• Proceedings of the Earthquake Engineering Society of Korea Conference
• /
• 2003.03a
• /
• pp.85-92
• /
• 2003

Hysteretic behaviors of a seismic isolator are identified by using the regularized output error estimator (OEE) based on the secant stiffness model. A proper regularity condition of tangent stiffness for the current OEE is proposed considering the regularity condition of Duhem hysteretic operator. The proposed regularity condition is defined by 12-norm of the tangent stiffness with respect to time. The secant stiffness model for the OEE is obtained by approximating the tangent stiffness under the proposed regularity condition by the secant stiffness at each time step. A least square method is employed to minimize the difference between the calculated response and measured response for the OEE. The regularity condition of the secant stiffness is utilized to alleviate ill-posedness of the OEE and to yield numerically stable solutions through the regularization technique. An optimal regularization factor determined by geometric mean scheme (GMS) is used to yield appropriate regularization effects on the OEE.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.3
• /
• pp.327-332
• /
• 2007

A variational inequality defined by the second-order cone is considered, and it is shown that a necessary and sufficient condition for a solution of the variational inequality holds under some regularity condition.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.957-975
• /
• 2000

We find a regularity criterion for the Ostwald-de Waele models like Serrin's condition to the Navier-Stokes equations. Moreover, we show short time existence and estimate the Hausdorff dimension of the set of singular times for the weak solutions.

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.735-745
• /
• 1996

This is the sequel to our paper "On projective representations of a group and its subgroups I" [4]. In Section 4[4] we proved some global properties on regularity condition. The purpose of this paper is to study local properties, that is, we shall ask how the regularity condition on subgroups is related to that on group. Throughout the paper we use the same notations as in [4].as in [4].

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.871-884
• /
• 2000

Polyharmonic operator with Dirichlet boundary condition is considered in a n-dimensional cone. The regularity properties of weak solutions are studied. In particular, it is proved the Holder contionuity of solutions near the vertex of the cone for dimensions n=2m+3,2m+4, where 2m is the order of the polyharmonic operator.

• Journal of the Korean Mathematical Society
• /
• v.37 no.4
• /
• pp.565-577
• /
• 2000

We consider regularity questions arising in the degenerate elliptic vector valued variational inequalities -div(｜▽u｜p-2∇u)$\geq$b(x, u, ∇u) with p$\in$(1, $\infty$). It is a generalization of the scalar valued inequalities, i.e., the obstacle problem. We obtain the C1,$\alpha$loc regularity for the solution u under a controllable growth condition of b(x, u, ∇u).

• Journal of applied mathematics & informatics
• /
• v.41 no.6
• /
• pp.1173-1180
• /
• 2023

In this paper, rings in which essential maximal right ideals are GP-injective are studied. Whether the rings with this condition satisfy von Neumann regularity is the goal of this study. The obtained research results are twofold: First, it was shown that this regularity holds even when the reduced ring is replaced with π-IFP and NI-ring. Second, it was shown that this regularity also holds even when the maximal right ideal is changed to GW-ideal. This can be interpreted as an extension of the existing results.

• Journal of the Korean Mathematical Society
• /
• v.50 no.3
• /
• pp.627-639
• /
• 2013

The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder's fixed point theorem. We construct the fundamental solution, establish the H$\ddot{o}$lder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions of the given equation.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.143-159
• /
• 2013

This paper is concerned with the long time behavior for the solution semiflow of the coupled two-compartment Gray-Scott equations with the homogeneous Neumann boundary condition on a bounded domain of space dimension $n{\leq}3$. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the equations possesses a global attractor in $H^k({\Omega})^4$ ($k{\geq}0$) space.

• Bulletin of the Korean Mathematical Society
• /
• v.44 no.1
• /
• pp.151-156
• /
• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.