• 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.40 no.1
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• pp.17-28
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• 2003

Let X be a closed, oriented, Riemannian 4-manifold with ${{b_2}^+}(x)\;>\;1$ and of simple type. Suppose that ${\sigma}\;:\;X\;{\rightarrow}\;X$ is an involution preserving orientation with an oriented, connected, compact 2-dimensional submanifold $\Sigma$ as a fixed point set with ${\Sigma\cdot\Sigma}\;{\geq}\;0\;and\;[\Sigma]\;{\neq}\;0\;{\in}\;H_2(X;\mathbb{Z})$. We show that if _X(\Sigma)\;+\;{\Sigma\cdots\Sigma}\;{\neq}\;0$ then the $Spin^{C}$ bundle $\={P}$ is not $\mathbb{Z}_2-equivariant$, where det $\={P}\;=\;L$ is a basic class with $c_1(L)[\Sigma]\;=\;0$.

• Tunnel and Underground Space
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• v.4 no.1
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• pp.31-37
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• 1994

The effects of blasting and ground vibratons on curing concrete have not been well studied. As a results unrealistic and costly ground vibration constraints have been placed on blasting and piling when it occurs in the vicinity of curing concrete. To study the effects of ground vibrations, a shaking table was made to produce peak particle velocities in the nearly same frequency range as found in construction blasting. Concrete blocks of 33.3X27.7X16.2cm were molded and placed on the shaking table. Different sets of concrete blocks were subjected to peak vibrations of 0.25, 0.5, 1.0, 5.0 and 10cm/sec. The impulses were applied at two hour intervals for thirty seconds. Along with unvibrated concrete blocks, the vibrated concrete samples with 60.3mm in diameters were measured for elastic moduli, sonic velocity, tensile and uniaxial compressive strength. Test results showed that the vibrations in curing concrete generally have effects on the uniaxial compressive strength or physical properties of the concrete.

• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.613-625
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• 2016

Contact interaction of a beam (flexible element) with an elastic half-plane is considered, when a soft inhomogeneous (functionally graded) interlayer is present between them. The beam is bent under the action of a distributed load applied to the surface and a reaction of the elastic interlayer and the half-space. Solution of the contact problem is obtained for different values of thickness and parameters of inhomogeneity of the layer. The interlayer is assumed to be significantly softer than the underlying half-plane; case of 100 times difference in Young's moduli is considered as an example. The influence of the interlayer thickness and gradient of elastic properties on the distribution of the contact stresses under the beam is studied.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• The Pure and Applied Mathematics
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• v.29 no.1
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• pp.59-68
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• 2022

For a finite group G ⊂ GL(n, ℂ), the G-Hilbert scheme is a fine moduli space of G-clusters, which are 0-dimensional G-invariant subschemes Z with H⁰(𝒪_Z ) isomorphic to ℂ[G]. In many cases, the G-Hilbert scheme provides a good resolution of the quotient singularity ℂⁿ/G, but in general it can be very singular. In this note, we prove that for a cyclic group A ⊂ GL(n, ℂ) of type ${\frac{1}{r}}$(1, …, 1, a) with r coprime to a, A-Hilbert Scheme is smooth and irreducible.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.659-675
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• 2023

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

• Tunnel and Underground Space
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• v.11 no.4
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• pp.328-338
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• 2001

Horizontal tunnel face reinforcement using Fiber Glass Tube(FGT) or steel pipe and pipe roofing techniques are frequently used when the stability of newly excavated tunnel is not guaranteed. However, the mechanical behavior of tunnels using these techniques has not been fully understood so far. Therefore, engineering rule of thumb is commonly applied during designing procedure, and it is difficult to adopt these techniques rationally. In this study, the application of a simplified numerical analysis method based on composite mechanics is verified. The mean field theory and the strain energy theory are used to obtain the equivalence elastic moduli of reinforced soil and rock. Furthermore, a parametric study on the deformational behavior of tunnel face is performed for various patterns of prereinforcement.

• Tunnel and Underground Space
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• v.5 no.2
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• pp.134-143
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• 1995

Effects of blasting vibrations on curing concrete have not been well studied. As a result, unreasonable and strong blasting vibration constraints have been placed on blasting when it occurs in the vicinity of curing concrete. To study the effects of blasting on curing concrete blocks of 33.3X27.7X16.2 cm were molded and placed on the quarry. Several sets of concrete blocks were subjected separately to peak vibrations of 0.25, 0.5. 1.0, 5.0, and 10cm/sec. The impulses of blasting vibrations were applied with thirty-minute intervals. Along with unvibrated concrete blocks, the vibrated concrete samples cored with 60.3 mm in diameter were measured for elastic moduli, sonic velocity and uniaxial compressive strength. Test results can be summarized as follows; 1. The blasting vibrations between 6 and 8 hours after pour generally lowered on the uniaxial compressive strength of the concrete. 2. A low blasting vibration of 0.25 cm/sec did not affect the uniaxial compressive strength. As the magnitude of the blasting vibration increases, compressive strength of concrete is decreased. 3. Physical properties of the P-wave velocity, Young's modulus, and Poisson's ratio showed a weakly decreasing trend in the concrete blocks vibrated between 6 and 8 hours after pour.

• Journal of Korean Tunnelling and Underground Space Association
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• v.14 no.1
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• pp.37-53
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• 2012

There is considerable uncertainty in ground properties used in tunnel designs. In this study, a back analysis was performed to find optimal ground properties based on the artificial neural network facility of MATLAB program of using tunnel monitoring data. Total 81 data were constructed by changing elastic modulus and coefficient of lateral pressure which have great influence on tunnel convergence. A sensitivity analysis was conducted to establish an optimal training model by varying the number of hidden layers, the number of nodes, learning rate, and momentum. Meanwhile, the optimal training model was selected by comparing MSE (Mean Squared Error) and coefficient of determination ($R^2$) and was used to find the correct elastic moduli of layers and the coefficient of lateral pressure. In future, it is expected that the suggested method of this study can be applied to determine the optimum tunnel support pattern under given ground conditions.