• Journal of the Institute of Electronics Engineers of Korea SP
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• v.42 no.5 s.305
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• pp.47-54
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• 2005

In general, wavelet coefficients are composed of a few large coefficients and a lot of small coefficients. In this paper, we propose image denoising algorithm using Bernoulli-Gaussian mixture model based on sparse characteristic of wavelet coefficient. The Bernoulli-Gaussian mixture is composed of the multiplication of Bernoulli random variable and Gaussian mixture random variable. The image denoising is performed by using Bayesian estimation. We present an effective denoising method through simplified parameter estimation for Bernoulli random variable using local expected squared error. Simulation results show our method outperforms the states-of-art denoising methods when using orthogonal wavelets.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.83-83
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• 2021

수리구조물로 인한 유황변화와 함께 기후변화로 기인하는 강우변동성 및 온도 증가는 수생태 전반에 악영향을 미치는 주요 인자로 작용하고 있다. 특히, 최근 가뭄으로 인한 유황감소 및 폭염 등으로 여름철 녹조의 발생 빈도 및 강도 증가가 지속적으로 증가하고 있다. 본 연구에서는 하천에서 계측되고 있는 Cyanobacteria 개체수를 기반으로 녹조발생 여부를 전망할 수 있는 모형을 개발하고자 한다. Cyanobacteria 개체수를 기준으로 녹조발생 여부를 판단할 수 있도록 기준값(threshold)을 설정하고 binary 형태로 시계열을 구성하였다. 이를 Bernoulli 모형에 적합하여 녹조 발생 여부를 판단할 수 있도록 모형을 개발하였다. 하천을 따라 나타나는 녹조는 시공간적으로 유사한 특성을 가지며, 이러한 점을 고려하여 여러 관측지점을 동시에 모델링하는 것이 모형의 효율성과 예측성 측면에서 유리하다. 본 연구에서는 낙동강을 따라 여러 녹조관측지점을 대상으로 동시에 모델링이 가능하도록 다변량 Bernoulli 모형 기반의 녹조 예측 모형을 제시하고 과거 자료를 대상으로 모형의 적합성을 평가하였다. 다양한 지표를 기준으로 교차검증을 수행하였으며, 기존 물리적 모델에 비해 모형의 예측성능 및 효율성 측면에서 우수성을 확인할 수 있었다.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.81-87
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• 2002

The weighted Hardy＇s inequality is known as (equation omitted) where -$\infty$$\leq$a$\leq$b$\leq$$\infty$ and 1 < p < $\infty$. The purpose of this article is to provide a useful formula to express the weight r(x) in terms of s(x) or vice versa employing a Bernoulli equation having the other weight as coefficients.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.11-24
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• 2007

The main purpose of this paper is to use the properties of primitive characters, Gauss sums and Ramanujan's sum to study the hybrid mean value of generalized Bernoulli numbers, general Kloosterman sums and Gauss sums, and give two asymptotic formulae.

• Journal of the Korean Mathematical Society
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• v.44 no.1
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• pp.1-10
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• 2007

The purpose of this paper is to define generalized twisted q-Bernoulli numbers by using p-adic q-integrals. Furthermore, we construct a q-analogue of the p-adic generalized twisted L-functions which interpolate generalized twisted q-Bernoulli numbers. This is the generalization of Kim's h-extension of p-adic q-L-function which was constructed in [5] and is a partial answer for the open question which was remained in [3].

• Coupled systems mechanics
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• v.7 no.5
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• pp.635-647
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• 2018

Dynamic problems arising from the Euler-Bernoulli beam model with inhomogeneous elastic properties are considered. The method of Green's function and perturbation theory are employed to find the deflection in the beam correct to the first-order. Eigenvalue problems appearing from transverse vibrations of inhomogeneous beams in linear and nonlinear cases are also discussed.

• Journal of applied mathematics & informatics
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• v.34 no.1_2
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• pp.145-156
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• 2016

It is known that certain convolution sums can be expressed as a combination of divisor functions and Bernoulli formula. In this article, we consider relationship between fifth-order combinatoric convolution sums of divisor functions and Bernoulli polynomials. As applications of these identities, we give a concrete interpretation in terms of the procedural modeling method.

• Journal of the Korean Mathematical Society
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• v.42 no.6
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• pp.1137-1152
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• 2005

In this article we prove the existence of the solution to the mixed problem for Euler-Bernoulli beam equation with memory condition at the boundary and we study the asymptotic behavior of the corresponding solutions. We proved that the energy decay with the same rate of decay of the relaxation function, that is, the energy decays exponentially when the relaxation function decay exponentially and polynomially when the relaxation function decay polynomially.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.987-998
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• 2015

In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers of the second kind.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.277-283
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• 2008

The paper deals with the values at the negative integers of a certain Dirichlet series related to the Riemann zeta function and with the expression of these values in terms of Bernoulli numbers.