• Journal of the Korean Mathematical Society
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• v.42 no.3
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• pp.529-541
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• 2005

An operator T belonging to the algebra B(H) of bounded linear transformations on a Hilbert H into itself is said to be posinormal if there exists a positive operator $P{\in}B(H)$ such that $TT^*\;=\;T^*PT$. A posinormal operator T is said to be conditionally totally posinormal (resp., totally posinormal), shortened to $T{\in}CTP(resp.,\;T{\in}TP)$, if to each complex number, $\lambda$ there corresponds a positive operator $P_\lambda$ such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P_{\lambda}^{\frac{1}{2}}(T-{\lambda}I)|^{2}$ (resp., if there exists a positive operator P such that $|(T-{\lambda}I)^{\ast}|^{2}\;=\;|P^{\frac{1}{2}}(T-{\lambda}I)|^{2}\;for\;all\;\lambda)$. This paper proves Weyl's theorem type results for TP and CTP operators. If $A\;{\in}\;TP$, if $B^*\;{\in}\;CTP$ is isoloid and if $d_{AB}\;{\in}\;B(B(H))$ denotes either of the elementary operators $\delta_{AB}(X)\;=\;AX\;-\;XB\;and\;\Delta_{AB}(X)\;=\;AXB\;-\;X$, then it is proved that $d_{AB}$ satisfies Weyl's theorem and $d^{\ast}_{AB}\;satisfies\;\alpha-Weyl's$ theorem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.699-704
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• 2004

Empirical mode decomposition(EMD) method has been recently proposed to analyze non-linear and non-stationary data. This method allows the decomposition of one-dimensional signals into intrinsic mode functions(IMFs) and is used to calculate a meaningful multi-component instantaneous frequency. In this paper, it is assumed that each mode of damped vibration signal could be well separated in the form of IMF by EMD. In this case, we can have a new powerful method to calculate natural frequencies and dampings from damped vibration signal which usually has multiple modes. This proposed method has been verified by both simulation and experiment. The result by EMD method which has used only output vibration data is almost identical to the result by FRF method which has used both input and output data, thereby proving usefulness and accuracy of the proposed method.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.11
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• pp.1143-1149
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• 2008

In a nuclear power plant, loose part monitoring and its diagnostic technique is one of the major issues for ensuring the structural integrity of the reactor system. Typically, accelerometers are mounted on the surface of a reactor vessel to localize impact location cavsed by the impact of metallic substances on the reactor system. However, in some cases, the number of the accelerometers is not enough to estimate the impact location precisely. In such a case, one of alternative plan is to utilize another type sensors that can measure the vibration of the reactor structure even though the measuring frequency ranges are different from each others. The AE sensors installed on the reactor structure can be utilized as additional sensors for loose part monitoring. In this paper, we proposed a new method to estimate impact location by using both accelerometer signal and AE signal, simultaneously. The feasibility of the proposed method is verified by an experiment. The experimental results demonstrate that we can enhance the reliability and precision of the loose part monitoring.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.7 no.2
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• pp.83-94
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• 2003

Let K be a nonempty closed convex subset of a real Hilbert space H. Approximation solvability of a system of nonlinear variational inequality (SNVI) problems, based on the convergence of projection methods, is given as follows: find elements $x^*,\;y^*{\in}H$ such that $g(x^*),\;g(y^*){\in}K$ and $$<\;{\rho}T(y^*)+g(x^*)-g(y^*),\;g(x)-g(x^*)\;{\geq}\;0\;{\forall}\;g(x){\in}K\;and\;for\;{\rho}>0$$ $$<\;{\eta}T(x^*)+g(y^*)-g(x^*),\;g(x)-g(y^*)\;{\geq}\;0\;{\forall}g(x){\in}K\;and\;for\;{\eta}>0,$$ where T: $H\;{\rightarrow}\;H$ is a relaxed $g-{\gamma}-r-cocoercive$ and $g-{\mu}-Lipschitz$ continuous nonlinear mapping on H and g: $H{\rightarrow}\;H$ is any mapping on H. In recent years general variational inequalities and their algorithmic have assumed a central role in the theory of variational methods. This two-step system for nonlinear variational inequalities offers a great promise and more new challenges to the existing theory of general variational inequalities in terms of applications to problems arising from other closely related fields, such as complementarity problems, control and optimizations, and mathematical programming.

• Korean Journal of Optics and Photonics
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• v.27 no.6
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• pp.203-211
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• 2016

We have studied the hybrid method for reconstructing apodized chirped fiber Bragg gratings, using both an analytic estimation of grating parameters and an optimization algorithm. The Hilbert transform of the reflection spectrum was utilized to estimate grating parameters, and then the layer-peeling algorithm was used to obtain refined parameter values by the differential-evolution optimization process. Calculations for a fiber Bragg grating with wavelength chirp rate 2 nm/cm were obtained with an accuracy of $6{\times}10^{-5}nm/cm$ for the chirp rate and $3{\times}10^{-9}nm/cm$ for the index modulation, with much improved calculation speed and high reliability.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.19-34
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• 2011

A bounded linear operator T on a complex Banach space X is said to have property (I) provided that T has Bishop's property (${\beta}$) and there exists an integer p > 0 such that for a closed subset F of ${\mathbb{C}}$ ${X_T}(F)={E_T}(F)=\bigcap_{{\lambda}{\in}{\mathbb{C}}{\backslash}F}(T-{\lambda})^PX$ for all closed sets $F{\subseteq}{\mathbb{C}}$, where $X_T$(F) denote the analytic spectral subspace and $E_T$(F) denote the algebraic spectral subspace of T. Easy examples are provided by normal operators and hyponormal operators in Hilbert spaces, and more generally, generalized scalar operators and subscalar operators in Banach spaces. In this paper, we prove that if T has property (I), then the quasi-nilpotent part $H_0$(T) of T is given by $$KerT^P=\{x{\in}X:r_T(x)=0\}={\bigcap_{{\lambda}{\neq}0}(T-{\lambda})^PX$$ for all sufficiently large integers p, where ${r_T(x)}=lim\;sup_{n{\rightarrow}{\infty}}{\parallel}T^nx{\parallel}^{\frac{1}{n}}$. We also prove that if T has property (I) and the spectrum ${\sigma}$(T) is finite, then T is algebraic. Finally, we prove that if $T{\in}L$(X) has property (I) and has decomposition property (${\delta}$) then T has a non-trivial invariant closed linear subspace.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1355-1370
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• 2019

A curve $X{\subset}\mathbb{P}^r$ has maximal rank if for each $t{\in}\mathbb{N}$ the restriction map $H^0(\mathcal{O}_{\mathbb{P}r}(t)){\rightarrow}H^0(\mathcal{O}_X(t))$ is either injective or surjective. We show that for all integers $d{\geq}r+1$ there are maximal rank, but not arithmetically Cohen-Macaulay, smooth curves $X{\subset}\mathbb{P}^r$ with degree d and genus roughly $d^2/2r$, contrary to the case r = 3, where it was proved that their genus growths at most like $d^{3/2}$ (A. Dolcetti). Nevertheless there is a sector of large genera g, roughly between $d^2/(2r+2)$ and $d^2/2r$, where we prove the existence of smooth curves (even aCM ones) with degree d and genus g, but the only integral and non-degenerate maximal rank curves with degree d and arithmetic genus g are the aCM ones. For some (d, g, r) with high g we prove the existence of reducible non-degenerate maximal rank and non aCM curves $X{\subset}\mathbb{P}^r$ with degree d and arithmetic genus g, while (d, g, r) is not realized by non-degenerate maximal rank and non aCM integral curves.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.623-637
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• 2019

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

• Wind and Structures
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• v.31 no.6
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• pp.561-573
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• 2020

Unsteady self-excited forces are commonly represented by parametric models such as rational functions. However, this requires complex multiparametric nonlinear fitting, which can be a challenging task that requires know-how. This paper explores the alternative nonparametric modeling of unsteady self-excited forces based on relations between flutter derivatives. By exploiting the properties of the transfer function of linear causal systems, we show that damping and stiffness aerodynamic derivatives are related by the Hilbert transform. This property is utilized to develop exact simplified expressions, where it is only necessary to consider the frequency dependency of either the aeroelastic damping or stiffness terms but not both simultaneously. This approach is useful if the experimental data on aerodynamic derivatives that are related to the damping are deemed more accurate than the data that are related to the stiffness or vice versa. The proposed numerical models are evaluated with numerical examples and with data from wind tunnel experiments. The presented method can evaluate any continuous fitted table of interpolation functions of various types, which are independently fitted to aeroelastic damping and stiffness terms. The results demonstrate that the proposed methodology performs well. The relations between the flutter derivatives can be used to enhance the understanding of experimental modeling of aerodynamic self-excited forces for bridge decks.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.11a
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• pp.804-807
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• 2013

최근 클라우드 컴퓨팅에 대한 관심이 고조됨에 따라, 이를 활용한 데이터베이스 아웃소싱(Outsourcing)에 대한 연구가 활발히 진행되고 있다. 그러나 아웃소싱 된 데이터베이스는 사용자 개인 정보, 증권, 또는 의료 정보 등 민감한 정보를 포함하기 때문에 서비스 제공자로부터 수행한 질의 결과 데이터가 데이터 소유자로부터 생성된 데이터이며, 정확한 질의 결과를 포함하는지 확인하기 위한 질의 결과 무결성 검증 기법의 필요성이 대두되었다. 기존 질의 결과 무결성 검증 기법은 질의 결과에 포함되는 무결성 검증 데이터의 크기가 증가하여 검증 데이터 전송 오버헤드 증가 및 데이터 노출 위험 증가 문제를 지닌다. 따라서, 본 논문에서는 데이터 보호를 지원하는 암호화 데이터 기반 질의 결과 무결성 검증 기법을 제안한다. 제안하는 질의 결과 무결성 검증 기법은 암호화된 데이터 그룹을 주기 함수를 이용하여 재분할하고, 최종 데이터 그룹 id를 힐버트 커브를 통해 변환한다. 따라서, 검증 데이터 오버헤드를 감소시켜 효율적인 질의 처리를 지원하며, 그룹 id 변경을 통해 검증 데이터 유출 위험을 방지한다. 성능평가를 통해, 제안하는 기법이 기존 기법에 비해 질의 처리 시간 측면에서 평균 2배, 검증 데이터 오버헤드 측면에서 최대 20배의 성능을 개선함을 보인다.