• 대한수학회지
• /
• 제59권6호
• /
• pp.1171-1184
• /
• 2022

We study the real-analytic continuation of local real-analytic solutions to the Cauchy problems of quasi-linear partial differential equations of first order for a scalar function. By making use of the first integrals of the characteristic vector field and the implicit function theorem we determine the maximal domain of the analytic extension of a local solution as a single-valued function. We present some examples including the scalar conservation laws that admit global first integrals so that our method is applicable.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제15권1호
• /
• pp.57-72
• /
• 2008

This paper is concerned with the numerical solutions to steady state nonlinear elliptical partial differential equations (PDE) of the form $u_{xx}+u_{yy}+Du_{x}+Eu_{y}+Fu=G$, where D, E, F are functions of x, y, u, $u_{x}$, and $u_{y}$, and G is a function of x and y. Dirichlet boundary conditions in a rectangular region are considered. We propose alternating direction shooting method for solving such nonlinear PDE. Numerical results show that the alternating direction shooting method performed better than the commonly used linearized iterative method.

• 대한수학회지
• /
• 제32권3호
• /
• pp.541-551
• /
• 1995

The nonlinear Klein Gordon equation $$ (1) \frac{\partial t^2}{\partial^2 u} - \Delta u + V_u(u) = f $$ where $\Delta$ is the Laplacian operator in $R^d (d = 1, 2, 3), V_u(u)$ is the derivative of the "potential function" V, and f is a source term independent of the solution u, in various areas of mathematical physics.l physics.

• 대한산업공학회지
• /
• 제20권3호
• /
• pp.105-116
• /
• 1994

This paper presents an inventory model with partial backorders for the situation in which demand is deterministic, lead time follows normal distribution and back order ratio during the stockout period varies in proportion to the length of backorder period In this situations, an objective function is formulated to minimize a time-proportional backorder cast and a fixed penalty cost per unit lost. And then the procedure of iterative solution method for the model is developed to find optimal reorder paint and order quantity and a numerical example to illustrate the proposed method is presented.

• Communications for Statistical Applications and Methods
• /
• 제9권3호
• /
• pp.753-763
• /
• 2002

When there is one change-point in the hazard rate model, a change-point estimator with the partial score process is suggested and compared with the previously developed estimators. The limiting distribution of the partial score process we used is a function of the Brownian bridge. Simulation study gives the comparison of change-point estimators.

• 대한수학회논문집
• /
• 제11권4호
• /
• pp.1105-1116
• /
• 1996

A partial ordering is developed among weakly positive quadrant dependent (WPQD) bivariate random vectors. This permits us to measure the degree of WPQD-ness and to compare pairs of WPQD random vectors. Some properties and closures under certain statistical operations are derived. An application is made to measures of dependence such as Kendall's $\tau$ and Spearman's $\rho$.

• 응용통계연구
• /
• 제22권1호
• /
• pp.189-195
• /
• 2009

A dynamic graphical procedure is suggested to estimate optimal response transformation parameter and a curvature function of covariates in the regression model. Augmented partial residual plot is chosen for specifying a curvature. The proposed method is compared with a different approach (Soo, 2007) and is investigated efficiency by applying it to the real and the artificial data. The method is also extended to the 3D graphical situations.

• 대한수학회논문집
• /
• 제22권1호
• /
• pp.111-119
• /
• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• 대한수학회보
• /
• 제50권5호
• /
• pp.1587-1598
• /
• 2013

In this paper, we obtain some gradient estimates for positive solutions to the following nonlinear parabolic equation $$\frac{{\partial}u}{{\partial}t}={\triangle}u-b(x,t)u^{\sigma}$$ under general geometric flow on complete noncompact manifolds, where 0 < ${\sigma}$ < 1 is a real constant and $b(x,t)$ is a function which is $C^2$ in the $x$-variable and $C^1$ in the$t$-variable. As an application, we get an interesting Harnack inequality.

• Journal of the Korean Data and Information Science Society
• /
• 제18권4호
• /
• pp.1145-1155
• /
• 2007

In this paper, we consider the permutation tests for the multivariate data under the two-sample problem setting. We review some testing procedures, which are parametric and nonparametric and compare them with the permutation ones. Then we consider to try to apply the permutation tests to the multivariate data having the continuous and discrete components together by choosing some suitable combining function through the partial testing. Finally we discuss more aspects for the permutation tests as concluding remarks.