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TWO NECESSARY AND SUFFICIENT CONDITIONS FOR THE CLASSICAL ORTHOGONAL POLYNOMIALS

  • Park, Suk-Bong
    • Journal of applied mathematics & informatics
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    • v.23 no.1_2
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    • pp.581-588
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    • 2007
  • We reconsider the classical orthogonal polynomials which are solutions to a second order differential equation of the form $$l_2(x)y'(x)+l_1(x)y'(x)={\lambda}_ny(x)$$. We investigate two characterization theorems of F. Marcellan et all and K.H.Kwon et al. which gave necessary and sufficient conditions on $l_1(x)\;and\;l_2(x)$ for the above differential equation to have orthogonal polynomial solutions. The purpose of this paper is to give a proof that each result in their papers respectively is equivalent.

Inhibitory Effect of Cymbopogon Citratus Ethanol Extracts on Adipogenesis in 3T3-L1 Preadipocytes (레몬그라스 에탄올 추출물의 3T3-L1 지방세포 분화 억제효과)

  • Jo, Yong Seok;Ju, Sung Min;Hwang, Keum Hee;Kim, Min Sook;Kim, Kwang Sang;Jeon, Byung Hun
    • Journal of Physiology & Pathology in Korean Medicine
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    • v.33 no.1
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    • pp.17-24
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    • 2019
  • Cymbopogon citratus, commonly know as lemongrass, prossesses strong antioxidant, anti-tumor and anti-inflammatory properties. Howerver, its anti-obesity activity remains to be elucidated. This study investigated the effect of ethanol extract of Cymbopogon citratus on adipogenesis, and its underlying mechanism, in 3T3-L1 preadipocytes. The results demonstrated that ethanol extracts of Cymbopogon citratus effectively suppressed intercellular lipid accumulation at non-toxic concentrations, and was associated with the down-regulation of adipocyte-specific transcription factors, including $C/EBP{\alpha}$ and $PPAR{\gamma}$, and phosphorylation of $AMPK{\alpha}$. Furthermore, ethanol extracts of Cymbopogon citratus increased p21 and p21 expression, while the expression of CDK2, cyclin A and cyclin B1 was reduced. As a result, ethanol extracts of Cymbopogon citratus seems to induce G0/G1 cell cycle arrest of 3T3-L1 cells. On the other hand, ERK and Akt signaling pathways were not involved in anti-adipogenesis by ethanol extracts of Cymbopogon citratus. Taken together, theses results suggest that ethanol extracts of Cymbopogon citratus inhibits adipocyte differentiation in 3T3-L1 cells and can be used as a safe and efficient natural substance to manage anti-obesity.

The method to estimate 3-D coordinates of lower trunk muscles using orientation angles during a motion (몸통 운동시 지향각(Orientation angles)을 이용한 허리 근육의 3차원 위치 좌표 추정 기법)

  • Lim, Young-Tae
    • Korean Journal of Applied Biomechanics
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    • v.12 no.1
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    • pp.125-133
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    • 2002
  • The purpose of this study was to develop a method for estimating 3-D coordinates of lower trunk muscles using orientation angles during a motion. Traditional 3-D motion analysis system with DLT technique was used to track down the locations of eight reference markers which were attached on the back of the subject. In order to estimate the orientations of individual lumbar vertebrae and musculoskeletal parameters of the lower trunk muscle, the rotation matrix of the middle trunk reference frame relative to the lower trunk reference frame was determined and the angular locations of individual lumbar vertebrae were estimated by partitioning the orientation angles (Cardan angles) that represent the relative angles between the rotations of the middle and lower trunks. When the orientation angles of individual intervertebral joints were known at a given instant, the instantaneous coordinates of the origin and insertion for all selected muscles relative to the L5 local reference frame were obtained by applying the transformation matrix to the original coordinates which were relative to a local reference frame (S1, L4, L3, L2, or L1) in a rotation sequence about the Z-, X- and Y-axes. The multiplication of transformation matrices was performed to estimate the geometry and kinematics of all selected muscles. The time histories of the 3-D coordinates of the origin and insertion of all selected muscles relative to the center of the L4-L5 motion segment were determined for each trial.

Existence theorems of an operator-valued feynman integral as an $L(L_1,C_0)$ theory

  • Ahn, Jae-Moon;Chang, Kun-Soo;Kim, Jeong-Gyoo;Ko, Jung-Won;Ryu, Kun-Sik
    • Bulletin of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.317-334
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    • 1997
  • The existence of an operator-valued function space integral as an operator on $L_p(R) (1 \leq p \leq 2)$ was established for certain functionals which involved the Labesgue measure [1,2,6,7]. Johnson and Lapidus showed the existence of the integral as an operator on $L_2(R)$ for certain functionals which involved any Borel measures [5]. J. S. Chang and Johnson proved the existence of the integral as an operator from L_1(R)$ to $C_0(R)$ for certain functionals involving some Borel measures [3]. K. S. Chang and K. S. Ryu showed the existence of the integral as an operator from $L_p(R) to L_p'(R)$ for certain functionals involving some Borel measures [4].

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Blunted Indomethacin-Induced Downregulation of Aquaporins by Nitric Oxide Synthesis Inhibition in Rats

  • You, Ju-Hee;Lee, Sung-Su;Bae, Eun-Hui;Ma, Seong-Kwon;Kim, Soo-Wan;Lee, Jong-Un
    • The Korean Journal of Physiology and Pharmacology
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    • v.10 no.4
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    • pp.213-216
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    • 2006
  • The present study was aimed to determine whether nitric oxide (NO) plays a role in the regulation of aquaporin (AQP) channels in the kidney. Male Brattleboro rats ($250{\sim}300\;g$ body weight) were used. The experimental group was treated with $N^G$-nitro-L-arginine methyl ester (L-NAME, 100 mg/L drinking water) for 1 week, and cotreated with indomethacin (5 mg/kg, twice a day, i.p.) for the last two days. Control groups were treated with either L-NAME for 1 week, indomethacin for 2 days, or without any drug treatment. The abundance of AQP1, AQP2 and AQP3 proteins in the kidney was determined by Western blot analysis. Indomethacin downregulated AQP channels, whereas L-NAME by itself showed no significant effects on them. The indomethacin-induced downregulation of AQP2 and AQP3 was significantly blunted in L-NAME-treated rats, while that of AQP1 was not affected. These results suggest that endogenous NO, when stimulated, may downregulate AQP channels that are specifically regulated by AVP/cAMP pathway in the kidney.

Age and Growth of Three-lined Tonguefish (Cynoglossus abbreviatus) (Soleidae; Teleostei) (용서대 (Cynoglossus abbreviatus)의 연령과 성장)

  • BAECK Gun Wook;HUH Sung-Hoi
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.37 no.1
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    • pp.51-56
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    • 2004
  • Age and growth of three-lined tonguefish (Cynoglossus abbreviatus) were studied using samples from the waters off Yosu, Korea, from June to December, 2001. Sagittal otoliths had relatively clear annuli. Each annulus was formed once a year in April. The peak of the gonadosomatic index occurred also in April. The oldest fish observed in this study was 5 years old for females and 4 years old for males. The relationship between the otolith radius (R) and total length (L) was as follows: L=14.921R-2.5318 for females and L=13.527R-0.5584 for males. The relationship between total length and body weight (W) was as follows: $W=0.0008L^{3.54}$ for females and $W=0.0029L^{3.14}$ for males. The growth in length of the fish was expressed by the von Bertalanffy's growth equation as: $$L_t=44.54(1-e^{-0.16(t+2.69)})\;for\;females\;and\;L_t=41.52(1-e^{-0.15(t+3.34)})\;for\;males$$.

Shoot Regeneration from Leaf Explants of Digitalis purpurea L. (디기탈리스의 잎 절편으로부터 신초의 재분화)

  • Hwang, Sung-Jin;Lee, Hye-Jung;Hwang, Baik
    • Korean Journal of Medicinal Crop Science
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    • v.11 no.5
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    • pp.397-401
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    • 2003
  • Digitalis purpurea L. is a medicinal herb and have been used to congestive heart failure, mycocardial infarction, edema, angina etc. A protocol has been developed for in vitro propagation of adventitious shoot buds directly from leaf segments of D. purpurea Leaf explants of D. purpurea directly formed shoot buds when cultured on a MS medium supplemented with $2\;mg/l$ BA and $0.1\;mg/l$ IAA for 5 weeks. Adventitious shoots were multiplied by subculturing on the $B_5$ medium and shoot elongation was developed by subculturing on the WPM medium. Root formation from the shoot regenerated was achieved on MS basal medium containing 1 mg/ IBA.

Foraminal Synovial Cyst Associated with Ankylosing Spondylitis

  • Kim, Heyun-Sung;Ju, Chang-Il;Kim, Seok-Won
    • Journal of Korean Neurosurgical Society
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    • v.50 no.1
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    • pp.54-56
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    • 2011
  • Ankylosing spondylitis (AS) is frequently associated with inflammatory lesions of the spine and continuous fatigue stress fractures; however, an association with an intraspinal synovial cyst has not been previously reported. A 55-year-old man with a five year history of AS who presented with back pain and a right radiculopathy was admitted to the hospital. Five years previously, he underwent a percutaneous vertebroplasty for an osteoporotic L1 compression fracture, and was diagnosed with AS at that time. Plain radiographs showed aggravated kyphosis and a stress fracture through the ossified posterior element, below the prior vertebroplasty. Magnetic resonance images revealed a right foraminal cystic lesion at the L2-L3 level with effacement of the nerve root. A 1.6 cm cystic lesion that appeared to arise from the L2-L3 facet joint without direct communication was excised from the L2-L3 foramen. Pathological examination confirmed synovial cyst. The patient's symptoms resolved immediately after surgery except for a mild dysesthesia of the right leg. We report herein a rare case of foraminal synovial cyst associated with AS accompanying posterior element fracture with a review of literature.

Age and Growth of Red Tongue Sole (Cynoglossus joyneri) in the Southern Sea of Korea (남해 참서대 (Cynogiossus joyneri)의 연령과 성장)

  • BAECK Gun Wook;HUH Sung-Hoi
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.37 no.4
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    • pp.307-311
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    • 2004
  • Age and growth of red tongue sole (Cynoglossus joyneri), were studied using samples from the coastal waters off Yeosu, Korea, from January to December, 2001. Sagittal otoliths had relatively clear annuli. Marginal index of otolith dropped sharhly in August suggesting that each annulus was formed once a year In August. Monthly changes in the gonadosomatic index indicated that spawning peaked between July and September. The oldest fish observed in this study was 4 years old for both of females and males. Relationships between the otolith radius (R) and total length (L) were: L=14.1R-0.098 for females, and L=11.9R+1.83 for males. Relationships between total length and body weight $(W)\;were:\;W=0.0021L^{3.24}\;for\;females,\;and\;W=0.0014L^{3.39}$ for males. Growth in length of the fish was expressed by the von Bertalanffy's growth equation as:$L_{t}=29.06\;(1-e^{-0.19(t+2.40)})\;for\;females\;and\;L_{t}=27.44 (1-e^{-0.17(t+2.84)})$ for males.

Electrochemical Behavior of the Reduction of Thin Films of $Ag_3Fe(CN)_6$

  • Moon Seongbae;Moon Jung Dae
    • Bulletin of the Korean Chemical Society
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    • v.15 no.12
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    • pp.1042-1045
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    • 1994
  • A thin film of silver ferricyanide (Ag$_3$Fe(CN)$_6$) on a platinum or gold substrates can be reduced electrochemically to the salt of silver ferrocyanide in potassium nitrate solution. The color of these films are orange and these films are shown to be electrochromic. The voltammogram is shown the asymmetry of the oxidation compared to the reduction wave under various supporting electrolytes. The standard heterogeneous electron-transfer rate for these films and bare Pt electrode were 0.49 ${\times}$ l0$^{-2}$ and 1.30 ${\times}$ l0$^{-2}$ cm/s, respectively, obtained using a rotating disc electrode. Rough D$_0$ values, evaluated from the Levich equation, for Fe(CN)$_6^{3-/4-}$ at both SF thin film and a bare Pt disc electrode were shown as 1.2l ${\times}$ l0-6 and 0.94 ${\times}$ l0$^{-6}$ cm$^2$/s, respectively. The conductivities, as determined from the slops of the i-V curves for a ca. 1 mm sample for dried SF potassium rich and deficient bulk samples pressed between graphite electrodes, were 9.34 ${\times}$ l0$^{-9}$ and 5.80 ${\times}$ l0$^{-9}$ (${\Omega}$${\cdot}$cm)$^{-1}$, respectively.