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SELF-ADJOINT INTERPOLATION ON Ax = y IN ALG$\cal{L}$

  • Kwak, Sung-Kon;Kang, Joo-Ho
    • Journal of applied mathematics & informatics
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    • v.29 no.3_4
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    • pp.981-986
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    • 2011
  • Given vectors x and y in a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equations $Tx_i=y_i$, for i = 1, 2, ${\cdots}$, n. In this paper the following is proved : Let $\cal{L}$ be a subspace lattice on a Hilbert space $\cal{H}$. Let x and y be vectors in $\cal{H}$ and let $P_x$ be the projection onto sp(x). If $P_xE=EP_x$ for each $E{\in}\cal{L}$, then the following are equivalent. (1) There exists an operator A in Alg$\cal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and $A=A^*$. (2) sup $sup\;\{\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}\;:\;E\;{\in}\;{\cal{L}}\}$ < ${\infty}$, $y\;{\in}\;sp(x)$ and < x, y >=< y, x >.

Optimization of Batch Expression of Sesame Oil (참기름의 회분식 착유의 최적화)

  • 민용규;정헌상
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.24 no.5
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    • pp.785-789
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    • 1995
  • In order to optimize the batch expression of sesame oil, recovery of expressed oil(REO) from roasted and unroasted sesame seeds were observed at different temperature, pressure, pressing duration and moisture content, and relatinship between REO and effects of expression factors were analysed. REO was high at 2.5~4.5% moisture content, 30~$50^{\circ}C$ and 30~50MPa, and decreased abruptly with increasing moisture content above 4.5%. The optimum temperature, pressure, pressing duration and moisture content were $40.1^{\circ}C$, 54.4MPa, 21.7min and 1.3% for unroasted seeds and $44.4^{\circ}C$, 37.8MPa, 14.4min and 2.52% for roasted seeds, respectively. REO in optimum condition was 84.6% in unroasted seed and 81.7% in roasted seed. From the statistic analysis between effects of expression factors and REO, importance of their effects was decreased in the order of moisture content, pressure, temperature and pressing duration. And also interaction effects were high in $pressure{\times}moisture$ content, $temperature{\times}moisture$ content and temperature pressure. The multiple regression equation between REO(Y) and temperature(T), pressure(P), moisture content(M), and pressing duration(D) were as follows ; $Y=18.20$ $35.66P$$24.52M-4.45P^{2}-1.20TM-4.02PM-6.62M^{2},\;r^{2}=0.89$, for unrosated sesame seed, $Y=117.93$$16.40P-58.61M-2.75P^{2}$$1.79TM-1.65PM$$7.16M^{2},\;r^{2}$$=0.91$ for roasted sesame seed.

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Studies on the Physico-Chemical Characteristics of Different Casing Materials Affecting Mycelial Growth and Yield of Cultivated Mushroom, Agaricus bisporus (Lange) Sing. (양송이의 균사생장(菌絲生長) 및 자실체(子寶體) 수량(收量)에 미치는 복토재료(覆土材料)의 이화학적(理化學的) 성질(性質)에 관(關)한 연구(硏究))

  • Kim, Dong-Soo
    • The Korean Journal of Mycology
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    • v.3 no.1
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    • pp.1-19
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    • 1975
  • Since the importance of casing in fruit body formation of Agaricus bisporus has been emphasized, physico-chemical characteristics of casing materials were discussed by many workers and a mixture of peat and mineral soil as proper casing material has been adopted in many of mushroom growing countries. Because of limited resources of peat in Korea, it is necessary to find practical performance and substitutional materials for casing. The effect of casing on mycelial growth and mushroom yield of A. bisporus varied with materials, its combination and practices etc. The experiments to be discussed in this paper are concerned with pH and Ca of casing material which influence A bisporus, and changes of physico-chemical characteristics with mixing ratio of casing materials and its effect on A. bisporus. The optimum range of moisture content of each material, management of watering and application of physico-chemical characteristics casing materials was also investigated and re-use of weathered spent compost for casing material was described. 1. The effect of calcium on mycelial growth of A. bisporus at various pH in Halbschalentest showed different results with calcium sources. Best results were obtained around neutrality and fresh weight of fruit bodies grown in the range of pH 7 to 8 was highest among the tested levels. 2. Available moisture, pore space, organic matter, cation exchangeable capacity and exchangeable cation was increased by an increase of mixing ratio of peat in casing materials, while an adverse effect was obtained by addition of sand. 3. Mycelial growth on clay loam was more rapid at a lower bulk density of 0.75g/cc and at 20% moisture content on a dry weight basis at the same bulk density. 4. Mixing ratio of casing materials, 60 to 80 per cent by volume of peat mixed with 20 to 40 per cent of clay loam produced the highest yield of fresh fruit bodies and sand the lowest. However, per cent of open cap was highest in peat and lowest in sand. 5. Days required for fruit body initiation was shortened in mixtures of peat and clay loam by one to three days compared with other materials and the formation of flushes was clear. 6. The effect of some physico-chemical characteristics of casing materials on the fresh weight of fruit bodies were estimated by a multiple regression equation; Y=-923.86+$8.18X_1+8.04X_2+7.90X_3+0.12X_4+2.03X_5-0.82X_6-0.54X_7$ where $X_1,X_2,X_3,X_4,X_5,X_6,X_7$ are sand, silt, clay, available moistuer, porosity, organic matter and exchangeable cation respectively. The productivity of certain casing material could be predicted from this equation. 7. Fresh weight of fruit bodies was positively correlated with porosity exchangeable cation, organic matter, available moisture, silt and clay of materials; while sand was negatively correlated. On the contrary, sand was the unique factor reducing per cent of open cap. 8. Distribution of three phases of high productive casing material was concentrated in the range of 10 to 30 per cent solids, 15 to 30 per cent liquids, and 50 to 60 per cent in air volume. 9. Fresh weight of fruit bodies from peat was not affected with heavy watering but in clay loam and sandy loam severe crop losses occurred. Fresh weight of individual fruit was increased and open caps were decreased with heavy watering but light watering resulted in adverse effects: its effect was especially great in peat. 10. Optimum range of moisture content by weight on a dry basis was different with each casing material. To maintain optimum moisture content concerned with yield of fruit bodies and open cap, sandy loam and peat mixtures required daily watering of 0.6, 0.6 to 1. 2 and 1.2 to 2.4 liters per $3.3m^2$ of bed area, respectively. 11. Maximum yield of fruit body was recorded in the range of pF 2. 0 to 2. 5 of casing materials if organic matter content was below 4.2 per cent and in pF 1. 3 to 1.8 if above 7.1%. 12. pF curve of a certain casing material could be draws from moisture content at various pF values by multiple regression equations provided texture, organic matter and calcium of the casing material are given. Optimum moisture range of the casing materials also could be estimated by the equation. 13. It was possible to improve the phyico-chemical characteristics of clay loam and sandy loam by addition of weathered spent compost although the effect was less than in the case of peat. Fresh weight of fruit bodies wsa increased by addition of weathered spent compost but its effect was not as remarkable as peat. Accordingly, further studies will be required.

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Experimental Study Trends on the Acupuncture Moxibustion Treatment for Visceral Hypersensitivity: Based on the Data of PubMed (내장감각과민의 침구 치료에 대한 실험연구 현황: PubMed를 중심으로)

  • Han, Chang Woo;Choi, Jun-Yong;Park, Seong Ha;Kim, So Yeon
    • Korean Journal of Acupuncture
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    • v.36 no.2
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    • pp.93-103
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    • 2019
  • Objectives : The aim of this study is to review the current trends in experimental studies on the acupuncture moxibustion treatment for visceral hypersensitivity. Methods : PubMed was searched for experimental studies about visceral hypersensitivity and acupuncture/moxibustion. Data were extracted and tabulated from the selected articles about experimental method, intervention, result and mechanism. Results : Total 23 articles were reviewed. Chronic visceral hypersensitivity animal model was applied in 17 studies (74%). Visceral hypersensitivity was measured by abdominal withdrawal reflex scoring or/and abdominal electromyogram. Acupoints like ST25, ST36, ST37, BL25, LI11, BL32 and PC6 were treated by electroacupuncture or moxibustion. All articles reported that electroacupuncture or moxibustion treatment is significantly effective in reducing visceral hypersensitivity. Treatment mechanisms were studied, related to mast cell, serotonin (5-HT) and receptor (5-HT3R and 5-HT4R), substance P (SP), vasoactive intestinal polypeptide (VIP), c-fos positive cell, corticotropin-releasing hormone (CRH), purinergic 2X (P2X)2, P2X3, P2X4, P2X7, N-methyl-D-aspartate (NMDA) receptor (NR1 and NR2B), prokinectin (PK) 1 and PK2. Conclusions : Evidences on acupuncture/moxibustion treatment for visceral hypersensitivity in animal studies warrant more research on effective acupoins, electro-acupuncture methods and treatment durations.

Ion-exchange Separation and Spectrophotometric Determination of Trace Amount of Aluminium with Thorinin the Presence of Triton X-100 (Triton X-100 존재하에 Thorin에 의한 미량의 알루미늄 이온의 분광학적 정량 및 이온-교환 분리)

  • Park, Chan-Il;Cha, Ki-Won;Jung, Duck-Chae
    • Analytical Science and Technology
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    • v.12 no.6
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    • pp.515-520
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    • 1999
  • The spectrophotometric determination of Al(III) with thorin have been investigated. The optimum condition of pH, concentration of ligand and surfactant, and stability were evaluated. The thorin ligand offers selective separation of Al(III) from sample solution containing Fe(III), Ni(II), Cu(II), Pb(II) and Cu(II). Various surfactants were tested and Triton X-100 showed the best stability and the maximum absorbance in an aqueous solution of Al(III)-Thorin-Triton X-100 complex appears about 526 nm. The method was applied for the determination of Al(III) in mixed sample solution. Separation and preconcentration was performed with a short column filled with resorcinol-formaldehyde resin. Control of the pH during the column operation is essential because the adsorption capacities are very sensitive to change in pH. Their separation was carried out in 0.2 M acetic acid-sodium acetate buffer solution (pH 4.5) and 1.0 M $HNO_3$media.

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Crystal Structure of N,N'-di-tert-butoxycabonyl-2, 7-diazabicyclo[3.3.0]oct-4-ene. (N,N'-di-tert-butoxycabonyl-2,7-diazabicyclo[3.3.0]oct-4-ene의 결정구조)

  • 김문집;이재혁
    • Korean Journal of Crystallography
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    • v.8 no.2
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    • pp.132-137
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    • 1997
  • The crystal structure of N,N'-di-tert-butoxycabonyl-2,7-diazabicyclo[3.3.0]oct-4-ene has been determined from single crystal x-ray diffraction study; C16H26N2O4, Triclinic, P1, a=11.119(1) Å, b=13.638(1) Å, c=6.214(1) Å, α=92.14(1)°, β=103.49(1)°, γ=73.35(1)°, V=877.4(2)Å3, T=293(2)K, Z=2, CuKα(λ=1.5418Å). The structure was solved by direct method and refined by full-matrix least squares to a final R=5.38% for 2389 unique observed F0>4σ(F0) reflections and 225 parameters.

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Synthesis of Nucleophilic Adducts of Thiols (Ⅳ). Addition of Glutathione to $\beta$-Nitrostyrene Derivatives

  • Kim, Tae-Rin;Choi, Sung-Yong;Choi, Won-Sik
    • Bulletin of the Korean Chemical Society
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    • v.4 no.2
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    • pp.92-95
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    • 1983
  • The addition products of glutathione to ${\beta}$ -nitrostyrene derivatives were synthesized. ${\beta}$ -Nitrostyrene (1a), p-methyl-${\beta}$-nitrostyrene (1b), 3,4,5-trimethoxy-${\beta}$-nitrostyrene (1c), o-, m- and p-chloro-${\beta}$-nitrostyrene (1e, 1f, 1g) and o-, m- and p-methoxy-${\beta}$-nitrostyrene (1h, 1i, 1j) undergo addition reactions with glutathione to form S-(2-nitro-1-phenylethyl)-L-glutathione (5a), S-[2-nitro-1-(p-methyl)phenylethyl]-L-glutatione (5b), S-[2-nitro-1-(3', 4', 5'-trimethoxy)phenylethyl]-L-glutathione (5c), S-[2-nitro-1-(o-chloro)phenylethyl]-L-glutathione (5e), S-[2-nitro-1-(m-choro)phenylethyl]-L-glutathione (5f), S-[2-nitro-1-(p-chloro)phenylethyl]-L-glutathione (5g), S-[2-nitro-x-(o-methoxy)-phenylethyl]-L-glutathion e(5h), S-[2-nitro-x-(m-methoxy)phenylethyl]-L-glutathion e (5i), and S-[2-nitro-1-(p-methoxy)phenylethy])-L-glutathione (5j), respectively. The structure of adducts were identified by UV and IR-spectra, molecular weight measurement, and elemental analysis.

The Prevalent Rates of Abnormal Serum Aminotransferase Levels and Total Cholesterol Levels among Adolescents with Obesity (청소년기 비만아에서 이상 혈청 간효소치 및 총콜레스테롤치의 유병율)

  • Jang, Hyun Oh;Lee, Chong Guk;Kang, Yun Ju
    • Clinical and Experimental Pediatrics
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    • v.45 no.12
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    • pp.1484-1490
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    • 2002
  • Purpose : The purpose of this study was to look at prevalences of abnormal serum aminotransferase levels and abnormal serum total cholesterol levels among adolescents with obesity in Seoul area. Methods : Body mass index[$BMI(kg/m^2)$], serum aspartate aminotransferase(AST) alanine aminotransferase( ALT), and total cholesterol levels were measured in 26,876 adolescents(male : 13,287, female : 13,589) of first grade of high school in Seoul between the ages of 15 and 16 years, enrolled in a large health examination survey by Seoul School Health Center(SSHC) in 2001. Obesity was defined as BMI more than 95th percentile for age and sex and normal weight was defined as BMI between 25th percentile and 75th percentile for age and sex. Abnormal levels of AST, ALT and total cholesterol were defined as more than 95th percentile for age and sex. Results : The BMI at 95th percentile was 28.7 in males and 26.9 in females. The prevalence of abnormal AST levels was higher in obesity group than in normal weight group. In males, those were 23.7% and 3.7%, respectively(P<0.01, $x^2-value$ : 529.2). In females, those were 11.8% and 4.9 %, respectively(P<0.01, $x^2-value$ : 56.3). The prevalence of abnormal ALT levels was significantly higher in the obesity group compared with the normal weight group. In males, those were 33.9% and 1.7%, respectively(P<0.01, $x^2-value$ : 1,693.4). In females, those were 22.3% and 3.9%, repectively(P<0.01, $x^2-value$ : 397.6). The prevalence of abnormal total cholesterol levels was higher in the obesity group than in the normal weight group. In males, those were 16.8% and 3.5%, respectively(P<0.01, $x^2-value$ : 268.3). In females, those were 9.0% and 5.4%, respectively(P<0.01, $x^2-value$ : 14.2). Conclusion : This study revealed that the prevalences of abnormal AST, ALT and total cholesterol level were higher in the obese group than in the normal weight group.

THE FRACTIONAL WEAK DISCREPANCY OF (M, 2)-FREE POSETS

  • Choi, Jeong-Ok
    • Bulletin of the Korean Mathematical Society
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    • v.56 no.1
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    • pp.1-12
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    • 2019
  • For a finite poset $P=(X,{\preceq})$ the fractional weak discrepancy of P, denoted $wd_F(P)$, is the minimum value t for which there is a function $f:X{\rightarrow}{\mathbb{R}}$ satisfying (1) $f(x)+1{\leq}f(y)$ whenever $x{\prec}y$ and (2) ${\mid}f(x)-f(y){\mid}{\leq}t$ whenever $x{\parallel}y$. In this paper, we determine the range of the fractional weak discrepancy of (M, 2)-free posets for $M{\geq}5$, which is a problem asked in [9]. More precisely, we showed that (1) the range of the fractional weak discrepancy of (M, 2)-free interval orders is $W=\{{\frac{r}{r+1}}:r{\in}{\mathbb{N}}{\cup}\{0\}\}{\cup}\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$ and (2) the range of the fractional weak discrepancy of (M, 2)-free non-interval orders is $\{t{\in}{\mathbb{Q}}:1{\leq}t<M-3\}$. The result is a generalization of a well-known result for semiorders and the main result for split semiorders of [9] since the family of semiorders is the family of (4, 2)-free posets.

Differences in the Electronic Structures of Bulk and Powder FeV2O4 Spinel Oxide Investigated by Using Synchrotron Radiation (방사광을 이용한 FeV2O4 스피넬 산화물의 덩치상태와 분말상태의 전자구조 차이 연구)

  • Hwang, Ji-Hoon;Kim, D.H.;Lee, Eun-Sook;Kang, J.S.;Kim, W.C.;Kim, C.S.;Han, S.W.;Hong, S.C.;Park, B.G.;Kim, J.Y.
    • Journal of the Korean Magnetics Society
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    • v.21 no.6
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    • pp.198-203
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    • 2011
  • The electronic structure of ferrimagnetic spinel oxide of $FeV_2O_4$ has been investigated by employing soft x-ray absorption spectroscopy (XAS) and soft x-ray magnetic circular dichroism (XMCD). The Fe 2p and V 2p XAS spectra show that the valence states of Fe and V ions are ${\sim}Fe^{2.3+}$ mixed-valent states and ${\sim}V^{3+}$ states, respectively. In Fe 2p XMCD spectra, finite XMCD signals are observed for divalent $Fe^{2+}$ states only, but not for $Fe^{3+}$ states. This finding indicates that the magnetic moments of $Fe^{2+}$ ions are ordered ferromagnetically but that those of $Fe^{3+}$ ions are cancelled, implying that $Fe^{2+}$ ions play an important role in determining magnetic properties of $FeV_2O_4$.