• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.309-316
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• 2005

In this paper, we develop continuum-based design sensitivity analysis (DSA) methods using both direct differential method (DDM) and adjoint variable method (AVM) for non-shape design problems. The developed DSA method is further utilized for the topology design optimization of 3-dimensional structures. In numerical examples, the analytical DSA results are verified using finite difference ones. The topology optimization method yields very reasonable results in physical point of view.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.9-18
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• 2015

In this paper, we verify the optimal topology design for heat conduction problems in steady stated which is obtained numerically using the adjoint design sensitivity analysis(DSA) method. In adjoint variable method(AVM), the already factorized system matrix is utilized to obtain the adjoint solution so that its computation cost is trivial for the sensitivity. For the topology optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of the structure and the allowable volume, respectively. For the experimental validation of the optimal topology design, we compare the results with those that have identical volume but designed intuitively using a thermal imaging camera. To manufacture the optimal design, we apply a simple numerical method to convert it into point cloud data and perform CAD modeling using commercial reverse engineering software. Based on the CAD model, we manufacture the optimal topology design by CNC.

• Bulletin of the Korean Mathematical Society
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• v.51 no.2
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• pp.357-371
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• 2014

We shall show that the Riesz idempotent $E_{\lambda}$ of every *-paranormal operator T on a complex Hilbert space H with respect to each isolated point ${\lambda}$ of its spectrum ${\sigma}(T)$ is self-adjoint and satisfies $E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*$. Moreover, Weyl's theorem holds for *-paranormal operators and more general for operators T satisfying the norm condition $||Tx||^n{\leq}||T^nx||\,||x||^{n-1}$ for all $x{\in}\mathcal{H}$. Finally, for this more general class of operators we find a sufficient condition such that $E_{\lambda}\mathcal{H}=ker(T-{\lambda})= ker(T-{\lambda})^*$ holds.

• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.313-324
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• 1995

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.885-892
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• 2015

In this paper, we mainly obtain the following assertions: (1) If T is a quasi-*-n-paranormal operator, then T is finite and simply polaroid. (2) If T or $T^*$ is a quasi-*-n-paranormal operator, then Weyl's theorem holds for f(T), where f is an analytic function on ${\sigma}(T)$ and is not constant on each connected component of the open set U containing ${\sigma}(T)$. (3) If E is the Riesz idempotent for a nonzero isolated point ${\lambda}$ of the spectrum of a quasi-*-n-paranormal operator, then E is self-adjoint and $EH=N(T-{\lambda})=N(T-{\lambda})^*$.

• Journal of the Optical Society of Korea
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• v.13 no.2
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• pp.286-293
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• 2009

In this paper, we present an optimal shape design method for a dielectric microlens which is used to focus an incoming infrared plane wave in wideband, by exploiting the finite difference time domain (FDTD) technique and the topology optimization technique. Topology optimization is a scheme to search an optimal shape by adjusting the material properties, which are design variables, within the design space. And by introducing the adjoint variable method, we can effectively calculate a derivative of the objective function with respect to the design variable. To verify the proposed method, a shape design problem of a dielectric microlens is tested when illuminated by a transverse electric (TE)-polarized infrared plane wave. In this problem, the design variable is the dielectric constant within the design space of a dielectric microlens. The design objective is to maximally focus the incoming magnetic field at a specific point in wideband.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-984
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• 2011

This paper discusses the hypercyclicity of weighted composition operators acting on the space of holomorphic functions on the open unit ball $B_N$ of $\mathbb{C}^N$. Several analytic properties of linear fractional self-maps of $B_N$ are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Journal of the korean Society of Automotive Engineers
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• v.15 no.1
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• pp.81-88
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• 1993

A direct treatment of the min-max type objective function of the dynamic response optimization problem is proposed. Previously, the min-max type objective function was transformed to an artificial design variable and an additional point-wise state variable constraint function was imposed, which increased the complexity of the optimization problem. Especially, the design sensitivity analysis for the augmented Lagrangian functional with the suggested treatment is established by using the adjoint variable method and a computer program to implement the proposed algorithm is developed. The optimization result of the proposed treatment are obtained for three typical problems and compared with those of the previous treatment. It is concluded that the suggested treatment in much more efficient in the computational effort than the previous treatment with giving the similar optimal solutions.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.661-676
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• 2017

Let T be a bounded linear operator acting on a complex Hilbert space ${\mathfrak{H}}$. In this paper we introduce the class, denoted ${\mathcal{Q}}(A(k),m)$, of operators satisfying $T^{m{\ast}}(T^{\ast}{\mid}T{\mid}^{2k}T)^{1/(k+1)}T^m{\geq}T^{{\ast}m}{\mid}T{\mid}^2T^m$, where m is a positive integer and k is a positive real number and we prove basic structural properties of these operators. Using these results, we prove that if P is the Riesz idempotent for isolated point ${\lambda}$ of the spectrum of $T{\in}{\mathcal{Q}}(A(k),m)$, then P is self-adjoint, and we give a necessary and sufficient condition for $T{\otimes}S$ to be in ${\mathcal{Q}}(A(k),m)$ when T and S are both non-zero operators. Moreover, we characterize the quasinilpotent part $H_0(T-{\lambda})$ of class A(k) operator.