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수학적 창의성과 개방형 문제(open ended problem)

  • Gwon, O-Nam;Jo, Yeong-Mi;Park, Jeong-Suk;Park, Ji-Hyeon;Kim, Yeong-Sil
    • Communications of Mathematical Education
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    • v.16
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    • pp.217-218
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    • 2003
  • 제7차 교육과정의 기본방향인 '21세기의 세계화 정보화 시대를 주도할 자율적이고 창의적인 한국인 육성'에서 볼 수 있듯이, 새로운 교육과정에서는 학생들의 창의력을 신장시키기 위한 방안으로 교과별 교육과정이나 재량활동 운영 등을 제시한 바 있다. 수학교육에서도 이러한 시대적 흐름에 발맞추어 수학적 창의력의 신장이 강조되고 있는 상황이다. 그동안 이론적인 측면과 실제적인 측면에서 수학적 창의성에 대한 성과가 축적되었다. 이론적인 측면에서 볼 때, Haylock(1987)등에 의해 창의력과 수학적 창의력의 구분되었으며, 특히 '수학적' 창의력에 대한 다양한 정의가 제안되었다. 실제적인 측면에서도 수학적 창의력을 측정하려는 평가 도구들이 그 동안 여러 가지로 개발하였다. 그러나, 이러한 수학적 창의력에 관한 전반적인 연구는 종국적으로 교실 수학수업에 반영되어야 함에도 불구하고, 그리 만족스럽지 못한 상황이다. 특히, 교실에서 수학수업을 실제로 담당하는 교사들이 수학적 창의력을 위한 수업을 하고자 하더라도 당장 가까이에서 구할 수 있는 교수 학습 자료가 여전히 부족한 상황이다. 물론 그 동안 교실 수학수업에서 사용할 수 있는 창의력 개발 프로그램이 전무한 것은 아니다. 그런데 그들 대부분은 게임이나 퍼즐을 이용한 것으로 그 수준이 단순 흥미유발에 그치고 있거나 소수의 영재아를 위한 소재를 중심으로, 특히 수학적 사고 과정을 따르기보다는, 시행착오를 거쳐 원하는 결과를 얻을 가능성이 많으며, 수학과의 연계성이 불분명한 채로 단순놀이에 그치는 경우가 적지 않아, 수업과 연관되어 창의력의 신장이라는 측면에서 볼 때, 적용하기 어려운 사례가 많다. 이러한 상황을 개선하는 데 기여하고자, 현재 교과교육공동연구 지원사업의 하나로 한국 학술 진흥재단의 지원을 받아, '개방형 문제(open-ended problems)'를 중심 소재로 한 '수학적 창의성'을 신장하기 위한 교수학습 프로그램을 개발하여, 중학교 1학년을 대상으로 연구를 진행하고 있다. 개방형 문제라 함은 명백한 정의가 어렵지만 Pehkeon(1995)는 개방형문제의 정의를 명백히 하기위한 시도로서 그 반대로 닫힌 문제에 대한 정의로부터 시작하여, 어떤 문제가 닫혀있다고 하는 것은 그 문제의 출발 상황과 목표 상황이 닫혀 있는 것, 즉 명백히 설명되어있을 때라면 개방형 문제는 이와 반대의 개념임을 시사하였다. Silver(1995)는 개방형 문제를 문제 자체가 다른 해석이 가능하거나 서로 다를 인정할만한 답을 가질 수 있는 문제 또는 풀이과정이 다양한 문제, 자연스럽게 다른 문제들을 제안하거나 일반화를 제시할 수 있는 문제라고 정의하였다. 따라서 개방형 문제란 출발상황이나 목표 상황의 일부가 닫혀있지 않을 때를 말하고 문제의 조건을 만족하는 해답이 여러 가지로 존재하는 문제를 뜻한다. 수학적 창의력을 개발하는 데, 다른 문제 유형보다도, 개방형 문제가 유리하다는 점은 이미 여러 학자들에 의해 주장되어왔다. 미국 국립영재교육센터(NRCG/T)는 기존의 사지선다형이나 단답형 문제와 질문들은 학생들의 사고 능력에 관한 정보를 거의 알려주지 못하기 때문에 한 가지 이상의 답을 요구하는 ‘open-ended' 또는 ’open-response' 문제와 질문을 가지고 수학 분야에서의 창의적 사고 능력과 표현능력을 측정해야 한다고 하였고, 개방형 문제가 일반적으로 정답이 하나인 문제보다 고차원적인 사고를 요구하게 하는 문제 형태라고 하였다. 본 연구에서는 이러한 근거를 바탕으로 개방형 문제의 유형을 다양한 답이 존재하는 문제, 다양한 해결 전략이 가능한 문제, 답이 없는 문제, 문제 만들기, 일반화가 가능한 문제 등으로 보고, 수학적 창의성 중 특히 확산적 사고에 초점을 맞추어 개방형 문제가 확산적 사고의 요소인 유창성, 독창성, 유연성 등에 각각 어떤 영향을 미치는지 20주의 프로그램을 개발, 진행하여 그 효과를 검증하고자 한다. 개방형 문제를 활용한 수학적 창의력 신장 프로그램을 개발하고 현장 학교에 실험 적용하여 그 효과를 분석하고자 하는 본 연구는 창의력 신장에 비중을 두는 수학과 교수-학습 과정에 실제적인 교수 학습 자료를 제공하는 것뿐만 아니라 교사들에게는 수학교실에서 사용 가능한 실제적인 활용방안을, 학생들에게는 주어진 문제를 여러 가지 각도에서 생각하면서 다양한 사고를 경험하는 기회를 가질 수 있어, 수학을 보는 학생들의 태도에도 긍정적인 변화를 가져올 수 있을 것이라 기대한다.

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Chlorophyll Contents and Growth Performances of the Five Deciduous Hardwood Species Growing Under Different Shade Treatments (광도 변화에 따른 5개 활엽수종의 엽록소 함량과 생장 특성)

  • Cho, Min-Seok;Kwon, Ki-Won;Kim, Gil-Nam;Woo, Su-Young
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.10 no.4
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    • pp.149-157
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    • 2008
  • We investigated chlorophyll contents and growth performances of five deciduous hardwood species growing in central temperate zone of Korean forest. Cornus controversa, Fraxinus rhynchophylla, Betula schmidtii, Prunus leveilleana, and Acer mono seedlings were grown under four different light intensity regime (full sunlight, $65{\sim}72%$, $29{\sim}40%$, and, $7{\sim}12%$ of the full sunlight) for the experiment. The chlorophyll contents of all of the species were highest in $7{\sim}12%$ of the full sunlight, while lowest under the full sunlight. The relative growth rate of root collar diameter and height were decreased with increasing shading level except for Acer mono that showed the highest relative growth rate under $29{\sim}40%$ of the full sunlight. Total biomass and root volumes of the seedlings studied decreased as the light intensity decreased with different shade levels. For Acer mono, however, the biomass and root volumes were highest in $29{\sim}40%$ of the full sunlight. The relative growth rate of root comparing to shoot decreased as shading increased, and as a result, the ratio of aboveground to belowground biomass increased. As the shading level increased, specific leaf area (SLA), leaf area ratio (LAR), and leaf weight ratio (LWR) of most species increased.

Downscaling of Sunshine Duration for a Complex Terrain Based on the Shaded Relief Image and the Sky Condition (하늘상태와 음영기복도에 근거한 복잡지형의 일조시간 분포 상세화)

  • Kim, Seung-Ho;Yun, Jin I.
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.18 no.4
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    • pp.233-241
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    • 2016
  • Experiments were carried out to quantify the topographic effects on attenuation of sunshine in complex terrain and the results are expected to help convert the coarse resolution sunshine duration information provided by the Korea Meteorological Administration (KMA) into a detailed map reflecting the terrain characteristics of mountainous watershed. Hourly shaded relief images for one year, each pixel consisting of 0 to 255 brightness value, were constructed by applying techniques of shadow modeling and skyline analysis to the 3m resolution digital elevation model for an experimental watershed on the southern slope of Mt. Jiri in Korea. By using a bimetal sunshine recorder, sunshine duration was measured at three points with different terrain conditions in the watershed from May 15, 2015 to May 14, 2016. The brightness values of the 3 corresponding pixel points on the shaded relief map were extracted and regressed to the measured sunshine duration, resulting in a brightness-sunshine duration response curve for a clear day. We devised a method to calibrate this curve equation according to sky condition categorized by cloud amount and used it to derive an empirical model for estimating sunshine duration over a complex terrain. When the performance of this model was compared with a conventional scheme for estimating sunshine duration over a horizontal plane, the estimation bias was improved remarkably and the root mean square error for daily sunshine hour was 1.7hr, which is a reduction by 37% from the conventional method. In order to apply this model to a given area, the clear-sky sunshine duration of each pixel should be produced on hourly intervals first, by driving the curve equation with the hourly shaded relief image of the area. Next, the cloud effect is corrected by 3-hourly 'sky condition' of the KMA digital forecast products. Finally, daily sunshine hour can be obtained by accumulating the hourly sunshine duration. A detailed sunshine duration distribution of 3m horizontal resolution was obtained by applying this procedure to the experimental watershed.

Histological studies on in vitro Propagation of Pulsatilla koreana Nakai (할미꽃 기내증식(器內增殖)에 관(關)한 조직학적(組織學的) 연구(硏究))

  • Lee, Man-Sang;Oh, Ki-Hong
    • Korean Journal of Medicinal Crop Science
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    • v.1 no.2
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    • pp.137-157
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    • 1993
  • This study was carried out to investigate the optimal condition for multiple propagation through leaf tissue culture and to apply anther culture techniques to Pulsatilla koreana Nakai breeding. Leaf and anther of Pulsatilla koreana Nakai were cultured on MS, MT, LS and $B_5$ media supplemented with several growth regulators and nitrogen sources under various conditions. For callus induction and differentiation from the Pulsatilla koreana leaf segments were more effective in the combination of zeatin and auxin than auxin alone. The color of the callus was green when treated with IBA alone. Shoot differentiation was more effective when treated with zeatin than auxin alone, especially the best hormoal combination for shoot differentiation was zeatin 1.0mg/l +NAA 0.1mg/l, while 2,4-D inhibited shoot differentiation. The appeared rate of S pollen was 35% in vivo, while that of S pollen by low temperature$(4^{\circ}C)$ pretreatment for 4 days was increased by 53% and the optimum culture time for callus induction from anther was uni-nucleate stage. $B_5$ basal medium supplemented with NAA 0.5mg/l and zeatin 1 mg/l was the most effective on callus formation and the best results of plant regeneration were obtained from combination of NAA 0.5mg/l and zeatin 0.5mg/l in anther culture. $NH_{4}NO_3$ as more effectives as the nitrogen source than $KNO_3$ and the combination with zeatin 2.0mg /L was the best effective. The best combination for plant regeneration in callus induced from anther was $NH_{4}NO_3$ 1650mg/l + $KNO_3$ 3800mg/l + zeatin 2.0mg/l. Ploidy level of anther-derived plants appeared 28% haploid, 47% diploid and the others were triploid, tetraploid and mixploid. In compare with E.S.T, M.D.H and P.X banding patterns were distinguished among callus, haploid and diploid plants in electrophoresis.

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Recovery of $SF_6$ gas from Gaseous Mixture ($SF_6/N_2/O_2/CF_4$) through Polymeric Membranes (고분자 분리막을 이용한 혼합가스($SF_6/N_2/O_2/CF_4$)로부터 $SF_6$의 회수)

  • Lee, Hyun-Jung;Lee, Min-Woo;Lee, Hyun-Kyung;Choi, Ho-Sang;Lee, Sang-Hyup
    • Membrane Journal
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    • v.21 no.1
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    • pp.22-29
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    • 2011
  • During the maintenance, repair and replacement process of circuit breaker, $SF_6$ reacted with input air in arc discharge, which led to the production of by-product gases (eg, $N_2$, $O_2$, $CF_4$, $SO_2$, $H_2O$, HF, $SOF_2$, $CuF_2$, $WO_3$). Among these various by-product gases, $N_2$, $O_2$, $CF_4$ is major component. Therefore, the effective separation process is necessary to recycle the $SF_6$ gas from the mixture gas containing $N_2$, $O_2$, $CF_4$. In this study, the membrane separation process was applied to recycle the $SF_6$ gas from the mixture gas containing $N_2$, $O_2$, $CF_4$. The concentration of $SF_6$ gas in gas produced from the electric power industry is over than 90 vol%. Therefore, we made the simulated gas containing $N_2$, $O_2$, $CF_4$, $SF_6$ which the concentration of $SF_6$ gas is minimum 90 vol%. From the results of membrane separation process of $SF_6$ gas from $N_2$, $O_2$, $CF_4$ $SF_6$ mixture gases, PSF membrane shown the highest recovery efficiency 92.7%, in $25^{\circ}C$ and 150 cc/min of retentate flow rate. On the other hand, PC membrane shown the highest recovery efficiency 74.8%, in $45^{\circ}C$ and 150 cc/min of retentate flow rate. Also, the highest rejection rate of $N_2$, $O_2$, $CF_4$ is 80, 74 and 58.9% seperately in the same operation condition of highest recovery efficiency. From the results, we supposed the membrane separation process as the effective $SF_6$ separation and recycle process from the mixture gas containing $N_2$, $O_2$, $CF_4$, $SF_6$.

Free Radical Scavenging Effect and Extraction Condition of Ethanol Extracts and Fractions of Wild Grape Seed (Vitis coignetiea) (머루종자의 적정 추출조건 및 추출 분획물의 Free Radical 소거능 효과)

  • Kim, Nan-Young;Kim, Young-Kuk;Bae, Ki-Ja;Choi, Jae-Ho;Moon, Jea-Hak;Park, Geun-Hyung;Oh, Deog-Hwan
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.34 no.6
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    • pp.755-758
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    • 2005
  • Wild grape is a traditional medicine plant in north-eastern part of Asia and has been known to have healing properties for various illnesses. This study was to determine the optimum extraction condition and antioxidant activity of ethanol extracts of wild grape (V. coignetiae) seed. Also, organic solvent fractions of hexane, chloroform, ethyl acetate and butanol were obtained from the ethanol extract of wild grape seed at different temperatures. Total ethanol extraction yield of wild grape seed ranged from $4\%\;to\;12\%$ depending on the ethanol concentration, extraction temperature and time condition. The highest extraction yield of $11.9\%$ was obtained at $90\%$ ethanol condition for 12 hour at $70^{\circ}C$. However, the strongest free radical scavenging effect $(RC_{50})$ with $20.93\mu g/mL$ was observed in $70\%$ ethanol extract of wild grape seed extracted for 6 hour at $70^{\circ}C,\;while\;RC_{50}\;with\;40.42$\mu g/mL$ was observed in $90\%$ ethanol extract for 12 hour at $70^{\circ}C$. Antioxidant activity of ethanol extracts of wild grape seed increased as total phenol contents increased. Among each fraction obtained from organic solvents, ethyl acetate fraction was found to have the strongest $RC_{50}\;(8.6\mu g/mL)$ and 636.77 mg GAE/g phenol contents .

Treatment of Malodorous Waste Air by a Biofilter Process Equipped with a Humidifier Composed of Fluidized Aerobic and Anoxic Reactor (폐가스 가습조(유동상호기 및 무산소조)를 포함한 바이오필터공정을 이용한 악취폐가스의 처리)

  • Lim, Kwang-Hee
    • Korean Chemical Engineering Research
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    • v.56 no.1
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    • pp.85-95
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    • 2018
  • In this research, a biofilter system equipped with a biofilter process and a humidifier composed of a fluidized aerobic and an anoxic reactor, was constructed to treat odorous waste air containing hydrogen sulfide, ammonia and VOC, frequently generated from pig and poultry housing facilities, compost manufacturing factories and publicly owned facilities. Its optimum operating condition was revealed and discussed. In the experiment of complex feed, the ammonia of fed-waste air was removed by ca. 75% and more than 20% at the stage of the humidifier and the biofilter, respectively. The toluene of the fed-waste air was removed by ca. 20% and more than 70% at the stage of the humidifier and the biofilter, respectively. Therefore the water-soluble ammonia and the water-insoluble toluene were treated mainly at the stage of the humidifier and the biofilter, respectively. In addition, hydrogen sulfide was almost absorbed at the stage of the humidifier so that it was not detected at the biofilter process. In the experiment of ammonia-containing feed, the ammonia of fed-waste air was removed by ca. 65% and 35% at the stage of the humidifier and the biofilter, respectively. Its removal efficiency of ammonia at the stage of the humidifier was 10% less than that in the experiment of complex feed, due to no supply of such carbon source as toluene required in the process of denitrification. In the experiments of complex feed, ammonia-containing feed with and without (instead, glucose) the addition of yeast extract, the absorption rates of ammonia-nitrogen were ca. 0.28 mg/min, 0.23 mg/min and 0.27 mg/min, respectively. The corresponding denitrification rates in the anoxic reactor were 0.42 mg/min, 0.55 mg/min and 0.27 mg/min, respectively. In addition, in the modeling of bubble column(the fluidized aerobic reactor of the humidifier) process, the value of specific surface area(a) of bubbles multiplied by enhanced mass transfer coefficient (E $K_y$) was evaluated to be 0.12/hr.

A Study on the Shaped-Beam Antenna with High Gain Characteristic (고이득 특성을 갖는 성형 빔 안테나에 대한 연구)

  • Eom, Soon-Young;Yun, Je-Hoon;Jeon, Soon-Ick;Kim, Chang-Joo
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.18 no.1 s.116
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    • pp.62-75
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    • 2007
  • This paper describes a shaped-beam antenna for increasing the antenna gain of a radiating element. The proposed antenna structure is composed of an exciting element and a multi-layered disk array structure(MDAS). The stack micro-strip patch elements were used as the exciter for effectively radiating the electromagnetic power to the MDAS over the broadband, and finite metallic disk array elements - which give the role of a director for shaping the antenna beam with the high gain - were finitely and periodically layered onto it. The efficient power coupling between the exciter and the MDAS should be carried out in such a way that the proposed antenna has a high gain characteristic. The design parameters of the exciter and the MDAS should be optimized together to meet the required specifications to meet the required specifications. In this study, a shaped-beam antenna with high gain was optimally designed under the operating conditions with a linear polarization and the frequency band of $9.6{\sim}10.4\;GHz$. Two methods constructed using thin dielectric film and dielectric foam materials respectively were also proposed in order to implement the MBAS of the antenna. In particular, through the computer simulation process, the electrical performance variations of the antenna with the MDAS realized by the thin dielectric film materials were shown according to the number of disk array elements in the stack layer. Two kinds of antenna breadboard with the MDAS realized with the thin dielectric film and dielectric foam materials were fabricated, but experimentation was conducted only on the antenna breadboard(Type 1) with the MDAS realized with the thin dielectric film materials according to the number of disk array elements in the stack layer in order to compare it with the electrical performance variations obtained during the simulation. The measured antenna gain performance was found to be in good agreement with the simulated one, and showed the periodicity of the antenna gain variations according to the stack layer number of the disk array elements. The electrical performance of the Type 1 antenna was measured at the center frequency of 10 GHz. As the disk away elements became the ten stacks, a maximum antenna gain of 15.65 dBi was obtained, and the measured return loss was not less than 11.4 dB within the operating band. Therefore, a 5 dB gain improvement of the Type 1 antenna can be obtained by the MDAS that is excited by the stack microstrip patch elements. As the disk array elements became the twelve stacks, the antenna gain of the Type 1 was measured to be 1.35 dB more than the antenna gain of the Type 2 by the outer dielectric ring effect, and the 3 dB beam widths measured from the two antenna breadboards were about $28^{\circ}$ and $36^{\circ}$ respectively.

Anti-Stress Effect of Punica granatum L. Extract against Sleep Deprivation-Induced Impairment (석류 열수 추출물의 수면박탈을 유도한 Rat 모델에서의 항스트레스 효과)

  • Na, Ju-Ryun;Kim, Sunoh;Jo, Ara;Bae, Donghyuck;Oh, Kyo-Nyeo;Kim, Yong Jae;Lee, Yoo-Hyun;Jun, Woojin
    • Journal of the Korean Society of Food Science and Nutrition
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    • v.45 no.11
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    • pp.1533-1543
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    • 2016
  • The anti-stress effects of Punica granatum L. (family Lythraceae, PG) on $H_2O_2$/corticosterone (CORT)-induced stress in cells and sleep-deprived rats were investigated. The PG extract showed neuroprotective effects in SH-SY5Y cells against $H_2O_2$/CORT-induced stress. Sleep deprivation led to behavioral, hormonal, and biochemical alterations in the animal model. The effects of P. granatum on physiological, behavioral, and biochemical parameters aggravated by sleep deprivation were investigated. Sleep deprivation impaired physiological (survival, body weight, and drowsiness scores) and behavioral (rotarod, passive avoidance, hot hyperalgesia, and Y maze) parameters as well as biochemical factors (cortisol, serotonin, dopamine, testosterone, and growth factor I contents in serum). These parameters were significantly recovered by PG extract in a concentration-dependent manner. The PG extract also enhanced catalase, superoxide dismutase, and non-enzymatic antioxidative activities such as glutathione compared to sleep-deprived rats. On the basis of these results, our findings suggest that Punica granatum prevents impairment of body functions induced by sleep deprivation and related oxidative damage.

IS AN OXYGEN INHIBITION LAYER ESSENTIAL FOR THE INTERFACIAL BONDING BETWEEN RESIN COMPOSITE LAYERS? (Layering시 복합레진 층간의 계면 결합에서 oxygen inhibition layer가 필수적인가?)

  • Kim, Sun-Young;Cho, Byeong-Hoon;Baek, Seung-Ho;Lee, In-Bog
    • Restorative Dentistry and Endodontics
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    • v.33 no.4
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    • pp.405-412
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    • 2008
  • This study was aimed to investigate whether an oxygen inhibition layer (OIL) is essential for the interfacial bonding between resin composite layers or not. A composite (Z-250, 3M ESPE) was filled in two layers using two aluminum plate molds with a hole of 3.7 mm diameter. The surface of first layer of cured composite was prepared by one of five methods as followings, thereafter second layer of composite was filled and cured: Group 1 - OIL is allowed to remain on the surface of cured composite; Group 2 - OIL was removed by rubbing with acetone-soaked cotton; Group 3 - formation of the OIL was inhibited using a Mylar strip; Group 4 - OIL was covered with glycerin and light-cured; Group 5 (control) - composite was bulk-filled in a layer. The interfacial shear bond strength between two layers was tested and the fracture modes were observed. To investigate the propagation of polymerization reaction from active area having a photo-initiator to inactive area without the initiator, a flowable composite (Aelite Flow) or an adhesive resin (Adhesive of ScotchBond Multipurpose) was placed over an experimental composite (Exp_Com) which does not include a photoinitiator and light-cured. After sectioning the specimen, the cured thickness of the Exp_Com was measured. The bond strength of group 2, 3 and 4 did not show statistically significant difference with group 1. Groups 3 and 4 were not statistically significant different with control group 5. The cured thicknesses of Exp_Com under the flowable resin and adhesive resin were 20.95 (0.90) urn and 42.13 (2.09), respectively.