• Communications of the Korean Mathematical Society
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• v.19 no.4
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• pp.691-700
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• 2004

Let X and Y be operators acting on a Hilbert space and let (equation omitted) be a subspace lattice of orthogonal projections on the space containing 0 and I. We investigate normal interpolation problems in Alg(equation omitted): Given operators X and Y acting on a Hilbert space, when does there exist a normal operator A in Alg(equation omitted) such that AX = Y?

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.545-558
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• 2013

In this paper, the formulas for calculating the extremal ranks and inertias of the Hermitian least squares solutions to matrix equation AX = B are established. In particular, the necessary and sufficient conditions for the existences of the positive and nonnegative definite solutions to this matrix equation are given. Meanwhile, the least squares problem of the above matrix equation with Hermitian R-symmetric and R-skew symmetric constraints are also investigated.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.111-128
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• 2001

In this paper, we consider the oscillation of the second-order neutral difference equation Δ²(x/sub n/ - px/sub n-r/) + q/sub n/f(x/sub n/ - σ/sub n/) = 0 as well as the oscillatory behavior of the corresponding ordinary difference equation Δ²z/sub n/ + q/sub n/f(R(n,λ)z/sub n/) = 0

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.329-337
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• 2005

This paper is to establish a functional equation satisfied by the generating function for counting rooted cubic c-nets and then to determine the parametric expressions of the equation directly. Meanwhile, the explicit formulae for counting rooted cubic c-nets are derived immediately by employing Lagrangian inversion with one or two parameters. Both of them are summation-free and in which one is just an answer to the open problem (8.6.5) in [1].

• Journal of KSNVE
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• v.7 no.6
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• pp.975-984
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• 1997

A direct boundary element method (DBEM) is developed for thin bodies whose surfaces are rigid or compliant. The Helmholtz integral equation and its normal derivative integral equation are adoped simultaneously to calculate the pressure on both sides of the thin body, instead of the jump values across it, to account for the different surface conditions of each side. Unlike the usual assumption, the normal velocity is assumed to be discontinuous across the thin body. In this approach, only the neutral surface of the thin body has to be discretized. The method is validated by comparison with analytic and/or numerical results for acoustic scattering and radiation from several surface conditions of the thin body; the surfaces are rigid when stationary or vibrating, and part of the interior surface is lined with a sound-absoring material.

• The Pure and Applied Mathematics
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• v.11 no.1
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• pp.15-22
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• 2004

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.173-182
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• 2015

In this paper, the blow-up rate of $L^2$-norm for the semi-linear wave equation with a power nonlinearity is obtained in the bounded domain for any p > 1. We also get the blow-up rate of the derivative under the condition 1 < p < $1+\frac{4}{N-1}$ for $N{\geq}2$ or 1 < p < 5 for N = 1.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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• pp.1291-1302
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• 2011

We establish the local well-posedness for the Cauchy problem of the nonlinear Schr$\ddot{o}$odinger equation with harmonic potential in $H^s(\mathbb{R}^n)$, where $s{\in}\mathbb{R}$, s > 0.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.175-186
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• 2018

Let (M, J, ${\theta}$) be a complete pseudohermintian (2n+1)-manifold. In this paper, we derive the subgradient estimate for positive solutions to a nonlinear subelliptic equation ${\Delta}_bu+au{\log}u+bu=0$ on M, where $a{\leq}0$, b are two real constants.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.23-40
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• 1998

Mixed finite element method is developed to approxi-mate the solution of the initial-boundary value problem for a strongly nonlinear second-order hyperbolic equation in divergence form. Exis-tence and uniqueness of the approximation are proved and optimal-order $L\infty$-in-time $L^2$-in-space a priori error estimates are derived for both the scalar and vector functions approximated by the method.