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Oscillations of Difference Equations with Several Terms

  • Ocalan, Ozkan
    • Kyungpook Mathematical Journal
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    • v.46 no.4
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    • pp.573-580
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    • 2006
  • In this paper, we obtain sufficient conditions for the oscillation of every solution of the difference equation $$x_{n+1}-x_n+\sum_{i=1}^{m}p_ix_{n-k_i}+qx_{n-z}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$ and $z{\in}\{-1,0\}$. Furthermore, we obtain sufficient conditions for the oscillation of all solutions of the equation $${\Delta}^rx_n+\sum_{i=1}^{m}p_ix_{n-k_i}=0,\;n=0,1,2,{\cdots},$$ where $p_i{\in}\mathbb{R}$, $k_i{\in}\mathbb{Z}$ for $i=1,2,{\cdots},m$. The results are given terms of the $p_i$ and the $k_i$ for each $i=1,2,{\cdots},m$.

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Influence of Refeeding of Protein, Carbohydrate and Fat on Hepatic Insulin-Like Growth Factor-I mRNA Level in Fasted Chicks

  • Kita, K.;Hangsanet, K.;Okumura, J.
    • Asian-Australasian Journal of Animal Sciences
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    • v.11 no.3
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    • pp.245-248
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    • 1998
  • The influence of refeeding either protein, carbohydrate or fat on hepatic insulin-like growth factor-I (IGF-I) mRNA level in chicks which had been fasted for 2 days was examined. The hepatic IGF-I mRNA was measured by ribonuclease protection assay. Fasting reduced hepatic IGF-I mRNA levels to less than half of those in the fed control. When chicks were refed either a control, protein or carbohydrate diet, IGF-I mRNA levels significantly increased to those in the fed control until 2 hours of refeeding. Refeeding of fat did not alter hepatic IGF-I mRNA levels. The significant correlation between liver weight and hepatic IGF-I gene expression suggests that when chicks are refed after 2-d fasting, the acute increase in hepatic IGF-I gene expression brought about after refeeding may be partly regulated by the increase in liver protein metabolism.

Fabrication and Performance of Microcolumnar CsI:Tl onto Silicon Photomultiplier (실리콘광증배관 기반의 미세기둥 구조 CsI:Tl 제작 및 평가)

  • Park, Chan-Jong;Kim, Ki-Dam;Joo, Koan-Sik
    • Journal of IKEEE
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    • v.20 no.4
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    • pp.337-343
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    • 2016
  • This study conducted the gamma ray spectroscopic analysis of the microcolumnar CsI:Tl deposited onto the SiPMs using thermal evaporation deposition. The SEM measured thickness of microcolumnar CsI:Tl and of its individual columns. From the SEM observation, the measured thickness of CsI:Tl were $450{\mu}m$ and $600{\mu}m$. The gamma ray spectroscopic properties of microcolumnar CsI:Tl, $450{\mu}m$ and $600{\mu}m$ thick deposited onto the SiPMs were analyzed using standard gamma ray sources $^{133}Ba$ and $^{137}Cs$. The spectroscopic analysis of microcolumnar CsI:Tl deposited onto the SiPMs included the measurements of response linearity over the $^{137}Cs$ gamma ray intensity; and gamma ray energy spectrum. Furthermore from the gamma ray spectrum measurement of $^{133}Ba$ and $^{137}Cs$, $450{\mu}m$ thick CsI:Tl showed good efficiency when measured with $^{133}Ba$ and $600{\mu}m$ thick CsI:Tl was highly efficient when measured with $^{137}Cs$.

ON THE 2-ABSORBING SUBMODULES AND ZERO-DIVISOR GRAPH OF EQUIVALENCE CLASSES OF ZERO DIVISORS

  • Shiroyeh Payrovi;Yasaman Sadatrasul
    • Communications of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.39-46
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    • 2023
  • Let R be a commutative ring, M be a Noetherian R-module, and N a 2-absorbing submodule of M such that r(N :R M) = 𝖕 is a prime ideal of R. The main result of the paper states that if N = Q1 ∩ ⋯ ∩ Qn with r(Qi :R M) = 𝖕i, for i = 1, . . . , n, is a minimal primary decomposition of N, then the following statements are true. (i) 𝖕 = 𝖕k for some 1 ≤ k ≤ n. (ii) For each j = 1, . . . , n there exists mj ∈ M such that 𝖕j = (N :R mj). (iii) For each i, j = 1, . . . , n either 𝖕i ⊆ 𝖕j or 𝖕j ⊆ 𝖕i. Let ΓE(M) denote the zero-divisor graph of equivalence classes of zero divisors of M. It is shown that {Q1∩ ⋯ ∩Qn-1, Q1∩ ⋯ ∩Qn-2, . . . , Q1} is an independent subset of V (ΓE(M)), whenever the zero submodule of M is a 2-absorbing submodule and Q1 ∩ ⋯ ∩ Qn = 0 is its minimal primary decomposition. Furthermore, it is proved that ΓE(M)[(0 :R M)], the induced subgraph of ΓE(M) by (0 :R M), is complete.

Characterization of the Restriction Endonuclease Bki I from Brevibacterium divaricatum (Brevibacterium divaricatum의 제한효소 Bdi I의 특성)

  • 김용석;노현모
    • Korean Journal of Microbiology
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    • v.24 no.1
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    • pp.18-23
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    • 1986
  • A new type II restriction endonuclease, Bdi I, has been isolated from Brenibacterium divaricatum FERM 5948 by procedures of ammonium sulfate fractionation, DEAE-cellulose chromatography and heparin agarose chromatography. The purified Bdi I restriction endonudlease had the same cleavage patterns of Cla I whose recognition sequence is 5' ATCGAT 3'. From the result that ${\lambda}-Cla$ I DNA frahment could be cloned in pBR 322 digested with Bdi I, it has been proven that Bdi I cuts between T and C(5' AT/CGAT3') within the recognition sequence and produces 5'pCG cohesive end. The optimal temperature for the Bdi I restriction endonuclease activity was $37^{\circ}C$, and optimal salt (NaCl) concentration was 50-100 mM.

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Bacillus licheniformis SSA3-2M1 이 생산하는 Proteinases

  • 장영채;이경형;김성영;조윤래;김종규
    • Korean Journal of Microbiology
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    • v.30 no.4
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    • pp.239-245
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    • 1992
  • Buci1llr.s 11c~h~n~1rnSiSi.As 3-2MI which is responsible for the special taste of traditionalKorean soy sause produced two kinds of proteinase. The activity of the proteinasc I washigher about two fold than that of proteinase 11. The optimai, reaction pH of proteinaseI and I1 wcre found to be 7-1 1.5 and 7-9. respectively. Proteinase I1 was more stable andactive than proteinase I at pH ranges around 3 to 5. The optimal te~tlperature of proteinaseI and I1 were 502. The temperature stabilitl of proteinase I1 was Inore stable thanproteinase 1 at temperature range around 30-quot;~A. ctivities of proteinase I and I1 graduallydeclined above $30^{\circ}$C and 45C. respectively. Proteinasc 1 was more active than proteinaseI1 at salt concentration range around 25-3500. The K,,, values of casein and soy proteinfor proteinase I were 6.89 mglml and 3.98 mglml. In case of proteinase 11. they were 9.00mgiml anti 11.44 111g/ml. respectively. The activity of the crudc enzyme was increased by1 rnM Pb(CH3COO). but was decreased by 5 n1M and 10 rnM of HgS04 and ZnS04. Thetwo proteinases produced amino acids and peptides from the soybean protein. The peptideswere digested into amino acids. Both protcinases were found to be the main enzymes thatproduced amino acids which make the main taste of traditional Korean soy sauce.al Korean soy sauce.

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THE EFFECTS OF INSULIN-LIKE GROWTH FACTOR I (IGF-I) ON EXPRESSION OF VASCULAR ENDOTHELIAL GROWTH FACTOR (VEGF) MRNA IN MG-63 OSTEOBLASTLIKE CELLS (MG-63 세포주에서 Vascular Endothelial Growth Factor (VEGF) mRNA 발현에 대한 Insulin-like Growth Factor I (IGF-I)의 효과에 대한 연구)

  • Suh, Je-Duck;Myung, Hoon;Kang, Nara;Choung, Pill-Hoon
    • Journal of the Korean Association of Oral and Maxillofacial Surgeons
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    • v.31 no.5
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    • pp.363-369
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    • 2005
  • Purpose: To determine the role of Insulin-like Growth Factor-I (IGF-I) in the regulation of Vascular Endothelial Growth Factor (VEGF) expression in MG-63 cells and then to find the mechanism b which this regulation occurs. Materials and methods: MG-63 cells were grown to confluence in 60-mm dishes. To determine the effects of IGF-I on expression of VEGF mRNA according to time and concentration, the cells were treated with 10 nM IGF-I, following isolation of total RNA and Northern blot analysis after 1, 2, 4, 8, 12, 24 hours and after 2 hours of treatment with 0.5, 2, 10, 25, 50 nM IGF-I respectively, isolation of total RNA and Northern blot analysis were followed. To determine the mechanism of action of IGF-I, inhibitors such as hydroxyurea $(76.1\;{\mu}g/ml)$, actinomycin D $(2.5\;{\mu}g/ml)$, cycloheximide $(10\;{\mu}g/ml)$ were added 1 hour after treatment of 10 nM IGF-I. Results: 1. the expression of VEGF mRNA was increased with treatment of IGF-I. 2. The expression of VEGF mRNA was increased according to time-and concentration dependent manner of IGF-I. 3. The effect of IGF-I was decreased by hydroxyuera, actinomycin D, but not by cycloheximide. Conclusion: IGF-I regulate the expression of VEGF mRNA in the level of DNA synthesis and transcription. These results could suggest that IGF-I plays an important role in angiogenesis in the process of new bone formation and remodeling.

ON THE INTEGRAL CLOSURES OF IDEALS

  • Ansari-Toroghy, H.;Dorostkar, F.
    • Honam Mathematical Journal
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    • v.29 no.4
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    • pp.653-666
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    • 2007
  • Let R be a commutative Noetherian ring (with a nonzero identity) and let M be an R-module. Further let I be an ideal of R. In this paper, by putting a suitable condition on $Ass_R$(M), we obtain some results concerning $I^{*(M)}$ and prove that the sequence of sets $Ass_R(R/(I^n)^{*(M)})$, $n\;\in\;N$, is increasing and ultimately constant. (Here $(I^n)^{*(M)}$ denotes the integral closure of $I^n$ relative to M.)

EFFECT OF CAPSAICIN AND EUGENOL ON ICGRP (IMMUNOREACTIVE CALCITONIN GENE-RELATED PEPTIDE) RELEASE FROM RAT LUMBAR SPINAL CORD. (백서 척수에서 Capsaicin과 Eugenol이 iCGRP (immunoreactive calcitonin gene-related peptide) 분비 조절에 미치는 영향.)

  • 오원만;김원재;최남기;박상원;황인남;김선헌
    • Restorative Dentistry and Endodontics
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    • v.26 no.5
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    • pp.436-442
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    • 2001
  • Neuropeptide such as calcitonin gene-related peptide and substance P may mediate neurogenic inflammation, but little is known about the regulation of neuropeptide release from rat spinal cord. Eugenol has been reported to reduce odontogenic pain and is known to have a structure similar to capsaicin, a potent stimulant of certain nociceptors. This study was done to examine the effect of capsaicin and eugenol on immunoreactive calcitonin gene-related peptide (iCGRP) release from rat spinal cord and whether eugenol regulates capsaicin-sensitive release of iCCRP or it evokes capsaicin-sensitive release of iCGRP. The dor-sal half of rat lumbar spinal cord was chopped into 200$\mu$m slices. They were superfused (500$\mu$l/min) in vitro with an oxygenated Kreb's buffer. The EC$_{50}$ of capsaicin on iCGRP release was measured. Eugenol (600$\mu$M and 1.2mM) and vehicle (0.02% 2-hydroxyl-$\beta$-cyclodextrin) were administered prior to stimulation of rat lumbar spinal cord with capsaicin. The amount of iCGRP release from rat lumbar spinal cord was measured by radioimmunoassay. The results were as follows : 1. iCGRP release from rat lumbar spinal cord was dependent on concentration of capsaicin. The EC$_{50}$ of capsaicin on iCGRP release was 3$\mu$M. 2. In the vehicle treated group, capsaicin (3$\mu$M) evoked a 14-fold increase over basal iCGRP level. 3. Administration of 600$\mu$M and 1.2mM eugenol evoked a 2.2-fold increase and a 2.3-fold increase over basal iCGRP level respectively. 4. Administration of 600$\mu$M and 1.2mM eugenol increased capsaicin evoked release of iCGRP by more than 50%. These results indicate that eugenol evoke CGRP release from central nervous system and potentiate the pain-inducing action of capsaicin on it.

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Normal Interpolation on AX = Y in CSL-algebra AlgL

  • Jo, Young Soo;Kang, Joo Ho
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.293-299
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    • 2005
  • Let ${\cal{L}}$ be a commutative subspace lattice on a Hilbert space ${\cal{H}}$ and X and Y be operators on ${\cal{H}}$. Let $${\cal{M}}_X=\{{\sum}{\limits_{i=1}^n}E_{i}Xf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}$$ and $${\cal{M}}_Y=\{{\sum}{\limits_{i=1}^n}E_{i}Yf_{i}:n{\in}{\mathbb{N}},f_{i}{\in}{\cal{H}}\;and\;E_{i}{\in}{\cal{L}}\}.$$ Then the following are equivalent. (i) There is an operator A in $Alg{\cal{L}}$ such that AX = Y, Ag = 0 for all g in ${\overline{{\cal{M}}_X}}^{\bot},A^*A=AA^*$ and every E in ${\cal{L}}$ reduces A. (ii) ${\sup}\;\{K(E, f)\;:\;n\;{\in}\;{\mathbb{N}},f_i\;{\in}\;{\cal{H}}\;and\;E_i\;{\in}\;{\cal{L}}\}\;<\;\infty,\;{\overline{{\cal{M}}_Y}}\;{\subset}\;{\overline{{\cal{M}}_X}}$and there is an operator T acting on ${\cal{H}}$ such that ${\langle}EX\;f,Tg{\rangle}={\langle}EY\;f,Xg{\rangle}$ and ${\langle}ET\;f,Tg{\rangle}={\langle}EY\;f,Yg{\rangle}$ for all f, g in ${\cal{H}}$ and E in ${\cal{L}}$, where $K(E,\;f)\;=\;{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Y\;f_{i}{\parallel}/{\parallel}{\sum{\array}{n\\i=1}}\;E_{i}Xf_{i}{\parallel}$.

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