• Title/Summary/Keyword: polynomials

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State-Space Equation Model for Motion Analysis of Floating Structures Using System-Identification Methods (부유식 구조체 운동 해석을 위한 시스템 식별 방법을 이용한 상태공간방정식 모델)

  • Jun-Sik Seong;Wonsuk Park
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.37 no.2
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    • pp.85-93
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    • 2024
  • In this paper, we propose a method for establishing a state-space equation model for the motion analysis of floating structures subjected to wave loads, by applying system-identification techniques. Traditionally, the motion of floating structures has been analyzed in the time domain by integrating the Cummins equation over time, which utilizes a convolution integral term to account for the effects of the retardation function. State-space equation models have been studied as a way to efficiently solve floating-motion equations in the time domain. The proposed approach outlines a procedure to derive the target transfer function for the load-displacement input/output relationship in the frequency domain and subsequently determine the state-space equation that closely approximates it. To obtain the state-space equation, the method employs the N4SID system-identification method and an optimization approach that treats the coefficients of the numerator and denominator polynomials as design variables. To illustrate the effectiveness of the proposed method, we applied it to the analysis of a single-degree-of-freedom model and the motion of a six-degree-of-freedom barge. Our findings demonstrate that the presented state-space equation model aligns well with the existing analysis results in both the frequency and time domains. Notably, the method ensures computational accuracy in the time-domain analysis while significantly reducing the calculation time.

Experimental Design of S box and G function strong with attacks in SEED-type cipher (SEED 형식 암호에서 공격에 강한 S 박스와 G 함수의 실험적 설계)

  • 박창수;송홍복;조경연
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.8 no.1
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    • pp.123-136
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    • 2004
  • In this paper, complexity and regularity of polynomial multiplication over $GF({2^n})$ are defined by using Hamming weight of rows and columns of the matrix ever GF(2) which represents polynomial multiplication. It is shown experimentally that in order to construct the block cipher robust against differential cryptanalysis, polynomial multiplication of substitution layer and the permutation layer should have high complexity and high regularity. With result of the experiment, a way of constituting S box and G function is suggested in the block cipher whose structure is similar to SEED, which is KOREA standard of 128-bit block cipher. S box can be formed with a nonlinear function and an affine transform. Nonlinear function must be strong with differential attack and linear attack, and it consists of an inverse number over $GF({2^8})$ which has neither a fixed pout, whose input and output are the same except 0 and 1, nor an opposite fixed number, whose output is one`s complement of the input. Affine transform can be constituted so that the input/output correlation can be the lowest and there can be no fixed point or opposite fixed point. G function undergoes linear transform with 4 S-box outputs using the matrix of 4${\times}$4 over $GF({2^8})$. The components in the matrix of linear transformation have high complexity and high regularity. Furthermore, G function can be constituted so that MDS(Maximum Distance Separable) code can be formed, SAC(Strict Avalanche Criterion) can be met, and there can be no weak input where a fixed point an opposite fixed point, and output can be two`s complement of input. The primitive polynomials of nonlinear function affine transform and linear transformation are different each other. The S box and G function suggested in this paper can be used as a constituent of the block cipher with high security, in that they are strong with differential attack and linear attack with no weak input and they are excellent at diffusion.

Growth at Heading Stage of Rice Affected by Temperature and Assessment of the Target Growth Applicable to North Korea for Breeding in South Korea (기온에 따른 벼 출수기 생육 반응 및 남한에서 북한 적응 품종 육성을 위한 출수기 목표 생장량 추정)

  • Yang, Woonho;Choi, Jong-Seo;Lee, Dae-Woo;Kang, Shingu;Lee, Seuk-ki;Chae, Mi-Jin
    • Korean Journal of Agricultural and Forest Meteorology
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    • v.23 no.2
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    • pp.108-121
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    • 2021
  • Field studies at Suwon, Cheorwon, and Jinbu were carried out to determine the relationship between mean temperature from transplanting to heading (MT) and growth at heading stage of rice. P lant height (P H) and dry weight (DW) at heading stage were significantly correlated with MT, showing second degree polynomials. The optimal temperatures for PH and DW were 23.2 ℃ and 22.8 ℃, respectively. Little differences in rice growth among soils collected from the experimental sites and the temperature-response in a phytotron study supported that MT was the main determinant of the growth shown in the field study. Though number of days to heading increased as MT decreased, cumulative temperatures (CT) affected by sites and MT for given varieties were fairly constant. When applying specific CT for each of the varieties to the temperature in North Korea, (1) five regions (Kaesong, Haeju, Sariwon, Nampo, Pyongyang) were suitable for early to mid-maturing varieties and (2) 14 regions (Yongyon, Singye, Anju, Kusong, Sinuiju, Changjon, Wonsan, Hamhung, Pyonggang, Yangdok, Huichon, Supung, Sinpo, Kanggye) were suitable only for early-maturing varieties. In (1) regions, the similar extent of growth with that in Suwon could be achieved when mid-maturing varieties grown in Suwon are cultivated. Among (2) regions, early-maturing varieties are expected to demonstrate the similar extent of growth with that in Cheorwon in 9 regions except Hamhung, Kanggye, Pyonggang, Yangdok, and Sinpo. For Hamhung and Kanggye, the target PH was assessed as 4cm higher than that shown in Cheorwon. P lant height of 8-14cm and DW of 2-4g per hill greater than those shown in Cheorwon were the target growth for P yonggang, Yangdok, and Sinpo to attain the similar amount of growth with that in Cheorwon. It is suggested that rice varieties for North Korea could be bred by adjusting the target growth at the breeding sites in South Korea.

Development of a split beam transducer for measuring fish size distribution (어체 크기의 자동 식별을 위한 split beam 음향 변환기의 재발)

  • 이대재;신형일
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.37 no.3
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    • pp.196-213
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    • 2001
  • A split beam ultrasonic transducer operating at a frequency of 70 kHz to use in the fish sizing echo sounder was developed and the acoustic radiation characteristics were experimentally analyzed. The amplitude shading method utilizing the properties of the Chebyshev polynomials was used to obtain side lobe levels below -20 dB and to optimize the relationship between main beam width and side lobe level of the transducer, and the amplitude shading coefficient to each of the elements was achieved by changing the amplitude contribution of elements with 4 weighting transformers embodied in the planar array transducer assembly. The planar array split beam transducer assembly was composed of 36 piezoelectric ceramics (NEPEC N-21, Tokin) of rod type of 10 mm in diameter and 18.7 mm in length of 70 kHz arranged in the rectangular configuration, and the 4 electrical inputs were supplied to the beamformer. A series of impedance measurements were conducted to check the uniformity of the individual quadrants, and also in the configurations of reception and transmission, resonant frequency, and the transmitting and receiving characteristics were measured in the water tank and analyzed, respectively. The results obtained are summarized as follows : 1. Average resonant and antiresonant frequencies of electrical impedance for four quadrants of the split beam transducer in water were 69.8 kHz and 83.0 kHz, respectively. Average electrical impedance for each individual transducer quadrant was 49.2$\Omega$ at resonant frequency and 704.7$\Omega$ at antiresonant frequency. 2. The resonance peak in the transmitting voltage response (TVR) for four quadrants of the split beam transducer was observed all at 70.0 kHz and the value of TVR was all about 165.5 dB re 1 $\mu$Pa/V at 1 m at 70.0 kHz with bandwidth of 10.0 kHz between -3 dB down points. The resonance peak in the receiving sensitivity (SRT) for four combined quadrants (quad LU+LL, quad RU+RL, quad LU+RU, quad LL+RL) of the split beam transducer was observed all at 75.0 kHz and the value of SRT was all about -177.7 dB re 1 V/$\mu$Pa at 75.0 kHz with bandwidth of 10.0 kHz between -3 dB down points. The sum beam transmitting voltage response and receiving senstivity was 175.0 dB re 1$\mu$Pa/V at 1 m at 75.0 kHz with bandwidth of 10.0 kHz, respectively. 3. The sum beam of split beam transducer was approximately circular with a half beam angle of $9.0^\circ$ at -3 dB points all in both axis of the horizontal plane and the vertical plane. The first measured side lobe levels for the sum beam of split beam transducer were -19.7 dB at $22^\circ$ and -19.4 dB at $-26^\circ$ in the horizontal plane, respectively and -20.1 dB at $22^\circ$ and -22.0 dB at $-26^\circ$ in the vertical plane, respectively. 4. The developed split beam transducer was tested to estimate the angular position of the target in the beam through split beam phase measurements, and the beam pattern loss for target strength corrections was measured and analyzed.

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