• 대한수학회보
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• 제49권4호
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• pp.829-850
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• 2012

In this paper, we adopt symmetric interior penalty discontinuous Galerkin (SIPG) methods to approximate the solution of nonlinear viscoelasticity-type equations. We construct finite element space which consists of piecewise continuous polynomials. We introduce an appropriate elliptic-type projection and prove its approximation properties. We construct semidiscrete discontinuous Galerkin approximations and prove the optimal convergence in $L^2$ normed space.

• 한국위성정보통신학회논문지
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• 제8권1호
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• pp.77-82
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• 2013

최근 주목을 받고 있는 Particle Filtering은 실제 객체 추적에서 발생하는 비선형, 비 가우시안 분포를 가지는 상태 벡터의 사후확률을 추정하기 위한 Monte Carlo 시뮬레이션에 기반을 둔 추적 방법론이다. 우리는 본 논문에서 Particle Filtering을 이용한 객체 추적성능을 향상시킬 수 있는 두 가지 방법론을 제안한다. 첫 번째는 확률이 가장 낮은 샘플을 이전 프레임의 추정된 상태 벡터로 대치하는 피드백 방법론이고, 두 번째는 객체 확률 분포를 추정된 객체 후보영역에 역투영하여 신뢰구간을 구함으로써 추적 박스의 정확도를 향상시키는 방법이다. 또한, 실험을 통해 구한 추적 샘플의 진화 방정식을 제시하였다. 우리는 다양한 상황이 설정된 실험 데이터 셋을 구성하여 실험을 실시하여 제안한 방법론의 우수성을 입증하였다.

• 펄프종이기술
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• 제41권4호
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• pp.25-32
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• 2009

Forest biomass can be used as various types of raw materials such as pulp, wood pellets, solid charcoals and so on. This paper estimates the nation wide amount of forest biomass based on the projection of forest areas for its effective and economic use. Several trend equations are used in projecting the forest areas. In 2009, the forest biomass arising from thinning is estimated be 6,591,575 $m^3$. The estimates of forest biomass in 2015 and 2018 are 6,375,627 $m^3$ and 6,284,779 $m^3$, respectively. Since the forest areas are projected to be declining, the biomass generated by thinning will decrease. This implies that the new alternatives for supplying raw materials for biofuels must be prepared before then.

• 한국전기전자재료학회논문지
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• 제18권1호
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• pp.89-95
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• 2005

We derived a formula which can calculate the space distribution of refractive index variation by an applied electric field about Bi$_{12}$ GeO$_{20}$ single crystal. Stereographic projection maps of refractive index variation by an applied electric field were made out using numerical value to be calculated by this formula. By the calculated results, since an electric field had applied to [(equation omitted) 1 1] direction and [1 (equation omitted) 1] direction of Bi$_{12}$ GeO$_{20}$ crystal, positive variation of the refractive index of [(equation omitted) 1 1] direction and [1 (equation omitted) 1] direction was the largest. The incremented refractive index per unit electric field was +3.2410${\times}$10$^{-11}$ V$^{-1}$ for the wavelength of 6328 $\AA$. Since an electric field had applied to [1 1 1] direction and [(equation omitted) 1] direction, negative variation of the refractive index of [1 1 1] direction and [(equation omitted) 1] direction was the largest. The decremented refractive index per unit electric field was -3.2410${\times}$10$^{-11}$ V$^{-1}$ for the wavelength of 6328 $\AA$.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.311-326
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• 2011

In this paper, we adopt discontinuous Galerkin methods with penalty terms namely symmetric interior penalty Galerkin methods, to solve nonlinear viscoelasticity type equations. We construct finite element spaces and define an appropriate projection of u and prove its optimal convergence. We construct extrapolated fully discrete discontinuous Galerkin approximations for the viscoelasticity type equation and prove ${\ell}^{\infty}(L^2)$ optimal error estimates in both spatial direction and temporal direction.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제15권3호
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• pp.233-251
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• 2011

The Gauge-Uzawa method [GUM] in [9] which is a projection type algorithm to solve evolution Navier-Stokes equations has many advantages and superior performance. But this method has been studied for backward Euler time discrete scheme which is the first order technique, because the classical second order GUM requests rather strong stability condition. Recently, the second order time discrete GUM was modified to be unconditionally stable and estimated errors in [12]. In this paper, we contemplate several GUMs which can be derived by the same manner within [12], and we dig out properties of them for both stability and accuracy. In addition, we evaluate an stability condition for the classical GUM to construct an adaptive GUM for time to make free from strong stability condition of the classical GUM.

• Nuclear Engineering and Technology
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• 제28권5호
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• pp.488-499
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• 1996

We have extended the source projection analytic nodal discrete ordinates method (SPANDOM) for more flexible applicability in analysis of hexagonal assembly cores. The method (SPANDOM-FH) does not invoke transverse integration but instead solves the discrete ordinates equation analytically after the source term is projected and represented in hybrid form of high-order polynomials and exponential functions. SPANDOM-FH which treats a hexagonal node as one node is applied to two fast reactor benchmark problems and compared with TWOHEX. The results of comparison indicate that the present method SPANDOM-FH predicts accurately $k_eff$ and flux distributions in hexagonal assembly cores. In addition, SPANDOM-FH gives the continuous two dimensional intranodal scalar flux distributions in a hexagonal node. The reentering models between TWOHEX and SPANDOM were also compared and it was confirmed that SPANDOM's model is more realistic. Through the results of benchmark problems, we conclude that SPANDOM-FH has the sufficient accuracy for the nuclear design of fast breeder reactor (FBR) cores with hexagonal assemblies.

• Korean Journal of Mathematics
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• 제21권2호
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제20권4호
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• pp.295-308
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• 2016

We propose a projection-based analysis of a new hybridizable discontinuous Gale-rkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses $L^2$-projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p + 1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.

• Journal of Magnetics
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• 제16권4호
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• pp.408-412
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• 2011

We investigated theoretically the magnetic field dependence of the quantum optical transition of qusi 2-Dimensional Landau splitting system, in GaN and ZnO. We apply the Quantum Transport theory (QTR) to the system in the confinement of electrons by square well confinement potential. We use the projected Liouville equation method with Equilibrium Average Projection Scheme (EAPS). Through the analysis of this work, we found the increasing properties of the optical Quantum Transition Line Shapes(QTLSs) which show the absorption power and the Quantum Transition Line Widths(QTLWs) with the magnetic-field in GaN and ZnO. We also found that QTLW, ${\gamma}(B)_{total}$ of GaN < ${\gamma}(B)_{total}$ of ZnO in the magnetic field region B < 25 Tesla.