• Korean Journal of Mathematics
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• v.16 no.4
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• pp.527-535
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• 2008

Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies one pair of Torus-Sphere variational linking inequality. We show that I has at least two critical points when I satisfies one pair of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. We prove this result by use of the limit relative category and critical point theory on the manifold with boundary.

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1997.06a
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• pp.223-228
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• 1997

The gas dynamics in a stagnation point upflow OMVPE reactor were studied by Raman spectroscopy. The gas temperature was measured as a function of inlet gas velocity and aspect ratio for both H$_2$ and N$_2$ carrier gases. The centerline temperature gradient was latger at higher inlet velocities and with the use of N$_2$, and only weakly dependent on the aspect ratio. a tracer molecule, CH$_4$, was used to investigate the steady state behavior of reactants in the reactor, and the use of a sweeping flow was found to be a suitable method for preventing wall deposition. The transient switching response of the gas manifold was also investigated. Under certain conditions (low velocities, unmatched flows) recirculation flows were apparent. Numerical calculations of the reactor gas dynamics gave reasonable agreement with experimental results when detailed thermal boundary conditions were included.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.321-338
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• 2008

Let $\bar{M}$ be a smoothly bounded pseudoconvex complex manifold with a family of almost complex structures $\{L^{\tau}\}_{{\tau}{\in}I}$, $0{\in}I$, which extend smoothly up to bM, the boundary of M, and assume that there is ${\lambda}{\in}C^{\infty}$(bM) which is strictly subharmonic with respect to the structure $L^0|_{bM}$ in any direction where the Levi-form vanishes on bM. We obtain explicit estimates for the $\bar{\partial}$-Neumann problem in Sobolev spaces both in space and parameter variables. Also we get a similar result when $\bar{M}$ is strongly pseudoconvex.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.175-178
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• 1988

Let .SIGMA. be a smooth compact manifold without boundary having the same homotopy type as a sphere, which is called a homotopy sphere. Supose a group G acts smoothly on .SIGMA. with the fixed point set .SIGMA.$^{G}$ consists of two isolated fixed points p and q. In this case, tangent spaces $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA. at isolated fixed points, as isotropy representations of G are called Smith equivalent. Moreover .SIGMA. is called a supporting homotopy sphere of Smith equivalent representations $T_{p}$ .SIGMA. and $T_{q}$ .SIGMA.. The study on Smith equivalence has rich history, and for this we refer the reader to [P] or [Su]. The following question of pp.A.Smith [S] motivates the study on Smith equivalence.e.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.81-87
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• 2006

This paper describes a method for extracting surfaces from multi-material CT (Computed Tomography) data. Most contouring methods such as Marching Cubes algorithm assume that CT data are composed of only two materials. Some extended methods such as [3, 6] can extract surfaces from the multi-material (non-manifold) implicit representation. However, these methods are not directly applicable to CT data that are composed of three or more materials. There are two major problems that arise from fundamentals of CT. The first problem is that we have to use n(n-1)/2 threshold values for CT data contains n materials and select appropriately one threshold value for each boundary area. The second is that we cannot reconstruct only from CT data in which area three or more materials are adjacent each other. In this paper, we propose a method to solve the problems by using image analysis and demonstrate the effectiveness of the method with application examples construct polygon models from CT data of machine parts.

• 한국연소학회:학술대회논문집
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• 2002.11a
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• pp.215-222
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• 2002

It has been well acknowledged that intake system plays great role in the performance of reciprocating engine. Well-designed intake system is expected to not only increase engine efficiency but also decrease engine emission, which is one of the most urgent issues in the automotive society. Thorough understanding of the flow in intake system helps great to design adequate intake system. Even though both experimental and numerical methods are used to study intake flow, numerical analysis is more widely used due to its merits in time and economy. Intake system of In-line 6-Cylinder CNG engine was chosen for the analysis ICEM CFD HEXA was used to create 3-D structured grid and FIRE code was used for the flow analysis in the intake system. Due to the complexity of the geometry standard ${\kappa}-{\varepsilon}$ turbulence model was applied. Numerical analysis was performed for various inlet and outlet boundary conditions under both steady and transient flow. Inlet mass flow rate and outlet pressure variation were changing parameters with respect to engine speed. Flow parameters, such as velocity, pressure and flow distribution, were evaluated to provide adequate data of this intake system.

• Transactions of the Korean Society of Automotive Engineers
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• v.2 no.4
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• pp.112-119
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• 1994

This study is investigated into the dynamic effect of the manifold configuration during the gas exchange processes using both simulation and experiment, In theoretical study on the flow analysis, the characteristic method is applied to solve the compressible unsteady flow equation, involving the several steady flow boundary conditions. In order to excute the engine experiment efficiently, a data acquisition system is configured by using A/D converter and PC. Good results which coincided experimental data with simulation output were obtained, and it shows that this simulation method can be applied to obtain the optimal design parameters in the intake and exhaust systems.

• Journal of Power System Engineering
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• v.8 no.1
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• pp.24-29
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• 2004

In this study, a computer analysis has been developed for predicting the pipe pressure of the intake and exhaust manifold. To obtain the boundary conditions for a numerical analysis, one dimensional and non-steady gas dynamic calculation is performed by using the MOC(Method Of Characteristic). The main numerical parameters are the variation of the engine revolution to calculate the pulsating flow which the intake and exhaust valves arc working. The comparison of exhaust pressure in case of numerical results is quite matched with in case of experimental results. When engine revaluation is increased, the pressure amplitude showed a high value, but the pressure frequency was decreased.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.181-189
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• 2000

Let (X, J) be a closed, connected almost complex four-manifold. Let $X_1$ be the complement of an open disc in X and let ${\varepsilon}_1$be the contact structure on the boundary ${\varepsilon}X_1$ which is compatible with a symplectic structure on $X_1$, Then we show that (X, J) is symplectic if and only if the contact structure ${\varepsilon}_1$ on ${\varepsilon}X_1$ is isomorphic to the standard contact structure on the 3-sphere $S^3$ and ${\varepsilon}X_1$is J-concave. Also we show that there is a contact structure ${\varepsilon}_0\ on\ S^2\times\ S^1$which is not strongly symplectically fillable but symplectically fillable, and that $(S^2{\times}S^1,\;{\varepsilon})$ has infinitely many non-diffeomorphic minimal fillings whose restrictions on$\S^2\times\ S^1$are ${\sigma}$ where ${\sigma}$ is the restriction of the standard symplectic structure on $S^2{\times}D^2$.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.1-9
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• 1989

In 1980 and 1983, it was proved that P $D^{2}$-groups are surface groups ([2], [3]). Since then, topologists have been positively studying about P $D^{n}$ -groups (or $D^{n}$ -groups). For example, let a topological space X have a right .pi.-action, where .pi. is a multiplicative group. If each x.memX has an open neighborhood U such that for each u.mem..pi., u.neq.1, U.cap. $U_{u}$ =.phi., this right .pi.-action is said to be proper. In this case, if X/.pi. is compact then (1) .pi.$_{1}$(X/.pi).iden..pi.(X:connected, .pi.$_{1}$: fundamental group) ([4]), (2) if X is a differentiable orientable manifold with demension n and .rho.X (the boundary of X)=.phi. then $H^{k}$ (X;Z).iden. $H_{n-k}$(X;Z), ([6]), where Z is the set of all integers.s.