• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1029-1044
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• 2023

The purpose of this paper is to introduce the concept of joint essential numerical spectrum 𝜎_en(·) of q-tuple of operators on a Banach space and to study its properties. This notion generalize the notion of the joint essential numerical range.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.653-659
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• 1995

We prove that two essentially normal elements of a type $II_{\infty}$ factor von Neumann algebra are unitarily equivalent up to the compact ideal if and only if they have the identical essential spectrum and the same index data. Also we calculate the spectrum and essential spectrum of a non-unitary isometry of von Neumann algebra.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.357-361
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• 1999

The essential spectra for a class of Toeplitz operators on p, 1$\leq$p$\leq$$\infty$, are computed.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.123-135
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• 2023

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of α-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.

• Nonlinear Functional Analysis and Applications
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• v.26 no.4
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• pp.701-716
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• 2021

In this present article, we construct a new framework that's we call the weighted geometric realization of 2 and 3-simplexes. On this new weighted framework, we construct a nonself-adjoint 2-simplex Laplacian L and a self-adjoint 2-simplex Laplacian N. We propose general conditions to ensure sectoriality for our new nonself-adjoint 2-simplex Laplacian L. We show the relation between the essential spectra of L and N. Finally, we prove the absence of the essential spectrum for our 2-simplex Laplacians L and N.

• East Asian mathematical journal
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• v.17 no.1
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• pp.87-92
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• 2001

In this paper, we have the extended result of Bunce's theorem. And we show that if T is an irreducible p-hyponormal operator such that T*T-TT* is compact, then ${\sigma}_{ap}(T)={\sigma}_e(T)$ and ${\sigma}_p({\phi}(T))={\sigma}_e({\phi}(T))$.

• Journal of Acupuncture Research
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• v.28 no.2
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• pp.89-95
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• 2011

Objectives : The purpose of this study was to investigate the composition of Rehmannia glutinosa's essential oils with Rehmanniae Radix herbal acupuncture Methods : I obtained the essential oils of Rehmannia Radix by hydrodistillation extraction method and supercritical fluid extraction(SFE) method, and then I analyzed those by GC/MS(gas chromatography/mass spectrum). Results : 1. With GC(gas chromatography) and GC/MS(gas chromatography/mass spectrum) analysis. I identified 9 compounds in the Rehmanniae Radix's essential oil obtained through the SFE method. The main compounds were as follows : Hexachloroethane(2.24%), N-Butyl-benzenesulfonamide(2.05%), hexadecanoic acid(1.93%), hexadecanoic acid, ethyl ester(3.49%), 9,12-Octadecadienoic acid(z,z)(2.70%), (9E)-9-Octadecenoic acid(6.14%), ethyl linoleate(4.43%), ethyl oleate(5.80%). 2. I failed to get Rehmanniae Radix's essential oil obtained through the hydrodistillation method. 3. With GC(gas chromatography) and GC/MS(gas chromatography/mass spectrum) analysis. I identified 4 compounds in the Rehmanniae Radix's essential oil obtained through the hydrodistillation method. The main compounds were as follows : Ethylbis(trimethylsilyl)amine(1.04%), 2-(Trimethylsiloxy)benzoic methyl ester(2.65%), Hexadecanoic acid trimethylsilyl ester(12.61%), octadecanoic acid, trimethylsilyl ester(6.28%). Conclusions : The substances by hydrodistillation method may not perfectly match with the substances by supercritical fluid extraction(SFE) method in essential oils extracted form Rehmanniae Radix. But, the main substances was assumed Hexadecanoic acid and octadecanoic acid.

• Electronics and Telecommunications Trends
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• v.38 no.5
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• pp.100-113
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• 2023

This study was aimed to derive implications in terms of competition to establish a reasonable spectrum policy for fifth-generation (5G) spectrum allocation through an in-depth analysis of C-band spectrum auctions. As a result of examining auctions in five countries, namely, Belgium, Sweden, Canada, Brazil, and Hong Kong, we identified various characteristics. First, the minimum bandwidth that is essential for service competition is guaranteed. Second, in Brazil, the network construction cost of mobile network operators is regarded as a part of the spectrum price. Third, a joint allocation of spectrum is permitted in Sweden, and spectrum sharing after allocation for 5G services is allowed in Canada. Finally, the reserved spectrum is provided for new service providers in Belgium and Canada. Our findings may provide insights for establishing policies of 5G spectrum allocation and competition in the telecommunications service market in Korea.

• Journal of Information Processing Systems
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• v.12 no.2
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• pp.295-309
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• 2016

Spectrum sensing is an essential function that enables cognitive radio technology to explore spectral holes and resourcefully access them without any harmful interference to the licenses user. Spectrum sensing done by a single node is highly affected by fading and shadowing. Thus, to overcome this, cooperative spectrum sensing was introduced. Currently, the advancements in multiple antennas have given a new dimension to cognitive radio research. In this paper, we propose a multiple energy detector for cooperative spectrum sensing schemes based on the evidence theory. Also, we propose a reporting mechanism for multiple energy detectors. With our proposed system, we show that a multiple energy detector using a cooperative spectrum sensing scheme based on evidence theory increases the reliability of the system, which ultimately increases the spectrum sensing and reduces the reporting time. Also in simulation results, we show the probability of error for the proposed system. Our simulation results show that our proposed system outperforms the conventional energy detector system.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.401-408
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• 2014

If A is a unital Banach algebra, then the spectrum can be viewed as a function ${\sigma}$ : 𝕬 ${\rightarrow}$ 𝕾, mapping each T ${\in}$ 𝕬 to its spectrum ${\sigma}(T)$, where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of $\mathbb{C}$. This paper is concerned with the continuity of the spectrum ${\sigma}$ via Browder's theorem. It is shown that ${\sigma}$ is continuous when ${\sigma}$ is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.