• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1129-1135
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• 2022

The purpose of this research is to find an extension of the renowned Chernoff theorem on standard operator algebra. Infact, we prove the following result: Let H be a real (or complex) Banach space and 𝓛(H) be the algebra of bounded linear operators on H. Let 𝓐(H) ⊂ 𝓛(H) be a standard operator algebra. Suppose that D : 𝓐(H) → 𝓛(H) is a linear mapping satisfying the relation D(AⁿBⁿ) = D(Aⁿ)Bⁿ + AⁿD(Bⁿ) for all A, B ∈ 𝓐(H). Then D is a linear derivation on 𝓐(H). In particular, D is continuous. We also present the limitations on such identity by an example.

• Progress in Superconductivity and Cryogenics
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• v.22 no.4
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• pp.20-23
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• 2020

Among many variables in processing the high performance MgB2 bulk superconductors, simple and important approach is to optimize the size dependence of the Mg & B raw powders. The present study is dedicated towards the variation in superconducting properties of MgB2 depending upon the various combination of Mg & B powders with the two different particle sizes respectively. From morphological investigation of the MgB2 samples, narrow and long pores are observed when the larger Mg powders are used, whereas it is rather like the oval shapes with the smaller Mg powders. Also, it can be seen that the connectivity of the MgB2 samples is much enhanced with the smaller size of the B powders. Jc-H properties of the MgB2 samples also indicate that the highest Jc can be obtained when using the smaller size of the B powder with the combination of the smaller Mg powders than that of the larger Mg powders. If the cases with the larger B powers, it is more favorable to select the larger Mg powders with the better Jc-H properties considering shorter diffusion length of Mg and more homogeneous mixture between the Mg & B powders.

• KSBB Journal
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• v.19 no.4
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• pp.250-256
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• 2004

In this work we have cultivated several B. cereus strains in a complex LB medium in order to study the production of phospholipase C (PLC), and among them B. cereus 318 showed the highest productivity of PLC. Some components, i.e., 5 g/L glucose, 5 g/L yeast extract, 5 g/L peptone, 0.5∼1.0 g/L K$_2$HPO$_4$, 0.02∼0.04 g/L ZnSO$_4$$.$7H$_2$O and 3 g/L NaHCO$_3$ were found to be optimal for the high production of PLC by B. cereus 318. Optimal culture temperature and pH were found to be 30$^{\circ}C$ and pH 7.5 for the PLC production, respectively. Optimum reaction temperature and pH of the PLC produced by B. cereus 11 and 318 were 45$^{\circ}C$ and pH 4.0, while they were 50$^{\circ}C$ and pH 7.0 for the PLC by B. cereus 559. The PLC produced by B. cereus was activated by Mn$\^$2+/, Co$\^$2+/ and dimethyl sulfoxide (DMSO), but its activity was inhibited by Cu$\^$2+/ and partially by glycerol, isopropanol and sodium dodecyl sulfate (SDS).

• Membrane Journal
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• v.19 no.3
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• pp.228-236
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• 2009

ABA type triblock copolymer of poly(hydroxyl ethyl acrylate )-b-polystyrene-b-poly(hydroxyl ethyl acrylate), i.e. PHEA-b-PS-b-PHEA, was synthesized throughatom transfer radical polymerization (ATRP). This block copolymer was thermally crosslinked with 4,5-imidazole dicarboxylic acid (IDA) via the esterification between the -OH groups of PHEA in block copolymer and the -COOH groups of IDA. Upon doping with ${H_3}{PO_4}$ to form imidazole-${H_3}{PO_4}$ complexes, the proton conductivity of membranes continuously increased with increasing ${H_3}{PO_4}$ content. The PHEA-b-PS-b-PHEA/IDA/${H_3}{PO_4}$ polymer membrane with [HEA]:[IDA]:[${H_3}{PO_4}$]=3:4:4 exhibited a maximum proton conductivity of 0.01 S/cm at $100^{\circ}C$ under anhydrous conditions. Thermal gravimetric analysis (TGA) shows that the PHEA-b-PS-b-PHEA/IDA/${H_3}{PO_4}$ complex membranes were thermally stable up to $350^{\circ}C$, indicating their applicability in fuel cells.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.17 no.7
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• pp.442-450
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• 2016

This study aims to determine the antimicrobial activity of fermented Cheonggukjang extract using the new Strain, Bacillus amyloliquefaciens NBF11-1, which was first found on the surface of the node part of bamboo stems, but has been studied very little so far. Bacillus subtilis NG24, which is the traditional fermented strain of Cheonggukjang, was selected as the control group and a comparative analysis was performed. The experimental method included measurements of the antimicrobial activity, minimum inhibitory concentration (MIC) and heat and pH stability. B. amyloliquefaciens NBF11-1 had stronger antimicrobial activity than B. subtilis NG24 against the gram-positive bacteria, C. perfringens and S. aureus and the gram-negative bacteria, A. faecalis and E. coli among the six species of pathogenic bacteria studied. When the minimum inhibitory concentration was measured, B. amyloliquefaciens NBF11-1 in C. perfringens, S. aureus, A. faecalis, and E. coli had an inhibitory effect at concentrations of 0.01 %, 0.21 %, 0.45 % and 0.29 %, respectively, compared to B. subtilis NG24. When the heat and pH stability was measured, B. subtilis NG24 and B. amyloliquefaciens NBF11-1 Cheonggukjang extract did not show any decrease in activity when held at a temperature of $121^{\circ}C$ for 15 minutes and at pH values ranging from 2 to 10 and were therefore considered to be relatively stable against heat and pH changes.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.51-57
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• 2001

Let $\mathcal{B}(H)$ and $\mathcal{B}(K)$ denote the algebras of all bounded linear operators on Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, respectively. We show that if ${\phi}:\mathcal{B}(H){\rightarrow}\mathcal{B}(K)$ is an additive mapping satisfying ${\phi}({\mid}A{\mid}^2)={\mid}{\phi}(A){\mid}^2$ for every $A{\in}\mathcal{B}(H)$, then there exists a mapping ${\psi}$ defined by ${\psi}(A)={\phi}(I){\phi}(A)$, ${\forall}A{\in}\mathcal{B}(H)$ such that ${\psi}$ is the sum of $two^*$-homomorphisms one of which C-linear and the othere C-antilinear. We will also study some conditions implying the injective and rank-preserving of ${\psi}$.

• Kyungpook Mathematical Journal
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• v.49 no.1
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• pp.1-6
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• 2009

Let B(X) denote the algebra of operators on a complex Banach space X, H(X) = {h ${\in}$ B(X) : h is hermitian}, and J(X) = {x ${\in}$ B(X) : x = $x_1$ + $ix_2$, $x_1$ and $x_2$ ${\in}$ H(X)}. Let ${\delta}_a$ ${\in}$ B(B(X)) denote the derivation ${\delta}_a$ = ax - xa. If J(X) is an algebra and ${\delta}_a^{-1}(0){\subseteq}{\delta}_{a^*}^{-1}(0)$ for some $a{\in}J(X)$, then ${\parallel}a{\parallel}{\leq}{\parallel}a-(x^*x-xx^*){\parallel}$ for all $x{\in}J(X){\cap}{\delta}_a^{-1}(0)$. The cases J(X) = B(H), the algebra of operators on a complex Hilbert space, and J(X) = $C_p$, the von Neumann-Schatten p-class, are considered.

• Proceedings of the KIEE Conference
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• 2004.07d
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• pp.2347-2349
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• 2004

The iron loss in electric machines takes large part of machine losses and the reduction of iron loss brings the increase of the efficiency. In the rotating machines, however it is very difficult to calculate result because the measuring processes are very complex and laborious. As is well known, the relation between the flux density B and the magnetic field intensity H relation is not linear. For the iron loss, B and H must be measured and usually B becomes the reference wave(sine wave) and the following H is measured using H-coil. To make the B as sine wave, B is controlled by some devices. The error is controlled to become zero by the proposed algorithm which uses the bisection algorithm. The experiments are compared with the simulation results, and they show acceptable agreements.

• Journal of the Chungcheong Mathematical Society
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• v.17 no.1
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• pp.85-101
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• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.6
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• pp.3013-3022
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• 2013

Satisfying the large car impact condition of the high level SB5-B for "SMART Highway" longitudinal barriers, the possibility of increase of the small car impact velocity from 120km/h to 130km/h was investigated. Through computer simulation using input parameters calibrated to full-scale crash test results, various longitudinal semi-rigid barrier models were improved such that for the small car impact speed of 120km/h the change of longitudinal and transverse velocities of the impact vehicle can satisfy the THIV limit. The barrier model determined through this process satisfied the performance assessment criteria for SB5-B impact conditions. Varying the wing angle of slip block-outs of the passed barrier model, the possibility of increase of the small car impact velocity was investigated by FEA and a full-scale crash test was conducted. It has been shown that the possibility to increase the small car impact speed to 130km/h is high if the test facility condition for 130km/h impact velocity is better equipped.