• Communications of the Korean Mathematical Society
• /
• v.9 no.3
• /
• pp.753-765
• /
• 1994

The linearly constrained quadratic programming(QP) considered is : $$ min f(x) = c^T x + \frac{1}{2}x^T Hx $$ $$ (1) subject to A^T x \geq b,$$ where $c,x \in R^n, b \in R^m, H \in R^{n \times n)}$, symmetric, and $A \in R^{n \times n}$. If there are bounds on x, these are included in the matrix $A^T$. The Hessian matrix H may be positive definite or negative semi-difinite. For large problems H and the constraint matrix A are assumed to be sparse.

• Journal of the Korean Mathematical Society
• /
• v.47 no.1
• /
• pp.83-100
• /
• 2010

In this article, an optimal control problem associated with convection-diffusion equation is considered. Using Lagrange multiplier, the optimality system is obtained. The derived optimal system becomes coupled, non-symmetric partial differential equations. For discretizations and implementations, the finite element multigrid V-cycle is employed. The convergence analysis of finite element multigrid methods for the derived optimal system is shown. Some numerical simulations are performed.

• Communications for Statistical Applications and Methods
• /
• v.9 no.1
• /
• pp.101-113
• /
• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.325-335
• /
• 2002

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the center of symmetric and continuous underlying distributions. This selector statistics is based on the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying distributions. In this paper, we use the functions of sample quantiles as selector statistics and determine the suitable quantile points based on maximizing the distance index to discriminate distributions under consideration. In Monte Carlo study, this robust estimation method works pretty good in wide range of underlying distributions.

• Communications for Statistical Applications and Methods
• /
• v.8 no.1
• /
• pp.65-71
• /
• 2001

In this paper, optimal block designs for complete diallel crosses are proposed. These optimal block designs are constructed by using triangular partially balanced incomplete designs derived from symmetric balanced incomplete block designs. Also, it is shown that block designs for complete dialle crosses derived from complementary designs of triangular designs are optimal block designs.

• Communications for Statistical Applications and Methods
• /
• v.10 no.1
• /
• pp.145-151
• /
• 2003

We shall propose several estimators for the scale parameter in the uniform distribution when the parameter is functions of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically relative efficiencies for proposed estimators of the scale parameter in the small sample sizes.

• Proceedings of the KIEE Conference
• /
• 2000.07c
• /
• pp.1987-1989
• /
• 2000

In this paper, electric field distribution of dielectric sphere considering surface or volume resistivity is analysed by the use of rotational symmetric charge simulation method. We applied three methods such as ${\alpha},{\beta}$ modified $\beta$ method to check electric field calculation error. We find f method and modified $\beta$ method are suitable to simulate volume and surface resistivity respectively.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.491-499
• /
• 2019

The problem of finding fast computing methods for Bernoulli numbers has a long and interesting history. In this paper, the author provides new proofs for two lacunary recurrence relations with gaps of length four and eight for the Bernoulli numbers. These proofs invoked the fact that the nth powers of ${\pi}^2$, ${\pi}^4$ and ${\pi}^8$ can be expressed in terms of the nth elementary symmetric functions.

• The Mathematical Education
• /
• v.56 no.3
• /
• pp.235-255
• /
• 2017

This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach. Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures. This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.2 no.1
• /
• pp.38-50
• /
• 1994

To improve the efficiency of internal combustion engines, it is necessary to understand mixed air-fuel in-cylinder flow processes accurately at intake and compression strokes. There is experimental and numerical methods to analyse in-cylinder flow process. In numerical method, standard $k-{\varepsilon}$ model with wall function was mostly adopted in in-cylinder flow process. But this type model was not efficiently predicted in the near wall region. Therefore in the present study, low Reynolds number $k-{\varepsilon}$ model was adopted near the cylinder wall and standard $k-{\varepsilon}$ model in other region. Also QUICK scheme was used for convective difference scheme. This study takes axisymmetric reciprocating model engine motored at 200rpm with a centrally located valve, incorporated 60 degree seat angie, and flat piston surface excluding inlet port. Because in-cylinder flow processes are undergoing unsteady and compressible, averaged cylinder pressure and inlet velocity at arbitrary crank angle are determined from thermodynamic analytic method and incylinder states at that crank angle are iteratively determined from the numerical analytic method.