• 비파괴검사학회지
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• 제11권1호
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• pp.13-22
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• 1991

In this paper, 3-dimensional fracture phenomena in the local area near a through notch tip located between the surface and the canter were investigated by using embedded dyeing grids with the pitch of $50.8{\mu}$. It was confirmed that displacement V and square root of distance from notch tip $y^{1/2}$ are not proportional in the local area of $\sqrt{{\mid}y{\mid}}\;<\;0.3mm^{1/2}$ and the maximum shea strain ${\varepsilon}_{xymax}$ near a notch tip occurred at the curvature beginning point of the notch curve. It was also noted that the maximum strain ${\varepsilon}_{xymax}$ in the thickness direction occurred at the interior, where the ratio of the distance measured from surface to the half of thickness of specimen is 0.3.

• 한국해양공학회지
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• 제17권6호
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• pp.47-52
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• 2003

To determine the effect of transverse open crack on the dynamic behavior of simply-supported Euler-Bernoulli beam with the moving masses, an iterative modal analysis approach is developed. The influence of depth and position of the crack in the beam, on the dynamic behavior of the simply supported beam system, have been studied by numerical method. The cracked section is represented by a local flexibility matrix, connecting two undamaged beam segments that is, the crack is modeled as a rotational spring. This flexibility matrix defines the relationship between the displacements and forces across the crack section, and is derived by applying a fundamental fracture mechanics theory. As the depth of the crack is increased, the mid-span deflection of the simply-supported beam, with the moving mass, is increased. The crack is positioned in the middle point of the pipe, and the mid-span defection of the simply-supported pipe represents maximum deflection.

• 대한수학회보
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• 제55권6호
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• pp.1869-1889
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• 2018

We are concerned with the following fractional p-Laplacian inclusion: $$(-{\Delta})^s_pu+V(x){\mid}u{\mid}^{p-2}u{\in}{\lambda}[{\underline{f}}(x,u(x)),\;{\bar{f}}(s,u(x))]$$ in ${\mathbb{R}}^N$, where $(-{\Delta})^s_p$ is the fractional p-Laplacian operator, 0 < s < 1 < p < $+{\infty}$, sp < N, and $f:{\mathbb{R}}^N{\times}{\mathbb{R}}{\rightarrow}{\mathbb{R}}$ is measurable with respect to each variable separately. We show that our problem with the discontinuous nonlinearity f admits at least one or two nontrivial weak solutions. In order to do this, the main tool is the Berkovits-Tienari degree theory for weakly upper semicontinuous set-valued operators. In addition, our main assertions continue to hold when $(-{\Delta})^s_pu$ is replaced by any non-local integro-differential operator.

• 대한수학회논문집
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• 제10권4호
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• pp.943-947
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• 1995

Assume that X is locally compact and Hausdorff. Then, we show that $\alpha X = sup {X \cup_f S(f)$\mid$f \in S^{\alpha}}$ for any compactification $\alpha X$ of X if and only if for any 2-point compatification $\gamma X$ of X with $\gamma X - X = {-\infty, +\infty}$, there exists a clopen subset A of \gamma X$ such that $-\infty \in A$ and $+\infty \notin A$. As a corollary, we obtain that if X is connected and locally connected, then $\alpha X = sup {X \cup_f S(f)$\mid$f \in S^{\alpha}}$ for any compactification $\alpha X$ of X if and only if X is 1-complemented.

• 대한수학회보
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• 제32권2호
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• pp.303-308
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• 1995

We consider a torus T, that is, a compact surface with genus 1 and $\Omega = D^2 \times S^1$ topologically with $\partial\Omega = T$, where $D^2$ is the open unit disk and $S^1$ is the unit circle. Let $\omega = (x,y)$ denote the generic point on T. For a smooth immersion $u : T \to R^3$, we define the Dirichlet functional by $$ E(u) = \frac{2}{1} \int_{T} $\mid$\nabla u$\mid$^2 d\omega $$ and the volume functional by $$ V(u) = \frac{3}{1} \int_{T} u \cdot u_x \Lambda u_y d\omege $$.

• 대한수학회논문집
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• 제32권3호
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• pp.689-707
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• 2017

In this paper, a boundary version of Schwarz lemma is investigated. We take into consideration a function f(z) holomorphic in the unit disc and f(0) = 0, f'(0) = 1 such that ${\Re}f^{\prime}(z)$ > ${\frac{1-{\alpha}}{2}}$, -1 < ${\alpha}$ < 1, we estimate a modulus of the second non-tangential derivative of f(z) function at the boundary point $z_0$ with ${\Re}f^{\prime}(z_0)={\frac{1-{\alpha}}{2}}$, by taking into account their first nonzero two Maclaurin coefficients. Also, we shall give an estimate below ${\mid}f^{{\prime}{\prime}}(z_0){\mid}$ according to the first nonzero Taylor coefficient of about two zeros, namely z = 0 and $z_1{\neq}0$. The sharpness of these inequalities is also proved.

• 접착 및 계면
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• 제7권4호
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• pp.18-23
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• 2006

The influence of the notch length on the stress distribution of mid-bondline and adherend was investigated using elasto-plastic finite element method. The results from the simulation showed that peak stress of mid-bondline decreased markedly as adherend with notch in the middle of lap zone, and the stress in the middle of joint with low stress originally increased evidently. All the peak stresses decreased firstly and increased again as the length of notch increased. The relative higher peak stress appeared at the point near the notch of adherend where might be failed previously during the loading procedure.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2006년도 춘계학술발표회 논문집(I)
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• pp.82-85
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• 2006

In this study, the fatigue tests were performed on a series of reinforce concrete beams with type of aggregate to investigate the fatigue behavior. The four point loading system is used in the fatigue tests. In these tests, relations between the repeated loading cycles and mid-span deflections, number of repeated loading cycles when specimen was fractured were observed. On this basis, the mid-span deflections, the crack growth and failure mode of beams were studied. The result of tests, reinforce concrete beams with recycled aggregate were about similar failure mode with natural aggregate concrete beam.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.237-249
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• 2004

Consider the second order self-adjoint neutral difference equation of form $\Delta(a_n$\mid$\Delta(x_n\;-\;{p_n}{x_{{\tau}_n}}$\mid$^{\alpha}sgn{\Delta}(x_n\;-\;{p_n}{x_{{\tau}_n}}\;+\;f(n,\;{x_{g_n}}\;=\;0$. In this paper, we will give the classification of nonoscillatory solutions of the above equation; and by the fixed point theorem, we present some existence results for some kinds of nonoscillatory solutions of the equation.

• 대한수학회보
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• 제33권1호
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• pp.1-16
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• 1996

Earlier in 1935[12], M. S. Robertson introduced the class of quadrant preserving functions. More precisely, let Q be the class of all functions f(z) analytic in the unit disk $D = {z : $\mid$z$\mid$ < 1}$ such that f(0) = 0, f'(0) = 1, and the range f(z) is in the j-th quadrant whenever z is in the j-th quadrant of D, j = 1,2,3,4. This class Q contains the subclass of normalized, odd univalent functions which have real coefficients. On the other hand, this class Q is contained in the class T of odd typically real functions which was introduced by W. Rogosinski [13]. Clearly, if $f \in Q$, then f(z) is real when z is real and therefore the coefficients of f are all real. Recently, it was observed by Y. Abu-Muhanna and T. H. MacGregor [1] that any function $f \in Q$ is odd. Instead of functions "preserving quadrants", the authors [1] have introduced the notion of "preserving sectors".