• Kyungpook Mathematical Journal
• /
• v.45 no.2
• /
• pp.293-299
• /
• 2005

Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

• Journal of Microbiology and Biotechnology
• /
• v.25 no.3
• /
• pp.358-365
• /
• 2015

ε-Poly-L-lysine (ε-PL) is a homopolymer of L-lysine molecules connected between the epsilon amino and alpha carboxyl groups. This polymer is currently used as a natural preservative in food. Insufficient biomass is a major problem in ε-PL fermentation. Here, to improve cell growth and ε-PL productivity, various nitrogen-rich nutrients were supplemented into flask cultures after 16 h cultivation, marking the onset of ε-PL biosynthesis. Yeast extract, soybean powder, corn powder, and beef extract significantly improved cell growth. In terms of ε-PL productivity, yeast extract at 0.5% (w/v) gave the maximum yield (2.24 g/l), 115.4% higher than the control (1.04 g/l), followed by soybean powder (1.86 g/l) at 1% (w/v) and corn powder (1.72 g/l) at 1% (w/v). However, supplementation with beef extract inhibited ε-PL production. The optimal time for supplementation for all nutrients examined was at 16 h cultivation. The kinetics of yeast-extract-supplemented cultures showed enhanced cell growth and production duration. Thus, the most commonly used two-stage pH control fed-batch fermentation method was modified by omitting the pH 5.0-controlled period, and coupling the procedure with nutrient feeding in the pH 3.9-controlled phase. Using this process, by continuously feeding 0.5 g/h of yeast extract, soybean powder, or corn powder into cultures in a 30 L fermenter, the final ε-PL titer reached 28.2 g/l, 23.7 g/l, and 21.4 g/l, respectively, 91.8%, 61.2%, and 45.6% higher than that of the control (14.7 g/l). This describes a promising option for the mass production of ε-PL.

• Proceedings of the Korean Powder Metallurgy Institute Conference
• /
• 2006.09a
• /
• pp.457-458
• /
• 2006

• Honam Mathematical Journal
• /
• v.2 no.1
• /
• pp.13-18
• /
• 1980

모든 기호(記號)는 G.E Bredon의 저(著) Sheaf Theory의 기호(記號)를 따른다. A가 torsion free이며 elementary sheaf이라 하자. 그리고 L을 injective L-module이라 하자 $dim_{\varphi}X<{\infty}$이라면 support의 $family{\varphi}$와 locally subset z에 대하여 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{\varphi}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-p}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ 이며 support의 family c와 compact subset z에 대하여도 ${\Gamma}_{z}(^{\sim}Hom({\Gamma}_{c}(L),L){\otimes}A){\simeq}H_0{^{z}}(X:A)\;H_{-y}{^{z}}(X:A)=0,\;p=1,2,3,$⋯⋯ A가 elementary이면 locally closed z와 z에서 closed인 $z^{\prime}$ 그리고 $z^{\prime\prime}=z-z^{\prime}$에 대하여 exact sequence ⋯⋯${\rightarrow}H^{z^{\prime}}_{p}\;(X:A){\rightarrow}H^{z}_{p}(X:A){\rightarrow}H^{z^{\prime\prime}}_{p}\;(X:A){\rightarrow}$⋯⋯ 가 존재(存在)한다.

• 한국생물공학회:학술대회논문집
• /
• 2003.10a
• /
• pp.341-345
• /
• 2003

Effect of immobilization on the production of human granulocyte-macrophage colony-stimulating factor (hGM-CSF) by Nicotiana tabacum cells was investigated using polyurethane foam as immobilization matrices. The cell activity and the hGM-CSF production were maintained for 16 days in spite of 3 times of media exchange. Under the same conditions of temperature and agitation rate, maximum concentrations of hGM-CSF in a 500-mL spinner flask and 100-mL Erleuneyer flasks were 17.3 ${\mu}g/L$ and 9.8 ${\mu}g/L$, respectively. Consequently high hGM-CSF production could be possible in spinner flask when the rate and amount of media exchange were optimized.

• Kyungpook Mathematical Journal
• /
• v.55 no.1
• /
• pp.63-71
• /
• 2015

Let H be a separable infinite dimensional complex Hilbert space, and let $\mathcal{L}(H)$ denote the algebra of all bounded linear operators on H into itself. Let $A,B{\in}\mathcal{L}(H)$ we define the generalized derivation ${\delta}_{A,B}:\mathcal{L}(H){\mapsto}\mathcal{L}(H)$ by ${\delta}_{A,B}(X)=AX-XB$, we note ${\delta}_{A,A}={\delta}_A$. If the inequality ${\parallel}T-(AX-XA){\parallel}{\geq}{\parallel}T{\parallel}$ holds for all $X{\in}\mathcal{L}(H)$ and for all $T{\in}ker{\delta}_A$, then we say that the range of ${\delta}_A$ is orthogonal to the kernel of ${\delta}_A$ in the sense of Birkhoff. The operator $A{\in}\mathcal{L}(H)$ is said to be finite [22] if ${\parallel}I-(AX-XA){\parallel}{\geq}1(*)$ for all $X{\in}\mathcal{L}(H)$, where I is the identity operator. The well-known inequality (*), due to J. P. Williams [22] is the starting point of the topic of commutator approximation (a topic which has its roots in quantum theory [23]). In [16], the author showed that a paranormal operator is finite. In this paper we present some new classes of finite operators containing the class of paranormal operators and we prove that the range of a generalized derivation is orthogonal to its kernel for a large class of operators containing the class of normal operators.

• Korean Journal of Plant Tissue Culture
• /
• v.25 no.3
• /
• pp.189-194
• /
• 1998

The experiment was tried to identify culture media which was suitable for seed germination and seedling growth of wild orchids, Calanthe discolor and Habenaria radiata. When seeds of Calanthe discolor, which was treated with ultrasonics for 30 minutes, were sowed in Murashige and SKoog(MS) medium, germination was much more promoted than other treatments. Seedling of C. discolor grew more rapidly in 3g/L Hyponex and 2g/L tryptone(H$_3$T$_2$) medium and 3g/L Hyponex and 2g/L peptone(H$_3$P$_2$) medium, especially in H$_3$P$_4$ medium among those media, pseudobulb became more corpulent. Habenaria radiata, whose tubers were obtained from seedlings, were sprouted more vigorously in 3g/L Hyponex and 1g/L peptone(H$_3$P$_1$) medium and 1g/L Hyponex and 2g/L peptone(H$_1$P$_2$) medium; but multiplication of tubers, growth of daughter tubers and its corpulence were well established in 1g/L Hyponex and 2g/L peptone(H$_1$P$_2$) medium.

• Bulletin of the Korean Chemical Society
• /
• v.27 no.9
• /
• pp.1405-1417
• /
• 2006

The geometrical structures, potential energy surfaces, and energetics for the ligand exchange reactions of tetracoordinated platinum $(PtY_2L_2\;:\;Y,\;L=Cl^-,\;OH^-,\;OH_2,\;NH_3)$ complexes in the ligand-solvent interaction systems were investigated using the ab initio Hartree-Fock (HF) and Density Functional Theory (DFT) methods. The potential energy surfaces for the ligand exchange reactions used for the conversions of $(PtCl_4\;+\;H_2O)^{^\ast_\ast}\;to\;[PtCl_3(H_2O)\;+\;Cl^-]$ and $[Pt(NH_3)_2Cl_2\;+\;H_2O]$$[Pt(NH_3)_2Cl_2\;+\;H_2O]$ to $[Pt(NH_3)_2Cl(H_2O)\;+\;Cl^-] $ were investigated in detail. For these two exchange reactions, the transition states $([PtY_2L_2{\cdot}{\cdot}{\cdot}L^\prime])^{^\ast_\ast} $ correspond to complexes such as $(PtCl_4{\cdot}{\cdot}{\cdot}H_2O)^{^\ast_\ast}$ and $[Pt(NH_3)_2Cl_2{\cdot}{\cdot}{\cdot}H_2O]^{^\ast_\ast}$, respectively. In the transition state, $([PtCl_4{\cdot}{\cdot}{\cdot}H_2O]^{^\ast_\ast}$ and $[Pt(NH_3)_2Cl_2{\cdot}{\cdot}{\cdot}H_2O]]^{^\ast_\ast})$ have a kind of 6-membered $(Pt-Cl{\cdot}{\cdot}{\cdot}HOH{\cdot}{\cdot}{\cdot}Cl)$ and $(Pt-OH{\cdot}{\cdot}{\cdot}Cl{\cdot}{\cdot}{\cdot}HN)$ interactions, respectively, wherein a central Pt(II) metal directly combines with a leaving $Cl^-$ and an entering $H_2O$. Simultaneously, the entering $H_2O$ interacts with a leaving $Cl^-$. No vertical one metal-ligand interactions $([PtY_2L_2{\cdot}{\cdot}{\cdot}L^\prime]) $ are found at the axial positions of the square planar $(PtY_2L_2)$ complexes, which were formed via a vertically associative mechanism leading to $D_{3h}$ or $C_{2v}$-transition state symmetry. The geometrical structure variations, molecular orbital variations (HOMO and LUMO), and relative stabilities for the ligand exchange processes are also examined quantitatively. Schematic diagrams for the dissociation reactions of {PtCl4(H2O)n(n=2,4)} into {$PtCl_3(H_2O)_{(n-2)}\;+\;Cl^-(H_2O)_2$} and the binding energies {$PtCl_4(H_2O)_n$(n = 1-5)} of $PtCl_4$ with water molecules are drawn.

• Korean Journal of Food Science and Technology
• /
• v.29 no.6
• /
• pp.1241-1247
• /
• 1997

Gel-type fermented milk was prepared from milk or mixture of milk and apple juice/grape juice. Acid production (pH change) and growth of Lactobacillus acidophilus (KCTC 2182) were studied. The effects of juice addition on sensory property of fermented milk were also studied. The pH value of samples containing mixture of milk and apple juice/grape juice (25 mL : 25 mL to 5 mL : 45 mL) was lower than that of milk sample. However, number of viable cells of L. acidophilus at 21 hr in milk and samples containing juices was similar. During lactic fermentation for 24 hr, pH of all samples dropped significantly between 6 hr and 21 hr. pH values of mixture of milk and juices were lower than that of milk sample. Growth curve showed that lag phase continued to approximately 3 hr and log phase continued to approximately 15 hr in all samples. Number of viable cells in all samples was similar Sensory evaluation showed that overall acceptability of fermented milk prepared from apple juice/grape juice and milk (15 mL : 35 mL or 5 mL : 45 mL) was better than that of reference sample. The optimum ratio of mixture of juice and milk was 15 mL : 35 mL. The score values of sensory test of fermented milk prepared from mixture of grape juice and milk were slightly higher than those of mixture of apple juice and milk.

• Journal of Microbiology and Biotechnology
• /
• v.17 no.5
• /
• pp.721-727
• /
• 2007

Stability-enhanced mutants, H44, 11-94, 5A2-84, and F8, of L-threonine aldolase(L-TA) from Streptomyces coelicolor A3(2)(SCO1085) were isolated by an error-prone PCR followed by a high-throughput screening. Each of these mutant, had a single amino acid substitution: H177Y in the H44 mutant, A169T in the 11-94 mutant, D104N in the 5A2-84 mutant and F18I in the F8 mutant. The residual L-TA activity of the wild-type L-TA after a heat treatment for 20 min at $60^{\circ}C$ was only 10.6%. However, those in the stability-enhanced mutants were 85.7% for the H44 mutant, 58.6% for the F8 mutant, 62.1% for the 5A2-84 mutant, and 67.6% for the 11-94 mutant. Although the half-life of the wild-type L-TA at $63^{\circ}C$ was 1.3 min, those of the mutant L-TAs were longer: 14.6 min for the H44 mutant, 3.7 min for the 11-94 mutant, 5.8 min for the 5A2-84 mutant, and 5.0 min for the F8 mutant. The specific activity did not change in most of the mutants, but it was decreased by 45% in the case of mutant F8. When the aldol condensation of glycine and 3,4-dihydroxybenzaldehyde was studied by using whole cells of Escherichia coli containing the wild-type L-TA gene, L-threo-3,4-dihydroxyphenylserine(L-threo-DOPS) was successfully synthesized with a yield of 2.0 mg/ml after 20 repeated batch reactions for 100 h. However, the L-threo-DOPS synthesizing activity of the enzyme decreased with increased cycles of the batch reactions. Compared with the wild-type L-TA, H44 L-TA kept its L-threo-DOPS synthesizing activity almost constant during the 20 repeated batch reactions for 100 h, yielding 4.0 mg/ml of L-threo-DOPS. This result showed that H44 L-TA is more effective than the wild-type L-TA for the mass production of L-threo-DOPS.