• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.961-965
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• 2010

A reduced order observer with finite time convergence characteristics is proposed for linear time invariant systems. The proposed finite time reduced order observer(FTROO) is a dual observer scheme in which two reduced order Luenberger observers with asymptotic convergence characteristics and a finite time delay element are employed. The FTROO can be constructed so as to converge in the designer specified finite time independent of the eigenvalues of the reduced order observers. A numerical example is given to show the finite-time convergence characteristics of the proposed FTROO.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.385-398
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• 1997

High order finite element have a greater convergence rate than low order finite elements, and in general produce more accurate results. These elements have the disadvantage of being more computationally expensive and often require a longer time to solve the finite element analysis. High order elements have been used in this paper to obtain a new eigenvalue solution with out re-solving the new model. The optimisation of the eigenvalue via the differentiation of the Rayleigh quotient has shown that the additional nodes associated with the higher order elements can be condensed out and solved using the original finite element solution. The higher order elements can then be used to calculate an improved eigenvalue for the finite element analysis.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.735-749
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• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

• Structural Engineering and Mechanics
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• v.6 no.7
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• pp.727-746
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• 1998

Finite element models and numerical results are presented for bending and natural vibration using the unified third-order plate theory developed in Part 1 of this paper. The unified third-order theory contains the classical, first-order, and other third-order plate theories as special cases. Analytical solutions are developed using the Navier and L$\acute{e}$vy solution procedures (see Part 1 of the paper). Displacement finite element models of the unified third-order theory are developed herein. The finite element models are based on $C^0$ interpolation of the inplane displacements and rotation functions and $C^1$ interpolation of the transverse deflection. Numerical results of bending and natural vibration are presented to evaluate the accuracy of various plate theories.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1127-1144
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• 2013

In this paper, we consider the error estimates of the numerical solutions of a class of fourth order linear-quadratic elliptic optimal control problems by using mixed finite element methods. The state and co-state are approximated by the order $k$ Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise polynomials of order $k(k{\geq}1)$. $L^2$ and $L^{\infty}$-error estimates are derived for both the control and the state approximations. These results are seemed to be new in the literature of the mixed finite element methods for fourth order elliptic control problems.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.816-826
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• 2017

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.23-28
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• 2013

The structures of finite local rings of order ${\leq}$ 16 with nonzero Jacobson radical are investigated. The whole shape of non-commutative local rings of minimal order is completely determined up to isomorphism.

• East Asian mathematical journal
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• v.34 no.5
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• pp.601-614
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• 2018

In this paper, we introduce an extrapolated higher order characteristic finite element method to approximate solutions of nonlinear Sobolev equations with a convection term and we establish the higher order of convergence in the temporal and the spatial directions with respect to $L^2$ norm.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.889-897
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• 2001

Based on the prime graph of a finite simple group, its order is the product of its order components (see[4]). It is known that Suzuki-Ree groups [6], $PSL_2(q)$ [8] and $E_8(q)$ [7] are uniquely deternubed by their order components. In this paper we prove that the simple groups $A_p$ are also unipuely determined by their order components, where p and p-2 are primes.

• Journal of the korean Society of Automotive Engineers
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• v.3 no.3
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• pp.24-29
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• 1981

This paper is studied an efficient temperature distribution and heat transfer of two-dimensional rectangular cross-section by the higher-order triangular finite dynamic element and finite difference. This is achieved by employing a discretization technique based on a recently developed concept of finite dynamic elements, involving higher order dynamic correction terms in the associated stiffness and convection matrices. Numerical solution results of temperature distribution presented herein clearly optimum element and show that FEM10 is the most accurate temperature distribution, but heat transfer and computational effort is the most acquired.