• 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.

• Journal of Communications and Networks
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• v.11 no.2
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• pp.122-133
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• 2009

As wireless spectrum resources become more scarce while some portions of frequency bands suffer from low utilization, the design of cognitive radio (CR) has recently been urged, which allows opportunistic usage of licensed bands for secondary users without interference with primary users. Spectrum sensing is fundamental for a secondary user to find a specific available spectrum hole. Cooperative spectrum sensing is more accurate and more widely used since it obtains helpful reports from nodes in different locations. However, if some nodes are compromised and report false sensing data to the fusion center on purpose, the accuracy of decisions made by the fusion center can be heavily impaired. Weighted sequential probability ratio test (WSPRT), based on a credit evaluation system to restrict damage caused by malicious nodes, was proposed to address such a spectrum sensing data falsification (SSDF) attack at the price of introducing four times more sampling numbers. In this paper, we propose two new schemes, named enhanced weighted sequential probability ratio test (EWSPRT) and enhanced weighted sequential zero/one test (EWSZOT), which are robust against SSDF attack. By incorporating a new weight module and a new test module, both schemes have much less sampling numbers than WSPRT. Simulation results show that when holding comparable error rates, the numbers of EWSPRT and EWSZOT are 40% and 75% lower than WSPRT, respectively. We also provide theoretical analysis models to support the performance improvement estimates of the new schemes.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.59 no.1
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• pp.1-13
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• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.10A
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• pp.984-991
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• 2007

Cognitive Radio is an advanced enabling techlology for efficient utilization of under-utilized spectrum since it is able to sense the temporally available spectrum and adapt its parameters to fully utilize the frequency band. Recent investigation suggests that spectrum sensing is compromised when a cognitive radio user suffers from the environment with fading or shadowing. In order to combat the effect, collaborative sensing is considered to be a promising way, which combines the sensing result of each user to achieve good performance. However, the conventional collaborative sensing is not efficient when users suffer different fading environments. In this paper, we propose a weighted-collaborative scheme that considers using the weights of each collaborative CR user, which can achieve better sensing performance under both fast and slow fading environments. The analysis of the simulation resultsproves that the weighted-collaborative scheme improves sensing performance obviously and outperforms the conventional method.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.809-821
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• 2018

In the present paper, we extend the main results of Jeribi in [6] to weighted and pseudo-weighted spectra of operators in a nonseparable Hilbert space ${\mathcal{H}}$. We investigate the characterization, the stability and some properties of these weighted and pseudo-weighted spectra.

• 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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.10
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• pp.1867-1872
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• 2016

In the area of digital signal processing, it is necessary to improve the quality of the speech signal after removing the background noise which exists in a various real environments. The important thing to consider when removing the background noise acoustically is that to solve the problem, depending on the information of the human auditory mechanism is mainly the amplitude spectrum of the speech signal. This paper introduces the characteristics of a frequency-weighted spectrum shaping filter for the extraction of the amplitude spectrum of the speech signal with the primary purpose. Therefore, this paper proposes an algorithm using the methods of a Wiener filter and the frequency-weighted spectrum shaping filter according to the acoustic model, after extracted the amplitude spectral information in the noisy speech signal. The spectral distortion (SD) output of the proposed algorithm is experimentally improved more than 5.28 dB compared to a conventional method.

• Bulletin of the Korean Mathematical Society
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• v.60 no.5
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• pp.1141-1154
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• 2023

In this paper, we study the complex symmetric weighted composition-differentiation operator D_𝜓,𝜙 with respect to the conjugation JW_𝜉,𝜏 on the Hardy space H². As an application, we characterize the necessary and sufficient conditions for such an operator to be normal under some mild conditions. Finally, the spectrum of D_𝜓,𝜙 is also investigated.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.11
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• pp.2561-2576
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• 2013

The ship ad-hoc network (SANET) extends the coverage of the high data-rate terrestrial communications to the ships with the reduced cost in maritime communications. Cognitive radio (CR) has the ability of sensing the radio environment and dynamically reconfiguring the operating parameters, which can make SANET utilize the spectrum efficiently. However, due to the dynamic topology nature and no central entity for data fusion in SANET, the interference brought into the primary network caused by the hidden primary user requires to be carefully managed by a sort of decentralized cooperative spectrum sensing schemes. In this paper, we propose a self-weighted decentralized cooperative spectrum sensing (SWDCSS) scheme to solve such a problem. The analytical and simulation results show that the proposed SWDCSS scheme is reliable to detect the primary user in SANET. As a result, secondary network can efficiently utilize the spectrum band of primary network with little interference to primary network. Referring the complementary receiver operating characteristic (ROC) curves, we observe that with a given false alarm probability, our proposed algorithm reduces the missing probability by 27% than the traditional embedded spectrally agile radio protocol for evacuation (ESCAPE) algorithm in the best condition.