• 대한수학회보
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• 제49권6호
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• pp.1131-1145
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• 2012

The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $$\{({\alpha}(t,x^{\Delta}(t)))^{\Delta}-a(t){\phi}_p(x^{\sigma}(t))+f({\sigma}(t),x^{\sigma}(t))=0,\;{\Delta}-a.e.\;t{\in}I\\x^{\sigma}(0)=0,\\{\beta}_1x^{\sigma}(1)+{\beta}_2x^{\Delta}({\sigma}(1))=0,$$ where ${\beta}_1$, ${\beta}_2$ > 0, $I=[0,1]^{k^2}$, ${\alpha}({\cdot},x({\cdot}))$ is an operator of $p$-Laplacian type, $\mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.

• 한국방송∙미디어공학회:학술대회논문집
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• 한국방송공학회 1996년도 학술대회
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• pp.9-15
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• 1996

In this paper, we propose a new detector based on the median-shift sign. We call it the median-shift sign (MSS) detector, which is an extension of the classical sign detector. We first analyze the problem of detecting a dc signal in noise of known probability density function (pdf). The MSS detector with the optimum median-shift value, the optimum MSS detector, performs better than the sign detector in Gaussian noise: it has the best performance among the detectors compared in Laplacian and Cauchy noise. It is shown that the MSS detectors with constant median-shift values are nearly equal to the optimum MSS detector. We also analyze the problem of detecting a dc signal when only partial information is available on the noise. The MSS detectors with constant median-shift values are almost equal to the sign detector in Gaussian noise: they perform better than the sign and Wilcoxon detectors for most signal ranges in Laplacian and Cauchy noise.

• 대한수학회보
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• 제47권2호
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• pp.411-422
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• 2010

By using the fixed point index theory, we investigate the existence of at least two positive solutions for p-Laplace equation with sign-changing nonlinear terms $(\varphi_p(u'))'+a(t)f(t,u(t),u'(t))=0$, subject to some boundary conditions. As an application, we also give an example to illustrate our results.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1171-1184
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• 2010

In this paper, by using fixed point theorems in cones, the existence of positive solutions is considered for nonlinear m-point boundary value problem for the following second-order dynamic equations on time scales $({\phi}(u^{\Delta}))^{\nabla}+a(t)f(t,\;u(t))=0$, t $\in$ (0, T), $u(0)=\sum\limits^{m-2}_{i=1}a_iu(\xi_i)$, $\phi(u^{\Delta}(T))=\sum\limits^{m-2}_{i=1}b_i{\phi}(u^{\Delta}(\xi_i))$, where $\phi$ : R $\rightarrow$ R is an increasing homeomorphism and positive homomorphism and ${\phi}(0)=0$. In [27], we obtained the existence results of the above problem for an increasing homeomorphism and positive homomorphism with sign changing nonlinearity. The purpose of this paper is to supplement with a result in the case when the nonlinear term f is nonnegative, and the most point we must point out for readers is that there is only the p-Laplacian case for increasing homeomorphism and positive homomorphism due to the sign restriction. As an application, one example to demonstrate our results are given.

• 방송공학회논문지
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• 제17권2호
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• pp.388-399
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• 2012

본 논문에서는 지역 특징 추출 방법 중 하나인 SURF를 개선시켜 모바일 환경에 적합한 특징 추출 및 정합 방법에 대하여 기술한다. 모바일 환경에서 최적의 성능을 내기 위해 크게 세 가지 방법을 제안한다. 첫 번째는 SURF 기술자의 차원을 축소시키는 방법이다. 기존의 64차원과 여러 차원의 기술자들의 성능을 비교 분석한다. 두 번째로 고속 헤시안 검출기에서 헤시안 행렬의 대각합을 통해 계산되는 라플라시안 부호를 사용하여 정합 성능을 높인다. 즉, 부호가 같으면 같은 특성의 특징점으로 여겨 정합하고 그렇지 않으면 정합하지 않는다. 세 번째는 특징점간의 거리 측정 시 사용하는 거리 비율을 실험하고, 실험을 통해 얻어진 거리 비율을 사용하여 정합의 성능을 높였다. 마지막으로, 기존의 시스템과 제안한 시스템의 성능을 비교하여 제안한 시스템의 성능 향상을 검증하고, 제안한 시스템이 비교적 정합률의 성능 저하 없이 응답속도를 크게 개선함을 보였다.

• 전자공학회논문지B
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• 제32B권12호
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• pp.1591-1602
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• 1995

A hybrid approach which includes edge- and region-based methods is considered. The modified non-linear Laplacian(MNL) filter is used for feature extraction. The matching algorithm has three steps which are edge, signed region, and residual region matching. At first, the edge points are matched using the sign and direction of edges. Then, the disparity is propagated from edge to inside region. A variable window is used to consider the local method which give accurate matched points and area-based method which can obtain full-resolution disparity map. In addition, a new relaxation algorithm for considering matching possibility derived from normalized error and regional continuity constraint is proposed to reduce the mismatched points. By the result of simulation for various images, this algorithm is insensitive to noise and gives full- resolution disparity map.

• 대한수학회지
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• 제56권4호
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• pp.857-867
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• 2019

Suppose that G = (V, E) is a connected locally finite graph with the vertex set V and the edge set E. Let ${\Omega}{\subset}V$ be a bounded domain. Consider the following quasilinear elliptic equation on graph G $$\{-{\Delta}_{pu}={\lambda}K(x){\mid}u{\mid}^{p-2}u+f(x,u),\;x{\in}{\Omega}^{\circ},\\u=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}^{\circ}$ and ${\partial}{\Omega}$ denote the interior and the boundary of ${\Omega}$, respectively, ${\Delta}_p$ is the discrete p-Laplacian, K(x) is a given function which may change sign, ${\lambda}$ is the eigenvalue parameter and f(x, u) has exponential growth. We prove the existence and monotonicity of the principal eigenvalue of the corresponding eigenvalue problem. Furthermore, we also obtain the existence of a positive solution by using variational methods.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.113-131
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• 2024

In this paper we give conditions for the existence of, and describe the asymtotic behavior of, radial positive solutions of the nonlinear elliptic equation of Emden-Fowler type with convection term ∆_p u + 𝛼|u|^q-1u + 𝛽x.∇(|u|^q-1u) = 0 for x ∈ ℝ^N, where p > 2, q > 1, N ≥ 1, 𝛼 > 0, 𝛽 > 0 and ∆_p is the p-Laplacian operator. In particular, we determine ${\lim}_{r{\rightarrow}}{\infty}\,r^{\frac{p}{q+1-p}}\,u(r)$ when $\frac{{\alpha}}{{\beta}}$ > N > p and $q\,{\geq}\,{\frac{N(p-1)+p}{N-p}}$.