• Journal of the Korean Mathematical Society
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• v.61 no.1
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• pp.1-28
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• 2024

In this article, we associate a contact structure to the conjugacy class of a periodic surface homeomorphism, encoded by a combinatorial tuple of integers called a marked data set. In particular, we prove that infinite families of these data sets give rise to Stein fillable contact structures with associated monodromies that do not factor into products to positive Dehn twists. In addition to the above, we give explicit constructions of symplectic fillings for rational open books analogous to Mori's construction for honest open books. We also prove a sufficient condition for the Stein fillability of rational open books analogous to the positivity of monodromy for honest open books due to Giroux and Loi-Piergallini.

• Korean Journal of Mathematics
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• v.18 no.4
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• pp.489-496
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• 2010

In this paper we consider the Dirichlet problem for an fourth order elliptic equation on a open set in $R^N$. By using variational methods we obtain the multiplicity of nontrivial weak solutions for the fourth order elliptic equation.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.451-460
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• 2009

We consider the existence of solutions of a nonlinear biharmonic equation with Dirichlet boundary condition, ${\Delta}^2u+c{\Delta}u=f(x, u)$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$. We obtain two new results by linking theorem.

• Korean Journal of Mathematics
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• v.5 no.1
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• pp.29-33
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• 1997

In this paper we investigate the existence of positive solutions of a nonlinear biharmonic equation under Dirichlet boundary condition in a bounded open set ${\Omega}$ in $\mathbf{R}^n$, i.e., $${\Delta}^2u+c{\Delta}u=bu^{+}+s\;in\;{\Omega},\\u=0,\;{\Delta}u=0\;on\;{\partial}{\Omega}$$.

• Journal for History of Mathematics
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• v.16 no.4
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• pp.107-115
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• 2003

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.

• Elastomers and Composites
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• v.50 no.1
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• pp.30-34
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• 2015

Thermo-mechanical treatment process of a compressed open-cell rigid polyurethane foam (OC-RPUF), which was fabricated for the vacuum insulation panel (VIP), was studied to obtain an optimum condition for the dimensional stability by the relaxation of compressive stress. Thermo-mechanical deformation of the sample OC-RPUF was shown to occur from about $120^{\circ}C$. Yield stress of 0.36 MPa was shown at about 10% yield strain. And, densification of the foam started to occur from 75% compressive strain and could be continued up to max. 90%. Compression set of the sample restored after initial compression to 90% at room temperature was ca. 82%. Though the expansion occurred to about twice of the originally compressed thickness in case of temperature rise to $130^{\circ}C$, it could be overcome and the dimensional stability could be maintained if the constant load of 0.3 MPa was applied. As the result, a thermo-mechanical treatment process, i.e, annealing process at temperature of $130{\sim}140^{\circ}C$ for about 20 min as is the maximum compressed state at room temperature, should be required for dimensional stability as an optimum condition for the use of VIP core material.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.11-17
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• 2002

In this paper we give several necessary and sufficient conditions for an operator on the Hilbert space to obey Browder's theorem. And it is shown that if S has totally finite ascent and $T{\prec}S$ then $f(T)$ obeys Browder's theorem for every $f{\in}H({\sigma}(T))$, where $H({\sigma}(T))$ denotes the set of all analytic functions on an open neighborhood of ${\sigma}(T)$.

• Communications of the Korean Mathematical Society
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• v.24 no.4
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• pp.523-528
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• 2009

In this paper, we consider the existence of solutions to some generalized vector quasi-equilibrium-like problem under a c-diagonal quasi-convexity assumptions, but not monotone concepts. For an example, in the proof of Theorem 1, the c-diagonally quasi-convex concepts of a set-valued mapping was used but monotone condition was not used. Our problem is a new kind of equilibrium problems, which can be compared with those of Hou et al. [4].

• Journal of information and communication convergence engineering
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• v.4 no.2
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• pp.62-66
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• 2006

The objective of this thesis is to measure the limit of the real space where wireless Local Area Network (LAN) is used, and to apply this result as reference to set up a real Wireless LAN environment. The organized circumference was composed of Wireless LAN based on IEEE 802.11b of the American standard, and the examination is carried out on the campus. On the real condition of office environment and open space, the ratio of available distance to a signal at each distance was measured and this result was studied as data to embody wireless LAN on the campus. The measurement under an indoor environment was executed under circumstance having two walls and open space, however, was executed respectively under three circumstances: Where no obstacle, where one wall exists, and where two or more walls exist.

• Journal of applied mathematics & informatics
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• v.41 no.4
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• pp.697-705
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• 2023

We studied new notions of analogues of topological rings. Salih [10] acquaints us with the notion of irresolute topological ring in 2018. In this paper, we further studied the space closely and characterized indispensable properties of the space. We prove that every open subset of an irresolute topological ring is irresolute topological ring. We also obtained the equivalent condition of neighborhood of an element in an irresolute topological ring. It is proved that ring homeomorphism of an irresolute topological ring is irresolute if it is irresolute at identity element e in the irresolute topological ring 𝓡.