• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.419-429
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• 2015

In this paper, we study properties SVEP, Bishop's property (${\beta}$), property (${\delta}$), decomposability, property $({\beta})_{\epsilon}$, subscalarity, Kato spectrum, generalized Kato decomposition, finite ascent for bounded linear operators in Banach spaces.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.785-794
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• 2022

In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then X_A(F) = X_A+R(F) for all subset F ⊆ ℂ and 𝜎_loc(A) = 𝜎_loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.261-269
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• 2020

For any Banach spaces X and Y, let L(X, Y) denote the set of all bounded linear operators from X to Y. Let A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA. In this paper, we prove that AC and BA share the local spectral properties such as a finite ascent, a finite descent, property (K), localizable spectrum and invariant subspace.

• Near Infrared Analysis
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• v.1 no.2
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• pp.1-8
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• 2000

Using the net analyte signal, hybrid linear analysis was proposed to predict chemical concentration. In this paper, we select a sample from training set and apply orthogonal signal correction to obtain an improved pseudo unit spectrum for hybrid least analysis. using the mean spectrum of a calibration training set, we first show the calibration by hybrid least analysis is effective to the prediction of not only chemical concentrations but also physical property variables. Then, a pseudo unit spectrum from a training set is also tested with and without orthogonal signal correction. We use two data sets, one including five chemical concentrations and the other including ten physical property variables, to compare the performance of partial least squares and modified hybrid least analysis calibration methods. The results show that the hybrid least analysis with a selected training spectrum instead of well-measured pure spectrum still gives good performances, which is a little better than partial least squares.

• Journal of the Korean Vacuum Society
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• v.16 no.1
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• pp.40-45
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• 2007

ZnCdSe alloy semiconductor was widely used for the optoelectronic device. And CdSe is the end-point in this material. In this work, we measured the dielectric function spectrum of cubic CdSe with Vacuum Ultra Violet spectroscopic ellipsometry and analysed this data with parametric model. As a result, we observed some of transition energy point over 6 eV and obtained the database for dielectric function spectrum, which could be used for temperature or alloy composition dependence study on optical property of CdSe.

• 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.

• The Pure and Applied Mathematics
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• v.25 no.2
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• pp.127-133
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• 2018

We look at Toeplitz arrays on ${\mathbb{Z}}^d$ and study a characterizing property for pure discrete spectrum in terms of the periodic structures of the Toeplitz arrays.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.9
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• pp.2470-2480
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• 1996

The energy efficiency and bandwidth efficiency are two important criterion in designing a modulation scheme Especially the constant envelope property must be considered as in the non-linear channel tht exit, for example in the nonlinear amplifiers for satellite repeater. The Q$^{2}$AM(Quadrature Quadrature Amplitude Modulation) is a new modulation scheme which combines the Q$^{2}$PSK(Quadrature Quadrature Phase Shift Keying) scheme which increases the signal space dimension and the QAM scheme which increases the bandwidth efficiency using the multi-level signal. The Q$^{2}$AM scheme has by far superior spectrum efficiency compared with the existing modulation schemes. Applying this scheme in the non-linear communication system increses the bandwidth efficiency but cannot envelop property. In this paper, a new system architecture is suggested which satisfies the large spectrum efficiency and constant envelope property by implementing the linear block coding prior to the Q$^{2}$AM modulation. the system has improved in performance by gaining the constant envelope and the additional coding gain. We able to observe the performance improvement of the suggested system(at BER=10$^{-5}$ ) of 4.4 dB for the 16-QAM and 0.7 dB for the Q$^{2}$PSK under the exact spectrum efficiency.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.3
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• pp.63-69
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• 2017

In order to observe the noise property of the flat-panel digital radiography detector, measuring the normalized noise power spectrum (NNPS) from acquired x-ray images is conducted. However, the conventional NNPS measurement has an unstable property depending on the acquired image. Averaging the sample periodograms of the input image is usually performed to estimate the NNPS values and increasing the number of samples can provide a reliable NNPS measurement. In this paper, for a finite number of images, two measurement methods, which are based on averaging spectra, such as the image periodogram, are proposed and their performances are analyzed. Using x-ray images acquired from two types of radiography detectors, the two spectrum averaging methods are compared and it is shown that averaging spectra based on the maximal number of combinations of the image pairs provides the best performance in measuring NNPS.

• Journal of the Korean Mathematical Society
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• v.54 no.1
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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.