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ON THE NORM OF THE OPERATOR aI + bH ON Lp(ℝ)

  • Ding, Yong;Grafakos, Loukas;Zhu, Kai
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.4
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    • pp.1209-1219
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    • 2018
  • We provide a direct proof of the following theorem of Kalton, Hollenbeck, and Verbitsky [7]: let H be the Hilbert transform and let a, b be real constants. Then for 1 < p < ${\infty}$ the norm of the operator aI + bH from $L^p(\mathbb{R})$ to $L^p(\mathbb{R})$ is equal to $$\({\max_{x{\in}{\mathbb{R}}}}{\frac{{\mid}ax-b+(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}ax-b-(bx+a){\tan}{\frac{\pi}{2p}}{\mid}^p}{{\mid}x+{\tan}{\frac{\pi}{2p}}{\mid}^p+{\mid}x-{\tan}{\frac{\pi}{2p}}{\mid}^p}}\)^{\frac{1}{p}}$$. Our proof avoids passing through the analogous result for the conjugate function on the circle, as in [7], and is given directly on the line. We also provide new approximate extremals for aI + bH in the case p > 2.

Crystallograpbic and Magnetic Properties of $Ni_{0.65}Zn_{0.35}Cu_{0.3}Fe_{1.7}O_4$ ($Ni_{0.65}Zn_{0.35}Cu_{0.3}Fe_{1.7}O_4$의 결정학적 및 자기적 특성 연구)

  • 김우철;김삼진;김철성;이승화
    • Journal of the Korean Magnetics Society
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    • v.9 no.3
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    • pp.136-142
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    • 1999
  • $Ni_{0.65}Zn_{0.35}Cu_{0.3}Fe_{1.7}O_4$ has been studied with x-ray diffraction, Mossbauer spectroscopy, and vibrating sample magnetometer. The crystal structure is found to be a cubic spinel with the lattice constant $a_0=8.403{\AA}$. Mossbauer spectra of have been taken at various temperatures ranging from 12 K to 665 K. as the temperature increases toward $T_N$ a systematic line broadening effect in the Mossbauer spectrum is observed and interpreted to originate from different temperature dependencies of the magenetic hyperfine fields at various iron sites. Also, by using binomial distribution equation we obtained the hyperfine fields of tetrahedral[A] and octahedral sites[B], $H_{hf}(A)=470\;kOe,\; H_{hf}(B0)=495 \;kOe,\; H_{hf}(B1)=485\;kOe, \;H_{hf}(B2)=453\;kOe,\; H_{hf}(B3)=424\;kOe,\; H_{hf}(B4)=390\;kOe,\; H_{hf}(Bavr)=451\;kOe$ respectively at room temperature. The isomer shift indicates that the iron ions are ferric at tetrahedral[A] and octahedral sites[B], respectively. The Neel temperature is determined to be $T_N=665\;K$. The results of the VSM data gave the magnetic moment and coercivity values of $M_S=66\; emu/g\;and\;H_C=36\;Oe$.

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Physical and Sensory Characteristics of Korean Style Meat Products (한국형 육가공 제품류의 물리적 및 관능적 품질 특성)

  • Kim, I.S.;Jin, S.K.;Hah, K.H.;Lyou, H.J.;Park, K.H.
    • Journal of Animal Science and Technology
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    • v.47 no.1
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    • pp.49-56
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    • 2005
  • The Korean styled meat products such as grilled and/or roasted ham(Jikhwagui: J), Bulgogi ham(B), Kimbab ham(K) and sliced roasted ham(DDukgalbi: D) were obtained from different Korean meat processing companies and investigated for their salinity, saccharinity, pH, moisture and fat content, meat color and sensory evaluation. The results obtained were as follows; Percentage of saccharinity in J, B, K and D ranged 7.5 %(13) - 12.7% (J2), 5.3 0/«B2) -7.5 o/«BI), 5.2 0/«K4) - 6.6 o/«KI, K2, KS), and 6.60/«04) - 14.4o/«Dl), respectively. Percentage of salinity in J, B, K and D ranged 2.260/«13)- 2.38 0/«J4), 1.850/«B2) - 2.45 0/«B3), 1.94o/«KI) - 2.40% (K3), and 1.830/«02) - 2.19 o/«Dl), respectively. The pH value of J, B and K were ranged 6.30 - 6.44, 6.266.37 and 6.20 - 6.42, respectively, which are slightly higher than that of D(5.86 - 6.25). Content of average moisture were higher in B(61.0 %), K(59.94%) and J(59.63%) compared to the D(55.93%). In crude fat, B and D were ranged 14-21 %, which are very lower than those of K(59.94%) and J(59.63%). In meat color, $L^*$ value were above 50.0, except D2 and D3. $a^*$ value of B were slightly higher than those of other meat products. Compared to sensory evaluation, the overall acceptability of J is excellent in the range of saccharinity 12.7%, salinity 2.3 %, moisture 61 %, crude fat II - 12%, $L^*$ value 52 - 54, and $a^*$ value 12.3- 12.7. In the case of B, the overall acceptability is excellent in the range of saccharinity 6.6 - 7.5 %, salinity 1.90- 2.45 %, moisture 60 %, crude fat 15 %, $L^*$ value 56, and $a^*$ value 15. In the case of K, the overall acceptability is excellent in the range of saccharinity 6.5 %, salinity 2.4 %, moisture 61 %, crude fat 16%, $L^*$ value 53, and $a^*$ valuce 15. In the case of D, the overall acceptability is excellent in the range of saccharinity 14.0%, salinity 2.1 %, moisture 55%, crude fat 55%, $L^*$ value 50, and $a^*$ value 13.

Synthesis of (${\pm}$)-cis-8-amino-l-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno [1,2-b][1,4]oxazine ((${\pm}$)-cis-8-Amino-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno [1,2-b][1,4]oxazine의 합성)

  • Ma, Eun-Sook
    • YAKHAK HOEJI
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    • v.52 no.6
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    • pp.488-493
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    • 2008
  • 2-Aminothiazole ring as a bioisoster of catechol in dopamine has provided with good oral availability and lipophilic property. 2-Aminoindan, is a rigid form of dopamine, was evaluated as a dopamine D3 agonist with low neurotoxicity. Dopamine D3 agonist was evaluated as selective for the treatment of Parkinson's disease. In order to develop a novel dopamine D3 agonist, we tried to synthesize the aminothiazoloindenoxazine derivative that is a hybrid structure of aminoindenoxazine and thiazole ring. cis-2-Amino-1-indanol (2) was synthesized from 1,2-indandione-2-oxime by catalytic hydrogenation and it was treated with chloroacetyl chloride and NaH in benzene solution to give (${\pm}$)-cis-4,4a,5,9b-tetrahydroindeno[1,2-b][1,4]oxazin-3(2H)-one (6). Nitration of 6 by the mixed acid gave 8-nitro compound (7) and the carbonyl group of 7 was reduced with $LiAlH_4$ to afford compound (8). 8 was reduced to form (${\pm}$)-cis-8-amino-2,3,4,4a,5,9b-hexahydroindeno[1,2-b][1,4]oxazine (9) and finally it was cyclized with KSCN in glacial acetic acid to yield (${\pm}$)-cis-8-amino-2,3,4,4a,5,10b-hexahydrothiazolo[4,5-f]indeno[1,2-b][1,4]oxazine (10).

Cytotoxicity of Compound K (IH-901) and Ginsenoside Rh2, Main Biotransformants of Ginseng Saponins by Bifidobacteria, against Some Tumor Cells

  • Shin, Ji-Eun;Park, Eun-Kyung;Kim, Eun-Jin;Hong, Yoon-Hee;Lee, Kyung-Tae;Kim, Dong-Hyun
    • Journal of Ginseng Research
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    • v.27 no.3
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    • pp.129-134
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    • 2003
  • When ginsenoside $R_{*}$b1/ and $R_{b2}$ were anaerobically incubated with human fecal microflora, these ginsenosides were metabolized to compound K (IH-901). When ginsenoside $R_{g3}$ was anaerobically incubated with human fecal microflora, the ginsenoside $R_{g3}$ was metabolized it to ginsenoside $R_{h2}$. Among ginsenosides, IH-901 and 20(S)-ginsenoside $R_{h2}$ exhibited the most potent cyotoxicity against tumor cells: 50% cytotoxic concentrations of IH-901 in the media with and without fetal bovine serum (FBS) were 27.1-31.6 $\mu$M and 0.1-0.61 $\mu$M, and those of 20(S)-ginsenoside $R_{h2}$ were 37.5->50 and 0.7-7.1 $\mu$M, respectively. The cytotoxic potency of ginsenosides was IH-901>20(S)-ginsenoside R $h_{h2}$》20(S)-ginsenoside $R_{g3}$>ginsenoside $R_{b1}$(equation omitted) $R_{b2}$.EX>$R_{b2}$./.

Purification and Characterization of Lactate Dehydrogenase Isozymes in Channa argus (가물치(Channa argus) 젖산탈수소효소 동위효소들의 정제 및 특성)

  • Park, Eun-Mi;Yum, Jung-Joo
    • Journal of Life Science
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    • v.20 no.2
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    • pp.260-268
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    • 2010
  • The lactate dehydrogenase (EC 1.1.1.27, LDH) isozymes in tissues from Channa argus were purified and characterized by biochemical, immunochemical and kinetic methods. The activity of LDH in skeletal muscle was the highest at 380.4 units and those in heart, eye and brain tissues were 13.4, 3,5 and 5.4 units, respectively. Citrate synthase (EC 4.1.3.7, CS) activity in heart tissue was the highest at 20.7 units. LDH/CS in skeletal muscle, heart, eye and brain tissues were 172.9, 0.6, 0.32 and 0.47. Protein concentration in skeletal muscle tissue was 14.7 mg/g and specific activities of LDH in skeletal muscle, heart, eye and brain tissues were 25.88, 0.79, 0.31 and 1.38 units/mg, respectively. Therefore, skeletal muscle tissue was anaerobic and heart tissue was aerobic. The LDH isozymes in tissues were identified by polyacrylamide gel electrophoresis, immunoprecipitation and Western blot with antiserum against $A_4$, $B_4$, and eye-specific $C_4$. LDH $A_4$, $A_3B$, $A_2B_2$. $AB_3$ and $B_4$ isozymes were detected in every tissue, $C_4$, $AC_3$, $A_2C_2$ and $A_3C$ were detected in eye tissue, and $A_3C$ was found in brain tissue. LDH $A_4$, $A_3B$, $A_2B_2$, $AB_3$, $B_4$, eye-specific $C_4$ isozymes were purified by affinity chromatography and Preparative PAGE Cells. The LDH $A_4$ isozyme was purified in the fraction from elution with $NAD^+$ containing buffer of affinity chromatography. Eye-specific $C_4$ isozyme was eluted right after $A_4$, after which $B_4$ isozyme was eluted with plain buffer. As a result, one part of molecular structures in $A_4$, $B_4$ and eye-specific $C_4$ were similar, but were different from each other in $B_4$ and $C_4$. Therefore the subunit A may be conservative in evolution, and the evolution of subunit B seems to be faster than that of subunit A. The activity of LDH $A_4$, $A_2B_2$, $B_4$, and eye-specific $C_4$ isozymes remained at 39.98, 21.28, 19.67 and 16.87% as a result of the inhibition by 10 mM of pyruvate, so the degree of inhibition was very high. The $Km^{PYR}$ values were 0.17, 0.27 and 0.133 mM in $A_4$, $B_4$ and eye-specific $C_4$ isozymes, respectively. The optimum pH of LDH $A_4$, $B_4$, eye-specific $C_4$, $A_2B_2$, $A_3B$, and $AB_3$ were pH 6.5, pH 8.5, pH 5.5, pH 6.0-6.5, pH 5.0 and pH 7.5. The $A_4$ and heterotetramer isozymes stabilized a broad range of pH. Especially, LDH activities in skeletal muscle tissue were high, resulting in a high degree of muscle activity.LDH metabolism in eye tissue seems to be converted faster from pyruvate to lactate by eye-specific $C_4$ isozyme as eye-specific $C_4$ have the highest affinity for pyruvate, and right after the conversion, oxidation of lactate was induced by $A_4$ isozyme. It was found that expression of Ldh-C, affinity to substrate and reaction time of $C_4$ isozyme were different according to the ecological environmental and feeding capturing patterns.

Transcriptional repression of ANGPT1 by histone H3K9 demethylase KDM3B

  • Han, Arim;Chae, Yun-Cheol;Park, Jin Woo;Kim, Kee-Beom;Kim, Ji-Young;Seo, Sang-Beom
    • BMB Reports
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    • v.48 no.7
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    • pp.401-406
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    • 2015
  • Here we report that the H3K9 demethylase KDM3B represses transcription of the angiogenesis regulatory gene, ANGPT1. Negative regulation of ANGPT1 by KDM3B is independent of its Jumonji (JmjC) domain-mediated H3K9 demethylase activity. We demonstrate that KDM3B downregulates ANGPT1 via interaction with SMRT, and suggest that the repressor complex is formed at the promoter area of ANGPT1. Using MTT and wound healing assays, depletion of KDM3B was found to increase cell proliferation and cell motility, indicating that KDM3B has a role in angiogenesis. [BMB Reports 2015; 48(7): 401-406]

Synthesis of Cephalosporin Derivatives with Triazolylthiomethylpyrrolidines at the C-3 Side Chain (트리아조릴 티오메칠피로리딘을 3번 측쇄에 가진 세파로스포린 유도체의 합성)

  • 고옥현;홍준희
    • YAKHAK HOEJI
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    • v.46 no.5
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    • pp.313-319
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    • 2002
  • Synthesis of 7$\beta$-[(Z)-2-(2-aminothiazol-4-yl)-2-(1-carboxy-1-methylethoxyimino)acetamido]-3-[[(3S, 5S)-5-[4-phenyl-5-(4-methylphenyl or 2-thiophenyl)-4H-l, 2, 4- triazol-3-yl]thiomethylpyrrolidin-3-yl]]thiomethyl-3-cephem-4-carboxylic acids (7a, 7b) were described. (2S, 4S)-4-acethylthio-2-[4-phenyl-5-(4-methylphenyl or 2-thiophenyl)-4 H-1, 2, 4-triazol-3-yl]thiomethyl-1-tert-butoxycarbonylpyrrolidines (4a, 4b) were prepared from trans-4-hydroxy-L-proline with (2S, 4R)-absolute configuration as starting material. 4-Phenyl-5-(4-methylphenyl or 2-thiophenyl)-4 H-l, 2, 4-triazol-3-thiols (2a, 2b) were prepared from p-toluic anhydride and 2-thiophene carboxylic acid hydrazide, respectively. p-Methoxybenzyl 7$\beta$-(Z)-2-(2-for-mamidothiazol-4-yl)-2-(1-tert-butoxycarbonylisopropylimino]acetamido-3-[[ (3S, 5S)-5-[4-phenyl-5-(4-methylphenyl or 2-thio phenyl)-4H-1, 2, 3-triazol-3-yl]thiomethyl-1- tert-butoxycarbonylpyrrolidin-3-yl]]thiomethyl-3-cephem-4-carboxylates (6a, 6b) were achieved by using p-methoxybenzyl ]7P-(Z)-2-(2-formamidothiazol-4-yl)-2-(tert-butoxycarbonylisopropylimino] acetamido-3-chloromethyl-3-cephem-4-carboxylate (5) and (2S, 4S)-4-acethylthio-2-[4-phenyl-5-(4-methyl phenyl or 2-thiophenyl)-4H-1, 2, 4-triazol-3-yl]thiomethyl-1-tert-butoxycarbonyl pyrrolidines (4a, 4b). Removal of formyl, Boc, and p-methoxybenzyl protecting groups were carried out by triflu oroacetic acid and anisole to give the target compounds.

Thienobenzothiopyranones 111-New 4H-thieno[2,3-b][1]benzothiopyran-4-ones Carrying Different Heterocyclic Moieties of Expected Pharmacological Interest

  • El-Subbagh, H.I.;El-Emam, A.A.;El-Ashmawy, M.B.;Shehata, I.A.
    • Archives of Pharmacal Research
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    • v.13 no.1
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    • pp.24-27
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    • 1990
  • Reaction of 2-formyl-4H-thieno [2, 3-b] benzothiopyran-4-one (1) with different heterocyclic amines afforded the corresponding Schiff's bases (2-4). Diethyl malonate, ethyl cyanoacetate and malononitrile were reached with 1 to afford compounds 5, 7 and 8, respectively. Compound 5 was cyclized to the pyrazolidin-3, 4-dione (6) by the action of hydrazine hydrate, whereas compound 7 was utilized for the synthesis of the thiazolin-4 one derivatives (9-13).

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