• Title/Summary/Keyword: Prime number

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The fast DCT algorithm based on the new prime factor and common factor decomposition

  • Choi, Byeong-Ho;Kim, Jong-Uk;Suh, Ki-Bum;Chong, Jong-Wha;Bang, Gyo-Yoon
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10b
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    • pp.245-250
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    • 1992
  • In this paper, we present a nev algorithm for the fast computation of the discrete cosine transform(DCT). This algorithm consists of the three dimensional prime factor-decomposed algorithm(PFA) and three dimensional common factor-decomposed algorithm(CFA). We can compute N-point DCT for the number N decomposable Into three relative prime numbers using PFA and into three common numbers using CFA. We also show input and output index mapping for the three decomposition. it results in requiring fever multiplicaions than the previous algorithms. Particularly, for the large number N, it is more powerful in reducing the number of multiplication.

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A Numerical Analysis on Prediction of Cut-diameter according to Vane Outflow Angle in the Axial-flow Cyclone (축상유입식 사이클론의 베인 유출각도에 따른 절단입경 예측에 관한 수치해석)

  • Yi, Chung-Seob;Lee, Chi-Woo
    • Journal of the Korean Society of Manufacturing Process Engineers
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    • v.11 no.4
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    • pp.111-117
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    • 2012
  • Dust collecting performance of axial-vane type cyclone for oil mist was analyzed in this study. For predicting cut diameter size of cyclone, the number and angle of vane ($tan{{\beta}_2}^{\prime}$) was simulated by CFD. As the result, $tan{{\beta}_2}^{\prime}$ was decreased as the number of vane was increased and the angle of inclination(${{\beta}_2}^{\prime}$) decreased, and it cause strong swirl flow. Therefore, it could be confirmed that as the number of vane was increased and the angle of inclination was decreased, cut diameter size was decreased. Also, by verifying the results of CFD through experiment, the cut diameter size could be $2{\mu}m$ at $4m^3/min$ of flow rate.

A Study on Dust Collection Efficiency of Axial-vane Type Cyclone for Oil Mist (오일미스트용 축상 유입식 사이클론의 집진효율에 관한 연구)

  • Yi, Chung-Seob;Shin, Hae-Joong;Lee, Chi-Woo
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.21 no.3
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    • pp.415-420
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    • 2012
  • Dust collecting performance of axial-vane type cyclone for oil mist was analyzed in this study. For predicting cut diameter size of cyclone, the number and angle of vane (${\beta}_2{^{\prime}}$) was calculated by CFD. As the result, ${\beta}_2{^{\prime}}$ was decreased as the number of vane was increased and the angle of inclination (${\beta}_2{^{\prime}}$) decreased, and it cause strong swirl flow. Therefore, it could be confirmed that as the number of vane was increased and the angle of inclination was decreased, cut diameter size was decreased. Also, by verifying the results of CFD through experiment, the cut diameter size could be 2 ${\mu}m$ at 4 $m^3/min$ of flow rate.

The effect of dynamic operating conditions on nano-particle emissions from a light-duty diesel engine applicable to prime and auxiliary machines on marine vessels

  • Lee, Hyungmin;Jeong, Yeonhwan
    • International Journal of Naval Architecture and Ocean Engineering
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    • v.4 no.4
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    • pp.403-411
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    • 2012
  • This study presents the nano-sized particle emission characteristics from a small turbocharged common rail diesel engine applicable to prime and auxiliary machines on marine vessels. The experiments were conducted under dynamic engine operating conditions, such as steady-state, cold start, and transient conditions. The particle number and size distributions were analyzed with a high resolution PM analyzer. The diesel oxidation catalyst (DOC) had an insignificant effect on the reduction in particle number, but particle number emissions were drastically reduced by 3 to 4 orders of magnitude downstream of the diesel particulate filter (DPF) at various steady conditions. Under high speed and load conditions, the particle filtering efficiency was decreased by the partial combustion of trapped particles inside the DPF because of the high exhaust temperature caused by the increased particle number concentration. Retarded fuel injection timing and higher EGR rates led to increased particle number emissions. As the temperature inside the DPF increased from $25^{\circ}C$ to $300^{\circ}C$, the peak particle number level was reduced by 70% compared to cold start conditions. High levels of nucleation mode particle generation were found in the deceleration phases during the transient tests.

A Parallel Processing Model for Selecting Prime Implicants of a Logic Function for a Near Minimal Sum of Products Form (논리 함수를 최소의 Sum of Products와 가까운 형태로 나타내기 위한 프라임 임프리컨트 선택 별렬 처리 모델)

  • Kim, Won-Jun;Hwang, Hee-Yeung
    • The Transactions of the Korean Institute of Electrical Engineers
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    • v.39 no.12
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    • pp.1288-1295
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    • 1990
  • In this paper, we propose a parallel processing model for the efficient selection of Prime Implicants of Logic Functions. This model consists of simple parallel processing nodes, connections between them, Max Net (a part of Hamming Net) and quasi essential Prime Implicant selection standard in simplified cost form. Through these, this model selects essential Prime Implicants in a certain period of time regardless of the number of given Prime Implicants and minterms and also selects quasi essential Prime Implicants in short time.

Game-based Learning Content Development for Learning Principles of Finding Prime Numbers (소수를 찾는 원리 학습을 위한 게임 기반 학습 콘텐츠 개발)

  • Kim, Han-Tae;Hong, Myoung-Pyo;Choi, Yong-Suk
    • Proceedings of the Korean Information Science Society Conference
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    • 2011.06b
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    • pp.272-275
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    • 2011
  • 본 논문에서는 수학에서 사용하는 소수(Prime number)를 찾는 원리에 대한 학습을 위한 게임 기반 학습(Game based learning) 콘텐츠인 Prime Miner라는 게임을 제안한다. Prime Miner는 게임이 가지고 있는 장점과 소수의 원리를 결합하여 게임을 통해 학습자의 흥미를 이끌어 학습에 몰입할 수 있도록 도우며, 학습자가 게임 규칙을 통해 소수의 원리를 합리적으로 배울 수 있도록 유도한다. 본 논문에서는 Prime Miner의 게임 원리와 학습자가 Prime Miner를 통해 소수 학습을 하는 방법을 설명한다. 또한 퍼즐게임에서 종종 발생하는 더 이상 게임을 진행할 수 없는 상태인 교착상태(Deadlock)를 피하기 위한 숫자 타일의 배치에 관한 방법도 제시한다.

Design and Analysis of Efficient Parallel Hardware Prime Generators

  • Kim, Dong Kyue;Choi, Piljoo;Lee, Mun-Kyu;Park, Heejin
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.16 no.5
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    • pp.564-581
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    • 2016
  • We present an efficient hardware prime generator that generates a prime p by combining trial division and Fermat test in parallel. Since the execution time of this parallel combination is greatly influenced by the number k of the smallest odd primes used in the trial division, it is important to determine the optimal k to create the fastest parallel combination. We present probabilistic analysis to determine the optimal k and to estimate the expected running time for the parallel combination. Our analysis is conducted in two stages. First, we roughly narrow the range of optimal k by using the expected values for the random variables used in the analysis. Second, we precisely determine the optimal k by using the exact probability distribution of the random variables. Our experiments show that the optimal k and the expected running time determined by our analysis are precise and accurate. Furthermore, we generalize our analysis and propose a guideline for a designer of a hardware prime generator to determine the optimal k by simply calculating the ratio of M to D, where M and D are the measured running times of a modular multiplication and an integer division, respectively.

Effect of Thermo-Mechanical Treatment on the Damping Capacity of Alloy with Deformation Induced Martensite Transformation (가공유기 마르텐사이트 변태를 갖는 합금의 감쇠능에 미치는 가공열처리의 영향)

  • Han, Hyun-Sung;Kang, Chang-Yong
    • Korean Journal of Materials Research
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    • v.29 no.3
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    • pp.160-166
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    • 2019
  • This study investigates the effect of thermo-mechanical treatment on the damping capacity of the Fe-20Mn-12Cr-3Ni-3Si alloy with deformation induced martensite transformation. Dislocation, ${\alpha}^{\prime}$ and ${\varepsilon}-martensite$ are formed, and the grain size is refined by deformation and thermo-mechanical treatment. With an increasing number cycles in the thermo-mechanical treatment, the volume fraction of ${\varepsilon}-martensite$ increases and then decreases, whereas dislocation and ${\alpha}^{\prime}-martensite$ increases, and the grain size is refined. In thermo-mechanical treated specimens with five cycles, more than 10 % of the volume fraction of ${\varepsilon}-martensite$ and less than 3 % of the volume fraction of ${\alpha}^{\prime}-martensite$ are attained. Damping capacity decreases by thermo-mechanical treatment and with an increasing number of cycles of thermo-mechanical treatment, and this result shows an opposite tendency for general metal with deformation induced martensite transformation. The damping capacity of the thermo-mechanical treated damping alloy with deformation induced martensite transformation greatly affect the formation of dislocation, grain refining and ${\alpha}^{\prime}-martensite$ and then ${\varepsilon}-martensite$ formation by thermo-mechanical treatment.

A Step-by-Step Primality Test (단계적 소수 판별법)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.13 no.3
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    • pp.103-109
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    • 2013
  • Miller-Rabin method is the most prevalently used primality test. However, this method mistakenly reports a Carmichael number or semi-prime number as prime (strong lier) although they are composite numbers. To eradicate this problem, it selects k number of m, whose value satisfies the following : m=[2,n-1], (m,n)=1. The Miller-Rabin method determines that a given number is prime, given that after the computation of $n-1=2^sd$, $0{\leq}r{\leq}s-1$, the outcome satisfies $m^d{\equiv}1$(mod n) or $m^{2^rd}{\equiv}-1$(mod n). This paper proposes a step-by-step primality testing algorithm that restricts m=2, hence achieving 98.8% probability. The proposed method, as a first step, rejects composite numbers that do not satisfy the equation, $n=6k{\pm}1$, $n_1{\neq}5$. Next, it determines prime by computing $2^{2^{s-1}d}{\equiv}{\beta}_{s-1}$(mod n) and $2^d{\equiv}{\beta}_0$(mod n). In the third step, it tests ${\beta}_r{\equiv}-1$ in the range of $1{\leq}r{\leq}s-2$ for ${\beta}_0$ > 1. In the case of ${\beta}_0$ = 1, it retests m=3,5,7,11,13,17 sequentially. When applied to n=[101,1000], the proposed algorithm determined 96.55% of prime in the initial stage. The remaining 3% was performed for ${\beta}_0$ >1 and 0.55% for ${\beta}_0$ = 1.

Floristic study of Songnisan National Park in Korea (속리산 국립공원의 관속식물상)

  • Choi, Hyeok-Jae;Oh, Byoung-Un
    • Korean Journal of Plant Taxonomy
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    • v.39 no.4
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    • pp.277-291
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    • 2009
  • The flora in the region of Songnisan National Park ($N36^{\circ}28^{\prime}05^{{\prime}{\prime}}{\sim}36^{\circ}46^{\prime}38^{{\prime}{\prime}}$, $E\;127^{\circ}47^{\prime}06^{{\prime}{\prime}}{\sim}127^{\circ}57^{\prime}50^{{\prime}{\prime}}$) was surveyed from April 2000 to July 2006. Vascular plants in 26 collections included a total of 723 taxa: 115 families, 392 genera, 629 species, 4 subspecies, 72 varieties and 18 forms. Ninety-three of these taxa were first records for the region. In the flora of Songnisan National Park, 27 taxa were Korean endemic plants, 19 taxa were rare and endangered plants as designated by the Korea Forest Service. Forty-five of the taxa were with the levels III, IV, V in the floristic regional indicator plants which was designated by Korean Ministry of Environment, and 29 taxa were alien plants now naturalized in Korea. Owing to their unusual phytogeography and low number of populations, the taxa Crypsinus hastatus (Thunb.) Copel., Paeonia japonica (Makino) Miyabe & Takeda, Jeffersonia dubia (Maxim.) Benth. & Hook.f. ex Baker & S.Moore, Bupleurum euphorbioides Nakai, Phacellanthus tubiflorus Siebold & Zucc., Lilium cernuum Kom., Gastrodia elata Blume and Cephalanthera erecta var. subaphylla (Miyabe & Kud ) Ohwi were considered the most important. Based on these results, it is clear that appropriate plans to conserve the natural habitat of Songnisan National Park must be made immediately.