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ON CHOWLA'S HYPOTHESIS IMPLYING THAT L(s, χ) > 0 FOR s > 0 FOR REAL CHARACTERS χ

  • Stephane R., Louboutin
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.1
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    • pp.1-22
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    • 2023
  • Let L(s, χ) be the Dirichlet L-series associated with an f-periodic complex function χ. Let P(X) ∈ ℂ[X]. We give an expression for ∑fn=1 χ(n)P(n) as a linear combination of the L(-n, χ)'s for 0 ≤ n < deg P(X). We deduce some consequences pertaining to the Chowla hypothesis implying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date no extended numerical computation on this hypothesis is available. In fact by a result of R. C. Baker and H. L. Montgomery we know that it does not hold for almost all fundamental discriminants. Our present numerical computation shows that surprisingly it holds true for at least 65% of the real, even and primitive Dirichlet characters of conductors less than 106. We also show that a generalized Chowla hypothesis holds true for at least 72% of the real, even and primitive Dirichlet characters of conductors less than 106. Since checking this generalized Chowla's hypothesis is easy to program and relies only on exact computation with rational integers, we do think that it should be part of any numerical computation verifying that L(s, χ) > 0 for s > 0 for real Dirichlet characters χ. To date, this verification for real, even and primitive Dirichlet characters has been done only for conductors less than 2·105.

Immunotoxicity Study of Separated Antigen from Helicobacter pylori. (Helicobacter pylori로부터 유래된 항원의 항원성에 관한 연구)

  • Park, Chang-Ho;Bae, Man-Jong
    • Journal of Life Science
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    • v.18 no.4
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    • pp.494-502
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    • 2008
  • The anaphylaxis shock reaction on the whole cells of H. pylori exhibited a symptom of slight illness for the first and second medication of causing antigen at an antigen concentration of WC (H) $60\;{\mu}g/100\;{\mu}l$ for WC (H) and no anaphylaxis shock symptom was observed at an antigen concentration of $20\;{\mu}g/100\;{\mu}l$ for WC (L). In the case of anaphylaxis shock reaction on the crude urease, no symptom was observed at an antigen concentration of $20\;{\mu}g/100\;{\mu}l$ for both urease (L) and urease (H). In the heterologous passive cutaneous anaphylaxis (PCA) test using a guinea pig-rat, no positive reaction was detected in all the medication groups of WC (H), WC (L), urease (H) and urease (L). In the skin sensitization test, it was observed that the best antigen concentration not causing skin disorder at each of $80\;{\mu}g/100\;{\mu}l$, $40\;{\mu}g/100\;{\mu}l$, $20\;{\mu}g/100\;{\mu}l$, and $20\;{\mu}g/100\;{\mu}l$ was $40\;{\mu}g/100\;{\mu}l$.

The Effects of Bee Venom and Melittin acupuncture solution on cPLA2, TNF-α and Calcium Concentration in RAW 264.7 Cells (봉약침액(蜂藥鍼液)과 Melittin 약침액(藥鍼液)이 RAW 264.7 Cell의 cPLA2, TNF-α 및 Calcium Concentration에 미치는 영향(影響))

  • Park, Young-eun;Song, Ho-sueb
    • Journal of Acupuncture Research
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    • v.21 no.5
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    • pp.179-190
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    • 2004
  • Objectives : The purpose of this study was to investigate the effect of Bee Venom and Melittin acupuncture solution on the lipopolysaccharide and sodium nitroprusside- induced expression of cytosolic phospholipase $A_2$, tumor necrosis factor-${\alpha}$ and calcium concentration in RAW 264.7 cells, a murine macrophage cell line. Methods : The expression of cytosolic phospholipase $A_2$ and tumor necrosis factor-${\alpha}$ was determined by western blotting with corresponding antibodies, and the generation of intracellular calcium concentration was investigated by delta scan system in RAW 264.7 cells. Results : 1. Compared with control, expressions of lipopolysaccharide-induced cytosolic phospholipase $A_2$ were decreased significantly by $5{\mu}g/mL$ of bee venom and 5, $10{\mu}g/mL$ of melittin acupuncture solution and decreased by 0.5, $1{\mu}g/mL$ of bee venom. 2. Compared with control, expressions of sodium nitroprusside-induced phospholipase $A_2$ were decreased significantly by 0.5, 1, $5{\mu}g/mL$ of bee venom and by 5, $10{\mu}g/mL$ of melittin acupuncture solution. 3. Compared with control, expressions of lipopolysaccharide-induced tumor necrosis factor-${\alpha}$ were decreased significantly by $10{\mu}g/mL$ of melittin acupuncture solution and were not changed significantly by 0.5, 1, $5{\mu}g/mL$ of bee venom and $5{\mu}g/mL$ of melittin acupuncture solution. 4. Compared with control, expressions of sodium nitroprusside-induced tumor necrosis factor-${\alpha}$ were decreased significantly by 1, $5{\mu}g/mL$ of bee venom and 5, $10{\mu}g/mL$ of melittin acupuncture solution and decreased by $0.5{\mu}g/mL$ of bee venom 5. Compared with control, lipopolysaccharide-induced intracellular calcium concentrations were decreased by 0.5, 1, $5{\mu}g/mL$ of bee venom and $10{\mu}g/mL$ of melittin acupuncture solution and increased by $5{\mu}g/mL$ of melittin acupuncture solution. 6. Compared with control, sodium nitroprusside-induced intracellular calcium concentrations were decreased by 0.5, 1, $5{\mu}g/mL$ of bee venom and 5, $10{\mu}g/mL$ of melittin acupuncture solution.

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Computation of Irrigation Interval and Amount as affected by Growing Substrate and Soil Depth Planted with Zoysia japonica in Green Roof during a Dry Summer (여름철 무강우 시 들잔디 옥상녹화 식재지반에 따른 관수주기 및 관수량 산정)

  • Ju, Jin-Hee;Bae, Gyu-Tae;Kim, Won-Tae;Yoon, Yong-Han
    • Journal of Environmental Science International
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    • v.21 no.3
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    • pp.289-296
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    • 2012
  • The purpose of this study was to identify the irrigation intervals and the amount of suitable growing substrate needed to achieve the desired shallow-extensive green roof system during a dry summer in Korea. In terms of treatment, three types (SL, $P_6P_2L_2$, $P_4P_4L_2$) with varying soil mixture ratios and two types (15 cm, 25 cm) with varying soil depths were created. The results have been analyzed after measuring growth and soil water contents. The difference of growth by treatment was significant in terms of green coverage, height, leaf width and photosynthesis. In measurement of chlorophyll content, no difference was detected when measured against soil depth. According to the growth measurement of Zoysia japonica with respect to differing soil mixture ratios in the 15 cm-deep treatment, a statistical difference was detected at the 0.05 significance level in photosynthesis. In case of green coverage, height, chlorophyll content and leaf width, no statistical significance was observed. In case of the 25 cm-deep treatment, a statistical significance was observed in height and photosynthesis. In terms of green coverage, chlorophyll content and leaf width, no statistical significance was detected. In comparisons of soil moisture tension and soil water contents, the irrigation interval and amount were 8 days and 14.9 L in the SL (15 cm) treatment, respectively. The irrigation interval showed for 10 days a 1.3-fold increase, and the irrigation amount was 27.4 L 1.8-fold more than SL (25 cm), respectively. For $P_6P_2L_2$ (15 cm) treatment, the irrigation interval and amount were 12 days and 20.7 L, respectively. However, an irrigation interval under $P_6P_2L_2$ (25 cm) was for 15 days 1.3 times longer than $P_6P_2L_2$ (15 cm), and an irrigation amount of 40 L was 1.9 times more than that under $P_6P_2L_2$ (15 cm). In $P_4P_4L_2$ (15 cm) treatment, it was indicated that the irrigation interval was 15 days, and the irrigation amount was 19.2 L. It was not needed to irrigate for 16 days under $P_4P_4L_2$ (25 cm) treatment during the dry summer and the longest no-rain periods. The irrigation interval and amount under $P_4P_4L_2$ were 1.8-fold and 1.3-fold, respectively, more than SL treatment as affected by soil mixture ratio. Comparatively $P_4P_4L_2$ had more 1.3-fold and 0.9-fold in irrigation interval and amount more than $P_6P_2L_2$. Therefore, it can be noted that different soil depth and soil mixture ratios had a significant effect on the irrigation interval and amount.

Measurement of 1,4-dioxane in surface water by headspace GC-MS (GC-MS에 의한 지표수에서 1,4-Dioxane의 측정)

  • Hong, Seon-Haw;Lee, Jun-Bae;Lee, Soo-Hyung;Lim, Hyun-Hee;Shin, Ho-Sang
    • Analytical Science and Technology
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    • v.27 no.1
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    • pp.22-26
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    • 2014
  • 1,4-Dioxane was classified as a Group 2B carcinogen by the International Agency for Research on Cancer. The compound was measured in surface water with a headspace gas chromatographic mass spectrometric detection. A 5 mL water sample was placed in a 10 mL headspace vial and saturated with NaCl, and the solution was spiked with 1,4-dioxane-d8 as an internal standard and sealed with a cap. Water samples were collected from twenty-two basins of Gum-River on June and September 2012, respectively. As a result, 1,4-dioxane was detected in the concentration range of $0.49-43.0{\mu}g/L$ (mean $2.0{\mu}g/L$) in the frequency of about 30% in surface water samples.

Efficiency of a hybrid solid digestion-denitrification column in suspended solid and nitrate removal from recirculating aquaculture system

  • Pungrasmi, Wiboonluk;Chaisri, Ratchadaporn;Malaphol, Ekachai;Powtongsook, Sorawit
    • Environmental Engineering Research
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    • v.20 no.2
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    • pp.175-180
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    • 2015
  • This research focused on the solid and nitrate removal efficiency in a solid digestion-denitrification column. The 20 L up-flow column consisted of 18 L acrylic column with 2 L down-comer inlet tube located in the middle. In the first part, the wastewater with high suspended solids from the Tilapia fish tank was applied into the sedimentation unit at 5 variable flow rates i.e., 11.25, 25.71, 60, 105.88 and 360 L/h. The results indicated that the flow rate of 11.25 L/h (0.57 m/h) gave the highest solid removal efficiency of $72.72%{\pm}8.24%$. However, the total suspended solids removal was highest at 360 L/h (18.13 m/h). In the second part, methanol was added as an external organic carbon source for denitrification process in a hybrid column containing settled solids. The COD:N ratios of 0.5:1, 1:1, 2:1, 3:1, 4:1, 5:1 and 6:1 were investigated and compared with control without methanol addition. This experiment was operated at the HRT of 1 h with 450 L wastewater from recirculating aquaculture pond containing 100 mg-N/L sodium nitrate. The results indicated that the COD:N ratio of 3:1 gave the highest nitrate removal efficiency of $33.32%{\pm}21.18%$ with the denitrification rate of 5,102.88 mg-N/day.

The Effect of Plant Growth Regulators on Callus Induction and Shoot Regeneration from the Dwarf Type Variety, Hibiscus syriacus L.var. Ggoma (왜성 변이 품종 '꼬마' 무궁화의 캘러스 유도 및 지상부 형성에 식물생장조절물질이 미치는 영향)

  • Lee, Ji Yeon;Kang, Eun Jeong;Kim, Sang Hoon;Kim, Dong Sub;Kim, Jin-Baek;Ha, Bo-Keun;Kang, Si-Yong
    • Journal of Radiation Industry
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    • v.5 no.3
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    • pp.231-236
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    • 2011
  • 'Ggoma' is a new Hibiscus dwarf type variety developed by gamma irradiation at the Korea Atomic Energy Research Institute (KAERI). This study was conducted to determine the best optimum cultural callus formation and shoot regeneration condition. Sterilized leaf tissues were cultured on MS (Marashige and skoog's) medium containing 3% sucrose, 0.8% agar with different concentration and combination of TDZ, 2, 4-D, KT, BA, and 2iP for 4 weeks in vitro culture. MS medium containing 2,4-D $0.1mg\;l^{-1}$ and BA $0.5mg\;l^{-1}$ were most effective on callus formation and growth. After 4 weeks, callus was transferred on BA (0.5, 1, $1.5mg\;l^{-1}$) and TDZ (0.1, 0.2, $0.3mg\;l^{-1}$) for shoot formation. The best condition for inducing the shoot from callus was BA $1.5mg\;l^{-1}$ and TDZ $0.3mg\;l^{-1}$. This result will be useful for the rapid multiplication of Hibiscus syriacus L.var. Ggoma.

Identification of Pseudomonas fluorescens antagonistic to Pseudomonas tolaasii and its cultivation (버섯의 갈변병 유발세균 Pseudomonas tolaasii의 길항세균인 Pseudomonas fluorescens의 분리동정 및 배양조건)

  • 박범식;조남철전억한
    • KSBB Journal
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    • v.7 no.4
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    • pp.296-301
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    • 1992
  • A Pseudomonas fluorescens was selected from mushrooms and studied in both batch and fed-batch cultures in order to get maximal biomass concentration. P. fluorescens is an aerobic bacterium and antagonistic to Pseudomonas tolaasii which causes blotch disease on the mushroom cap. P fluarescens and P. tolaasii were identified by Gram staining, gelatin liquefaction, oxidase test, etc. and were characterized by pigment production, temperature sensitivity, salt tolerance and rapid pitting test, etc., Celts of P. fluorescens well in medium containing 30g/L of glucose, whereas the growth was inhibited at the glucose levels at higher than 30g/L. The highest values of specific growth rate and productivity were obtained when using 10g/1 of yeast extract. Optimum concentrations of $NH_4Cl$ and ${(NH_4Cl)}_2SO_4$ for culture were found to be 1.0g/L and 0.1g/L respectively. Optimum concentration of $MgSO_4{\cdot}7H_2O$ used as a sulfursource was 1.0g/L. It was also found that the cell concentrations reached the maximum level when grown on the medium containing 1.0g/L of $KH_2PO_4$ and 0.1g/L of $CaCl_2$. Also, the optimum culture conditions were $30^{\circ}C$ and pH 6.0. Cultivation of P. fluarescens at high dissolved oxygen (DO) concentration led to a decrease of bacterial productivity in batch culture. Maximum productivity was achieved at 40% DO concentration.

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Effect of Heavy Metal on Syngas Fermentation Using Clostridium autoethanogenum (Clostridium autoethanogenum을 이용한 합성가스 발효에 대한 중금속의 영향)

  • Im, Hongrae;Kwon, Rokgyu;Park, Soeun;Kim, Young-Kee
    • Applied Chemistry for Engineering
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    • v.31 no.4
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    • pp.423-428
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    • 2020
  • In this work, we investigated the effect of the concentration of medium components on microbial growth and ethanol production in order to improve ethanol productivity in the Clostridium autoethanogenum culture process using syngas as a sole carbon source. Molybenum, nickel and cobalt (as heavy metal ions) were selected as examined components, and the effects of components concentration on the cell growth and ethanol production was examined. Among molybdenum concentrations of 0, 0.001, 0.01 and 0.1 g/L. a slight increase in ethanol production was observed at 0.001 g/L, but significant differences in the microbial growth and ethanol production were not observed in the examined concentration range. In the case of nickel concentration of 0, 0.001, 0.01 and 0.1 g/L, the change in the microbial growth and ethanol production was investigated, and it was found that the ethanol production using 0.001 g/L increased by 26% compared to that of using the basal medium concentration (0.01g/L). The effect of cobalt concentrations (0, 0.018, 0.18 and 1.8 g/L) on the microbial growth and ethanol production was also investigated, and the inhibition of microbial growth was observed when the cobalt usage was over 0.18 g/L. In conclusion, cobalt did not show any further improvement of ethanol production by changing concentration, however, molybdenum and nickel showed increases in the produced ethanol concentration compared to that of using 1/10 times of the basal medium concentration.

Phenolic compounds of must and wine supplemented with Muscat Bailey A grape fruit stem (송이줄기 첨가에 따른 Muscat Bailey A 포도의 발효 중 발효액 및 포도주의 생리활성 물질 함량)

  • Jeong, Se-Hyun;Chang, Eun-Ha;Hur, Youn-Young;Jeong, Sung-Min;Nam, Jong-Chul;Koh, Sang-Wook;Choi, In-Myung
    • Food Science and Preservation
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    • v.22 no.1
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    • pp.91-99
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    • 2015
  • This study investigated the phenolic compounds of must and wine supplemented with different concentrations (0% (no added stems), 1%, 2%, 3%, and 5%) of fruit stems during winemaking using Muscat Bailey A (MBA) grapes. The red color, and total anthocyanin, total polyphenol, and tannin contents of the must and wine significantly (p<0.05) increased with increasing added amounts of grape fruit stems, while the volatile acid content decreased with increasing added amounts of grape fruit stems. Catechin (8.16~23.08 mg/L), gallic acid (2.32~3.28 mg/L), trans-resveratrol (1.38~3.27 mg/L), and ferulic acid (1.51~1.59 mg/L) were detected in the must and wine via HPLC. The bioactive substance contents increased with increasing added amounts of grape fruit stems, except for ferulic acid. The DPPH $IC_{50}$ activity was higher in the wine (12 mg/L) with 5% grape fruit stems than in ascorbic acid (67 mg/L). These results suggest that the fruit stems of MBA grapes can be used as functional materials for winemaking.