• 제목/요약/키워드: Continued fraction

검색결과 103건 처리시간 0.028초

한국산 재배대황엽의 약효성분 -엽의 후라보노이드- (Pharmaco-Constituents of Korean Cultivated Rhubarb Leaves -The Flavonoids from Leaves-)

  • 함인혜;오인세;황완균;김일혁
    • 약학회지
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    • 제38권4호
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    • pp.469-475
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    • 1994
  • As the continued studies for Korean cultivated rhubarb, MeOH extract of the leaves was fractionated with ether, ethylacetate, and n-butanol. From the ethyl acetate fraction of MeOH extract, one flavone glycoside, apigenin-8-${\beta}$-D-glucopyranoside(vitexin, $C_{21}H_{20}O_{10}$) and from the n-BuOH fraction of MeOH extract, two flavonol glycosids, kaempferol-3-O-(2,6-di-O-rhamnopyranosyl)-${\beta}$-D-galactopyranoside$(C_{33}H_{40}O_{19})$and quercetin-3-O-rutinoside(rutin, $C_{27}H_{30}O_{16}$) were isolated and identified through the physico-chemical properties and spectroscopic evidences(UV, IR, NMR, Mass) respectively.

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NOTE ON Q-PRODUCT IDENTITIES AND COMBINATORIAL PARTITION IDENTITIES

  • Chaudhary, M.P.;Salilew, Getachew Abiye
    • 호남수학학술지
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    • 제39권2호
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    • pp.267-273
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    • 2017
  • The objective of this note is to establish three results between q-products and combinatorial partition identities in a elementary way. Several closely related q-product identities such as (for example)continued fraction identities and Jacobis triple product identities are also considered.

NOTE ON MODULAR RELATIONS FOR THE ROGER-RAMANUJAN TYPE IDENTITIES AND REPRESENTATIONS FOR JACOBIAN IDENTITY

  • CHAUDHARY, M.P.;CHOI, JUNESANG
    • East Asian mathematical journal
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    • 제31권5호
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    • pp.659-665
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    • 2015
  • Combining and specializing some known results, we establish six identities which depict six modular relations for the Roger-Ramanujan type identities and two equivalent representations for Jacobian identity expressed in terms of combinatorial partition identities and Ramanujan-Selberg continued fraction. Two q-product identities are also considered.

A NEW ATTACK ON THE KMOV CRYPTOSYSTEM

  • Nitaj, Abderrahmane
    • 대한수학회보
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    • 제51권5호
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    • pp.1347-1356
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    • 2014
  • In this paper, we analyze the security of the KMOV public key cryptosystem. KMOV is based on elliptic curves over the ring $\mathbb{Z}_n$ where n = pq is the product of two large unknown primes of equal bit-size. We consider KMOV with a public key (n, e) where the exponent e satisfies an equation ex-(p+1)(q+1)y = z, with unknown parameters x, y, z. Using Diophantine approximations and lattice reduction techniques, we show that KMOV is insecure when x, y, z are suitably small.

병렬계산용 TTLS 알고리즘의 최적운용환경 (Optimized Operational Environment for Parallel TTLS Solver)

  • 김형중;김용준;이장규
    • 대한전기학회:학술대회논문집
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    • 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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    • pp.666-668
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    • 1988
  • A new tridiagonal Toeplitz linear system (TTLS) solver is proposed. The solver decomposes a strictly diagonally dominant TTLS equation into a number of subsystems using a limit convergent of an analytic solution of a continued fraction. Subsystem equations can be solved employing a modified Gaussian elimination method. The solver fully exploits parallelism. Optimized operational environment for the algorithm is discussed.

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PARTIAL SECOND ORDER MOCK THETA FUNCTIONS, THEIR EXPANSIONS AND PADE APPROXIMANTS

  • Srivastava, Bhaskar
    • 대한수학회지
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    • 제44권4호
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    • pp.767-777
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    • 2007
  • By proving a summation formula, we enumerate the expansions for the mock theta functions of order 2 in terms of partial mock theta functions of order 2, 3 and 6. We show a relation between Ramanujan's ${\mu}(q)$-function and his sixth order mock theta functions. In addition, we also give the continued fraction representation for ${\mu}(q)$ and 2nd order mock theta functions and $Pad\acute{e}$ approximants.

X-ray diffraction analysis of the effect of ball milling time on crystallinity of milled polyacrylonitrile-based carbon fiber

  • Lee, Sang-Hye;Kang, Dong-Su;Lee, Sang-Min;Roh, Jae-Seung
    • Carbon letters
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    • 제26권
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    • pp.11-17
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    • 2018
  • Milled carbon fiber (mCF) was prepared by a ball milling process, and X-ray diffraction (XRD) diffractograms were obtained by a $2{\theta}$ continuous scanning analysis to study mCF crystallinity as a function of milling time. The raw material for the mCF was polyacrylonitrile-based carbon fiber (T700). As the milling time increased, the mean particle size of the mCF consistently decreased, reaching $1.826{\mu}m$ at a milling time of 18 h. The XRD analysis showed that, as the milling time increased, the fraction of the crystalline carbon decreased, while the fraction of the amorphous carbon increased. The (002) peak became asymmetric before and after milling as the left side of the peak showed an increasingly gentle slope. For analysis, the asymmetric (002) peak was deconvoluted into two peaks, less-developed crystalline carbon (LDCC) and more-developed crystalline carbon. In both peaks, Lc decreased and $d_{002}$ increased, but no significant change was observed after 6 h of milling time. In addition, the fraction of LDCC increased. As the milling continued, the mCF became more amorphous, possibly due to damage to the crystal lattices by the milling.

Effect of Stage of Growth and Cultivar on Chemical Composition of Whole Maize Plant and Its Morphological Fractions

  • Firdous, R.;Gilani, A.H.
    • Asian-Australasian Journal of Animal Sciences
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    • 제12권3호
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    • pp.366-370
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    • 1999
  • Samples of whole plant, leaf and stem of Akbar, Neelum, UM-81 and lZ-31 cultivars of maize fodder harvested up to 14 weeks at different growth stages were drawn and analysed for dry matter contents and various cell wall constituents such as NDF, ADF, hemicellulose, cellulose, lignin, cutin and silica. The dry matter contents of whole maize plant, leaf and stem increased significantly (p<0.01) with advancing plant age. Maximum dry matter was found in the leaf fraction of the plant. The cell wall components continued to increase significantly (p<0.001) in whole maize plant and its morphological fractions as the age advanced. Maximum values for NDF, ADF, cellulose and lignin were observed in stem followed by whole plant and leaf, whereas hemicellulose, cutin and silica contents were higher in leaf fraction of the plant. The cultivars were observed to have some effects on chemical composition of all plant fraction. The results indicated that maturity had a much greater effect on the concentration of all the structural components than did the cultivars. It was concluded that maize fodder should be cut preferably between 8th to 9th week of age (flowering stage) to obtain more nutritious and digestible feed for livestock. Among the maize cultivars, Neelum proved to be the best, due to its higher dry matter contents and lower lignin concentration.

발아기간별 맥주맥 단백질의 분획 및 조성변화 (Changes in Chromatographic Fractionation and Composition of the Proteins of Malting Barley Grain during Germination)

  • 서호수;조성환
    • 한국식품과학회지
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    • 제24권1호
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    • pp.1-6
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    • 1992
  • 일정조건에서 7일간 발아시킨 맥주맥 단백질을 용매별로 분리 추출하고 발아기간별, 그 조성변화를 조사한 결과, hordein이 가장 높은 비율로 존재하였고, 발아가 진행됨에 따라 albumin, hordein, residue 함량이 감소하였고, globulin, glutelin 및 NPN 함량은 증가하는 경향이었다. 아울러, 각 단백질 분획들의 전기영동패턴을 보면, albumin 분획은 분자량이 15,000, 36,000 및 41,000 dalton인 3개 분리대로 구성되어 있었으며 36.000 dalton의 분리대는 발아함에 따라 소열되었다. globulin 분획은 19,000, 23,000, 29,000, 35,000 및 61,000 dalton의 5개 분리대로 구성되어 있었으며 발아시킴으로서 41,000 dalton의 분리대가 생성되었고, 23,000 dalton의 분리대는 발아 5일에 완전히 소별되었다. hordein 분획은 26,000, 39,000, 43,000 및 56,000 dalton의 5개 분리대로 구성 되어 있었고, glutelin 분획은 4배의 분리대(20.000, 28.000, 42,000, 47,000 dalton)로 구성되어 있었다. 아미노산 조성은 glutamin acid, histidine, aspartic acid, serine, glycine, valine, alanine 및 leucine이 주요한 아미노산이었으며 발아에 따른 유의할 만한 변화는 없었다.

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Effect of Extracts from Safflower Seeds on Osteoblastic Differentiation and Intracellular Free Calcium Concentration in MC3T3-El Cells

  • Jang, Hye-Ock;Eom, Hyun-Sup;Roh, Sung-Bae;Yun, ll
    • The Korean Journal of Physiology and Pharmacology
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    • 제9권1호
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    • pp.55-62
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    • 2005
  • Very little research has been carried out on safflower seed for the prevention and treatment of the bone deficiency diseases, including osteoporosis, which are supported by scientific evidences. In the present study, $3{\mu}l$ of 0.1% dried crude extract or $2{\mu}l$ of 0.1% dried aqueous fraction were shown to significantly accelerate the rate of differentiation of osteoblast. Also, the crude extract and aqueous fraction increased the $[Ca^{2+}]_i$ of the cultured osteoblast cells: $3{\mu}l$ of 0.1% dried crude extract and $2{\mu}l$ of 0.1% dried aqueous fraction significantly increased the $[Ca^{2+}]_i$ of the cultured osteoblast cells ($8{\times}10^{-4}$) to the extent that it deserves a considerable attention. Furthermore, the crude extract and aqueous fraction increased the $[Ca^{2+}]_i$ of the cultured osteoblast cells, and $300{\mu}M$ $Cd^{2+}$, specific calcium channel blocker, completely blocked the increase. Therefore, the increased $[Ca^{2+}]_i$ of the cultured osteoblast cells by safflower seed component continued to activate calcium channel.