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Clinical features of congenital muscular torticollis (선천성 근성 사경의 임상적 특징)

  • Jun, Ji Eun;Ryu, Hye Kyeong;Shim, Jae Won;Shim, Jung Yeon;Jung, Hye Lim;Park, Moon Soo;Kim, Deok-Soo
    • Clinical and Experimental Pediatrics
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    • v.50 no.3
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    • pp.241-247
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    • 2007
  • Purpose : Congenital muscular torticollis (CMT) is a common and benign congenital disorder of the musculoskeletal system in neonates and infants. The pathophysiology is that the sternocleidomastoid muscle (SCM) is shortened on the involved side by fibrosis, leading to ipsilateral tilt and contralateral rotation of the face and chin. In this study, we investigated the clinical features of CMT, the role of ultrasonography (USG) in prediction of prognoses and the clinical significance of early detection and treatment. Methods : Forty seven patients (M:F=31:16) were diagnosed as a CMT between March 2003 and May 2006. We reviewed age at diagnosis, physical findings, USG findings, treatment and therapeutic outcome from their medical records. Results : The median age at diagnosis was 90 days (18 days-9 years, 7 months) and the right side of neck was affected in more patients (right : left=26:21). Of 24 patients with a palpable neck mass, 21 had USG; 19 cases showed sternocleidomastoid tumor (SMT). In cases with no neck mass, USG was performed in 11 patients; seven had postural torticollis (POST), three had SMT and one had muscular torticollis (MT). Among 40 patients with follow-up, 36 had total resolution. There was negative correlation between the age at diagnosis and the recovery time, whereas the final outcome was not correlated with USG findings. However, the patients without positive findings in USG had earlier resolution (1 month vs 2.6 months, P=0.0008). The patients with SMT had earlier diagnosis and excellent outcomes. The patients with MT were delayed to diagnosis and had the longest time to resolve. Lastly, the patients with POST had delayed diagnoses, but they had excellent outcomes. Conclusion : Since the patients with delayed diagnoses, in despite of benign courses, may take a long time to resolve and rarely need surgical treatment, it is important to diagnose and treat early. This study showed that USG findings of the SCM may be used as predictive factors.

The optimal conditions to improve retrovirus-mediated transduction efficiency to NIH 3T3 cells (레트로바이러스(retrovirus)의 NIH 3T3 세포로의 유전자 전달효율을 증가시키기 위한 적절한 조건들)

  • Lee, Jun Ah;Lee, Kang-Min;Lee, Hyun Jae;Lee, Yun Jeong;Kim, Dong Ho;Lim, Jung Sub;Park, Kyung-Duk
    • Clinical and Experimental Pediatrics
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    • v.50 no.10
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    • pp.1011-1017
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    • 2007
  • Purpose : We tried to assess the optimal conditions to improve low transduction efficiency and their effect on target cells. Methods : Cultured NIH 3T3 cells were incubated with retroviral vectors bearing an enhanced green fluorescent protein (eGFP) gene. We varied the ratio of viral vectors to target cells (1:1-1:8) and the number of transfections (${\times}1$, ${\times}2$), and compared transduction efficiencies. Also, the effects of polybrene on transduction efficiency and viability of target cells were assessed. Transduction of the eGFP gene was evaluated by observing NIH 3T3 cells under a fluorescence microscope and efficiencies were measured by the percentage of eGFP positive cells using FACscan. Results : As the ratio of retroviral vectors to target cells increased, transduction efficiency was greatly improved, from 7% (1:1) to 38% (1:4). However, transduction efficiency did not increase any more when the ratio increased from 1:4 to 1:8. Cells transfected twice showed higher transduction efficiencies than cells transfected once, at a ratio of 1:8. The eGFP gene transduced to NIH 3T3 cells sustained its expression during repeated passages. However, after the third passage (day 9), the percentage of eGFP positive cells began to decline. The degree of this decline in eGFP expression was lower in cells transfected twice than in cells transfected once (P<0.05). The addition of polybrene did not have any toxic effect on NIH 3T3 cells and greatly increased transduction efficiency (P=0.007). In addition to vector component, transduction efficiency was very sensitive to culture confluence. Cells cultured and transfected in 24-well plate showed higher transduction efficiency, although cells cultured in 6- well plate proliferated more (P=0.024). Conclusion : Our data could be used as a basis for retrovirus-based gene therapy. Further study will follow using human cells as target cells.

Why Central Banks Intervene? (왜 중앙은행은 개입하는가?)

  • Ko, Jong-Moon
    • The Korean Journal of Financial Management
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    • v.12 no.2
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    • pp.273-298
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    • 1995
  • 1960년대, 각국의 환율이 미국의 달러화에 연동(pegging)된 고정환율제도를 근간으로 하는 브레튼우즈(Bretton Woods)체제하에서 각국의 중앙은행은 환율을 일정한 범위 내로 유지하기 위한 정책수단으로 외환시장개입을 적극 활용하였다. 1973년 브레튼우즈체제하의 고정환율제도가 붕괴되고 변동환율제도가 채택된 이후에도 각국의 외환시장개입정책은 계속되었다. 1980년대에 레이건 행정부의 재정팽창정책과 미연방준비은행의 긴축통화정책으로 금리의 지속적인 상승과 미달러화의 큰폭의 절상이 이루어 졌다. 이에 국제무역의 위기를 우려한 미국, 독일, 프랑스, 영국, 일본 등 선진 5개국(Group-5, G5)은 1985년 9월 22일 미 달러화의 절하를 위해 외환시장에 공동으로 개입할 것을 주내용으로 한 플라자합의(Plaza Agreement)를 발표하였다. 그후에도 1987년 2월 23일 열린 루브르협정(Louvre Accord, G-6 Communique)에서 환율을 현수준으로 유지시키기 위한 목표환율대(Target zone)를 설정하고 외환시장개입을 통해 이를 유지하기로 합의한 바 있다. 이후의 구미각국은 환율의 관리를 위하여 국가가 공동으로 외환시장에 개입하곤 했다. 본 논문은 1987년 루브르협정 이후 미국, 독일 및 일본의 중앙은행의 외환시장 개입 정책이 소기의 목적을 달성했는지의 여부를 규명해 보고자 한다. 즉, Federal Reserve, Bundesbank 및 Bank of Japan의 외환시장개입이 현물환율시장(spot market)에서 각각의 변동성을 감소 시켰는지의 여부를 독일의 마르크화 및 일본의 엔화를 중심으로 규명해 보고자 한다. 1981년 루브르협정이후, 미국, 독일 및 일본의 중앙은행은 미국 달러화에 대한 마르크 및 엔화의 환율을 안정시키기 위해 꾸준히 외환시장에 개입해 왔다. 외환시장의 개입유형은 크게 태화외환시장개입(non-sterilized intervention)과 불태화외환시장개입(sterilized intervention)으로 구분할 수 있는데, 전자는 외환당국이 민간부문과 외화채권을 거래함으로써 본원통화의 크기가 변하는 개입형태를 의미하는 반면에 후자는 외환당국의 순외화자산의 크기변화가 본원통화의 변화를 초래하지 않는 경우이다. 즉, 불태화외환시장개입은 순외화자산의 증감이 순국내자산의 증감과 반비례해서 이루어지기 때문에 본원통화의 크기에는 변함이 없다. 외환시장개입이란 외환당국이 은행간 시장에서 민간시잔 참가자들과 행하는 적극적인 외환거래를 의미한다. 반면, 넓은 의미에서의 외환시장개입에는 수동적 외환시장개입이라고 불리는 고객거래가 포함된다. 후자의 거래는 국내통화 및 외화표시 자산의 상대적 공급규모를 변화시킨다는 의미에서 전통적외환시장개입과 동일한 효과를 갖기 때문에 광의의 외환시장 개입으로 분류된다. 외환시장의 개입목적은 크게 세 가지로 분류할 수 있다. 첫째, 환율의 안정적 운영이다. 환율수준이 자유롭게 변화되는 변동환율제도하에서 환율의 지나친 변동으로 인한 실물경제로의 부정적인 영향을 최소화하기 위해서 환율의 지나친 변동으로 인한 실물경제로의 부정적인 영향을 최소화하기 위해서 환율의 안정을 정책 목표로 설정하는 경우와 고정환율제도하에서 환율을 일정수준으로 유지시키기 위해서 외환당국이 외환시장에 개입하는 경우가 여기에 해당된다고 볼 수 있다. 둘째, 환율수준의 균형수준으로의 조정이다. 이때 야기될 수 있는 문제점으로는 환율균형 수준을 어떻게 정의, 추정할 것이냐 하는 점과 목표환율정책이 다른 정책목표와 상충될 수 있다는 점이다. 셋째, 외환당국이 공적외환보유액이나 구성을 변화시킬 목적으로 외환시장에 개입하는 경우이다. 이때의 외환시장개입은 현재의 환율수준이 개입으로 인하여 과도하게 이탈하는 문제가 발생하지 않을 것을 전제로 한다. 본고에서는 현물환율에 영향을 미치는 요소로 미국, 독일 및 일본의 중앙은행의 개입효과, 요일효과, 통화의 공급량(M1), 무역적자의 폭, 산업의 생산량, 생산가격지수(PPI), 소비자물가지수(CPI), 실업률, 옵션의 내재적 변동성 등을 고려한다. 환율의 변동성을 추정하는 식은 GARCH 모델이 사용된다. 본 추정모델은 Dominguez(1993)의 확장이다. Dominguez (1993)의 논문은 GARCH 모델을 써서 미국, 독일 및 일본의 중앙은행의 시장개입효과를 분석했으나, 거시변수를 고려대상에서 제외시켰다. 본 논문은 위의 방법에 거시변수를 삽입하고 모델을 변형시켜서 더 확실한 시장개입효과와 거시변수효과를 밝혔다. 또한 옵션의 내제적 변동성을 구하는 과정에서 American option model을 사용하는 대신, Bourtha & Courtadon (1987)등이 밝힌 바와 같이 American style option이라 할지라도, European Model을 쓰면 더욱더 간편하고, 예측력도 American Model에 뒤지지 않음을 이용하여, European Model을 써서 내재적 변동성을 구한 다음 이것을 독립변수로 이용하였다. 본 모델의 추정 결과는 3국의 시장개입정책이 현물환율과 옵션의 내재적 변동성을 증가시켜서 Louvre 협정이후 각국은 시장개입의 목적을 달성하지 못한 것으로 나타났다.

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Stellite bearings for liquid Zn-/Al-Systems with advanced chemical and physical properties by Mechanical Alloying and Standard-PM-Route

  • Zoz, H.;Benz, H.U.;Huettebraeucker, K.;Furken, L.;Ren, H.;Reichardt, R.
    • Proceedings of the Korean Powder Metallurgy Institute Conference
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    • 2000.04a
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    • pp.9-10
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    • 2000
  • An important business-field of world-wide steel-industry is the coating of thin metal-sheets with zinc, zinc-aluminum and aluminum based materials. These products mostly go into automotive industry. in particular for the car-body. into building and construction industry as well as household appliances. Due to mass-production, the processing is done in large continuously operating plants where the mostly cold-rolled metal-strip as the substrate is handled in coils up to 40 tons unwind before and rolled up again after passing the processing plant which includes cleaning, annealing, hot-dip galvanizing / aluminizing and chemical treatment. In the liquid Zn, Zn-AI, AI-Zn and AI-Si bathes a combined action of corrosion and wear under high temperature and high stress onto the transfer components (rolls) accounts for major economic losses. Most critical here are the bearing systems of these rolls operating in the liquid system. Rolls in liquid system can not be avoided as they are needed to transfer the steel-strip into and out of the crucible. Since several years, ceramic roller bearings are tested here [1.2], however, in particular due to uncontrollable Slag-impurities within the hot bath [3], slide bearings are still expected to be of a higher potential [4]. The today's state of the art is the application of slide bearings based on Stellite\ulcorneragainst Stellite which is in general a 50-60 wt% Co-matrix with incorporated Cr- and W-carbides and other composites. Indeed Stellite is used as the bearing-material as of it's chemical properties (does not go into solution), the physical properties in particular with poor lubricating properties are not satisfying at all. To increase the Sliding behavior in the bearing system, about 0.15-0.2 wt% of lead has been added into the hot-bath in the past. Due to environmental regulations. this had to be reduced dramatically_ This together with the heavily increasing production rates expressed by increased velocity of the substrate-steel-band up to 200 m/min and increased tractate power up to 10 tons in modern plants. leads to life times of the bearings of a few up to several days only. To improve this situation. the Mechanical Alloying (MA) TeChnique [5.6.7.8] is used to prOduce advanced Stellite-based bearing materials. A lubricating phase is introduced into Stellite-powder-material by MA, the composite-powder-particles are coated by High Energy Milling (HEM) in order to produce bearing-bushes of approximately 12 kg by Sintering, Liquid Phase Sintering (LPS) and Hot Isostatic Pressing (HIP). The chemical and physical behavior of samples as well as the bearing systems in the hot galvanizing / aluminizing plant are discussed. DependenCies like lubricant material and composite, LPS-binder and composite, particle shape and PM-route with respect to achievable density. (temperature--) shock-reSistibility and corrosive-wear behavior will be described. The materials are characterized by particle size analysis (laser diffraction), scanning electron microscopy and X-ray diffraction. corrosive-wear behavior is determined using a special cylinder-in-bush apparatus (CIBA) as well as field-test in real production condition. Part I of this work describes the initial testing phase where different sample materials are produced, characterized, consolidated and tested in the CIBA under a common AI-Zn-system. The results are discussed and the material-system for the large components to be produced for the field test in real production condition is decided. Outlook: Part II of this work will describe the field test in a hot-dip-galvanizing/aluminizing plant of the mechanically alloyed bearing bushes under aluminum-rich liquid metal. Alter testing, the bushes will be characterized and obtained results with respect to wear. expected lifetime, surface roughness and infiltration will be discussed. Part III of this project will describe a second initial testing phase where the won results of part 1+11 will be transferred to the AI-Si system. Part IV of this project will describe the field test in a hot-dip-aluminizing plant of the mechanically alloyed bearing bushes under aluminum liquid metal. After testing. the bushes will be characterized and obtained results with respect to wear. expected lifetime, surface roughness and infiltration will be discussed.

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Effect of Brown Seaweed Waste Supplementation on Lactational Performance and Endocrine Physiology in Holstein Lactating Cows (미역부산물의 첨가가 홀스타인 비유우의 비유성적과 내분비생리에 미치는 영향)

  • Lee, H.G.;Hong, Z.S.;Li, Z.H.;Xu, C.X.;Jin, X.;Jin, M.G.;Lee, H.J.;Choi, N.J.;Koh, T.S.;Choi, Yun-Jaie
    • Journal of Animal Science and Technology
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    • v.47 no.4
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    • pp.573-582
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    • 2005
  • This study was conducted to investigate effects of the brown seaweed waste(BSW) supplementation on milk production and related endocrine response in serum in Holstein dairy cows. A total of 14 Holstein dairy cows(initial mean live weight 625kg, average lactation days 225, Reproduction 2.4) were randomly allocated into control(basal diet) and treatment groups (4% BSW/basal diet) with 7 replications for 90 days. Dry matter intake was not affected by brown seaweed waste supplementation, but daily milk yield(kg) at the last experiment significantly increased (6.25kg) in treatment group compared with control group(p<0.05) at the last experiment. The plasma insulin-like growth factor(IGF)-1, triiodothyronine($T_3$) and thyroxine($T_4$) levels were significantly increased in treatment group compared with control group(p<0.05), although the concentration of plasma growth hormone(GH) was not significantly different. Milk composition was not significantly different between groups. The somatic cell count(SCC) in milk were significantly reduced in treatment group compared with control group(p<0.05), but antibodies(total IgG, G1, G2) were not significantly different between groups. Therefore we strongly believe that the increased milk yield is related to metabolic hormones as IGF-1, $T_3$ and $T_4$ and the mechanism of reducing SCC in milk must do more study related nonspecific immunsystem in the future.

Late aortic root dilatation and aortic regurgitation in repaired tetralogy of fallot (팔로 4징의 완전 교정술 후 장기 추적 관찰상 나타나는 대동맥근의 확장과 대동맥판 폐쇄부전)

  • Kim, Jeong Eun;Hur, Kyong;Kwon, Hae Sik;Yoo, Byung Won;Choi, Jae Young;Sul, Jun Hee
    • Clinical and Experimental Pediatrics
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    • v.50 no.10
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    • pp.976-981
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    • 2007
  • Purpose : Aortic valve or aortic root (AoRo) replacement is occasionally required because of AoRo dilatation and aortic regurgitation (AR) in repaired tetralogy of Fallot (TOF). We evaluated AoRo size and possible factors associated with its hemodynamic nature in patients with repaired TOF. Methods : We investigated 130 repaired TOF patients more than 15 years of age who followed-up by echocardiography from January 2002 to December 2003. Of 130 patients, we identified 17 patients with AoRo dilatation, which was defined as ratio of expected AoRo size by standard nomogram (AoRo ratio) >1.5 (dilator group), and 113 TOF controls, with AoRo ratio <1.5 (non-dilator group). Results : Mean indexed AoRo size ($mm/m^2$) in the first echo was $24{\pm}3.2$ in the dilator group and $18{\pm}3.4$ in the non-dilator group (P<0.0001). AoRo rate of change (mm/year) from the first to latest echo study was $1.6{\pm}3.8$ in dilator group and $0.05{\pm}1.6$ in the non dilator group (P=0.0021). Patients from the dilator group showed a higher prevalence of pulmonary atresia (P=0.031) and a history of aortopulmonary shunt before repair (P=0.048), moderate to severe AR (P=0.0065), and increased left ventricular end-diastolic dimensions (P=0.003). Conclusions : A subset of patients late after TOF repair may show progressive dilatation of AoRo. To identify and prevent long-term sequelae in this patient group, regular follow-up and speculation about AoRo after TOF repair is recommended.

Therapeutic comparison between low-dose sustained-release theophylline dry syrup and capsule in children with mild persistent asthma (유소아 경증 지속성 천식에서 저용량 서방형 테오필린 건조시럽과 캡슐 제형의 치료 효과 비교)

  • Lee, Hyun Seung;Lee, Hae Kyung;Kwon, Hi Jeong;Kim, Jeong Hee;Rha, Yeong Ho;Kim, Jin Tack;Kim, Young Ho;Lee, Hae Rhan;Pyun, Bok Yang
    • Clinical and Experimental Pediatrics
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    • v.50 no.3
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    • pp.284-291
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    • 2007
  • Purpose : Theophylline has recently been reported to have concurrent anti-inflammatory effects at low therapeutic plasma concentrations which are below the doses at which significants, clinically useful bronchodilatation is evident. Sustained-release formulation in capsule and dry syrup forms were developed to reduce its adverse effects and improve its clinical effects. We compared the therapeutic effects of theophylline dry syrup and capsules in children with mild asthma. Methods : Ninety children with mild asthma were randomized to receive either theophylline dry syrup (n=44) or theophylline capsules (n=46); 4 mg per kilogram of body weight, twice a day, for 12 weeks. Baseline and serial measurements of daytime and nighttime asthma symptom score were performed. Compliance scores, drug swallowing scores, and drug usability scores were measured every 4 weeks. Each scoring was rated on a scale of 0-4. Serum theophylline concentration were measured at 4 and at 12 weeks. To examine the anti-inflammatory effect of theophylline on asthma, Serum eosinophilic cationic protein as a marker of airway inflammation caused by eosinophil was measured 12 weeks pre- and post-administration. Results : The daytime and nighttime asthma symptom scores of the two groups after 4 weeks significantly improved over the baseline score. Daytime and nighttime asthma symptom scores in the dry syrup group were statistically lower at all time points except for the nighttime symptom scores at 4 weeks. Compliance scores, drug swallowing scores, and drug usability scores in the dry syrup group were significantly higher at the end time point. Only in the dry syrup group was the serum ECP at the end time point statistically lower than baseline. Conclusion : Low-dose sustained-release theophylline may be safe and effective in bronchial asthma and this effect may be mediated by its anti-inflammatory action mechanisms. Especially, when used in children with asthma, dry syrup formulation is recommended because of its higher compliance than capsule formulation.

Operative treatment for Proximal Humeral Fracture (상완골 근위부 골절의 수술적 요법)

  • Park Jin-Young;Park Hee-Gon
    • Journal of Korean Orthopaedic Sports Medicine
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    • v.2 no.2
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    • pp.168-175
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    • 2003
  • Fracture about proximal humerus may be classified as the articular segment or the anatomical neck, the greater tuberosity, the lesser tuberosity, and the shaft or surgical neck. Now, usually used, Neer's classification is based on the number of segments displaced, over 1cm of displaced or more than 45 degrees of angulation , rather than the number of fracture line . Absolute indication of a operative treatment a open fracture, the fracture with vascular injury or nerve injury , and unreductable fracture-dislocation . Inversely, the case that are severe osteoporosis, and eldly patient who can't be operated by strong internal fixation is better than arthroplasty used by primary prosthetic replacement and early rehabilitation program than open reduction and internal fixation. The operator make a decision for the patient who should be taken the open reduction and internal fixation, because it's different that anatomical morphology, bone density, condition of patient. The operator decide operation procedure. For example, percutaneous pinning, open reduction, plate & screws, wire tension bands combined with some intramedullary device are operation procedure that operator can decide . The poor health condition for other health problem, fracture with unstable vital sign and severe osteoporosis , are the relative contraindication. The stable fracture without dislocation is not the operative indication . The radiologic film of the prokimal humerus before the operation can not predict for fracture evaluation. It's necessary to good radiologic film for evaluation of fracture form. The trauma serise is better than the other radiologic film for evaluation. The accessary radiologic exam is able to help for evaluation of bone fragment and anatomy. The CT can be helpful in evaluating these injury, especially if the extract fracture type cannot be determined from plain roenterogram of the proximal humerus, bone of humerus head. If the dislocation is severe anatomically , we could consider to do three dimentional remodelling. The MRI doing for observing of bony morphology before the operation is not better than CT If we were suspicious of vascular injury, we could consider the angiography.

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NEAR REAL-TIME ESTIMATION OF GEOMAGNETIC LOCAL K INDEX FROM GYEONGZU MAGNETOMETER (경주 지자기관측소 자료를 이용한 준실시간 K 지수 산출에 관한 연구)

  • Choi, K.C.;Cho, K.S.;Moon, Y.J.;Kim, K.H.;Lee, D.Y.;Park, Y.D.;Lim, M.T.;Park, Y.S.;Lim, H.R.
    • Journal of Astronomy and Space Sciences
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    • v.22 no.4
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    • pp.431-440
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    • 2005
  • Local K-index is an indicator representing local geomagnetic activity in every 3 hour. For estimation of the local K-index, a reasonable determination of solar quiet curve (undisturbed daily variation of geomagnetic field) is quiet essential. To derive the solar quiet curve, the FMI method, which is one of representative algorithms, uses horizontal components (H and D) of 3 days magnetometer data from the previous day to the next day for a specific day. However, this method is not applicable to real time forecast since it always requires the next day data. In this study, we have devised a new method to estimate local K-index in near real-time by modifying the FMI method. The new method selects a recent quiet day whose $K_p$ indices, reported by NOAA/SEC are all lower than 3, and replace the previous day and the next day data by the recent quiet day data. We estimated 2,672 local K indices from Gyeongzu magnetometer in 2003, and then compared the indices with those from the conventional FMI method. We also compared the K indices with those from Kakioka observatory. As a result, we found that (1) K indices from the new method are nearly consistent with those of the conventional FMI method with a very high correlation (R=0.96); (2) onr local K indices also have a relatively high correlation (R=0.81) with those from Kakioka station. Our results show that the new method can be used for near real-time estimation of local K indices from Gyeongzu magnetometer.

Analysis on Efficiency of Hierarchical Structure for a Grid Transit Network (격자형 대중교통 노선망의 위계구조 효율성 분석)

  • Park, Jun-Sik;Go, Seung-Yeong;Jeon, Gyeong-Su
    • Journal of Korean Society of Transportation
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    • v.25 no.4
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    • pp.123-133
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    • 2007
  • This study analyzed whether a transit network with hierarchy is efficient or not, and if transit network hierarchy has cost efficiency, then which condition guarantees the efficiency of the transit network hierarchy. The authors modeled the total cost of the transit network and suggested the conditions in which the transit network hierarchy has cost efficiency through comparing the cost of the transit network with and without hierarchy. The efficiency of transit network hierarchy is guaranteed when the travel cost savings induced by using a higher hierarchy transit network is larger than the increasing non-travel cost, which is the sum of access cost, waiting cost, and operating cost, induced by the introduction of a higher hierarchy transit network. This result is consistent with common sense and with the concept of cost and benefit analysis. If a passenger traveling within the area divided by a higher hierarchy transit network uses only a lower hierarchy transit network and the passenger traveling out of the area divided by the higher hierarchy transit network uses both lower and higher hierarchy transit networks, the travel demand using the higher hierarchy transit network is inversely proportional to the square of the line spacing. This means that the transit network becomes more efficient and small increases of travel demand guarantee the efficiency of the transit network hierarchy as the connectivity of the network becomes higher. This result shows that transit networks have economies of aggregation. This study is the first analytical research on transit network hierarchy and is expected to be a basis for numerical research. However, numerical research should complement this study, since analytical research has some limitations for considering a real network.