• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.73-93
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• 2005

In this paper, we attempt to present a new numerical approach to solve non-linear backward stochastic differential equations. First, we present some definitions and theorems to obtain the conditions, from which we can approximate the non-linear term of the backward stochastic differential equation (BSDE) and we get a continuous piecewise linear BSDE correspond with the original BSDE. We use the relationship between backward stochastic differential equations and stochastic controls by interpreting BSDEs as some stochastic optimal control problems, to solve the approximated BSDE and we prove that the approximated solution converges to the exact solution of the original non-linear BSDE in two different cases.

• 한국정보처리학회논문지
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• 제3권6호
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• pp.1553-1567
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• 1996

표면 보간법을 응용하는 분야에는 모델링 자연현상 가시화 등을 비롯하여 여러 가지를 들 수 있다. 사면체 분할법은 사차원적 표면 형성을 위한 전 처리 단계 중의 하나이다. 사차원 공간상에서 피스와이즈(piecewise) 선형보간법의 질은 삼차원에서 의 자료 점의 분포에 영향을 받을 뿐 아니라 자료 값에도 영향을 받는다. 자료 값을 고려한 사면체 분할법이 추정의 질을 개선시킬 있음을 사차원 공간의 가시화를 통하 여 보여준다. 본 논문에서는 Delaunay 사면분할법의 구 기준(Sphere criterion)과 자 료 의존형 사면체 분할법 중의 하나인 최소 제공제곱 근사기준(least squares fitting criterion)을 논의하였다. 본 논문은 또한 새로운 자료 값을 고려한 기준인 gradient difference와 jump in normal direction derivative들을 논의하였다.

• 전자공학회논문지
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• 제52권9호
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• pp.36-44
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• 2015

본 논문에서는 광각 카메라에서 발생하는 비네팅 왜곡과 배럴 왜곡을 효율적으로 보정하기 위한 낮은 복잡도의 프로세서를 제안하고, 이를 구현한 결과를 보인다. 제안하는 프로세서에서는 비네팅 왜곡과 배럴 왜곡 보정 시 복잡한 연산을 수반하는 고차 다항식과 같은 피팅 함수를 구간 선형 근사하여 보정 품질을 유지하면서도 연산 복잡도를 크게 낮추었다. 이를 기반으로, 배럴 왜곡과 비네팅 왜곡을 중첩적으로 보정하도록 설계하여 전체적인 하드웨어 복잡도를 낮추었다. 제안하는 프로세서는 $0.11{\mu}m$ CMOS 공정을 사용하여 18.6K의 논리 게이트로 구현되었으며, $2048{\times}2048$ 크기의 영상에 대하여 최대 200Mpixels/s의 속도로 보정이 가능하다.

• 대한수학회보
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• 제50권1호
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• pp.321-341
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• 2013

In this paper, we discuss the a posteriori error estimates of the semidiscrete mixed finite element methods for quadratic optimal control problems governed by linear hyperbolic equations. The state and the co-state are discretized by the order $k$ Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise polynomials of order $k(k{\geq}0)$. Using mixed elliptic reconstruction method, a posterior $L^{\infty}(L^2)$-error estimates for both the state and the control approximation are derived. Such estimates, which are apparently not available in the literature, are an important step towards developing reliable adaptive mixed finite element approximation schemes for the control problem.

• 설비공학논문집
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• 제9권1호
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• pp.43-54
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• 1997

This paper presents an approximate analytical solution to a two-region one-dimensional model for the charging process of stratified thermal storage tanks with variable inlet temperature in the presence of momentum-induced mixing. Based on the superposition principle, an arbitrary-varying inlet temperature is decomposed into inherent discontinuous steps and continuous intervals approximated as a finite number of piecewise linear functions. This approximation allows the temperature of the upper perfectly-mixed layer to be expressed in terms of constant, linear and exponential functions with respect to time. Applying the Laplace transform technique to the model equation for the lower thermocline layer subject to each of three representative interfacial conditions yields compact-form solutions, a linear combination of which constitutes the final temperature profile. A systematic method for deriving solutions to the plug-flow problem having polynomial-type boundary conditions is also established. The effect of adiabatic exit boundary on solution behaviors proves to be negligible under the actual working conditions, which justifies the assumption of semi-infinite domain introduced in the solution procedure. Finally, the approximate solution is validated by comparing it with an exact solution obtained for a specific variation of inlet temperature. Excellent agreements between them suffice to show the necessity and utility of this work.

• Structural Engineering and Mechanics
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• 제45권1호
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• pp.95-110
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• 2013

In the recent decade, practical of wavelet technique is being utilized in various domain of science. Particularly, engineers are interested to the wavelet solution method in the time series analysis. Fundamentally, seismic responses of structures against time history loading such as an earthquake, illustrates optimum capability of systems. In this paper, a procedure using particularly discrete Haar wavelet basis functions is introduced, to solve dynamic equation of motion. In the proposed approach, a straightforward formulation in a fluent manner is derived from the approximation of the displacements. For this purpose, Haar operational matrix is derived and applied in the dynamic analysis. It's free-scaled matrix converts differential equation of motion to the algebraic equations. It is shown that accuracy of dynamic responses relies on, access of load in the first step, before piecewise analysis added to the technique of equation solver in the last step for large scale of wavelet. To demonstrate the effectiveness of this scheme, improved formulations are extended to the linear and nonlinear structural dynamic analysis. The validity and effectiveness of the developed method is verified with three examples. The results were compared with those from the numerical methods such as Duhamel integration, Runge-Kutta and Wilson-${\theta}$ method.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.707-719
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• 2014

In this paper, we investigate a variational discretization approximation of elliptic optimal control problems with control constraints. The state and the co-state are approximated by piecewise linear functions, while the control is not directly discretized. By using some proper intermediate variables, we derive a second-order convergence in $L^2$-norm and superconvergence between the numerical solution and elliptic projection of the exact solution in $H^1$-norm or the gradient of the exact solution and recovery gradient in $L^2$-norm. Then we construct a posteriori error estimates by using the superconvergence results and do some numerical experiments to confirm our theoretical results.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1989년도 하계종합학술대회 논문집
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• pp.116-120
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• 1989

The optimal control problem of linear Lumped Parameter Systems (LPS) and Distributed Parameter Systems (DPS) is studied by employing the technique of Walsh functions (WF). By the using the elegant operational properties of WF, a direct computational algorithm for evaluating the optimal control and trajectory of LPS and DPS is developed. Without the need of solving the traditional matrix Riccati equation, the WF approach in shown very simple in form and convenient for use of a computer. The approximation is in the sense of least squares employing WF as the basis and the results are in the piecewise constant and discrete form.

• 한국가스학회지
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• 제4권4호
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• pp.58-64
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• 2000

가스 저장$\cdot$ 공급 시설을 포함한 화학공정에서 측정된 데이터를 효과적으로 이용하기 위하여 정보의 손실의 최소화하면서 데이터를 압축하여 저장하고 재생할 수 있는 방법에 대한 연구가 진행되어 왔다 기존에 제안되었던 데이터 압축 저장 방법들의 단점을 극복하기 위하여, 부분 선형화 근사 방법과 k-means 클러스터링 알고리즘을 응용한 새로운 공정 데이터의 압축 방법을 제안하였다. 제안된 방법을 실공정 데이터에 적용하여 본 결과, 본 연구에서 제안된 방법이 기존의 방법보다 재현 능력이 우수함을 확인할 수 있었다.

• 대한전자공학회:학술대회논문집
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• 대한전자공학회 2006년도 하계종합학술대회
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• pp.425-426
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• 2006

Overdriving schemes are used to improve the response time of liquid crystal display. Typically they are implemented by using LUTs (look-up table) within an image processor. However, the size of LUT is limited by the physical memory size and system cost. In this paper, we present an improved method for LUT implementation using linear interpolation and piecewise least-square polynomial regression. Using the proposed method, the performance of LUT can be improved and memory size of that can be reduced.