• Title, Summary, Keyword: sieve theory

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ON A WARING-GOLDBACH PROBLEM INVOLVING SQUARES, CUBES AND BIQUADRATES

  • Liu, Yuhui
    • 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].

Diffusion-Selectivity Analysis of Permanent Gases through Carbon Molecular Sieve Membranes

  • Kang, Jong-Seok;Park, Ho-Bum;Lee, Young-Moo
    • Korean Membrane Journal
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    • v.5 no.1
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    • pp.43-53
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    • 2003
  • The selectivity of a gas in the carbon molecular sieve membrane (CMSM) can be expressed as the ratio of the product of the diffusivity and the solubility of two different gases. The diffusivity is also expressed as the product of the entropy and the total energy (kinetic and potential energy) in the nano-sized pore of the membrane. The present study calculates the entropic-energy and selectivity of penetrant gases such as H$_2$, O$_2$, N$_2$, and CO$_2$ from the gas-in-a box theory to physically analyze the diffusivity of penetrant gas in slit-shaped pore of CMSM focusing on the restriction of gas motion based on the size difference between penetrant gas pairs. The contribution of each energy term is converted to entropic term separately. By the conjugated calculation for each entropic-energy, the entropic effects on diffusivity-selectivity for gas pairs such as H$_2$/N$_2$, CO$_2$/N$_2$, and O$_2$/N$_2$ were analyzed within active pore of CMSM. In the activated diffusion domain, the calculated value of entropic-selectivity lies between 9.25 and 111.6 for H$_2$/N$_2$, between 3.36 and 6.0 for CO$_2$/N$_2$, and between 1.25 and 16.94 for O$_2$/N$_2$, respectively. The size decrement of active pore in CMSM had the direct effect on the reduction of translational entropic-energy and the contribution of vibrational entropic-energy for N$_2$, O$_2$, and H$_2$ was almost negligible. However, the vibrational entropic term of CO$_2$ might extravagantly affect on the entropic-selectivity.

A Study on Estimation of Loss Rate of Hydraulic Fills (준설토의 유실율 평가방법에 관한 연구)

  • 김홍택;노종구;김석열;강인규;김승욱;박재억
    • Proceedings of the Korean Geotechical Society Conference
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    • pp.185-192
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    • 2000
  • Recently, the hydraulic fill method is commonly used in many reclamation projects due to lack of fill materials. The method of hydraulic fill in reclamation is executed by transporting the mixture of water-soil particles into a reclaimed land through dredging pipes, then the dredged soil particles settle down in the water or flow over an out flow weir with the water. In the present study, practice each three method in order to suggest method of determining the loss rate of the dredged fills. The first sieve and hydrometer analysis were performed with the soil samples obtained before and after dredging and then apply theory of particle breakage, the second compare with the volume of dredged soil between at the dredging area and the target pond and the last compare with weight of dredged soil between before and after dredging at the dredging area and in the target pond for estimating the amount of soil particles residual at the reclaimed area and the loss of soil particles passed through the weir. In addition to compare with the loss ratio between as using Marsal's modified theory of particle breakage and measured weight and volume in the field.

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Application of Artificial Neural Network Theory for Evaluation of Unconfined Compression Strength of Deep Cement Mixing Treated Soil (심층혼합처리된 개량토의 일축압축강도 추정을 위한 인공신경망의 적용)

  • Kim, Young-Sang;Jeong, Hyun-Chel;Huh, Jung-Won;Jeong, Gyeong-Hwan
    • Proceedings of the Korean Geotechical Society Conference
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    • pp.1159-1164
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    • 2006
  • In this paper an artificial neural network model is developed to estimate the unconfined compression strength of Deep Cement Mixing(DCM) treated soil. A database which consists of a number of unconfined compression test result compiled from 9 clay sites is used to train and test of the artificial neural network model. Developed neural network model requires water content of soil, unit weight of soil, passing percent of #200 sieve, weight of cement, w-c ratio as input variables. It is found that the developed artificial neural network model can predict more precise and reliable unconfined compression strength than the conventional empirical models.

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DIOPHANTINE INEQUALITY WITH FOUR SQUARES AND ONE kTH POWER OF PRIMES

  • Zhu, Li
    • Journal of the Korean Mathematical Society
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    • v.56 no.4
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    • pp.985-1000
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    • 2019
  • Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.