• 대한수학회보
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• 제43권4호
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• pp.715-722
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• 2006

In this paper, we show that if T is a hyponormal operator on a non-separable Hilbert space H, then $Re\;{\omega}^0_{\alpha}(T)\;{\subset}\;{\omega}^0_{\alpha}(Re\;T)$, where ${\omega}^0_{\alpha}(T)$ is the weighted Weyl spectrum of weight a with ${\alpha}\;with\;{\aleph}_0{\leq}{\alpha}{\leq}h:=dim\;H$. We also give some conditions under which the product of two ${\alpha}-Weyl$ operators is ${\alpha}-Weyl$ and its converse implication holds, too. Finally, we show that the weighted Weyl spectrum of a hyponormal operator satisfies the spectral mapping theorem for analytic functions under certain conditions.

• 전기의세계
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• 제31권3호
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• pp.209-217
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• 1982

This paper considers a finite spectrum assignment Problem for a functional retarded linear differential system with delays in control only. In this problem, by generalizing from an abstract linear system characterized by Semigroups on a Hilbert space to a finite dimensional linear system, we unify the relationship between a control-delayed system and its non-delayed system, and then by using the spectrum of the generator-decomposition of Semigroup, we try to get a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned sets of n points in the complex plane. The comparative examinations between the standard spectrum assignment method and the method of spectral projection for the feedback law which consists of proportional and finite interval terms over present and past values of control variables are also considered. The analysis is carry down to the elementary spectral projection level because, in spite of all the research efforts, so far there has been no significant attempt to obtain the feedback implementation directly from the abstract representation forms in the case of multivariables.

• 대한수학회보
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• 제39권4호
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• pp.571-575
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• 2002

In this paper we show that Weyl's theorem holds for f(T) when an Hilbert space operator T is “algebraically totally-paranormal” and f is any analytic function on an open neighbor-hood of the spectrum of T.

• 대한수학회지
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• 제45권3호
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• pp.771-780
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• 2008

Let $M_C=\(\array{A&C\\0&B}\)$ be a $2{\times}2$ upper triangular operator matrix acting on the Hilbert space $H{\bigoplus}K\;and\;let\;{\sigma}_w(\cdot)$ denote the Weyl spectrum. We give the necessary and sufficient conditions for operators A and B which ${\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w\(\array{A&C\\0&B}\)\;or\;{\sigma}_w\(\array{A&C\\0&B}\)={\sigma}_w(A){\cup}{\sigma}_w(B)$ holds for every $C{\in}B(K,\;H)$. We also study the Weyl's theorem for operator matrices.

• 지구물리와물리탐사
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• 제19권2호
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• pp.84-90
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• 2016

신규 센서의 성능과 노후화된 센서의 성능 평가를 하는 것은 지진 감시 및 지진연구에 있어서 매우 중요하다고 할 수 있다. 특히 센서 주파수 응답은 지진자료의 보정을 위해서 필수적으로 사용되고 있다. 이 연구에서는 주파수 스펙트럼비를 이용한 지진 기록계의 보정 방법과 시간영역 대역통과필터(bandpass filter)와 힐버트(Hilbert) 변환을 이용한 지진계 주파수 응답을 계산하는 방법을 제시하고자 하였다. 실내 진동대 실험에서 가속도 센서(CMG-5T 1g, 2g 센서)를 설치하고 제안된 방법으로 센서 주파수 응답스펙트럼을 구하였을 때 좋은 결과를 얻을 수 있었다. 또한 2011년 도호쿠 대지진에 대하여 서울대학교 관측소(SNU)의 STS-2와 ES-T에서 얻어진 자료에 대하여 제안된 방법을 적용한 결과 STS-2 광대역 센서의 저주파수 대역에 대한 주파수 응답을 얻을 수 있었다. 대역통과필터와 힐버트 변환 방법을 이용할 경우, 주파수 스펙트럼비를 이용한 방법보다 신호대 잡음이 낮은 부분에서도 명확한 주파수 응답스펙트럼을 보여주었다.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.637-650
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• 2018

In this paper first we show properties of isosymmetric operators given by M. Stankus [13]. Next we introduce an [m, C]-symmetric operator T on a complex Hilbert space H. We investigate properties of the spectrum of an [m, C]-symmetric operator and prove that if T is an [m, C]-symmetric operator and Q is an n-nilpotent operator, respectively, then T + Q is an [m + 2n - 2, C]-symmetric operator. Finally, we show that if T is [m, C]-symmetric and S is [n, D]-symmetric, then $T{\otimes}S$ is [m + n - 1, $C{\otimes}D$]-symmetric.

• Smart Structures and Systems
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• 제10권3호
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• pp.253-269
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• 2012

A split spectrum processing (SSP) method is proposed to accurately determine the time-of-flight (ToF) of damage-scattered waves by comparing the instantaneous amplitude variation degree (IAVD) of a wave signal captured from a damage case with that from the benchmark. The fundamental symmetrical ($S_0$) mode in aluminum plates without and with a notch is assessed. The efficiency of the proposed SSP method and Hilbert transform in determining the ToF of damage-scattered $S_0$ mode is evaluated for damage identification when the wave signals are severely contaminated by noise. Broadband noise can overwhelm damage-scattered wave signals in the time domain, and the Hilbert transform is only competent for determining the ToF of damage-scattered $S_0$ mode in a noise-free condition. However, the calibrated IAVD of the captured wave signal is minimally affected by noise, and the proposed SSP method is capable of determining the ToF of damage-scattered $S_0$ mode accurately even though the captured wave signal is severely contaminated by broadband noise, leading to the successful identification of damage (within an error on the order of the damage size) using a triangulation algorithm.

• Geomechanics and Engineering
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• 제11권5호
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• pp.607-624
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• 2016

Rockburst is becoming more serious in Chinese coal mine. One of the effective methods to control rockburst is blasting. In the paper, we monitored and analyzed the blasting waves at different blast center distances by the Hilbert-Huang transform (HHT) in a coal mine. Results show that with the increase of blast center distance, the main frequency and amplitude of blasting waves show the decreasing trend. The attenuation of blasting waves is slower in the near blast field (10-75 m), compared with the far blast field (75-230 m). Besides, the frequency superposition phenomenon aggravates in the far field. A majority of the blasting waves energy at different blast center distances is concentrated around the IMF components 1-3. The instantaneous energy peak shows attenuation trend with the blast center distance increase, there are two obvious energy peaks in the near blast field (10-75 m), the energy spectrum appears "fat", and the total energy is greater. By contrast, there is only an energy peak in the far blast field, the energy spectrum is "thin", and the total energy is lesser. The HHT three dimensional spectrum shows that the wave energy accumulates in the time and frequency with the increasing of blast center distance.

• 대한수학회지
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• 제54권1호
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• pp.281-302
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• 2017

For a Banach space operator $A{\in}B(\mathcal{X})$, let ${\sigma}(A)$, ${\sigma}_a(A)$, ${\sigma}_w(A)$ and ${\sigma}_{aw}(A)$ denote, respectively, its spectrum, approximate point spectrum, Weyl spectrum and approximate Weyl spectrum. The operator A is polaroid (resp., left polaroid), if the points $iso{\sigma}(A)$ (resp., $iso{\sigma}_a(A)$) are poles (resp., left poles) of the resolvent of A. Perturbation by compact operators preserves neither SVEP, the single-valued extension property, nor the polaroid or left polaroid properties. Given an $A{\in}B(\mathcal{X})$, we prove that a sufficient condition for: (i) A+K to have SVEP on the complement of ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) for every compact operator $K{\in}B(\mathcal{X})$ is that ${\sigma}_w(A)$ (resp., ${\sigma}_{aw}(A)$) has no holes; (ii) A + K to be polaroid (resp., left polaroid) for every compact operator $K{\in}B(\mathcal{X})$ is that iso${\sigma}_w(A)$ = ∅ (resp., $iso{\sigma}_{aw}(A)$ = ∅). It is seen that these conditions are also necessary in the case in which the Banach space $\mathcal{X}$ is a Hilbert space.

• 대한수학회지
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• 제52권2호
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• pp.403-416
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• 2015

An operator T on a complex Hilbert space $\mathcal{H}$ is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for $\mathcal{H}$. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Several corollaries and illustrating examples are provided.