• Geomechanics and Engineering
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• v.17 no.3
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• pp.237-245
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• 2019

In deep mixed rock strata, a double shield TBM (DS-TBM) is easy to be entrapped by a large force during tunneling. In order to reduce the probability of the entrapment, we need to investigate a favorable driving direction, either driving with or against dip, which mainly associates with the angle between the tunneling axis and strike, ${\theta}$, as well as the dip angle of rock strata, ${\alpha}$. We, therefore, establish a 3DEC model to show the changes of displacements and contact forces in mixed rock strata through LDP (longitudinal displacement profile) and LFP (longitudinal contact force profile) curves at four characteristic points on the surrounding rock. This is followed by a series of numerical models to investigate the favorable driving direction. The computational results indicate driving with dip is the favorable tunneling direction to reduce the probability of DS-TBM entrapment, irrespective of ${\theta}$ and ${\alpha}$, which is not in full agreement with the guidelines proposed in RMR. From the favorable driving direction (i.e., driving with dip), the smallest contact force is found when ${\theta}$ is equal to $90^{\circ}$. The present study is therefore beneficial for route selection and construction design in TBM tunneling.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.1
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• pp.39-46
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• 1993

In this paper, an offset paraboloidal reflector antenna satisfied efficiency of over 60% and sidelobe envelope line of 29-25$log\theta$ was designed and manufactured for Ku-band VSAT(Very Small Aperture Terminal) antenna. The radiation patterns of experimental antenna were computed by applying the series expansion method using the Zernike polynomials. The measured patterns are in good agreement with the computed results. The Gain, efficiency, and sidelobe envelop line fairly well satisfy the design specifications except first sidelobe level.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.159-166
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• 1999

For classical elliptic pseudodifferential operators $A({\lambda})$ of order $m$ > 0 with parameter ${\lambda}$ of weight ${\chi}$ > 0, it is known that $logDet_{\theta}A({\lambda})$ admits an asymptotic expansion as ${\theta}{\rightarrow}+{\infty}$. In this paper we show, with some assumptions, that the coefficients of ${\lambda}^-{\frac{n}{\chi}}$ can be expressed by the values of zeta functions at 0 for some elliptic ${\psi}$DO's on $M{\times}S^1{\times}{\cdots}{\times}S^1$ multiplied by $\frac{m}{c_{n-1}}$.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• Honam Mathematical Journal
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• v.31 no.4
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• pp.463-478
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• 2009

Let k be an imaginary quadratic field, ℌ the complex upper half plane, and let ${\tau}{\in}k{\cap}$ℌ, q = exp(${\pi}i{\tau}$). And let n, t be positive integers with $1{\leq}t{\leq}n-1$. Then $q^{{\frac{n}{12}}-{\frac{t}{2}}+{\frac{t^2}{2n}}}{\prod}^{\infty}_{m=1}(1-q^{nm-t})(1-q^{nm-(n-t)})$ is an algebraic number [10]. As a generalization of this result, we find several infinite series and products giving algebraic numbers using Ramanujan's $_{1{\psi}1}$ summation. These are also related to Rogers-Ramanujan continued fractions.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.397-400
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• 2006

In this study, we experimentally investigate the possibility of skin-friction drag reduction by series of transverse cavities in a turbulent boundary layer flow. The effects of cavity depth (d), cavity length (l) and cavity spacing (s) on the skin friction drag are examined in the range of $Re_{\theta}\;=\;4030\;{\sim}\;7360$, $d/{\theta}_0\;=\;0.13\;{\sim}1.03$, l/d = 1 ~ 4 and s/d = 5 ~ 20. We perform experiments for twenty different cavity geometries and directly measure total drag force using in-house force measurement system. In most cases, the skin friction drag is increased. At several cases, however, small drag reduction is obtained. The variation of the skin ftiction drag is more sensitive to the cavity length than to the cavity depth or cavity spacing, and drag is reduced at $s/l\;{\geq}\;10$ and $l/{\theta}_0\;{\leq}\;0.26$ irrespective of the cavity depth. At $l/\bar{\theta}_0\;=\;0.13$ and s/l = 10, maximum 2% drag reduction is achieved. When the skin friction drag is reduced, there is little interaction between the flows inside and outside cavity, and the flow changed by the cavity is rapidly recovered at the following crest. A stable vortex is formed inside a cavity in the case of drag reduction. This vortex generates negative skin friction drag at the cavity bottom wall. Although there is form drag due to the cavity itself, total drag is reduced due to the negative skin friction drag.

• Journal of the Korean Geotechnical Society
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• v.29 no.12
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• pp.57-67
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• 2013

Micropile technology has evolved continuously since its instruction by Fernando Lizzi in the 1950s. The effects of group micropile have been researched by many researchers. The effects of group micropile differ and change with pile length, pile spacing (S), pile angle (${\theta}$) and pile embedded conditions. In the present study, the effects of resistance increase and settlement reduction from micropiles were investigated through a series of axial load tests. For the study, axial load tests were performed using mat, group micropiles and micropiled-raft (MPR) in various pile spacing and pile angle conditions. As the result, the effects of resistance of micropiled-raft were 80% (3D) to 110% (7D) of the total resistance of mat and group micropile. The effects of settlement restraint of micropiled-raft were 20% (S=3D, ${\theta}=45^{\circ}$) to 70% (7D, ${\theta}=15^{\circ}$) of settlement of mat foundation.

• Korean Journal of Soil Science and Fertilizer
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• v.39 no.5
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• pp.259-267
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• 2006

Hydraulic conductivity is the rate of water flux on hydraulic gradient. The van Genuchten Mualem (VGM) model is frequently used for describing unsaturated state of soils, that is composed with the function of soil water potential and soil water content and requests various parameters. This study is to get the value of VGM parameters used Rosetta computer program based on neural network analysis method and to calculate VGM parameters. VGM parameters included Ko(effective saturated hydraulic conductivity), ${\theta}r$(residual soil water content), ${\theta}s$(saturated soil water content), L, n and m. The unsaturated hydraulic conductivity at 10 kPa was calculated by using Rosetta program. Unsaturated hydraulic conductivities of 17 soil series at 1, 3, 5, 7 kPa were also obtained by applying saturated hydraulic conductivity by disk tension infiltrometer based on Gardner and Wooding's equation. Water flow at the water potential of 3 kPa was very low except Namgye, Hagog, Baegsan, Sangju, Seogcheon, Yesan soil series. Unsaturated hydraulic conductivity at 1 kPa showed the highest value for Samgag soil series and was in order of Yesan, Hwabong, Hagog and Baegsan soil series. Those of Gacheon, Seocheon and Ugog soil series were very low. When the value by VGM was compared with the value by disc tension infiltrometer, there was a tendency with exponential function to soils without gravel but there was no tendency to soils including gravel. Conclusively, it would be limited that VGM model for unsaturated hydraulic conductivity analysis applies to Korean agricultural land including gravel and having steep slope, shallow soil depth.

• Bulletin of the Korean Mathematical Society
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• v.49 no.3
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• pp.529-572
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• 2012

A basis of a subspace of $S_4({\Gamma}_0(79))$ is given and the formulas for the number of representations of positive integers by some direct sums of the quadratic forms $x^2_1+x_1x_2+20x^2_2$, $4x^2_1{\pm}x_1x_2+5x^2_2$, $2x^2_1{\pm}x_1x_2+10x^2_2$ are determined.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.11-18
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• 1999

To estimate the mean and the variance of a lognormal distribution, Finney (1941) derived the uniformly minimun variance unbiased estimators(UMVUE) in the form of infinite series. However, the conditions ${\sigma}^{2}\;>\;n\;and\;{\sigma}^{2}\;<\;\frac{n}{4}$ for computing $E(\hat{\theta}_{AM})\;and\;E(\hat{\eta}^{2}_{AM})$ are necessary. In this paper, we give an alternative derivation of the UMVUE's.