• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.107-116
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• 2005

We show an algorithm to draw the famous picture of Kleinian modular group PSL(2, $\mathbb{Z}$), which appears in describing the moduli space of elliptic curves.

• Journal of the Korean Geotechnical Society
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• v.23 no.3
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• pp.141-147
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• 2007

Various approaches have been developed for the dynamic response analysis of piles. In one of the approaches, the soil-pile interaction is approximated by using parallel nonlinear springs, namely the p-y curves. Currently available p-y curve recommendations are based on static and cyclic lateral load tests. Other researchers have attempted to extend the p-y curves by incorporating the effects of liquefaction on soil-pile interaction and derived scaling factors of p-y curves to account fur the liquefaction. However, opinions on the scaling factors vary. In this study, the sealing factors, which reflect the variation of the elastic moduli of surrounding soils, were established combining the relationship between excess pore pressures and the natural frequencies of a soil-pile system obtained from Ig shaking table tests and the relationship between the elastic moduli of surrounding soils and the natural frequencies of a soil-pile system obtained from numerical analyses. As a result, the scaling factors were presented in an exponential function.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.341-365
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• 2011

In this paper, we establish general stratawise higher jet evaluation transversality of J-holomorphic curves for a generic choice of almost complex structures J (tame to a given symplectic manifold (M, $\omega$)). Using this transversality result, we prove that there exists a subset $\cal{J}^{ram}_{\omega}\;{\subset}\;\cal{J}_{\omega}$ of second category such that for every $J\;{\in}\;\cal{J}^{ram}_{\omega}$, the dimension of the moduli space of (somewhere injective) J-holomorphic curves with a given ramication prole goes down by 2n or 2(n - 1) depending on whether the ramication degree goes up by one or a new ramication point is created. We also derive that for each $J\;{\in}\;\cal{J}^{ram}_{\omega}$ there are only a finite number of ramication profiles of J-holomorphic curves in a given homology class $\beta\;{\in}\;H_2$(M; $\mathbb{Z}$) and provide an explicit upper bound on the number of ramication proles in terms of $c_1(\beta)$ and the genus g of the domain surface.

• Korea-Australia Rheology Journal
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• v.20 no.1
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• pp.27-34
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• 2008

Clay suspensions in liquid polymers exhibit a time-dependent behaviour that includes viscoelastic as well as thixotropic features. Because of the presence of interacting clay platelets, particulate networks can develop, which are broken down during flow and rebuild upon cessation of the flow. Here, the use of thixotropic techniques in probing flow-induced structures in nanocomposites is explored with data on a hectorite-poly(isobutylene) model system. By means of fast stress jump measurements the hydrodynamic contributions to the steady state stresses are determined as well as those caused by the stretching of the clay floes. Flow reversal measurements do not provide a clear indication of flow-induced anisotropy in the present case. The recovery of the clay microstructure upon cessation of flow is followed by means of overshoot and dynamic measurements. The development of a particulate network is detected by the appearance and growth of a low frequency plateau of the storage moduli. The modulus-frequency curves after various rest times collapse onto universal master curves, regardless of the pre-shear history or temperature. The scaling factors for this master curve are the crossover parameters. The crossover moduli are nearly a linear function of the crossover frequency, the relation being identical for recovery after shearing at different shear rates. This function depends, however, on temperature.

• International Journal of Highway Engineering
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• v.11 no.1
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• pp.1-12
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• 2009

A new mix design procedure for cold in-place recycling using foamed asphalt (CIR-foam) has been developed for Iowa Department of Transportation. Some strengths and weaknesses of the new mix design parameters were considered and modified to improve the laboratory test procedure. Based on the critical mixture parameters identified, a new mix design procedure was developed and validated to establish the properties of the CIR-foam mixtures. As part of the validation effort to evaluate a new CIR-foam mix design procedure, dynamic moduli of CIR-foam mixtures made of seven different reclaimed asphalt pavement (RAP) materials collected throughout the state of Iowa were measured and their master curves were constructed. The main objectives of this study are to provide: 1) standardized testing procedure for measuring the dynamic modulus of CIR-foam mixtures using new simple performance testing (SPT) equipment; 2) analysis procedure for constructing the master curves for a wide range of RAP materials; and 3) impacts of RAP material characteristics on the dynamic modulus. Dynamic moduli were measured at three different temperatures and six different loading frequencies and they were consistent among different RAP sources. Master curves were then constructed for the CIR-foam mixtures using seven different RAP materials. Based upon the observation of the constructed master curves, dynamic moduli of CIR-foam mixtures were less sensitive to the loading frequencies than HMA mixtures. It can be concluded that at the low temperature, the dynamic modulus is affected by the amount of fines in the RAP materials whereas, at the high temperature, the dynamic modulus is influenced by the residual binder characteristics.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.905-915
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• 1994

Let $M_g$ be the moduli space of isomorphism classes of genus g smooth curves. It is a quasi-projective variety of dimension 3g - 3, when $g > 2$. It is known that a complete subvariety of $M_g$ has dimension $< g-1 [D]$. In general it is not known whether this bound is rigid. For example, it is not known whether $M_4$ has a complete surface in it. But one knows that there is a complete curve through any given finite points [H]. Recently, an explicit example of a complete curve in moduli space is given in [G-H]. In [G-H] they constructed a complete curve of $M_3$ as an intersection of five hypersurfaces of the Satake compactification of $M_3$. One way to get a complete curve of $M_3$ is to find a complete one dimensional family $p : X \to B$ of plane quartics which gives a nontrivial morphism from the base space B to the moduli space $M_3$. This is because every non-hyperelliptic smooth curve of genus three can be realized as a nonsingular plane quartic and vice versa. This paper has come out from the effort to find such a complete family of plane quartics. Since nonsingular quartics form an affine space some fibers of p must be singular ones. In this paper, due to the semistable reduction theorem [M], we search singular plane quartics which can occur as singular fibers of the family above. We first list all distinct plane quartics in terms of singularities.

• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.565-583
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• 2007

We offer a refinement of the classical Clifford inequality about special linear series on smooth irreducible complex curves. Namely, we prove about curves of genus g and odd gonality at least 5 that for any linear series $g^r_d$ with $d{\leq}g+1$, the inequality $3r{\leq}d$ holds, except in a few sporadic cases. Further, we show that the dimension of the set of curves in the moduli space for which there exists a linear series $g^r_d$ with d<3r for $d{\leq}g+l,\;0{\leq}l{\leq}\frac{g}{2}-3$, is bounded by $2g-1+\frac{1}{3}(g+2l+1)$.

• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.485-494
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• 2023

Let Y be the quintic del Pezzo 4-fold defined by the linear section of Gr(2, 5) by ℙ⁷. In this paper, we describe the locus of double lines in the Hilbert scheme of coincs in Y. As a corollary, we obtain the desigularized model of the moduli space of stable maps of degree 2 in Y. We also compute the intersection Poincaré polynomial of the stable map space.

• Tunnel and Underground Space
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• v.6 no.2
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• pp.144-156
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• 1996

The deformation behaviors under uniaxial compressive cyclic loading were investigated for fresh rocks and freeze-thaw cycled samples. The Pocheon granite which is one of the most popular building stone in Korea was selected for tests. 0.5 Hz and 50% of dynamic strength were used as test conditions for frequency and fatigue span, respectively. For freezethaw procedure, sample were frozen for 3 hours under the temperature of -2$0^{\circ}C$ and then followed 3 hours thawing under the temperature of +2$0^{\circ}C$. Twenty seven samples were used as untreated and seventy three for freeze-thaw samples. No failure occurred up to 15000 cycles at the stress level of 60% of dynamic strength, indicating that the lowest strees level for fatigue failure may be around 60% of dynamic strength. Permanent strain and damping capacity curves show that there were three stages when rock behaves like under creep. Young's moduli were increased and Possion's ratios were decreased with the increase of the number of cycles. Possion's ratios varied more rapidly than Young's moduli did with the increase of the number of cycles. This may represent that most microcracks developed by fatigue stress are parallel to the axis of loading. The deformation behavior of freeze-thaw cycled samples were almost the same as that of untreated samples. However, the result of freeze-thaw cycled samples showed lower regression constant, indicating that the physical durability of rock is much lowered because of cyclic temperature variation.

• Composites Research
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• v.18 no.2
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• pp.30-37
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• 2005

In this paper, geometrically non-linear finite element analyses were performed to study the mechanical behavior of the material system of the envelope of stratospheric airships. The microstructure of the load-bearing plain weave layer was identified and modeled. The Updated Lagrangian formulation was employed to consider the geometric non-linearity as well as the induced structural non-linearity for the fiber tows. The stress-strain behavior was predicted and the effective elastic modulus was calculated by numerical experiments. It was found the non-linear stress-strain curves were largely different from those by linear analysis. And non-linear elastic moduli were much higher than linear elastic moduli. The difference was more distinguishable when the tow waviness ratio was smaller.