• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Bulletin of the Korean Mathematical Society
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• v.23 no.2
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• pp.167-170
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• 1986

Let M be a von Neumann algebra and .alpha., .betha. be *-automorphisms of M satisfying the operator equation .alpha.+.alpha.$^{-1}$ =.betha.+.betha.$^{-1}$ This operator equation has been extensively studied and many important decomposition theorems have been obtained by several authors (for instance see [4], [5], [2], [1]). Originally, this operator equation arose in the paper of Van Daele on the new approach of the Tomita-Takesaki theory in the case of modular operators ([7]). In the case of one-parameter automorphism groups, this equation has produced a bounded and completely positive map which can play a role similar to the infinitesimal generator (for details see [6] and [1]). A recent and one of the most important applications of this equation has been in developing an anglogue of the Tomita-Takesaki theory for Jordan algebras by Haagerup [3]. One general result of this theory is the following.

• Journal of radiological science and technology
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• v.35 no.1
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• pp.1-7
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• 2012

Dual Energy X-ray Absorptiometry(DEXA) is commonly used to diagnose Osteoporosis. The errors of DEXA bone density operation are caused by operator, bone mineral density meter, blood testing, patient. We focus on operator error then study about how much influence operator's region of intest(ROI) in bone testing result. During from March to July in 2011. 50 patients ware selected respectively from 30, 40, 50, 60, and 70 age groups who came to Korea University Medical Center(KUMC) for their Osteoporosis treatment. A-test was performed with usually ROI and B-test was performed with most widely ROI. Then, We compare A-test and B-test for find maximum difference of T-score error which occurred operator ROI controlling. Standard deviation of T-score of B-test showed 0.1 higher then A-test in femur neck. Standard deviation of B-test showed 0.2 higher then A-test in Ward's area which in Greater trocanter and Inter trocanter. Standard deviation of B-test showed 0,1 lower then A-test in L-1. Bone density testing about Two hundred patients results are as follow. When operator ROI was changed wider than normal ROI, bone density of femur was measured more higher but bone density of L-spine was measured more lower then normal bone density. That means, sometime DEXA bone density testing result is dependent by operator ROI controlling. This is relevant with the patient's medicine and health insurance, thus, tester always keep the size of ROI for to prevent any problem in the patient.

• IE interfaces
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• v.22 no.2
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• pp.104-115
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• 2009

The objective of the study is to evaluate the effectiveness of Crew Resource Management (CRM) training program for operators in the Main Control Room (MCR) simulator of APR-1400 Nuclear Power Plant. The experiments were conducted for two different crews of operators performing six different emergency operating scenarios during four-week period. Each crew consisted of the five operators: senior reactor operator, safety technical advisor, reactor operator, turbine operator, and electric operator. All crews (Crew A and B) participated in the training program for the technical knowledge and skills which were required to operate the simulator of the MCR during the first week. To verify the effectiveness of the CRM training program; however, only Crew A was selected to attend the CRM training after the technical knowledge and skills training. The results of the experiments showed that the CRM training program improved the individual attitudes of Crew A significantly. Team skills of Crew A were found to be significantly better than those of Crew B. The CRM training did not have positive effects on enhancing the individual performance of Crew A; however, as compared to that of Crew B. Implication of these findings was discussed further in detail.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1299-1309
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• 2021

Demeter [1] and Kuk and Lee [5] proved the unboundedness of the trilinear Hilbert transforms H_a,b,c under the critical index 1/2 for some parameters a, b and c. We show the unboundedness of H_a,b,c for any parameters.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1443-1455
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• 2017

Let $M_{z^N}(N{\in}{\mathbb{Z}}^d_+)$ be a bounded multiplication operator on a class of Hilbert spaces with orthogonal basis $\{z^n:n{\in}{\mathbb{Z}}^d_+\}$. In this paper, we prove that each reducing subspace of $M_{z^N}$ is the direct sum of some minimal reducing subspaces. For the case that d = 2, we find all the minimal reducing subspaces of $M_{z^N}$ ($N=(N_1,N_2)$, $N_1{\neq}N_2$) on weighted Bergman space $A^2_{\alpha}({\mathbb{B}}_2)$(${\alpha}$ > -1) and Hardy space $H^2({\mathbb{B}}_2)$, and characterize the structure of ${\mathcal{V}}^{\ast}(z^N)$, the commutant algebra of the von Neumann algebra generated by $M_{z^N}$.

• KSBB Journal
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• v.5 no.3
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• pp.195-200
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• 1990

The growth behavior of recombinant Escherichia coli cells having plasmid pIF-III-B, which carries human alpha-interferon gene under the control of lpp promoter, lac promoter and lac operator, was studied by using of various E. coli host strains. Expression of the alpha-IFN gene is controllable by using inducer IPTG because the plasmid also contains lacI gene which produces lac regressors. The repressors block the transcription of alpha-IFN gene. There were considerable differences in cell growth according to the host strains used. Cell growth was inhibited not only by plasmid pIF-III-B itself but also by the induction of alph-a-IFN gene expression. Growth inhibition caused by the plasmid itself was more serious than that caused by the induction of alpha-IFN gene expression.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.477-484
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• 2020

For a non-zero complex number b and for m and n in 𝒩₀ = {0, 1, 2, …} let Ψ_n,m(b) denote the class of normalized univalent functions f satisfying the condition ${\Re}\;\[1+{\frac{1}{b}}\(\frac{D^{n+m}f(z)}{D^nf(z)}-1\)\]\;>\;0$ in the unit disk U, where Dⁿ f(z) denotes the Salagean operator of f. Sharp bounds for the Fekete-Szegö functional |a₃ - 𝜇a²₂| are obtained.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.29B no.10
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• pp.90-99
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• 1992

In this paper, we propose a neural network model for speech recognition. The model consists of feature extraction parts and recognition parts. The interconnection model based on ${\Delta}^2$G operator was used for frequency analysis. Two features, global feature and local feature, were extracted from this model. Recognition parts consist of global grouping stage and local grouping stage. When the input pattern was coded by slope method, the recognition rate of speakers, A and B, was 100%. When the test was performed with the data of 9 speakers, the recognition rate of 91.4% was obtained.

• Communications of the Korean Mathematical Society
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• v.36 no.2
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• pp.247-256
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• 2021

Using variational methods, we show the existence of a unique weak solution of the following singular biharmonic problems of Kirchhoff type involving critical Sobolev exponent: $$(\mathcal{P}_{\lambda})\;\{\begin{array}{lll}{\Delta}^2u-(a{\int}_{\Omega}{\mid}{\nabla}u{\mid}^2dx+b){\Delta}u+cu=f(x){\mid}u{\mid}^{-{\gamma}}-{\lambda}{\mid}u{\mid}^{p-2}u&&\text{ in }{\Omega},\\{\Delta}u=u=0&&\text{ on }{\partial}{\Omega},\end{array}$$ where Ω is a smooth bounded domain of ℝⁿ (n ≥ 5), ∆² is the biharmonic operator, and ∇u denotes the spatial gradient of u and 0 < γ < 1, λ > 0, 0 < p ≤ 2^# and a, b, c are three positive constants with a + b > 0 and f belongs to a given Lebesgue space.