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ON NEWTON'S METHOD FOR SOLVING A SYSTEM OF NONLINEAR MATRIX EQUATIONS

  • Kim, Taehyeong;Seo, Sang-Hyup;Kim, Hyun-Min
    • East Asian mathematical journal
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    • 제35권3호
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    • pp.341-349
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    • 2019
  • In this paper, we are concerned with the minimal positive solution to system of the nonlinear matrix equations $A_1X^2+B_1Y +C_1=0$ and $A_2Y^2+B_2X+C_2=0$, where $A_i$ is a positive matrix or a nonnegative irreducible matrix, $C_i$ is a nonnegative matrix and $-B_i$ is a nonsingular M-matrix for i = 1, 2. We apply Newton's method to system and present a modified Newton's iteration which is validated to be efficient in the numerical experiments. We prove that the sequences generated by the modified Newton's iteration converge to the minimal positive solution to system of nonlinear matrix equations.

백화산(白華山) 삼림식생(森林植生) -식물사회학적(植物社會學的) 연구(硏究)- (Forest Vegetation of Mt. Baek-Hwa -A Phytosociological Study-)

  • 조현제;이윤원;이동섭;홍성천
    • 한국산림과학회지
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    • 제80권1호
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    • pp.42-53
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    • 1991
  • 1. 경상북도(慶尙北道) 상주군(尙州郡)과 충청북도(忠淸北道) 영동군(永同郡)의 경계(境界)를 이루는 백화산(白華山) 일대(一帶)에 대하여 식물사회학적(植物社會學的) 삼림군락분류(森林群落分類)와 소산식물상(所産植物相)의 조사(調査)를 행(行)하였다. 삼림식생(森林植生)은 자연림(自然林)으로 계곡부(溪谷部)와 산정부(山頂部)의 일부지역(一部地域)에 느티나무와 달피나무가 소규모(小規模)의 잔재림(殘在林)으로 분포(分포(布))하고 있지만 거의 전지역(全地域)이 이차림(二次林)이나 식림(植林)과 같은 대상식생(代償植生)으로 구성(構成)되어 있다. 2. 백화산(白華山) 일대(一帶)의 삼림군락(森林群落)은 신갈나무, 쇠물푸레 등(等)이 특징(特徵)지우는 신갈나무 쇠물푸레군락(群落)(Table 1 : I)의 산지림(山地林)과 물푸레나무, 고로쇠나무 등(等)이 특징(特徵)지우는 물푸레나무-고로쇠나무군락(群落)(Table 1 : II)의 계곡림(溪谷林)의 2개(個) 상급식생단위(上級植生單位)로 크게 구분(區分)되었으며 이들의 하급식생단위(下級植生單位)는 다음과 같다. I. 산지림(山地林)(I-A. 당단풍-지리대사초군(群), I-B. 소나무군(群) : I-B-a. 전형소군(典型小群), I-B-b. 철쭉나무소군(小群)) II. 계곡림(溪谷林)(II-A. 당단풍군(群), II-B. 느티나무군(群) : II-B-a. 전형소군(典型小群), II-B-b. 비목나무소군(小群), II-C. 졸참나무-굴피나무군(群) : II-C-a. 전형소군(典型小群), II-C-b. 비목나무소군(小群)) 3. 삼림군락(森林群落)의 수직분포(垂直分布)를 조사(調査)한 결과(結果), 산지림(山地林)은 해발(海拔) 600m를 경계(境界)로 상부(上部)는 당단풍-지리대사초군(群)(I-A)과 전형소군(典型小群)(I-B-a), 하부(下部)는 철쭉나무소군(小群)(I-B-b)이 주로 분포(分布)하고 있었으며, 해발(海拔) 600m이하(以下)에서 주로 발달(發達)하는 계곡림(溪谷林)은 해발(海拔) 350m를 경계(境界)로 상부(上部)는 당단풍군(群)(II-A)과 느티나무군(群)(II-B), 하부(下部)는 졸참나무-굴피나무군(群)(II-C)이 분포(分布)하고 있었다. 4. 군락(群落)의 잠재우점성(潛在優占性)을 검토(檢討)한 결과(結果), 산지림(山地林)은 중부(中部) 이상(以上)에서는 신갈나무가 당분간(當分間) 도중극상(途中極相)을 중부(中部), 이하(以下)는 서어나무가 기후적(氣候的) 극상(極相)을 계곡림(溪谷林)은 인위적(人爲的) 영향(影響)을 배제(排除)하면 잔존종(殘存種)과 치묘(稚苗) 및 치수(稚樹)의 생육상태(生育狀態)로 보아 느티나무와 물푸레나무가 지형(地形) 및 토지적(土地的) 극상(極相)을 이루는 가운데 고로쇠나무, 까치박달, 비목나무 등(等)이, 국소적(局所的)으로 혼생(混生) 우점(優占)할 것으로 사료(思料)되었다. 5. 일치법(一致法)에 의해 산지림(山地林)과 계곡림(溪谷林)의 구분요인(區分要因)을 검토(檢討)한 결과(結果), 해발(海拔)보다는 지형(地形)에 의해 좌우(左右)되었다. 6. 백화산(白華山) 일대(一帶) 현존식물상(現存植物相)을 조사(調査)한 결과(結果), 소산식물(所産植物)은 총(總) 709종류(種類)로 108과(科), 371속(屬), 613종(種), 2아종(亞種), 88변종(變種) 및 6품종(品種)이었다.

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지질다당체유도 BV2세포손상에 대한 상백피 추출물의 항염증작용 (Anti-inflammatory Action of Extract of Mori Cortex against Lipopolysaccharide-induced BV2 Microglia)

  • 박신형;최영현;엄현섭;지규용
    • 동의생리병리학회지
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    • 제24권3호
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    • pp.463-469
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    • 2010
  • This research is performed to obtain positive evidences of Mori cortex, a kind of oriental medicinal herbs, in the cellular levels. The extracts of M. cortex have shown anti-inflammatory effects against cutaneous inflammation and clinical effects on pulmonary asthma and congestion in oriental medicine. Thus BV2 cells were chosen because microglia are considered as the main immunocompetent cells in the central nervous system. Lipopolysaccharide (LPS)-induced microglial activation of cultured BV2 cells and subsequent release of nitric oxide (NO) and Prostaglandin E2 (PGE2) were effectively suppressed by methylene chloride extract of Morus alba L. (MEMA). From the inflammation-mediated mRNA and protein analyses, we showed that inducible NO synthase (iNOS), cyclooxygenase-2 (COX-2), interleukin-$1{\beta}$ (IL-$1{\beta}$) and tumor necrosis alpha (TNF-${\alpha}$) induced by LPS were markedly decreased by MEMA treatment. From the observation of nuclear factor-kB (NF-${\kappa}B$) which is controlling and mediating inflammation through COX-2 and iNOS, there showed that p65, a subunit of NF-${\kappa}B$, was increased in nuclear and $I{\kappa}B$, a competitor of NF-${\kappa}B$, was recovered in cytosol after MEMA treatment. These are corresponding with results of iNOS, COX-2, IL-$1{\kappa}$ and TNF-${\alpha}$, and confirm some suppressive effect against transcriptional activation of NF-${\kappa}B$. In conclusion, the anti-inflammatory action of M. cortex against BV2 microglia cells is expected to protect nerve tissues through suppression of neuronal inflammation in various neurodegenerative diseases.

The Inhibitory Effect of Lycii Fructus on LPS-stimulated NF-${\kappa}B$ Activation and iNOS Expression in RAW 264.7 Macrophages

  • Kim, Beum-Seuk;Song, Yun-Kyung;Lim, Hyung-Ho
    • 대한한의학회지
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    • 제29권1호
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    • pp.47-59
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    • 2008
  • Objective : Anti-inflammatory effects of the extract of Lycii Fructus on lipopolysaccharide (LPS)-induced inflammation in RAW 264.7 macrophage cells were investigated. Method : In order to assess the cytotoxic effect of Lycii Fructus on the raw 264.7 macrophages 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide(MTT) assay was performed. Reverse transcription-polymerase chain reaction(RT-PCR) analysis of the mRNA levels of tumor necrosis factor-$\alpha$(TNF-$\alpha$) and inducible nitric oxide synthase(iNOS) was performed in order to provide an estimate of the relative level of expression of these genes. The protein level of the inhibitor of nuclear factor-${\kappa}B(I{\kappa}B)$ and nuclear factor-${\kappa}B$(NF-${\kappa}B$) activity was investigated by Western blot assay. NO production was investigated by NO detection. Result : Lycii Fructus suppressed NO production by inhibiting the LPS-induced expressions of iNOS and TNF-$^-\alpha$ mRNA and iNOS protein in RAW 264.7 macrophage cells. Also, Lycii Fructus suppressed activation of NF-${\kappa}B$ in the nucleus. Conclusion : These results show that the extract of Lycii Fructus has anti-inflammatory effect probably by suppressing iNOS expressions through the down-regulation of NF-${\kappa}B$ binding activity.

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Pig Skin Gelatin Hydrolysates Attenuate Acetylcholine Esterase Activity and Scopolamine-induced Impairment of Memory and Learning Ability of Mice

  • Kim, Dongwook;Kim, Yuan H. Brad;Ham, Jun-Sang;Lee, Sung Ki;Jang, Aera
    • 한국축산식품학회지
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    • 제40권2호
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    • pp.183-196
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    • 2020
  • The protective effect of pig skin gelatin water extracts (PSW) and the low molecular weight hydrolysates of PSW generated via enzymatic hydrolysis with Flavourzyme® 1000L (LPSW) against scopolamine-induced impairment of cognitive function in mice was determined. Seventy male ICR mice weighing 20-25 g were randomly assigned to seven groups: Control (CON); scopolamine (SCO, 1 mg/kg B.W., intraperitoneally (i.p.); tetrahydroaminoacridine 10 [THA 10, tacrine; 10 mg/kg B.W. per oral (p.o.) with SCO (i.p.)]; PSW 10 (10 mg/kg B.W. (p.o.) with SCO (i.p.); PSW 40 (40 mg/kg B.W. (p.o.) with SCO (i.p.); LPSW 100 (100 mg/kg B.W. (p.o.) with SCO (i.p.); LPSW 400 (400 mg/kg B.W. (p.o.) with SCO (i.p.). All treatment groups, except CON, received scopolamine on the day of the experiment. The oxygen radical absorbance capacity of LPSW 400 at 1 mg/mL was 154.14 μM Trolox equivalent. Administration of PSW and LPSW for 15 weeks did not significantly affect on physical performance of mice. LPSW 400 significantly increased spontaneous alternation, reaching the level observed for THA and CON. The latency time of animals receiving LPSW 400 was higher than that of mice treated with SCO alone in the passive avoidance test, whereas it was shorter in the water maze test. LPSW 400 increased acetylcholine (ACh) content and decreased ACh esterase activity (p<0.05). LPSW 100 and LPSW 400 reduced monoamine oxidase-B activity. These results indicated that LPSW at 400 mg/kg B.W. is a potentially strong antioxidant and contains novel components for the functional food industry.

ON THE CAUCHY PROBLEM FOR SOME ABSTRACT NONLINEAR DIFFERENTIAL EQUATIONS

  • Hamza A.S. Abujabal;Mahmoud M. El-Boral
    • Journal of applied mathematics & informatics
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    • 제3권2호
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    • pp.279-290
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    • 1996
  • In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

초오의 항알레르기 염증반응 및 기전탐색에 관한 연구 (Experimental Study about Pathway of Aconiti Ciliare Tuber on Allergic Reaction of Inflammation)

  • 김원일
    • 한국한의학연구원논문집
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    • 제16권3호
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    • pp.155-166
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    • 2010
  • Objetives : The purpose of this study was to examine the pathway of anti-allergic effects of Aconiti Ciliare Tuber (ACT). Methods : We examined cell viability, ${\beta}$-hexosaminidase release, pro-inflammatory cytokines secretion and mRNA expressions, nuclear factor-kappa B (NF-${\kappa}B$) (p65) activation, inhibitor kappa B-alpha ($I{\kappa}B-{\alpha}$) degradation, and MAPKs activation from RBL-2H3 cells pre-treatment by ACT of 1.0 mg/ml, 2.0 mg/ml separately. Results : We observed that ACT reduced the secretion of ${\beta}$-hexosaminidase, TNF-${\alpha}$, IL-4 and the expression of COX-2 mRNA in RBL-2H3 cells. Futhermore, ACT inhibited the levels of activation of NF-${\kappa}B$ (p65) protein, ERK MAPK, and degradation of $I{\kappa}B-{\alpha}$ in RBL-2H3 cells. Conclusions : These results show that ACT has an anti-histamine effect and inhibitory effect of NF-${\kappa}B$ (p65) through regulation of $I{\kappa}B-{\alpha}$ degradation. This improves that ACT could be used as an anti-allergic medicine.

천맥탕(天麥湯)의 알레르기 염증반응 및 기전탐색에 관한 연구 (Experimental Study about the Pathway of Inflammatory Allergic Reaction of Cheonmaec-tang)

  • 김용현;이승연;김원일
    • 대한한방소아과학회지
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    • 제24권1호
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    • pp.93-103
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    • 2010
  • Objectives The purpose of this study was to examine the pathway of anti-allergic effects of Cheonmaec-tang (CMT). Methods We examined the cell viability, $\beta$-hexosaminidase release, pro-inflammatory cytokines secretion and mRNA expressions, nuclear factor-kappa B (NF-${\kappa}B$) (p65) activation, inbibitor kappa B-alpha ($I{\kappa}B-{\alpha}$) degradation, and MAPKs activation in RBL-2H3 cells pre-treated by CMT of 2.0 mg/ml, 4.0 mg/ml separately. Results We observed that CMT reduced the secretion of $\beta$-hexosaminidase, TNF-$\alpha$, IL-4 and the expression of COX-2 mRNA in RBL-2H3 cells. Furthermore, CMT inhibited the levels of activation of NF-${\kappa}B$ (p65) protein, ERK MAPK, and degradation of $I{\kappa}B-{\alpha}$ in RBL-2H3 cells. Conclusions These results show that CMT has an anti-histamine effect and inhibitory effect of NF-${\kappa}B$ (p65) through regulation of $I{\kappa}B-{\alpha}$ degradation. These suggest that CMT could be used as an anti-allergic medicine.

Sodium n-Octanoate(SOC)와 n-Octylammonium Chloride(OAC)의 혼합마이셀화에 관한 연구 (Mixed Micellar Properties of Sodium n-Octanoate(SOC) with n-Octylammonium Chloride(OAC) in Aqueous Solution)

  • 이병환
    • 대한화학회지
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    • 제46권6호
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    • pp.495-501
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    • 2002
  • Sodium n-Octanoate(SOC)와 n-Octylammonium Chloride(OAC)의 혼합마이셀화에 대하여 연구하기 위하여 임계마이셀농도(CMC)와 반대이온 결합상수(B)값을 SOC의 겉보기 몰분율($\alpha_1$)을 변화시키면서 측정하였다. SOC/OAC 혼합시스템의 마이셀화에 대한 여러 가지 열역학적 함수값($x_i$, $Y_i$, $C_i$, ${\alpha}_i^M$${\Delta}H_{mix}$)을 비이상적 혼합마이셀화 모델에 의하여 계산하고 분석하였다. 그 결과 이러한 혼합계면활성제의 마이셀화는 이상적 거동으로부터 큰 음의 벗어남을 알 수 있었다. 그리고 SOC,OAC 및 그들 혼합체($\alpha_1$=0.5)의 마이셀화에 대한 열역학적 함수값(${\Delta}G^0_m$, ${\Delta}H^0_m$${\Delta}S^0_m$)을 계산하기 위하여 온도에 따른 CMC 및 B 값의 변화를 측정하였다. 이러한 변화로부터 계산한 열역학적 함수값을 상호 비교함으로써 순수 및 혼합계면활성제의 마이셀화에 대하여 분석하였다.