• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.161-169
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• 1999

Generalized nonnegative trigonometric polynomials are defined as the products of nonnegative trigonometric polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We improve and extend the large sieve involving pth powers of trigonometric polynomials so that it holds for generalized trigonometric polynomials.

• The KIPS Transactions:PartA
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• v.8A no.1
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• pp.36-41
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• 2001

In this paper, we first design an parallel quadratic sieve algorithm for factoring method. We then present parallel factoring algorithm for factoring a large odd integer by repeatedly using the parallel quadratic sieve algorithm based on the divide-and-conquer strategy on SIMD machines with DMM. We show that this algorithm is optimal in view of the product of time and processor numbers.

• Magazine of the Korean Society of Agricultural Engineers
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• v.12 no.1
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• pp.1854-1860
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• 1970

Results of this study on the influence of percent passing of No. 200 sieve on soil compaction are as follows; 1. The higher maximum dry density of soil is, the lower optimum moisture content is. Maximum dry density is highest value and optimum moisture content is the lowest value in twocases that percents of No. 200 sieve are 30% in soils of which percents retained on No. 10 sieve are 5% and 10% respectively. 2. Maximum dry density increases according as uniformity coefficient increase. Maximum dry density is the highest when uniformity coefficient is approximately 300 in soil of which maximum diameter is 4.76mm. 3. Maximum dry density has a tendency to become large according as value of Cu Caincrease. Correlation between maximum dry density and $Log_{10}$(CuCa) shows straight line. 4. Maximum dry density increases according as n increase and reaches the peak when n equal 0.35 in condition that the index of talbot formula n is less than 0.35 in soil of which maximum diameter is 4.76mm. 5. Maximum dry density has a tendency to increase according as value of Cg $(Cg=\frac{P_{50}^2}{P_{10}{\times}{P_{200}}$) decrease.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.37A no.12
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• pp.1031-1037
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• 2012

We study an algorithm that can efficiently find square roots and cube roots by modifying Tonelli-Shanks algorithm, which has an application in Number Field Sieve (NFS). The Number Field Sieve, the fastest known factoring algorithm, is a powerful tool for factoring very large integer. NFS first chooses two polynomials having common root modulo N, and it consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root. The last step of NFS needs the process of square root computation in Number Field, which can be computed via square root algorithm over finite field.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.36 no.10C
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• pp.614-620
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• 2011

RSA, the most commonly used public-key cryptosystem, is based on the difficulty of factoring very large integers. The fastest known factoring algorithm is the Number Field Sieve(NFS). NFS first chooses two polynomials having common root modulo N and consists of the following four major steps; 1. Polynomial Selection 2. Sieving 3. Matrix 4. Square Root, of which the most time consuming step is the Sieving step. However, in recent years, the importance of the Polynomial Selection step has been studied widely, because one can save a lot of time and memory in sieving and matrix step if one chooses optimal polynomial for NFS. One of the ideal ways of choosing sieving polynomial is to choose two polynomials with same degree. Montgomery proposed the method of selecting two (nonlinear) quadratic sieving polynomials. We proposed two cubic polynomials using 5-term geometric progression.

• Journal of IKEEE
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• v.23 no.2
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• pp.438-447
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• 2019

As the IoT-based hyper-connected society grows, public-key cryptosystem such as RSA is frequently used for encryption, authentication, and digital signature. Public-key cryptosystem use very large (safe) prime numbers to ensure security against malicious attacks. Even though the performance of the device has greatly improved, the generation of a large (safe)prime is time-consuming or memory-intensive. In this paper, we propose ET-MR and ET-MR-MR using Euler sieve so it runs faster while using less memory. We present a running time prediction model by probabilistic analysis and compare time and memory of our method with conventional methods. Experimental results show that the difference between the expected running time and the measured running time is less than 4%. In addition, the fastest running time of ET-MR is 36% faster than that of TD-MR, 8.5% faster than that of DT-MR and the fastest running time of ET-MR-MR is 65.3% faster than that of TD-MR-MR and similar to that of DT-MR-MR. When k=12,381, the memory usage of ET-MR is 2.7 times more than that of DT-MR but 98.5% less than that of TD-MR and when k=65,536, the memory usage of ET-MR-MR is 98.48% less than that of TD-MR-MR and 92.8% less than that of DT-MR-MR.

• Journal of Ocean Engineering and Technology
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• v.21 no.3 s.76
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• pp.26-32
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• 2007

A series of large-scale experiments were carried out in order to examine wave-induced liquefaction in a loosely packed sandbed, its afterward high densification and liquefaction by oscillatory pore pressure. The experiments were conducted in a Large Hydro-Geo Flume that can nearly solve the problems of scale effects of the sandbed, and the 50% sieve diameter of sand was 0.2 mm. The generation of residual pore pressure and its afterward high densification which had observed by Takahashi et al. (1999) in a wave flume experiment using fine sand with the size of 0.08 mm. As a result, the relative density of the sandbed after high densification was increased up to 79% and liquefaction by oscillatory pore pressure was not observed.

• Asian-Australasian Journal of Animal Sciences
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• v.8 no.3
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• pp.267-273
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• 1995

The differences in rumen particle pool size, passage rate and rumen degradability in sheep receiving three varieties of orchardgrass hay harvested at pre-heading (H1), early-bloom (H2) and late-bloom (H3) were investigated using four ruminal-cannulated wethers (68 kg) fed 1,300 g of the hay once a day. Representative samples of whole rumen contents were collected at different times after feeding and the quantities of rumen particle pools [large particle pool (LPP), retained on a $1,180{\mu}m$ sieve; small particle pool (SPP), retained on a 47 but passed a $1,180{\mu}m$ sieve; and soluble fraction (SOL), passed a $47{\mu}m$ sieve (SOL)] were determined by a wet-sieving technique. The fullowing results were obtained: 1) The dry weight of whole rumen contents were significantly lower (p < 0.05) for HI than for H2 or H3. The reduction rate of whole rumen contents was slightly but significantly greater for HI that, the other hay varieties. 2) The LPP disappearance rates were 26.2, 25.3 and 21.7 g DM/h for H1, H2 and H3, respectively, and no statistical differences were found among the hay varieties. Appreciable changes were not observed with SPP and SOL throughout measurements for all hay varieties; however the SPP was markedly greater (p <0.05) for H2 and ill than for HI, while SOL did not differ among hay varieties. 3) The SPP passage rate (g DM/h) and effective rumen degradability (%) for HI, H2 and ill were, respectively, 9.7, 56.6; 16.9, 42.3; and 18.0, 28.9. The ruminal tum-over rate for SPP appeared to be higher for HI than for the other hay varieties.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1659-1666
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• 2018

Let $P_r$ denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper, it is proved that for every sufficiently large even integer N, the equation $$N=x^2+p_1^2+p_2^3+p_3^3+p_4^4+p_5^4$$ is solvable with x being an almost-prime $P_4$ and the other variables primes. This result constitutes an improvement upon that of $L{\ddot{u}}$ [7].

• Wind and Structures
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• v.19 no.3
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• pp.271-294
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• 2014

The impact of artefacts in archived wind observations on the design wind speed obtained by extreme value analysis is demonstrated using case studies. A signpost protocol for detecting candidate artefacts is described and its performance assessed by comparing results against previously validated data. The protocol targets artefacts by exploiting the serial correlation between observations. Additional "sieve" algorithms are proposed to identify types of correctable artefact from their "signature" in the data. In extreme value analysis, artefacts displace valid observations only when they are larger, hence always increase the design wind speed. Care must be taken not identify large valid values as artefacts, since their removal will tend to underestimate the design wind speed.