• Korean Journal of Mathematics
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• 제22권4호
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• pp.633-644
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• 2014

We get one theorem that there exists a unique solution for the fourth order semilinear elliptic Dirichlet boundary value problem when the number 0 and the coefficient of the semilinear part belong to the same open interval made by two successive eigenvalues of the fourth order elliptic eigenvalue problem. We prove this result by the contraction mapping principle. We also get another theorem that there exist at least two solutions when there exist n eigenvalues of the fourth order elliptic eigenvalue problem between the coefficient of the semilinear part and the number 0. We prove this result by the critical point theory and the variation of linking method.

• 대한수학회보
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• 제55권1호
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• pp.297-310
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• 2018

In this paper, a nonlinear high-order difference scheme is proposed to solve the Extended-Fisher-Kolmogorov equation. The existence, uniqueness of difference solution and priori estimates are obtained. Furthermore, the convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete $L^{\infty}-norm$. Some numerical examples are given in order to validate the theoretical results.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권1호
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• pp.13-20
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• 2005

This paper addresses a new blind channel equalization method using fourth-order cumulants of channel inputs and a three-layer neural network equalizer. The proposed algorithm is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum-phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple recordering and scaling. By using this estimated deconvolution matrix, which is the inverse of the over-sampled unknown channel, a three-layer neural network equalizer is implemented at the receiver. In simulation studies, the stochastic version of the proposed algorithm is tested with three-ray multi-path channels for on-line operation, and its performance is compared with a method based on conventional second-order statistics. Relatively good results, withe fast convergence speed, are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

• 한국통신학회논문지
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• 제31권6C호
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• pp.629-636
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• 2006

Array 신호처리에서 복소 지수함수의 합으로 구성된 신호의 파라미터를 추정하는데 고차 통계를 이용할 수 있다. 본 논문에서는 기존의 MPM(matrix pencil method)보다 효과적으로 DOA를 판별하기 위해 MPM에 4차 cumulant와 moment 통계량을 적용하였다. 4차 cumulant 통계량은 선형 배열안테나에 입사하는 신호에 포함된 Gaussian 잡음을 효과적으로 감소시킬 수 있다. Gaussian 잡음이 존재하는 환경에서 기존의 방법과 4차 통계량을 이용한 방법을 시뮬레이션 함으로써 SNR과 DOA 분해능에 대하여 성능을 분석하였다. 결과로써 4차 통계량을 이용한 MPM이 기존의 MPM보다 우수함을 보였으며, 또한 4차 moment보다는 4차 cumulant 적용이 더 우수함을 증명하였다.

• 한국광학회지
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• 제2권4호
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• pp.214-218
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• 1991

레이저로 여기된 원자에서 방출하는 형광과 여기용 레이저 빛이 중첩 되었을 때 일어나는 4차 간섭현상을 조사하였다. 간섭무늬 선명도(visibility)가 50% 이상의 비고전적 효과가 나타나는 조건을 검토하였으며 2차 간섭무늬 선명도와 비교하였다. 여기레이저를 원자에 입사시킨 후 오랜 시간이 경과하면 $\Omega/\beta$>>1 일 때 2차 간섭현상을 소멸하는 데 반하여 4차 간섭은 존재함을 알 수 있다.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.601-612
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• 2023

The existence of solution of the fractional order differential equations is very important mathematical field. Thus, in this work, we discuss, under some hypothesis, the existence of a positive solution for the nonlinear fourth order fractional boundary value problem which includes the p-Laplacian transform. The proposed method in the article is based on the fixed point theorem. More precisely, Krasnosilsky's theorem on a fixed point and some properties of the Green's function were used to study the existence of a solution for fourth order fractional boundary value problem. The main theoretical result of the paper is explained by example.

• Proceedings of the Jangjeon Mathematical Society
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• 제20권2호
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• pp.183-191
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• 2017

We get one theorem that there exist solutions for the fourth order semi- linear elliptic Dirichlet boundary value problem with fully nonlinear term. We prove this result by the critical point theory and the variation of linking method.

• 대한전자공학회논문지SP
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• 제43권2호
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• pp.87-92
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• 2006

Array 신호처리에서 복소 지수함수의 합으로 구성된 신호의 파라미터를 추정하는데 고차 통계를 이용할 수 있다. 본 논문에서는 4차 cumulant를 이용한 고차 Matrix Pencil method(MPM)를 제안하였다. 4차 cumulant는 Gaussian 잡음를 억제할 수 있기 때문에, MPM의 응답은 기존의 방법에 비하여 더 좋은 잡음 면역을 가지고 있다. 본 논문에서는 높은 정확성을 가지는 MPM의 모든 장점을 유지하면서 성공적으로 고차 MPM을 공식화하였다. 그리고 Numerical simulation을 통해서 본 논문에서 제안된 4차 cumulant를 이용한 방법이 Gaussian 잡음환경에서 더 우수한 DOA 분해능을 가지고 있음을 증명하였다.

• Journal of applied mathematics & informatics
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• 제32권3_4호
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• pp.511-527
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• 2014

This paper provides a new application similar to the Local Defect Correction (LDC) technique to solve Poisson problem -u"(x) = f(x) with Dirichlet boundary conditions. The exact solution is supposed to have high activity in some region of the domain. LDC is combined with a fourth order compact scheme which is recently developed in Abbas (Num. Meth. Partial differential equations, 2013). Numerical tests illustrate the interest of this application.

• 센서학회지
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• 제21권2호
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• pp.109-113
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• 2012

We propose an improved interpolating equation to express temperature-resistance characteristics for modern industrial platinum resistance thermometers (PRTs). Callendar-van Dusen equation which has been widely used for platinum resistance thermometer fails to fully describe temperature characteristics of high quality PRTs and leaves systematic residual when the calibration point include temperatures above $300^{\circ}C$. Expanding Callendar-van Dusen to higher-order polynomial drastically improves the uncertainty of the fitting even with reduced degrees of freedom of the fitting. We found that in the fourth-order polynomial fitting, the third-order and fourth-order coefficients have a strong correlation. Using the correlation, we suggest an improved interpolating equation in the form of fourth-order polynomial, but with three fitting parameters. Applying this interpolating equation reduced the uncertainty of the fitting to 32 % of that resulted from the traditional Callendar-van Dusen. This improvement was better than that from a simple third-order polynomial despite that the degrees of the freedom of the fitting was the same.