• Bulletin of the Korean Mathematical Society
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• v.43 no.1
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• pp.63-75
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• 2006

We study the homology of based gauge groups associated with the principal Spin(n) bundles over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the Dyer-Lash of operations.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.4
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• pp.788-796
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• 2017

This paper proposes a new measurement method to improve the shortcomings of an existing integral method for measuring heat flux in plug-type heat flux gauges in the high-temperature and high-pressure environments of liquid-rocket combustors. Using the existing integral measurement method, the calculation of the surface area for the heat flux in the gauge exhibits error in relation to the actual surface area. To solve this problem, transient profiles obtained from ANSYS Fluent were used to calculate unsteady heat flux as it adjusted to the measured temperature. First, a heat flux gauge was designed and manufactured specifically for use in the high-temperature and high-pressure conditions that are similar to those of liquid rocket combustors. A calibration test was performed to prove the reliability of the manufactured gauge. Then, a combustion experiment was conducted, in which the gauge was used to measure unsteady heat flux in a liquid rocket combustor that used kerosene and liquid oxygen as propellants. Reasonable heat flux values were obtained using the gauge. Therefore, the proposed measurement method is considered to offer significant improvement over the existing integral method.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.1023-1032
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• 2011

In this paper, a new Ekeland type variational principle on gauge spaces is established. As applications, we give Caristi-Kirk type fixed point theorems on gauge spaces, and Dane$\check{s}$' drop theorem on seminormed spaces. Also, we show that the Palais-Smale condition implies coercivity on semi-normed spaces.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.1
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.699-709
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• 2008

We study homology of the gauge group associated with the principal $G_2$ bundle over the four-sphere using the Eilenberg-Moore spectral sequence and the Serre spectral sequence with the aid of homology and cohomology operations.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.933-944
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• 1994

Let $\pi : P \to S^4$ be a principal G-bundle over $S^4$ whose the structure group G is a compact, connected, simple Lie group. Since $\pi_3(G) = \pi_4 (BG) = Z$, we can classify the principal bundle $P_k$ over $S^4$ by the map $S^4 \to BG$ of degree k. Atiyah and Jones [2] showed that $C_k = A_k/g^b_k$ is homotopy equivalent to $\Omega^3_k G \simeq \Omega^4_k BG$ where $A_k$ is the space of the all connections in $P_k$ and $g^b_k$ is the based gauge group which consists of all base point preserving automorphisms on $P_k$. Here $\Omega^nX$ is the space of all base-point preserving continuous map from $S^n$ to X. Let $M_k$ be the space of based gauge equivalence classes of all connections in $P_k$ satisfying the Yang-Mills self-duality equations, which we call the moduli space of G instantons.

• Proceedings of the KSR Conference
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• 2003.05a
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• pp.592-596
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• 2003

In general the limit of EMU bases on the construction gauge. But to save the cost for construction, there is often a case that the gauge of construction for bogie is narrower than the existing gauge. Finally, out-board bogie type cannot be applicable because of the space. In this case, we can use the in-board bogie type which the support distance of both suspensions is narrower than out-board bogie. But we cannot use an in-board bogie indifferently because car with in-board bogie must also have the same performance as out-board bogie in wider gauge. Accordingly, we have to consider how many moments in the suspensions are applied due to the narrower support distance. And the characteristics of suspensions in the in-board bogie must be decided from the moments.

• Journal of the Korean Mathematical Society
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• v.25 no.2
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• pp.259-264
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• 1988

• East Asian mathematical journal
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• v.37 no.5
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• pp.591-598
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• 2021

In this paper we study the Cauchy problem for the Chern-Simons gauged O(3) sigma model. We prove the local existence of solutions with low regularity initial data, observing null forms of the system and applying bilinear estimates for wave-Sobolev space H^{s, b}.

• Korean Journal of Mathematics
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• v.21 no.2
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• pp.125-150
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• 2013

The stabilized Gauge-Uzawa method (SGUM), which is a second order projection type algorithm to solve the time-dependent Navier-Stokes equations, has been newly constructed in 2013 Pyo's paper. The accuracy of SGUM has been proved only for time discrete scheme in the same paper, but it is crucial to study for fully discrete scheme, because the numerical errors depend on discretizations for both space and time, and because discrete spaces between velocity and pressure can not be chosen arbitrary. In this paper, we find out properties of the fully discrete SGUM and estimate its errors and stability to solve the evolution Navier-Stokes equations. The main difficulty in this estimation arises from losing some cancellation laws due to failing divergence free condition of the discrete velocity function. This result will be extended to Boussinesq equations in the continuous research (part II) and is essential in the study of part II.