• Journal of Applied Reliability
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• v.12 no.3
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• pp.215-224
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• 2012

This paper deals with a design of fault tolerant state feedback controllers for continuous time nonlinear time delay systems with actuator failures. The goal is to find an asymptotically stabilizing controller such that the closed loop system achieves the prescribed $H_{\infty}$ performance objective in the actuator fault cases. Based on a sum of squares (SOS) approach, a design method for $H_{\infty}$ fault tolerant controller is presented. In order to demonstrate our design method, a numerical example is provided.

• Honam Mathematical Journal
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• v.38 no.1
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• pp.47-57
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• 2016

In the discrete formulation of the bubble stabilized Legendre Galerkin methods, the system of equations includes the artificial viscosity term as the parameter. We investigate the estimation of this parameter to get the least-squares solution which minimizes the sum of the squares of errors at each node points. Some numerical results are reported.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.55-68
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• 2007

First-order least-squares method of a distributed optimal control problem for the incompressible Navier-Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing velocity-flux variables and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $L^2$ norm of the residual equations of the system. The optimal error estimates for least-squares finite element approximations are obtained.

• Journal of the Korean Mathematical Society
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• v.46 no.5
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• pp.1007-1025
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• 2009

First-order least-squares method of a distributed optimal control problem for the incompressible Stokes equations is considered. An optimality system for the optimal solution are reformulated to the equivalent first-order system by introducing the vorticity and then the least-squares functional corresponding to the system is defined in terms of the sum of the squared $H^{-1}$ and $L^2$ norms of the residual equations of the system. Finite element approximations are studied and optimal error estimates are obtained. Resulting linear system of the optimality system is symmetric and positive definite. The V-cycle multigrid method is applied to the system to test computational efficiency.

• Journal of the Korean Statistical Society
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• v.8 no.1
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• pp.23-36
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• 1979

In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

• The Pure and Applied Mathematics
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• v.11 no.2
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• pp.103-115
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• 2004

A computational algorithm is developed for fitting given data in the plane or in 3-space by implicitly defined quadrics. Implicity implies that the type of the quadric is part of the model and need not be known in advance. Starting with some estimate for the coefficients of the quadric the method will alternatively determine the shortest distances from the given points onto the quadric and adapt the coefficients such as to reduce the sum of those squared distances. Numerical examples are given.

• Korea journal of population studies
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• v.28 no.2
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• pp.131-164
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• 2005

The central focus of this research paper is to explore the recent structural core empirical unemployment reason of IT new professional manpower who graduated in higher education level in Korea. The final goal of this issue is to estimate and analyze rambling impediment in IT manpower labor market between 26 detail occupations and between detail occupations and 3 educational levels of new graduates and entrants who entered in IT 6 occupational groups composing 26 particular occupations. This study uses the 2004 data published by the Ministry of ICT and relies upon both one-way analysis of variance and two-way analysis variance to tackle the issue. According to the ANOVA results, 2 main points were delineated In the one-way analysis of variance method. the total sum of squares (SST) is decomposed into two major components: within sum of squares (SSW) (6 detail occupations, 85%) and between sum of squares (SSG) (26 detail occupation, 15%) The other major finding is that total sum of squares (SST) is decomposed into three major components: between detail occupations (SSG) (19.3%), between educations (SSB) and errors (SSE) (56%) in IT SIW development design group.

• Journal for History of Mathematics
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• v.29 no.4
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• pp.219-232
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• 2016

In this paper, the problem posed in Yeonhwando is presumed like the following: "Make the sum of eight numbers in each 13 octagons to be 292, and the sum of four numbers in each 12 squares to be 146 using every numbers once from 1 to 72." Regarding this problem, in this paper, firstly, it is commented that there can be a lot of derived solutions from the Yang Hui's solution. Secondly, the Yang Hui's solution is generalized by using sequence 1 in which the sum of neighbouring two numbers are 73, 73-x by turns, and sequence 2 in which the sum of neighbouring two numbers are 73, 73+x by turns. Thirdly, the Yang Hui's solution is generalized by using the alternating method.

• Investigative Magnetic Resonance Imaging
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• v.9 no.1
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• pp.36-42
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• 2005

Purpose : To develop a novel approach to calculate the sensitivity profiles of the phased array coil for use in non-uniform intensity correction. Materials and Methods : The proposed intensity correction method estimates the sensitivity profile of the coil to extract intensity variations that represent the scanned image. The sensitivity profile is estimated by fitting a non-linear curve to various angles of projections through the imaged object in order to eliminate the high-frequency image content. Filtered back projection is then used to compute the estimates of the sensitivity profile of each coil. The method was applied both to phantom and brain images from 8-channel phased-array coil and 4-channel phased-array coil, respectively. Results : Intensity-corrected images from the proposed method have more uniform intensity than those from the commonly used 'sum-of-squares' approach. By using the proposed correction method, the intensity variation was reduced to $6.1\%$ from $13.1\%$, acquired from the 'sum-of-squares'. Conclusion : The proposed method is more effective at correcting the intensity non-uniformity of the phased-array surface-coil images than the conventional 'sum-of-squares' method.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.37-49
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• 2004

We are interested in the problem of fitting a sphere to a set of data points in the three dimensional Euclidean space. In Spath [6] a descent algorithm already have been given to find the sphere of best fit in least squares sense of minimizing the orthogonal distances to the given data points. In this paper we present another new algorithm which computes a parametric represented sphere in order to minimize the sum of the squares of the distances to the given points. For any choice of initial approximations our algorithm has the advantage of ensuring convergence to a local minimum. Numerical examples are given.