• Title/Summary/Keyword: maximum of a polynomial

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Maximum Sugar Loss Lot First Production Algorithm for Cane Sugar Production Problem (사탕수수 설탕 생산 문제의 최대 당분 손실 로트 우선 생산 알고리즘)

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.19 no.12
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    • pp.171-175
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    • 2014
  • Gu$\acute{e}$ret et al. tries to obtain the solution using linear programming with $O(m^4)$ time complexity for cane sugar production problem a kind of bin packing problem that is classified as NP-complete problem. On the other hand, this paper suggests the maximum loss of lot first production greedy rule algorithm with O(mlogm) polynomial time complexity underlying assumption of the polynomial time rule to find the solution is exist. The proposed algorithm sorts the lots of sugar loss slope into descending order. Then, we select the lots for each slot production capacity only, and swap the exhausted life span of lots for lastly selected lots. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(mlogm) time complexity. Also, this algorithm better result than linear programming.

Sealing design optimization of nuclear pressure relief valves based on the polynomial chaos expansion surrogate model

  • Chaoyong Zong;Maolin Shi;Qingye Li;Tianhang Xue;Xueguan Song;Xiaofeng Li;Dianjing Chen
    • Nuclear Engineering and Technology
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    • v.55 no.4
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    • pp.1382-1399
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    • 2023
  • Pressure relief valve (PRV) is one of the important control valves used in nuclear power plants, and its sealing performance is crucial to ensure the safety and function of the entire pressure system. For the sealing performance improving purpose, an explicit function that accounts for all design parameters and can accurately describe the relationship between the multi-design parameters and the seal performance is essential, which is also the challenge of the valve seal design and/or optimization work. On this basis, a surrogate model-based design optimization is carried out in this paper. To obtain the basic data required by the surrogate model, both the Finite Element Model (FEM) and the Computational Fluid Dynamics (CFD) based numerical models were successively established, and thereby both the contact stresses of valve static sealing and dynamic impact (between valve disk and nozzle) could be predicted. With these basic data, the polynomial chaos expansion (PCE) surrogate model which can not only be used for inputs-outputs relationship construction, but also produce the sensitivity of different design parameters were developed. Based on the PCE surrogate model, a new design scheme was obtained after optimization, in which the valve sealing stress is increased by 24.42% while keeping the maximum impact stress lower than 90% of the material allowable stress. The result confirms the ability and feasibility of the method proposed in this paper, and should also be suitable for performance design optimizations of control valves with similar structures.

Time-varying modeling of the composite LN-GPD (시간에 따라 변화하는 로그-정규분포와 파레토 합성 분포의 모형 추정)

  • Park, Sojin;Baek, Changryong
    • The Korean Journal of Applied Statistics
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    • v.31 no.1
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    • pp.109-122
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    • 2018
  • The composite lognormal-generalized Pareto distribution (LN-GPD) is a mixture of right-truncated lognormal and GPD for a given threshold value. Scollnik (Scandinavian Actuarial Journal, 2007, 20-33, 2007) shows that the composite LN-GPD is adequate to describe body distribution and heavy-tailedness. This paper considers time-varying modeling of the LN-GPD based on local polynomial maximum likelihood estimation. Time-varying model provides significant detailed information of time dependent data, hence it can be applied to disciplines such as service engineering for staffing and resources management. Our work also extends to Beirlant and Goegebeur (Journal of Multivariate Analysis, 89, 97-118, 2004) in the sense of losing no data by including truncated lognormal distribution. Our proposed method is shown to perform adequately in simulation. Real data application to the service time of the Israel bank call center shows interesting findings on the staffing policy.

Evaluation of Probability Precipitation using Climatic Indices in Korea (기상인자를 이용한 우리나라의 확률강수량 평가)

  • Oh, Tae-Suk;Moon, Young-Il
    • Journal of Korea Water Resources Association
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    • v.42 no.9
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    • pp.681-690
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    • 2009
  • In this research, design precipitation was calculated by reflecting the climatic indices and its uncertainty assessment was evaluated. Climatic indices used the sea surface temperature and moisture index which observed globally. The correlation coefficients were calculated between the annual maximum precipitation and the climatic indices. and then climatic indices which have the larger correlation coefficient were selected. Therefore, the regression relationship was established by a locally weighted polynomial regression. Next, climatic indices were generated by montecarlo simulation using kernel function. Finally, the design rainfall was calculated by the locally weighted polynomial regression using generated climatic indices. At the result, the comparison of design rainfall between the reflection of the climatic indices and the frequency analysis did not indicate a significant difference. Also, this result can be used as basic data for calculation of probability precipitation to reflect climate change.

Analysis of Siloxane Adsorption Characteristics Using Response Surface Methodology

  • Park, Jin-Kyu;Lee, Gyeung-Mi;Lee, Chae-Young;Hur, Kwang-Beom;Lee, Nam-Hoon
    • Environmental Engineering Research
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    • v.17 no.2
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    • pp.117-122
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    • 2012
  • A central composite design and response surface methodology were applied to investigate the optimum conditions for maximum adsorption capacity in activated alumina as an adsorbent. The optimized conditions were determined for adsorption capacity using variables of flow rate and temperature. It was found that flow rate and temperature greatly influenced the adsorption capacity, as determined by analysis of variance analysis of these variables. Statistical checks indicated that second order polynomial equations were adequate for representing the experimental values. The optimum conditions for adsorption capacity were $0^{\circ}C$ and 2,718 mL/min, with the estimated maximum adsorption capacity of 17.82%. The experimental adsorption capacity was 17.75% under these optimum conditions, which was in agreement with the predicted value of 17.82%.

Dynamic Behavior of Plane Parabolic Arches with Initial Deflections (초기 처짐을 갖는 평면 포물선 아치의 동적 거동)

  • Cho , Jin-Goo;Park, Keun-Soo
    • Journal of The Korean Society of Agricultural Engineers
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    • v.46 no.2
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    • pp.67-75
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    • 2004
  • This study aims to investigate the dynamic behaviour of a parabolic arch with initial deflection by using the elasto-plastic finite element model where the von-Mises yield criteria have been adopted. The initial deflection of arch was assumed by the high order polynomial of ${\omega}_i$ = ${\omega}_o$${(1-{(2x/L)}^m)}^n$) and the sinusoidal profile of ${\omega}_i$ = ${\omega}_o$$\sin$(n$\pi$x/L). Several numerical examples were tested considering symmetric initial deflection modes when the maximum initial deflection of an arch is fixed as L/500, L/1000, L/2000 or L/5000. The effects of polynomials order on the dynamic behavior of arch were not conspicuous. The most unfavorite dynamic response occurs when the maximum initial deflection varies from L/1000 to L/4000 if the initial deflection mode is represented by high order polynomials.

Maximum Options-Equiped Class First-Production Algorithm for Car Sequencing Problem

  • Lee, Sang-Un
    • Journal of the Korea Society of Computer and Information
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    • v.20 no.9
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    • pp.105-111
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    • 2015
  • This paper suggests O(n) linear-time algorithm for car sequencing problem (CSP) that has been classified as NP-complete because of the polynomial-time algorithm to solve the solution has been unknown yet. This algorithm applies maximum options-equiped car type first production rule to decide the car sequencing of n meet the r:s constraint. This paper verifies thirteen experimental data with the six data are infeasible. For thirteen experimental data, the proposed algorithm can be get the solution for in all cases. And to conclude, This algorithm shows that the CSP is not NP-complete but the P-problem. Also, this algorithm proposes the solving method to the known infeasible cases. Therefore, the proposed algorithm will stand car industrial area in good stead when it comes to finding a car sequencing plan.

Effect of volume fraction on stability analysis of glass fibre reinforced composite plate

  • Mini, K.M.;Lakshmanan, Mahadevan;Mathew, Lubin;Kaimal, Girish
    • Steel and Composite Structures
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    • v.12 no.2
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    • pp.117-127
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    • 2012
  • This paper deals with an experimental investigation to study the effect of fibre content on the stability of composite plates with various aspect ratios. Epoxy based glass fibre reinforced composite plates with aspect ratio varying from 0.4 to 1 and with volume fractions of 0.36, 0.4, 0.46, 0.49 and 0.55 are used for the investigation. From the study it is observed that for plate with aspect ratio of 0.5 and 0.4 there is no buckling and the plate got crushed at the middle. As the volume fraction increases the buckling load also increases to a limit and then began to reduce with further increase in fibre content. The optimum range of fibre content for maximum stability is found between 0.49 and 0.55. Polynomial expressions are developed for the study of buckling behaviour of composite plates with different volume fractions in terms of load and aspect ratio.

Experimental study on the tensile strength of gravelly soil with different gravel content

  • Ji, Enyue;Chen, Shengshui;Zhu, Jungao;Fu, Zhongzhi
    • Geomechanics and Engineering
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    • v.17 no.3
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    • pp.271-278
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    • 2019
  • In recent years, the crack accidents of earth and rockfill dams occur frequently. It is urgent to study the tensile strength and tensile failure mechanism of the gravelly soil in the core for the anti-crack design of the actual high earth core rockfill dam. Based on the self-developed uniaxial tensile test device, a series of uniaxial tensile test was carried out on gravelly soil with different gravel content. The compaction test shows a good linear relationship between the optimum water content and gravel content, and the relation curve of optimum water content versus maximum dry density can be fitting by two times polynomial. For the gravelly soil under its optimum water content and maximum dry density, as the gravel content increased from 0% to 50%, the tensile strength of specimens decreased from 122.6 kPa to 49.8 kPa linearly. The peak tensile strain and ultimate tensile strain all decrease with the increase of the gravel content. From the analysis of fracture energy, it is proved that the tensile capacity of gravelly soil decreases slightly with the increasing gravel content. In the case that the sample under the maximum dry density and the water content higher than the optimum water content, the comprehensive tensile capacity of the sample is the strongest. The relevant test results can provide support for the anti-crack design of the high earth core rockfill dam.

Design of FIR Halfband Filters using Generalized Lagrange Polynomial (일반화된 라그랑지 다항식을 사용하는 FIR 하프밴드 필터 설계)

  • Bong, Jeongsik;Jeon, Joonhyeon
    • Journal of the Institute of Electronics and Information Engineers
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    • v.50 no.10
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    • pp.188-198
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    • 2013
  • Maximally flat (MAXFLAT) half-band filters usually have wider transition band than other filters. This is due to the fact that the maximum possible number of zeros at $z={\pm}1$ is imposed, which leaves no degree of freedom, and thus no independent parameters for direct control of the frequency response. This paper describes a novel method for the design of FIR halfband filters with an explicit control of the transition-band width. The proposed method is based on a generalized Lagrange halfband polynomial (g-LHBP) with coefficients parametizing a 0-th coefficient $h_0$, and allows the frequency response of this filter type to be controllable by adjusting $h_0$. Then, $h_0$ is modeled as a steepness parameter of the transition band and this is accomplished through theoretically analyzing a polynomial recurrence relation of the g-LHBP. This method also provides explicit formulas for direct computation of design parameters related to choosing a desired filter characteristic (by trade-off between the transition-band sharpness and passband & stopband flatness). The examples are shown to provide a complete and accurate solution for the design of such filters with relatively sharper transition-band steepness than MAXFLAT half-band filters.