• 제목/요약/키워드: Exponential equation

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Performance evaluation and reliability analysis of a complex system with three possibilities in repair with the application of copula

  • Nailwal, B.;Singh, S.B.
    • International Journal of Reliability and Applications
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    • 제12권1호
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    • pp.15-39
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    • 2011
  • This paper deals with the reliability analysis of a complex system with three possibilities at the time of repair. The considered system consists of two subsystems A and Bin series configuration (1-out-of-2: F). Subsystem A has n units which are connected in series whereas subsystem B consists of n units in parallel configuration. The configuration of subsystem A is of 1-out-of-n: F whereas subsystem B is of k-out-of-n: D and k+1-out-of-n: F nature. System has three states: Good, degraded and failed. Supplementary variable technique has been used for mathematical formulation of the model. Laplace transform is being utilized to solve the mathematical equation. Reliability, Availability, M.T.T.F., Busy Period and Cost effectiveness of the system have been computed. The repairs from state $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ have two types namely exponential and general. Joint probability distribution of repair rate from $S_7$ to $S_0$, $S_8$ to $S_0$, $S_9$ to $S_0$ and $S_{11}$ to $S_0$ is computed by Gumbel-Hougaard family of copula. Some particular cases of the system have also been derived to see the practical importance of the model.

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Reactor core analysis through the SP3-ACMFD approach Part II: Transient solution

  • Mirzaee, Morteza Khosravi;Zolfaghari, A.;Minuchehr, A.
    • Nuclear Engineering and Technology
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    • 제52권2호
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    • pp.230-237
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    • 2020
  • In this part, an implicit time dependent solution is presented for the Boltzmann transport equation discretized by the analytic coarse mesh finite difference method (ACMFD) over the spatial domain as well as the simplified P3 (SP3) for the angular variable. In the first part of this work we proposed a SP3-ACMFD approach to solve the static eigenvalue equations which provide the initial conditions for temp dependent equations. Having solved the 3D multi-group SP3-ACMFD static equations, an implicit approach is resorted to ensure stability of time steps. An exponential behavior is assumed in transverse integrated equations to establish a relationship between flux moments and currents. Also, analytic integration is benefited for the time-dependent solution of precursor concentration equations. Finally, a multi-channel one-phase thermal hydraulic model is coupled to the proposed methodology. Transient equations are then solved at each step using the GMRES technique. To show the sufficiency of proposed transient SP3-ACMFD approximation for a full core analysis, a comparison is made using transport peers as the reference. To further demonstrate superiority, results are compared with a 3D multi-group transient diffusion solver developed as a byproduct of this work. Outcomes confirm that the idea can be considered as an economic interim approach which is superior to the diffusion approximation, and comparable with transport in results.

콩군락의 단파폭사 흡수특성 II. 광합성유효폭사흡수와 건물생산 (Characteristics of Shortwave Radiation Absorption by Soybean Canopy II. Absorption of Photosynthetically Active Radiation and Its Relation to Dry Matter Production)

  • 이양수;윤성호;임정남;박연규
    • 한국작물학회지
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    • 제35권2호
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    • pp.156-164
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    • 1990
  • A field experiment was conducted to study both the distribution characteristics of photosynthetically active radiation (PAR) in the soybean canopy and their relationships with dry matter production. The soybean cultivars 'Hwanggeumkong' and 'Paldalkong' were sown with the spaces of 60$\times$15cm and 30$\times$15cm at Suwon on May 20 and on June 20 in 1989. The ratio of PAR to the total shortwave radiation was estimated by the empirical equation derived from sunshine hours and direct incoming radiation. The functional relationships between the PAR interception and the leaf area index were expressed as a function of Beer's law. The extinction coefficients(k) in the functions ranged from 0.77 to 0.92. The values of k were greater at higher planting density, but they were affected neither by planting dates nor by varieties. The reflection ratio of PAR($\alpha$) was determined by the exponential function as below; $\alpha$=$\alpha$p-($\alpha$p-$\alpha$o) exp(-kㆍLAI) where $\alpha$p was the reflectance at the maximum LAI and $\alpha$o was that of the bare soil. The ap ranged from 0.025 to 0.035 and $\alpha$o ranged from 0.11 to 0.12, respectively. The reflected PAR ranged from 0.049 to 0.064 and the transmitted PAR ranged from 0.168 to 0.340 until maximum dry weights were observed. The slope from the linear regression of dry matter on absorbed PAR, conversion efficiency, ranged from 1.30 to 2.3g MJ$^{-1}$ during the growing season until maximum dry weight was reached. The total dry matter yield above ground (TDM) increased with the increases in the conversion efficiency. TDM was higher in Hwanggeumkong than Paldalkong and higher in the space of 30$\times$15cm than 60$\times$15cm, Paldalkong showed higher harvest index than Hwanggeumkong. than Hwanggeumkong.

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가리비, Patinopecten yessoensis 소화맹낭의 계절변화 (Seasonal Variations of Digestive Diverticula in the Scallop, Patinopecten yessoensis)

  • 장영진
    • 한국양식학회지
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    • 제4권1호
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    • pp.19-30
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    • 1991
  • 가리비, Patinopecten yesso두냔의 소화맹낭 및 그 상피세포의 지방에 대한 계절변동과 생식소 발달과의 관계를 알아보기 위하여, 일본 북해도의 오호츠크해에 면한 망주만산 방류양식 개체를 1982년 9월부터 1984년 5월까지 월별로 채집하여 조사한 결과는 다음과 같다. 1. 소화맹낭의 지수는 $5{\~}6$월에 가장 높았으며, 12월 및 유빙에 최저치를 나타냈다. 2. 소화맹낭의 조직단면적 1 $mm^{2}$당 세관수는 $9{\~}10$월에 최소치를 나타냈으나, 3월에 최다치를 보였다. 3. 생식소 지수(X)와 소화맹낭의 지방세관 비율(Y)은 $Y=145.6X^{-0793}$의 역지수함수적 관계를 나타냈다. 4. 소화맹낭의 지방은 생식소의 발달과 함께 생식소로 전이되는 계절변동을 보였다.

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뱀장어의 초기사육에 관한 연구 (REARING OF THE EARLY STAGE OF THE EEL ANGUILLA JAPONICA)

  • 김인배;조재윤
    • 한국수산과학회지
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    • 제7권4호
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    • pp.179-186
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    • 1974
  • 1973년 4월부터 1974년 6월 말까지 뱀장어의 효과적인 초기사육을 위하여 일연의 실험을 한 결과는 다음과 같다. 1. 뱀장어의 초기사육의 최적성장수온은 $20\~34^{\circ}C$의 범위내에서 실험한 결과 $30^{\circ}C$로 나타났다. 2. $20\~30^{\circ}C$ 사이에서 10일간의 성장배수는 R=0.0056296$T^{1.80740}$이라는 곡선식으로 나타났다. 3. 오랫동안 축양하여 두었던 실뱀장어도 채포후 바로 사육하는 것에 비해 성장이 나쁘지 않았다. 4. 사육중 크지 않고 성장이 나빴던 것도 이번 시험사육결과 정상적인 성장을 하였다. 5. ammonia는 5ppm 이하에서는 섭이에 영향을 주지 않으나 6ppm에서는 섭이량이 현저히 줄었다. 6. 뱀장어의 고밀도 사육시 배설물의 제거는 좋은 수질을 유지하는 데 매우 중요하다.

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수정된 제1종 부분 응답 전송 시스템 모델을 이용한 여현 펄스 푸리에 변환의 새로운 순환 공식 (A New Recursive Formula to Derive the Fourier Transforms of Cosine-Pulses Using Modified Class-I PRS Model)

  • 오용선;조형래;강민구;김한종;강창언
    • 한국통신학회논문지
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    • 제17권12호
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    • pp.1343-1352
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    • 1992
  • 본 논문에서는 일정한 구간 내에 한정되고 최대치가 균일하도록 설정된 임의 차수 여현펄스의 푸리에 변환을 유도하기 위한 새롭고 용이한 방법을 제안하였다. 제안된 방법은 수치적 해법에 원활하게 적용될 수 있도록 함수의 각 차수에 따라 순환적으로 유도되는 공식에 초점을 두고 있다. 반면에, 유도된 관계식은 용이하게 계산될 수 있는 두함수의 합에 의하여 나타나므로 해석적 해법의 관점에서도 기존의 방법보다 간결한 과정을 제공한다. 특히, 저자 등에 의하여 발견된 계수 분리법에 의하여 공식은 완전 순환적 알고리듬으로 표현되며, 그 결과로 나타나는 자동방정식은 초기 'Sinc'함수가 차수에 따라 지연되어 상수가 곱해진 형태의 합으로 주어진다. 이 때 곱해지는 각 상수는 이항계수로부터 용이하게 결정되며, 'Sinc'함수의 지연요소도 이항식 $(a+b)^n$의 전개식에서 해당되는 항의 지수차에 의하여 쉽게 얻어진다.

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Mechanism of shear strength deterioration of loess during freeze-thaw cycling

  • Xu, Jian;Wang, Zhangquan;Ren, Jianwei;Yuan, Jun
    • Geomechanics and Engineering
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    • 제14권4호
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    • pp.307-314
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    • 2018
  • Strength of loess that experienced cyclic freeze and thaw is of great significance for evaluating stability of slopes and foundations in loess regions. This paper takes the frequently encountered loess in the Northwestern China as the study object and carried out three kinds of laboratory tests including freeze-thaw test, direct shear test and SEM test to investigate the strength behaviors of loess after cyclic freeze and thaw, and the correlation with meso-level changes in soil structure. Results show that for loess specimens at four dry densities, the cohesion decreases with freeze-thaw cycles until a residual value is reached and thus an exponential equation is proposed. Besides, little change in the angle of internal friction was observed as freeze-thaw proceeds. This may depend on the varying of soil structure, based on which a clue can be found from the surface morphology and mesoscopic scanning of loess specimens. Clearly we observed significant changes in surface morphology of loess and it tends to aggravate at higher water contents or more cycles of freeze and thaw. Moreover, freeze-thaw cycling leads to obvious changes in the meso-structure of loess including lowering the particle aggregates and increasing both the proportion of fine particles and porosity area ratio. A damage variable dependent on the ratio of porosity area is introduced based on the continuum damage mechanics and its correlation with cohesion is discussed.

Gametogenic Cycle and the Size at 50% of Group Sexual Maturity in Male Chlamys (Azumapecten) farreri nipponensis (Kuroda, 1932) (Bivalvia: Pectinidae) in Western Korea

  • Park, Ki Yeol;Chung, Ee-Yung;Lee, Ki-Young;Park, Kwan Ha
    • 한국패류학회지
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    • 제29권1호
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    • pp.65-76
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    • 2013
  • We investigated the gametogenic cycle and spawning seasons of the male Chlamys (Azumapecten) farreri nipponensis by qualitative and quantitative analyses, and also the size at 50% of group sexual maturity was calculated by the data of first sexual maturity. In this study, the male gametogenic cycle of this species by qualitative analysis was divided into five successive stages: early active stage (January to March), late active stage (March to April), ripe stage (April to August), partially spawned stage (July to September), and spent/inactive stage (August to January). The male gametogenic cycle showed similar patterns with monthly changes in the gonadosomatic index and condition index. Particularly, spawning in male scallop occurred once a year from July to September, unlike the spawning period of this species (from June to August) reported by the previous researchers. In quantitative statistical analysis using an image analyzer system, the patterns of monthly changes in the percent (%) of the areas occupied by spermatogenic stages to the testis areas in males showed a maximum in June, and then sharply dropped from July to September, 2006. From these data, it is apparent that the spawning season of C. (A.) farreri nipponensis occurred once per year from July to early September, indicating a unimodal gametogenic cycle during the year. Shell heights at 50% of group sexual maturity (RM50) fitted to an exponential equation were estimated to be 49.90 mm in males (considered to be one year old), and it was 100% for male scallops over 61.0 mm (considered to be two years old).

A Study on Production of Nitrogen Oxides in Plasma Reactors

  • Lim, Gye-Gyu
    • Journal of Korean Society for Atmospheric Environment
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    • 제17권E3호
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    • pp.91-99
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    • 2001
  • Plasma reactor was used to generate a high potential difference between two surfaces of concentric pyrex tubes by electrical current. The annular gap of the reactor was calculated by trial and error from the breakdown voltage equation and set at 0.45 cm. The overall objective of this research was to know the effects of the frequency, humidity, and residence time on the formation of nitrogen oxides in a plasma reactor. The primary voltage varied from 50 to 90 volts and the frequency was varied in increments of 10 Hz from 60 to 650 Hz at the primary voltage of 90. The increase in the secondary voltage was not linear but exponential at high frequencies. At a maximum concentration of about 745 ppm, the frequency and secondary voltage was 600 Hz and 4,200 volts, respectively. All tests for the effects of humidity on NO$_{x}$ production were performed at the optimal setting of 90 colts and 600 Hz frequency. Since the NO$_{x}$ production was not an one dimensional phenomenon, competing reactions were assumed to occur in the discharge chamber. The sharp peak concentration of 1,810 ppm was observed at 38% of relative humidity, The enhanced production was choked off, and the production rate rapidly dropped to 3 ppm at above 40% of relative humidity. It is assumed that the corona attacks the most vulnerable molecules in the reaction chamber before attacking other more lightly bonded molecules, possibly at humidities above 38% and the optimized 90 volt setting. Thus, there was not enough energy left after attacking all water molecules to decompose an appreciable amount of $N_2$. If nitrogen breakdown does not occur, then oxides of nitrogen are not likely to be produced.ced.

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Chill Unit 축적과 휴면해제시기 공간변이 추정 프로그램 : CUMAP (CUMAP : A Chill Unit Calculator for Spatial Estimation of Dormancy Release Date in Complex Terrain)

  • 김광수;정유란;윤진일
    • 한국농림기상학회지
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    • 제6권3호
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    • pp.177-182
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    • 2004
  • 기온의 공간변이가 심한 넓은 지역에서 Chill Unit 축적량과 휴면해제일의 공간분포를 얻기 위해서 Utah Chill Unit 모형을 지리정보시스템과 결합하여 Chill Unit 공간적산기(CUMAP)을 개발하였다. CUMAP은 Grid 형태의 일 최고, 최저기온을 입력받아 시간내삽법에 의해 매시기온을 추정하고, Utah 모형에 의해 매시 Chill Unit을 계산한다. 하루 단위로 Chill Unit이 누적되면 Grid파일로 저장되며, 사용자가 정하는 저온요구량(임계값)에 도달하는 날짜를 역시 Grid파일로 생성한다. 전라북도 김제시 백구면 일대 포도재배지역에 대해 CUMAP을 적용하여 10m 해상도의 Chill Unit 일별 적산값과 휴면해제일 추정분포도를 작성하였다.