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ESTIMATES FOR RIESZ TRANSFORMS ASSOCIATED WITH SCHRÖDINGER TYPE OPERATORS

  • Wang, Yueshan
    • 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 $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

Stability of Tris(2-cyclohexylaminoethyl)amine-Zn(II) Complex (Tris(2-cyclohexylaminoethyl)amine-Zn(II) 착물의 안정성)

  • Yong Woon Shin;Hyun Sook Baek;Jae-Kyung Yang;Jineun Kim;Moo Lyong Seo
    • Journal of the Korean Chemical Society
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    • v.47 no.2
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    • pp.121-126
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    • 2003
  • Tris(2-cyclohexylaminoethyl)amine (L) was synthesized by the Schiff base condensation reaction of tris(2-aminoethyl)amine with cyclohexanone, followed by reduction. The thermodynamic characteristics, mole ratio and formation constant of [Zn(II)-L] complex were measured by the cyclic voltammetry and isothermal titration. In the case of Zn(II), well-defined cathodic and anodic peak were obtained at -1.02V and -0.48V vs Ag/AgCl , respectively. For the [Zn(II)-L] complex, both peaks were obtained at -1.19V and -0.45V vs Ag/AgCl, respectively. In addition, the peak height gradually increases as the scan rate increases, suggesting that the currents obtained were diffusion - controlled. The mole ratio and stability constant of the complex measured cyclic voltammerty were 1:1 and logK$_f$= 5.8, respectively. And the mole ratio and stability constant of the complexe calculated by isothermal titration method was 1:1 and logK =5.4, respectively. ${\Delta}$H, ${\Delta}$G and T${\Delta}$S for the complex formation were -53.0 kJ/mol, -31.1 kJ/mol, and -21.9 J/K at 25 ${\circ}$C, respectively.

Patho-anatomy and treatment of complex congenital cardiovascular anomalies associated with left superior vena cava: report of 16 cases (좌상공정맥을 합병한 복합심혈관기형의 병리해부와 수술 성적: 16례 보)

  • 정원상
    • Journal of Chest Surgery
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    • v.17 no.2
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    • pp.177-183
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    • 1984
  • From July 1975 to March 1984, 16 patients of complex congenital cardiovascular anomalies associated with left superior vena cava were seen at Han-Yang University Hospital. The age of patients was ranged from 2 to 15 years-old. The distribution of Sex was 7 patients in male, 9 patients in female. Persistent Left Superior Vena Cava [L.S.V.C.] was classified according to the proximal connection of L.S.V.C. into 3 groups. Group I which L.S.V.C. connected to coronary venous sinus was in 9 patients, Group II which L.S.V.C. connected to Left atrium was in 5 patients, Group III which L.S.V.C. hemodynamically connected to right atrium was in 2 patients. Pathoanatomical findings of complex congenital cardiovascular anomalies associated with L.S.V.C. in 16 cases were generally show unsystematic irregularity. In group I, A.S.D. were only in 3 cases, but in highest incidence and in group III, all two cases were supracardiac type of total anomalous drainage of pulmonary veins. Post-operatively, 3 patients among 14 patients of total correction, were died immediately, 1 patient of palliative shunt operation was died after 2 and half years, and Follow-up results of other remaining patients were excellent.

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Synthesis and Characterization of a $Di-{\mu}-oxo-bridged$ Molybdeum(V) Complexes (두 개 산소 가교형 몰리브덴(V)착물의 합성과 그 성질에 관한 연구)

  • Kim, Il-Chool;Kim, Yeoung-Chan
    • Journal of the Korean Applied Science and Technology
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    • v.16 no.3
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    • pp.205-210
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    • 1999
  • The Mo(V) $di-{\mu}-oxo$ type $[Mo_2O_4(H_2O)_2L]Cl_2$ complexes(L: 4,4'-Diphenyl-2,2'-dipyridyl, 4,4'-Dimethyl-2,2'-dipyridyl, 4,7-Diphenyl-1,10-phenanthroline) have been prepared by the reaction of $[Mo_2O_4(H_2O)_6]^{2+}$ with a series of chelate ligands. These complexes are completed by two terminal oxygens arranged trans to one another and each ligand forms a chelate types. In $Mo_2O_4(H_2O)_2L$ two $H_2O$ coordinated at trans site of terminal oxgens. The prepared complexes have been characterized by elemental analysis, infrared spectra, electronic spectra, $^1H$ nuclear magnetic resonance spectra, and thermal analysis(TG-DTA). In the potential range -0.00V to -1.00V at scan rate of $50mVs^{-1}$, a cathodic peak at -0.83V ${\sim}$ -0.88V (vs SCE) and an anodic peak at -0.54V ${\sim}$ -0.88V (vs SCE) have been observed in aquous solution. The ratio of the cathodic to anodic current(Ipc/Ipa) is almost 2, we infer that redox is irreversible as dimer forms broken.

Identification and Fermentation Characteristics of Lactic Acid Bacteria Isolated from Hahyangju Nuruk (하향주 누룩으로부터 분리한 젖산균의 동정 및 발효 특성)

  • Park, Chi-Duck;Jung, Hee-Kyoung;Park, Hwan-Hee;Hong, Joo-Heon
    • Food Science and Preservation
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    • v.14 no.2
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    • pp.188-193
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    • 2007
  • The purpose of this study was to isolate lactic acid bacteria, useful in the fermentation industry from Hahyangju Nuruk. Five strains were isolated, and identified as Lactobacillus based on growth inhibition by 10% (v/v) alcohol at pH 4.0. Isolated strains were identified to species, and named Lactobacillus plantarum L-3, L. sakei L-10, and L. curvatus strains L-8, L-11, and L-12. Morphological characteristics, physiological data, carbohydrate fermentation patterns, and 16S rRNA sequence data, were all used to characterize the bacterial isolates. L. plantarum L-3 showed the highest lactic acid productivity of all isolates, but grew only poony in the presence of 10% (v/v) alcohol at pH 4.0. The other strains exhibited lower lactic acid productivity than did L. plantarum L-3 and did not grow in the presence of 10% (v/v) alcohol at pH 4.0. The optimal temperature and pH for lactic acid production were $30^{\circ}C$ and pH 6.0 7.0, respectively. The lactic acid productivity of L. plantarum L-3, L. sakei L-10 and the three L. curvatus strains L-8, L-11, and L-12 were (% v/v of culture supematant) 1.55, 1.0, 1.06, 1.0, and 0.99, respectively, at $30^{\circ}C$ and pH 6.0. While L. plantarum L-3 suffered growth inhibition in the presence of 10% (v/v) alcohol, growth of the other strains was inhibited at 8% (v/v) alcohol.

EXTREMUM PROPERTIES OF DUAL Lp-CENTROID BODY AND Lp-JOHN ELLIPSOID

  • Ma, Tong-Yi
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.465-479
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    • 2012
  • For $0<p{\leq}{\infty}$ and a convex body $K$ in $\mathbb{R}^n$, Lutwak, Yang and Zhang defined the concept of dual $L_p$-centroid body ${\Gamma}_{-p}K$ and $L_p$-John ellipsoid $E_pK$. In this paper, we prove the following two results: (i) For any origin-symmetric convex body $K$, there exist an ellipsoid $E$ and a parallelotope $P$ such that for $1{\leq}p{\leq}2$ and $0<q{\leq}{\infty}$, $E_qE{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$; For $2{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, $2^{-1}{\omega_n}^{\frac{1}{n}}E_qE{\subseteq}{\Gamma}_{-p}K{\subseteq}{2\omega_n}^{-\frac{1}{n}}(nc_{n-2,p})^{-\frac{1}{p}}E_qP$ and $V(E)=V(K)=V(P)$. (ii) For any convex body $K$ whose John point is at the origin, there exists a simplex $T$ such that for $1{\leq}p{\leq}{\infty}$ and $0<q{\leq}{\infty}$, ${\alpha}n(nc_{n-2,p})^{-\frac{1}{p}}E_qT{\supseteq}{\Gamma}_{-p}K{\supseteq}(nc_{n-2,p})^{-\frac{1}{p}}E_qT$ and $V(K)=V(T)$.

The Effects of Sugar Addition in Yogurt Prepared from Egg White Powder and Casein (난백분말과 카제인으로 만든 요구르트에서 당의 첨가 효과)

  • 고영태;이주원
    • Korean journal of food and cookery science
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    • v.12 no.2
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    • pp.153-161
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    • 1996
  • A curd yogurt was prepared from egg white powder (EWP) and casein added with sugars (glucose, fructose, lactose). The effects of sugar addition on acid production and growth of Lactobacillus were studied. The effects of sugar addition on sensory property and volatile aroma compounds were also studied. Acid production by L. acidophilus in EWP 2% (W/V), casein 3% (w/v) and sugar 0.5,1 or 2% W/V) was lower than that of L. acidophilus in milk (control). Acid production in sample added with glucose or fructose of 1% or 2% (W/V) was higher than that of 0.5% (W/V), while acid production in lactose added sample was not affected with the concentration of lactose. Number of viable cells of L. acidophilus at 24 hr in milk, glucose added sample, fructose added sample and lactose added sample was 3.6${\times}$10/Sup 9/, 5.6${\times}$10$\^$8/, 6.0${\times}$10$\^$8/,and 3.2${\times}$10$\^$7/, respectively. Through 30hr fermentation, acid production and number of viable cells of L. acidophilus in milk were higher than those of sugar added samples. Sensory property of fructose added sample was slightly better than that of milk yogurt (reference), while that of lactose added sample was significantly inferior. Though the composition of volatile aroma compounds was slightly different according to sample, gas chromatographic analysis detected acetone, ethanol, diacetyl and acetoin in samples fermented by L. acidophilus.

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Micropropagation and RAPD Analysis of Somaclonal Variants in Lavandula spica cv. Marino (라벤다의 기내증식과 RAPD에 의한 체세포 변이체 분석)

  • Li, Xian Ri;Seong, Eun-Soo;Kim, Il-Seop;Yu, Chang-Yeon
    • Korean Journal of Medicinal Crop Science
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    • v.7 no.2
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    • pp.94-100
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    • 1999
  • To establish the mass propagation system of Lavandula spica cv. Marino, shoot tip, node, internode and leaf segment cultures were carried out. RAPD was applied to detect the somaclonal variation. Callus induction was very high in the medium supplemented with 1 mg/l 2.4-D, 2 mg/l NAA. especially and combined with 0.05 mg/l BAP from leaves. Shoot formation was high with $2{\sim}4\;mg/l$ BAP or 4 mg/l BAP + 0.2 mg/l NAA from shoot tip. Shoot proliferation was 9.1 times in the $B_{5}$ medium with 0.5 mg/l BAP and 0.01 mg/l NAA. Root formation was improved in NAA, which was the concentration of 0.1 to 1 mg/l and 1 mg/l IAA. Nursery survival rate was enhanced over 90% and growth was looked good in the acclimation soil consisting of peatmoss : vermiculite : perlite (1:1:1, v:v:v). Randomly amplified polymorphic DNA banding patterns based on polymerase chain reaction (PCR) were used to assess the genetic variation in plants regenerated from in vitro culture.

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Production of $poly-{\beta}-hydroxybutyric$ acid by methanol assimilating bacterium, Pseudomonas sp. ILS-003 (Methanol 자화성 세균 Pseudomonas sp. ILS-003에 의한 $poly-{\beta}-hydroxybutyric$ acid의 생산)

  • Lee, Il-Seok;Bang, Won-Gi
    • Applied Biological Chemistry
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    • v.34 no.3
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    • pp.273-278
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    • 1991
  • Methanol assimilating bacterium, Pseudomonas sp. ILS-003 was used to investigate the optimum conditions for the production of $poly-{\beta}-hydroxybutyric$ acid from methanol. For PHB production, the optimum initial pH was 6.4 and the optimum temperature was $30^{\circ}C$. Also the optimum methanol concentration was found to be 1.0%(v/v). In the PHB production, $(NH_4)_2SO_4$ was the most effective nitrogen source and the optimum concentration was 0.8 g/l, which was eqivalent to 17.4 in C/N ratio. Also, deficiency of the 2 valence metal ions in the medium had stimulating effect on PHB accumulation. Under the optimum substrate concentration, successive feeding of 0.25%(v/v) methanol was the most effective on PHB production. Under the optimum conditions, 1.94 g/l of PHB and 2.78 g/l of dry biomass were produced in 96 hours, and the yield was 69.8%(w/w).

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Study on Solid Phase Extraction and Spectrophotometric Determination of Vanadium with 2-(2-Quinolylazo)-5-Diethylaminophenol

  • Hu, Qiu-Fen;Yang, Guan-Gyu;Huang, Zhang-Jie;Yin, Jia-Yuan
    • Bulletin of the Korean Chemical Society
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    • v.25 no.2
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    • pp.263-266
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    • 2004
  • A sensitive, selective and rapid method has been developed for the determination ${\mu}$g/L level of vanadium ion based on the rapid reaction of vanadium(V) with 2-(2-quinolylazo)-5-diethylaminophenol (QADEAP) and the solid phase extraction of the colored chelate with $C_{18}$ cartridge. The QADEAP reacts with V(V) in the presence of citric acid-sodium hydroxide buffer solution (pH = 3.5) and cetyl trimethylammonium bromide (CTMAB) medium to form a violet chelate of a molar ratio 1 : 2 (V(V) to QADEAP). This chelate was enriched by solid phase extraction with $C_{18}$cartridge and the enrichment factor of 50 was obtained by elution of the chelates from the cartridge with ethanol. The molar absorptivity of the chelate is $1.28 {\times}10^5L\;mol^{-1}cm^{-1}$ at 590 nm in the measured solution. Beer's law is obeyed in the range of 0.01-0.6 ${\mu}$g/mL. The detection limit is 0.04 ${\mu}$g/L in the original samples. This method was applied to the determination of vanadium(V) in water and biological samples with good results.