• Structural Engineering and Mechanics
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• v.25 no.4
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• pp.383-403
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• 2007

The contact problem for an elastic layer resting on an elastic half plane is considered according to the theory of elasticity with integral transformation technique. External loads P and Q are transmitted to the layer by means of two dissimilar rigid flat punches. Widths of punches are different and the thickness of the layer is h. All surfaces are frictionless and it is assumed that the layer is subjected to uniform vertical body force due to effect of gravity. The contact along the interface between elastic layer and half plane will be continuous, if the value of load factor, ${\lambda}$, is less than a critical value, ${\lambda}_{cr}$. However, if tensile tractions are not allowed on the interface, for ${\lambda}$ > ${\lambda}_{cr}$ the layer separates from the interface along a certain finite region. First the continuous contact problem is reduced to singular integral equations and solved numerically using appropriate Gauss-Chebyshev integration formulas. Initial separation loads, ${\lambda}_{cr}$, initial separation points, $x_{cr}$, are determined. Also the required distance between the punches to avoid any separation between the punches and the layer is studied and the limit distance between punches that ends interaction of punches, is investigated. Then discontinuous contact problem is formulated in terms of singular integral equations. The numerical results for initial and end points of the separation region, displacements of the region and the contact stress distribution along the interface between elastic layer and half plane is determined for various dimensionless quantities.

• Journal of KSNVE
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• v.8 no.3
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• pp.504-512
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• 1998

For analyzing the torsional vibration of a multiple stepped gear system containing a pair of triple gears, a transfer matrix model based on Hibner's branch method is developed and the natural properties of the branched rotor system are calculated with using the $\lambda$-matrix formulation. A Campbell diagram, in which the excitation sources caused by the mass unbalances of the rotors and the transmitted errors of thegearings are considered, shows that, at the neighborhood of the operating speed, there are the four critical speeds amplifying the first mode and the fifth mode. For the surpression of the gear box vibration, two ways are suggested by referring the mode shapes.

• Korean Journal of Mathematics
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• v.19 no.3
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• pp.331-342
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• 2011

We consider the multiplicity of the solutions for a class of a system of critical growth beam equations with periodic condition on t and Dirichlet boundary condition $$\{u_{tt}+u_{xxxx}=av+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{{\alpha}-1}v_{+}^{\beta}+s{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,\\u_{tt}+v_{xxxx}=bu+\frac{2{\alpha}}{{\alpha}+{\beta}}u_{+}^{\alpha}v_{+}^{{\beta}-1}+t{\phi}_{00}\;\;in\;(-\frac{\pi}{2},\;\frac{\pi}{2}){\times}R,$$ where ${\alpha}$, ${\beta}$ > 1 are real constants, $u_+=max\{u,0\}$, ${\phi}_{00}$ is the eigenfunction corresponding to the positive eigenvalue ${\lambda}_00=1$ of the eigenvalue problem $u_{tt}+u_{xxxx}={\lambda}_{mn}u$. We show that the system has a positive solution under suitable conditions on the matrix $A=\(\array{0&a\\b&0}\)$, s > 0, t > 0, and next show that the system has another solution for the same conditions on A by the linking arguments.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.439-449
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• 2014

In this paper, we present some inequalities for the non-tangential derivative of f(z). For the function $f(z)=z+b_{p+1}z^{p+1}+b_{p+2}z^{p+2}+{\cdots}$ defined in the unit disc, with ${\Re}\(\frac{f^{\prime}(z)}{{\lambda}f{\prime}(z)+1-{\lambda}}\)$ > ${\beta}$, $0{\leq}{\beta}$ < 1, $0{\leq}{\lambda}$ < 1, we estimate a module of a second non-tangential derivative of f(z) function at the boundary point ${\xi}$, by taking into account their first nonzero two Maclaurin coefficients. The sharpness of these estimates is also proved.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.301-317
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• 2022

In this paper, we propose a change point detection procedure based on the modified information criterion in a generalized lambda distribution (GLD) model. Simulations are conducted to obtain empirical critical values of the proposed test statistic. We have also conducted simulations to evaluate the performance of the proposed methods comparing to the log-likelihood method in terms of power, coverage probability, and confidence sets. Our results indicate that, under various conditions, the proposed method modified information criterion (MIC) approach shows good finite sample properties. Furthermore, we propose a new goodness-of-fit testing procedure based on the energy distance to evaluate the asymptotic null distribution of our test statistic. Two real data applications are provided to illustrate the use of the proposed method.

• Journal of Korean Tunnelling and Underground Space Association
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• v.9 no.1
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• pp.49-62
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• 2007

A new earth pressure equation acting on the vertical shafts in cohesionless soils has been proposed by modifying the equations proposed by others. In order to verify the modified equation, model tests which can control uniform wall displacement with depth to radial direction were conducted. Model tests were performed with three different wall friction angles and two different relative densities. The measured values were larger than estimated values when assuming $\lambda=1$ ; smaller than those when assuming $\lambda=1-sin\phi$. The parameter, $\lambda$ is the ratio of tangential stress to vertical stress and is the most critical value in proposed equation. A method which can estimate the earth pressure on vertical shafts in layered soils is also proposed by reasonably assuming the failure surface of layered soils and using the modified equation. In order to verify the proposed method, in-situ measurement data have been collected from the three in-situ vertical shafts installed in layered soils. Most of earth pressures converted from measured data match reasonably well with estimated values using proposed method.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1541-1547
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• 2011

In this paper, using B.Ricceri's three critical points theorem, we prove the existence of at least three classical solutions for the problem $$\{u^{(4)}(t)={\lambda}f(t,\;u(t)),\;t{\in}(0,\;1),\\u(0)=u(1)=u^{\prime}(0)=u^{\prime}(1)=0,$$ under appropriate hypotheses.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.961-977
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• 2022

In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

• Journal of the Korean Magnetics Society
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• v.1 no.2
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• pp.15-21
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• 1991

The magnetic properties of the $Y_{1}Ba_{2}Cu_{3-x}Sn_{x}O_{7-y}$ superconductor were studied as a function of Sn concentration by utilizing both the vibrating sample magnetometer (VSM) and torque magnetometer. Unlike the cases where Fe and Co were substituted for Cu, the superconducting transition temperature was maintained above 90 K until x reached the value of 0.36. The lower critical field $H_{c1}(T)$ and upper critical field $H_{c2}(T)$ are measured as a function of temperature and external magnetic field, respectively. By aid of these results, $H_{c1}(0)$.($H_{c2}(0)$), the coherence length ${\varepsilon}_{0}$, the penetration depth ${\lambda}_{0}$, and the Ginzburg-Landau parameter k were oqtained. Flux pinning was also observed in the sample.

• Korean Journal of Agricultural Science
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• v.31 no.1
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• pp.26-34
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• 2004

In this study, motion characteristics and power requirement of rotary tilling according to shape of conventional rotary blade were measured. This study was performed to establish factors which needed to develop energy saving rotary blade. Starting point of edged curve of imported rotary blade was faster than that of domestic rotary blade after measuring and analyzing edged curve of rotary blade. So domestic rotary blade tills much soil than imported rotary blade. In analyzing motion of rotary blade, Rotary blade of A, D type was begun to contact at part 3. Analyzing back surface of rotary blade which contact to soil at critical $\lambda$ results in contacting at e-f part. In measuring power requirement of rotary blade, specific torque and specific work of rotary blade are $160{\sim}170kgf{\cdot}m/m^2$, $3,700kgf{\cdot}m/m^3$. It shows power requirement of rotary blade according to shape of rotary blade are very different.