• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.351-361
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• 2010

For a bounded linear operator T on a separable complex infinite dimensional Hilbert space $\mathcal{H}$, we say that T is a quasi-class (A, k) operator if $T^{*k}|T^2|T^k\;{\geq}\;T^{*k}|T|^2T^k$. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class (A, k) operators.

• 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.

• Journal of the Korean Mathematical Society
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• v.41 no.4
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• pp.617-627
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• 2004

Let (equation omitted) denote the class of bounded linear Hilbert space operators with the property that $\midA^2\mid\geq\midA\mid^2$. In this paper we show that (equation omitted)-operators are finitely ascensive and that, for non-zero operators A and B, A (equation omitted) B is in (equation omitted) if and only if A and B are in (equation omitted). Also, it is shown that if A is an operator such that p(A) is in (equation omitted) for a non-trivial polynomial p, then Weyl's theorem holds for f(A), where f is a function analytic on an open neighborhood of the spectrum of A.

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.75-80
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• 2013

Let T be a bounded linear operator on a complex Hilbert space $\mathfrak{H}$. An operator T is called class A operator if ${\mid}T^2{\mid}{\geq}{\mid}T{\mid}^2$ and is called class $A({\kappa})$ operator if $(T^*{\mid}T{\mid}^{2{\kappa}}T)^{\frac{1}{{\kappa}+1}}{\geq}{\mid}T{\mid}^2$ for a positive number ${\kappa}$. In this paper, we show that ${\sigma}$ is continuous when restricted to the set of class $A({\kappa})$ operators.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.50 no.6
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• pp.413-422
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• 2022

In this paper, the fault analysis of the momentum wheel, which is a high-speed rotary machinery of 'Control Moment Gyro' for medium and large satellite, was described. For fault diagnosis, envelope spectrum analysis was performed using Hilbert transformation method and signal demodulation method to find the impact signals periodically generated from amplitude modulated signals. Through this, the fault of the momentum wheel was diagnosed by analyzing whether there was a harmonic component of the rotational frequency and a bearing fault frequency in a specific frequency band with a high peak.

• Structural Engineering and Mechanics
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• v.39 no.6
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• pp.813-831
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• 2011

This paper presents an efficient version of Hilbert-Huang transform for nonlinear non-stationary systems analyses. An ensemble empirical mode decomposition (EEMD) is introduced to alleviate the problem of mode mixing between intrinsic mode functions (IMFs) decomposed by EMD. Yet the problem has not been fully resolved when a signal of a similar scale resides in different IMF components. Instead of using a trial and error method to select the "best" outcome generated by EEMD, a hybrid algorithm based on EEMD and EMD is proposed for multi-mode signal processing. The developed approach comprises the steps from a bandpass filter design for regrouping modes of the IMFs obtained from EEMD, to the mode extraction using EMD, and to the assessment of each mode in the marginal spectrum. A simulated two-mode signal is tested to demonstrate the efficiency and robustness of the approach, showing average relative errors all equal to 1.46% for various noise levels added to the signal. The developed approach is also applied to a real bridge structure, showing more reliable results than the pure EMD. Discussions on the mode determination are offered to explain the connection between modegrouping form on the one hand, and mode-grouping performance on the other.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.687-692
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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 caused 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.

• 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.

• 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.

• 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.