is formulated. And this correction process is analyzed by the quasi Newton method. Finally this method is verified through 3 dimensional vehicle model.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제1권1호
• /
• pp.75-82
• /
• 1997

An algorithm for computing the cubic spline interpolation coefficients for polynomials is presented in this paper. The matrix equation involved is solved analytically so that numerical inversion of the coefficient matrix is not required. For $f(t)=t^m$, a set of constants along with the degree of polynomial m are used to compute the coefficients so that they satisfy the interpolation constraints but not necessarily the derivative constraints. Then, another matrix equation is solved analytically to take care of the derivative constraints. The results are combined linearly to obtain the unique solution of the original matrix equation. This algorithm is tested and verified numerically for various examples.

• 전기의세계
• /
• 제20권5호
• /
• pp.19-22
• /
• 1971

This paper deals with the state-variable analysis of the arbitrary RLC lumped linear time-invariant networks. A formulation technique for determining a set of state equation using Bryant-Bashkow A Matrix and by means of the procedure setting up the terminal equation is discussed.

• 대한수학회보
• /
• 제41권2호
• /
• pp.199-211
• /
• 2004

For positive integers $\kappa$ and p$\geq$3, let(equation omitted) where $J_{p}$ is the p${\times}$p matrix whose entries are all 1. Then, we determine the minimum permanents and minimizing matrices over (1) the face of $\Omega$(D) and (2) the face of $\Omega$($D^{*}$), where (equation omitted).

• International Journal of Control, Automation, and Systems
• /
• 제1권4호
• /
• pp.459-463
• /
• 2003

In this paper, new results using bounds for the solution of the discrete Lyapunov matrix equation are proposed, and some of the existing works are generalized. The bounds obtained are advantageous in that they provide nontrivial upper bounds even when some existing results yield trivial ones.

• Journal of the Korean Data and Information Science Society
• /
• 제17권1호
• /
• pp.161-171
• /
• 2006

In this paper, we consider the random number generation method for multivariate Poisson distribution with specific covariance matrix. Random number generating method for the multivariate Poisson distribution is considered into two part, by first solving the linear equation to determine the univariate Poisson parameter, then convoluting independent univariate Poisson variates with appropriate expectations. We propose a numerical algorithm to solve the linear equation given the specific covariance matrix.

• 한국공간구조학회논문집
• /
• 제2권1호
• /
• pp.75-84
• /
• 2002

In this study, the 'force density method' for shape finding of cable net structures is presented. This concept is based on the force-length ratios or force densities which are defined for each branch of the net structures. This method renders a simple linear 'analytical form finding' possible. If the free choice of the force densities is restricted by further condition, the linear method is extended to a nonlinear one. The nonlinear one can be applied to the detailed computation of networks. In this paper, the general inverse matrix is introduced to solve the nonlinear equilibrium equation including Jacobian matrix which is rectangular matrix. Several examples for linear and nonlinear analysis applied additional constraints are presented. It is shown that the force density method is suitable for form finding of cable net and the general inverse matrix can be applied to solve the nonlinear equation without Lagrangian factors.

• Bulletin of the Korean Chemical Society
• /
• 제12권6호
• /
• pp.692-698
• /
• 1991

The reaction path Smoluchowski equation approach developed in a recent work to calculate the rate constant for a diffusive multidimensional barrier crossing process is extended to incorporate the configuration-dependent diffusion matrix. The resulting formalism is then applied to the investigation of stilbene photoisomerization dynamics. Adapting a model two-dimensional potential and a model diffusion matrix proposed by Agmon and Kosloff [J. Phys. Chem.,91 (1987) 1988], we derive an eigenvalue equlation for the relaxation rate constant of the stilbene photoisomerization. This eigenvalue equation is solved numerically by using the finite element method. The advantages and limitations of the present method are discussed.

• 호남수학학술지
• /
• 제30권2호
• /
• pp.399-409
• /
• 2008

We consider the most generalized quadratic matrix equation, Q(X) = $A_7XA_6XA_5+A_4XA_3+A_2XA_1+A_0=0$, where X is m ${\times}$ n, $A_7$, $A_4$ and $A_2$ are p ${\times}$ m, $A_6$ is n ${\times}$ m, $A_5$, $A_3$ and $A_l$ are n ${\times}$ q and $A_0$ is p ${\times}$ q matrices with complex elements. The convergence of Newton's method for solving some different types of quadratic matrix equations are considered and we show that the elementwise minimal positive solvents can be found by Newton's method with the zero starting matrices. We finally give numerical results.