• The Mathematical Education
• /
• v.21 no.3
• /
• pp.7-11
• /
• 1983

A measurable function f defined on a measurable subset A of the real line R is called pth power summable on A if │f│$^{p}$ is integrable on A and the set of all pth power summable functions on A is denoted by L$^{p}$ (A). For each member f in L$^{p}$ (A), we define ∥f∥$_{p}$ =(equation omitted) For real numbers p and q where (equation omitted) and (equation omitted), we discuss the Holder's inequality ∥fg∥$_1$<∥f∥$_{p}$ ∥g∥$_{q}$ , f$\in$L$^{p}$ (A), g$\in$L$^{q}$ (A) and the Minkowski inequality ∥＋g∥$_{p}$ <∥f∥$_{p}$ ＋∥g∥$_{p}$ , f,g$\in$L$^{p}$ (A). In this paper also discuss that L$_{p}$ (A) becomes a metric space with the metric $\rho$ : L$^{p}$ (A) $\times$L$^{p}$ (A) longrightarrow R where $\rho$(f,g)=∥f-g∥$_{p}$ , f,g$\in$L$^{p}$ (A). Then, in this paper prove the Riesz-Fischer theorem, i.e., the space L$^{p}$ (A) is complete and that the space L$^{p}$ (A) is separable.

• Journal of Life Science
• /
• v.19 no.8
• /
• pp.1033-1038
• /
• 2009

Maximal productions of gellan by Sphingomnas paucibilis NK2000 from 20 g/l glucose and 10 g/l soybean pomace were 7.46 g/l in a flask and 7.35 g/l in a 7 l bioreactor, when the initial pH of media was 6.8. Maximal production of gellan in a 7 l bioreactor under pH control by sodium hydroxide was 8.42 g/l, whereas that under control by potassium phosphate was 8.50 g/l. The optimal concentration of potassium phosphate in a medium for production of gellan by S. paucibilis NK2000 was found to be 5.0 g/l. Maximal production of gellan in a medium containing 5.0 g/l potassium phosphate without pH control was 8.93 g/l in a 7 l bioreactor. In this study, a simple process without pH control was developed to enhance the production of gellan, with optimized concentration of potassium phosphate in the medium.

• KSBB Journal
• /
• v.14 no.5
• /
• pp.628-632
• /
• 1999

Optimization of the medium and fermentation conditions for erythritol production has been studied. We have found that the optimal carbon source was glucose at the concentration of 400 g/L. The optimal temperature was 3$0^{\circ}C$ with excessive aeration. Improved erythritol productivity was achieved by reducing the yeast extract from 5 g/L to 3g/L while adding 2.7 g/L urea, 1.79g/L $K_2HPO_4, and 0.18g/L MgSO$_4$. 7$H_2O. The erythritol productivity increased from 0.747 g/L/h to 1.071 g/L/h and the yield increased from 31.4% to 45.2%. The byproduct glycerol was reduced from 96.6g/L to 45.7g/L as well. We have performed 5L fermentation with and without the pH control. The erythritol productivity with the pH control was about 30% lower than that without pH control. Excessive foaming of 5L fermentation has been observed during fermentation.

• KSBB Journal
• /
• v.7 no.2
• /
• pp.149-153
• /
• 1992

Pseudomanas fluorescens was selected from mushroom and studied in both batch and continuous culture in order to find out optimum conditions for cultivation. P. fluorescens is an aerobic bacterium and antagonistic to Pseudomonas tolaasii which causes blotch disease on the mushroom cap. Cells of P. fluorescens were grown well on medium containing 30g/L of glucose, whereas the growth was inhibited with the glucose concentration at higher than 30g/L. The highest value of specific growth rate and productivity were obtained when using 10g/L of yeast extract. Optimum concentrations of $NH_4Cl$ and $(NH_4)_2SO_4$ 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 sulfur source was 1.0g/L. It was also found that the cell concentrations were at 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.fluorescens at high initial dissolved oxygen (D.O) value led to a decrease of bacterial productivity in batch culture. Maximum productivity was achieved at 68 for the initial D.O value.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.3
• /
• pp.589-597
• /
• 1999

Let G be a closed subspace of a Banach space X and let (S,$\Omega$,$\mu$) be a $\sigma$-finite measure space. It was known that $L_1$(S,G) is proximinal in $L_1$(S,X) if and only if $L_p$(S,G) is proximinal in $L_p$(S,X) for 1$\infty$. In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if G is a proximinal subspace of X such that either G or the kernel of the metric projection $P_G$ is separable then, for 0 < p $\leq$ $\infty$. $L_p$(S,G) is proximinal in $L_p$(S,X)

• Analytical Science and Technology
• /
• v.15 no.1
• /
• pp.54-66
• /
• 2002

In order to study systematic survey of Kumho river pollution, water analysis for 24 items was conducted at 16 sites surrounding the Kumho river system for 3 times from May 2000 to February 2001. Analytical items for the study of water quality are as follows; water temperature, pH, BOD, COD, DO, SS, electrical conductivity, oil & grease, ABS, phenol, T-P, ${PO_4}^{3-}-P$, T-N, $NH_3-N$, ${NO_2}^--N$, ${NO_3}^--N$, Cu, Zn, Cr, Cd, Mn, Fe, Pb and As. The mean values obtained for water temperature, pH, BOD, COD, DO, SS, electrical conductivity, oil & grease, ABS, phenol T-P, T-N, Cu, Zn, Fe and Mn showed $17.84^{\circ}C$, 8.04, $2.54{\mu}g/mL$, $5.64{\mu}g/mL$, $7.07{\mu}g/mL$, $8.75{\mu}g/mL$, $600.4{\mu}S/cm$, $0.19{\mu}g/mL$, $0.015{\mu}g/mL$, $0.29{\mu}g/mL$, $0.21{\mu}g/mL$, $5.22{\mu}g/mL$, $0.005{\mu}g/mL$, $0.007{\mu}g/mL$, $0.044{\mu}g/mL$ and $0.001{\mu}g/mL$ respectively. As, Cd, Cr and Pb are not detected. The mean concentration of phenol, $NH_3-N$ and $NO_2-N$ were found to be increased compared to the prior study for 3 years from January 1997 to December 1999, that of BOD, COD, SS, oil & grease and ABS were found to be decreased and the others are nearly constant. The effect of Kumho river to the Nakdong river pollution are as follows. The mean concentration of BOD changed from $1.07{\mu}g/mL$ to $1.42{\mu}g/mL$ before and after of introducing of Kumho river water respectively. The mean concentration of COD, electrical conductivity, oil & grease, ABS, phenol, T-N and T-P changed from $1.99{\mu}g/mL$, $221{\mu}S/cm$, $0.15{\mu}g/mL$, $0.006{\mu}g/mL$, $0.06{\mu}g/mL$, $2.21{\mu}g/mL$ and $0.08{\mu}g/mL$ to $2.44{\mu}g/mL$, $392{\mu}S/cm$, $0.16{\mu}g/mL$, $0.015{\mu}g/mL$, $0.07{\mu}g/mL$, $2.81{\mu}g/mL$ and $0.19{\mu}g/mL$ respectively.

• Journal of the Korean Chemical Society
• /
• v.8 no.4
• /
• pp.192-199
• /
• 1964

Seasonal variations of the contents of some chemical constituents of the estuary water at two definite stations of the laver bed in Nack Dong River have been determined over one tidal cycle in spring tide from Nov. 1962 to Oct. 1963. The ranges of annual variations of the contents at station 1 and station 2 are as follows: water temp. $2.2-30.8^{\circ}C$, $3.3-28.0^{\circ}C$; pH 7.8-8.5, 7.9-8.4; chlorosity 0.025-19.66 g/l, 4.31-19.56 g/l; magnesium 0.00355-1.565 g/l, -1.524 g/l; calcium 0.00557-0.482 g/l, - -0.590 g/l; saturation % of dissolved oxygen 71.8-123.2%, 88.2-113.8%; silicate-Si 8.00-125.5 ${\mu}$g-at./l, 6.70-100.5 ${\mu}$g-at./l; phosphate-P 0.12-1.47 ${\mu}$g-at./l, 0.11-1.09 ${\mu}$g-at./l; ammonia-N 4.88-25.45 ${\mu}$g-at./l, 4.12-17.58 ${\mu}$g-at./l; nitrite-N 0.07-0.75 ${\mu}$g-at./l, 0.08-0.58 ${\mu}$g-at./l; nitrate-N 2.11-6.89 ${\mu}$g-at./l, 1.85-7.43 ${\mu}$g-at./l each. The annual tidal variations of the constituents at station 1 are more remarkable than of station 2. The chlorosity, magnesium and calcium contents are decreased nearing the slack after ebb, and increased abruptly then one hour after the slack. The contents of the other constituents are varied according to the chlorosity variety. The values of pH, chlorosity, magnesium and calcium contents are lower in summer than winter, while the difference of seasonal variations of the % saturation of dissolved oxygen is not remarkable. The phosphate-P and total nitrogen contents have a tendency of increasing within a definite range, while the silicate-Si increase proportionally, to the increasing of mixing percentage of fresh water. The average values of Si/P and N/P are several times greater than of the normal in sea water. The chemical composition considered from the value of Mg/Cl or Ca/Cl of estuarine water varies according to the variety of chlorosity, even at the high chlorosity of 19 g/l.

• Journal of Bio-Environment Control
• /
• v.26 no.2
• /
• pp.115-122
• /
• 2017

Objective of this research was to investigate the influence of lowered substrate pH on the reduction of bicarbonate injury in the vegetative growth of 'Ssanta' strawberry. The acid substrate was formulated by mixing sphagnum peat moss with pine bark (5:5, v/v) and the pH, EC, and CEC of the substrate were 4.07, $0.46dS{\cdot}m^{-1}$, and $91.3cmol^+{\cdot}kg^{-1}$, respectively. To adjust the pH of acid substrate, various amount of dolomitic lime [$CaMg(CO_3)_2$] were incorporated with the rate of 0 (untreated), 1, 2, 3, and $4g{\cdot}L^{-1}$. Then, mother plants were transplanted and grown with fertilizer solution containing $240mg{\cdot}L^{-1}$ of the $HCO_3{^-}$ and equal concentrations of essential nutrients to Hoagland solution. In growth of 'Ssanta' strawberry, fresh weight of mother plants were the highest in the treatment of $2g{\cdot}L^{-1}$ dolomitic lime such as 102.1 g followed by 94.7 g in $1g{\cdot}L^{-1}$, 91.2 g in $3g{\cdot}L^{-1}$, 75.7 g in $0g{\cdot}L^{-1}$ and 72.3 g in $4g{\cdot}L^{-1}$ treatments. The dry weight showed a similar tendency to fresh weight. At 140 days after transplanting, 5.8, 9.8, 11.8, 8.8, and 5.0 daughter plants were derived from each of the mother plants in the treatments of 0, 1, 2, 3, and $4g{\cdot}L^{-1}$ dolomitic lime, respectively. The highest occurrence of daughter plants were observed in the treatments $2g{\cdot}L^{-1}$ dolomitic lime. The substrate pH and bicarbonate concentration of 'Ssanta' strawberry seedlings in the 1 and $2g{\cdot}L^{-1}$ dolomitic lime treatments were maintained at a proper range such as 5.6 to 6.2. The micro-nutrient contents of above ground tissue in mother plants were the highest in $2g{\cdot}L^{-1}$ and the lowest in $4g{\cdot}L^{-1}$ dolomitic lime treatment. The above results indicate that incorporation rate of dolomitic lime in acid substrate with the pH of around 4 is $2g{\cdot}L^{-1}$ to raise the 'Ssanta' strawberry in propagation.

• Asian-Australasian Journal of Animal Sciences
• /
• v.15 no.8
• /
• pp.1128-1133
• /
• 2002

The whole plant of crop maize was chopped and ensiled in airtight 1-L capacity glass jars to determine the influence of residual sugar on anaerobic yeast growth and on the fermentation of lactic acid by L. buchneri in whole crop maize silage. There were a total of six treatments used in this experiment as follow: added 25 g de-mineralised water per kg chopped maize serving as control (con), 37.5 g glucose solution containing 12.5 g glucose ($g_1$), 75 g glucose solution containing 25 g glucose ($g_2$), 25 g L. buchneri suspension intended for $10^6$ cfu $g^{-1}$ (L.b.), $g_1+L.b.$ and $g_2+L.b.$ All silos were stored in the dark at $20^{\circ}C$ until end of experiment. Jars were opened on duplicates at day 2, 7, 14, 28, 56 or triplicates at day 91 after ensiling for measuring the pH, microbiological enumeration and fermentative products. Results indicated that acidification rates for all silages were very fast, no difference occurred among treatments before day 28. After day 28 the pH values for silages inoculated by L. buchneri. with or without sugar tended to increase especially for treated only with L. buchneri, resulting in higher (p<0.01) finial pH than uninoculated silages. Compared with control silage, the added sugar significantly (p<0.01) increased dry matter (DM) loss, L. buchneri enhanced (p<0.01) DM loss further at different sugar existence. Silages inoculated by L. buchneri only or in combination with sugar addition contained less (p<0.01) lactic acid than the correspondent silages without inoculation with L. buchneri. In comparison with control, ethanol production is about 3 or 6 fold higher due to addition 12.5 or 25 g glucose per kg chopped maize at ensiling. The added sugar resulted in less acetic acid concentration (p<0.01) than control, but inoculation with L. buchneri increased (p<0.01) acetic acid than correspondent uninoculated silages at different sugar levels. No butyric acid and propionic acid were found in uninoculted silages, silages inoculated with L. buchneri. produced more propionic acid, 1-propanol and butyric acid. Lactobacilli counts were not influenced by added sugar, but increased (p<0.01) with inoculation of L. buchneri. The added sugar increased significantly (p<0.01) the yeast count, whereas L. buchneri showed the contrary effect. No differences were found in the aerobic stability among all treatments. In conclusions, 1) the added sugars encourage the growth of yeast and yeasts convert extra sugar into ethanol in maize silages. 2) The added sugars and L. buchneri do not influence the aerobic stability of silages stored in anaerobic silos.

• Journal of Dairy Science and Biotechnology
• /
• v.37 no.2
• /
• pp.136-153
• /
• 2019

The present study aimed to investigate the effects of skin care foods on the synthesis of pro-collagen type I C peptide and suppression of matrix metalloproteinase (MMP)-1 secretion through an in vitro study using fibroblasts (Hs68 cells) and keratinocytes (HaCaT cells). Among the three skin care foods developed in this study, three beans cookie and avocado yoghurt influenced the production of pro-collagen type I C peptide and suppressed MMP-1 secretion; however, tiger nut Galsu drink did not exhibit these effects. All skin care foods, including three beans cookie and plain yoghurt ($50{\mu}g/mL$, p<0.001) influenced the suppression of MMP-1 in addition to other commercially available breast milk production support foods examined, such as Heath Heather ($50{\mu}g/mL$, p<0.001), Happy Mama ($50{\mu}g/mL$, p<0.01), BioLys ($50{\mu}g/mL$, p<0.001), Enfamama ($25{\mu}g/mL$, p<0.0001), and Pregnagen ($25{\mu}g/mL$, p<0.001). Avocado fruit yoghurt ($25{\mu}g/mL$, p<0.05), avocado fruit jam yoghurt ($50{\mu}g/mL$, p<0.01), Enfamama ($100{\mu}g/mL$, p<0.05), and Pregnagen ($100{\mu}g/mL$, p<0.05) influenced the production of pro-collagen type I C peptide and suppressed MMP-1 secretion. This result indicates that only avocado jam yoghurt significantly influenced both the prevention of skin keratinization and acceleration of recovery of skin fibrous structure. Therefore, avocado is a favorable ingredient for nutrition-balanced dietary foods or an essential ingredient in products for revitalization of human skin.