• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제22권2호
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• pp.91-100
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• 2018

In this paper, we propose a new method for template matching, patch ratio, to inpaint unknown pixels. Before this paper, many inpainting methods used sum of squared differences(SSD) or sum of absolute differences(SAD) to calculate distance between patches and it was very useful for closest patches for the template that we want to fill in. However, those methods don't consider about geometric similarity and that causes unnatural inpainting results for human visuality. Patch ratio can cover the geometric problem and moreover computational cost is less than using SSD or SAD. It is guaranteed about finding the most similar patches by Cauchy-Schwarz inequality. For ignoring unnecessary process, we compare only selected candidates by priority calculations. Exeperimental results show that the proposed algorithm is more efficent than Criminisi's one.

• 대한수학회지
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• 제45권2호
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• pp.455-466
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• 2008

Current studies on products of analytic functionals have been based on applying convolution products in D' and the Fourier exchange formula. There are very few results directly computed from the ultradistribution space Z'. The goal of this paper is to introduce a definition for the product of analytic functionals and construct a new multiplier space $F(N_m)$ for $\delta^{(m)}(s)$ in a one or multiple dimension space, where Nm may contain functions without compact support. Several examples of the products are presented using the Cauchy integral formula and the multiplier space, including the fractional derivative of the delta function $\delta^{(\alpha)}(s)$ for $\alpha>0$.

• 대한수학회논문집
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• 제18권2호
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• pp.263-280
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• 2003

We prove weighted L$^{p}$ estimates with respect to the non-isotropic norm for the (equation omitted)-equation on real ellipsoids, where weights are powers of the distance to the boundary. The non-isotropic norm is smaller than the usual norm, by a factor which is equal to the distance to the boundary in the complex tangential component and which is equal to the m-th root of the distance to the boundary in the complex normal component. Here n is the maximal order of contact of the boundary of the real ellipsoid with complex analytic curves.

• 대한수학회지
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• 제45권1호
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• pp.249-271
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• 2008

We prove the Hyers-Ulam stability of linear d-isometries in linear d-normed Banach modules over a unital $C^*-algebra$ and of linear isometries in Banach modules over a unital $C^*-algebra$. The main purpose of this paper is to investigate d-isometric $C^*-algebra$ isomor-phisms between linear d-normed $C^*-algebras$ and isometric $C^*-algebra$ isomorphisms between $C^*-algebras$, and d-isometric Poisson $C^*-algebra$ isomorphisms between linear d-normed Poisson $C^*-algebras$ and isometric Poisson $C^*-algebra$ isomorphisms between Poisson $C^*-algebras$. We moreover prove the Hyers-Ulam stability of their d-isometric homomorphisms and of their isometric homomorphisms.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.763-771
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• 2009

T.H. Kim, H.K. Xu, [Convergence of the modified Mann's iteration method for asymptotically strict pseudo-contractions, Nonlinear Anal.(2007),doi:l0.l016/j.na.2007.02.029.] proved the strong convergence for asymptotically strict pseudo-contractions by the classical CQ iterative method. In this paper, we apply the monotone CQ iterative method to modify the classical CQ iterative method of T.H. Kim, H.K. Xu, and to obtain the strong convergence theorems for asymptotically strict pseudo-contractions. In the proved process of this paper, Cauchy sequences method is used, so we complete the proof without using the demi-closedness principle, Opial's condition or others about weak topological technologies. In addition, we use a ingenious technology to avoid defining that F(T) is bounded. On the other hand, we relax the restriction on the control sequence of iterative scheme.

• Journal of Power Electronics
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• 제13권4호
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• pp.712-718
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• 2013

This paper proposes a control method for reducing the total harmonic distortion (THD) of the grid current of three-phase grid-connected inverter systems when the grid voltage is distorted. The THD of the grid current caused by grid voltage harmonics is derived by considering the phase delay and magnitude attenuation due to the hardware low-pass filter (LPF). The Cauchy-Schwarz inequality theory is used in order to search more easily for the minimum point of the THD. Both the gain and angle of the compensation voltage at the minimum point of the THD of the grid current are derived with the variation of cut-off frequencies of the hardware LPF. Simulation and experimental results show the validity of the proposed control methods.

• 비파괴검사학회지
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• 제32권3호
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• pp.296-301
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• 2012

This paper describes an analytic method for infrared thermography to detect surface cracks in thin plates. Traditional thermographic method uses the spatial contrast of a thermal field, which is often corrupted by noise in the experiment induced mainly by emissivity variations of target surfaces. This study developed a robust analytic approach to crack detection for thermography using the holomorphic function of a temperature field in thin plate under steady-state thermal conditions. The holomorphic function of a simple temperature field was derived for 2-D heat flow in the plate from Cauchy-Riemann conditions, and applied to define a contour integral that varies depending on the existence and strength of singularity in the domain of integration. It was found that the contour integral at each point of thermal image reduced the noise and temperature variation due to heat conduction, so that it provided a clearer image of the singularity such as cracks.

• 비파괴검사학회지
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• 제31권6호
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• pp.665-670
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• 2011

In this paper, a new approach to detect surface cracks from a noisy thermal image in the infrared thermography is presented using an holomorphic characteristic of temperature field in a thin plate under steady-state thermal condition. The holomorphic function for 2-D heat flow field in the plate was derived from Cauchy Riemann conditions to define a contour integral that varies according to the existence and strength of a singularity in the domain of integration. The contour integral at each point of thermal image eliminated the temperature variation due to heat conduction and suppressed the noise, so that its image emphasized and highlighted the singularity such as crack. This feature of holomorphic function was also investigated numerically using a simple thermal field in the thin plate satisfying the Laplace equation. The simulation results showed that the integral image selected and detected the crack embedded artificially in the plate very well in a noisy environment.

• Kyungpook Mathematical Journal
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• 제48권4호
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• pp.529-543
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• 2008

It is shown that every almost linear mapping h : $A{\rightarrow}B$ of a unital PoissonC*-algebra A to a unital Poisson C*-algebra B is a Poisson C*-algebra homomorph when $h(2^nuy)\;=\;h(2^nu)h(y)$ or $h(3^nuy)\;=\;h(3^nu)h(y)$ for all $y\;\in\;A$, all unitary elements $u\;\in\;A$ and n = 0, 1, 2,$\codts$, and that every almost linear almost multiplicative mapping h : $A{\rightarrow}B$ is a Poisson C*-algebra homomorphism when h(2x) = 2h(x) or h(3x) = 3h(x for all $x\;\in\;A$. Here the numbers 2, 3 depend on the functional equations given in the almost linear mappings or in the almost linear almost multiplicative mappings. We prove the Cauchy-Rassias stability of Poisson C*-algebra homomorphisms in unital Poisson C*-algebras, and of homomorphisms in Poisson Banach modules over a unital Poisson C*-algebra.