• Korean Journal of Mathematics
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• 제28권3호
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• pp.449-457
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• 2020

We focus on the interations of the weighted Berezin transform T_α on L^p(τ), where τ is the invariant measure on the complex unit ball B_n. Iterations of T_α on L¹_R(τ) the space of radial integrable functions played important roles in proving 𝓜-harmonicity of bounded functions with invariant mean value property. Here, we introduce more properties on iterations of T_α on L¹_R(τ) and observe differences between the iterations of T_α on L1(τ) and L^p(τ) for 1 < p < ∞.

• 전자공학회논문지B
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• 제30B권4호
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• pp.44-55
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• 1993

In this paper, we proposed a new optical method for the efficient recognition of Korean characters. There are six filters in the proposed method which employed the concepts of amplitude-modulated phase-only filter(AMPOF) and spatial frequency modulation(SFM). Here, amplitude modulation is used to achieve improved correlation discrimination and SFM is to reduce the number of filters. We also used a simplified synthetic discriminant function(SDF) for distortion invariance of input image. In order to recognize the partial rotation invariant Korean characters, the proposed distortion invariant minimum average correlation energy (MACE) filter is synthesized SFM, partial rotation invariant filter (PRIF), AMPOF and MACE for partial rotation invariance in the frequency domain. The advantage of the proposed filters is to supress the sidelobes of cross correlation peak away from the autocorrelation peak and to produce sharp correlation peaks. We performed simulation and optical experiment for some of Korea characters using the proposed method. The results show that the proposed method has more improved discriminant ability and reduced processing time than the conventional methods.

• 한국측량학회지
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• 제28권3호
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• pp.353-359
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• 2010

본 논문은 Scale Invariant Feature Transform(SIFT) 기술자를 이용한 매칭 방법을 개선하여 고해상도영상에서 보다 많은 매칭쌍(tie points)을 추출함으로써 고해상도영상 자동기하보정의 결과향상을 목적으로 한다. 이를 위해 기준(reference)영상과 대상(sensed)영상의 특징점(interest points)간의 위치관계를 추가적으로 이용하여 매칭쌍을 추출하였다. SIFT 기술자를 이용하여 어핀(affine)변환계수를 추정한 후, 이를 통해 대상영상의 특징점 좌표를 기준영상 좌표체계로 변환하였다. 변환된 대상영상의 특징점과 기준영상의 특징점간의 공간거리(spatial distance)정보를 이용하여 최종적으로 매칭쌍을 추출하였다. 추출된 매칭쌍으로 piecewise linear function을 구성하여 고해상도 영상간 자동기하보정을 수행하였다. 제안한 기법을 통하여, 기존 SIFT 기법에 의해 추출한 결과에 비해 영상 전역에 걸쳐 고르게 분포된 다수의 매칭쌍을 추출할 수 있었다.

• 대한수학회지
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• 제34권4호
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• pp.959-971
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• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• 한국농공학회지
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• 제37권3_4호
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• pp.34-47
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• 1995

It is experienced fact as a regular annual event that the structure to he designed on unreasonable flood for the agricultural structures including reservoirs have been brought not only loss of lives, but also enormous property damage. For the solution of this problem at issue, this study was conducted to develop an optimal runoff hydrograph model by comparison of the peak flows and time to peak between observed and simulated flows derived by linear time-invariant and linear time-variant models under the condition of having a short duration of heavy rainfall with uniform rainfall intensity at nine small watersheds which are within the range of 55.9 to 140.7 square kilometers in area in Han, Geum, Nagdong and Yeongsan Rivers. The results obtained through this study can be summarized as follows. 1. Storage constants and Gamma function arguments were calculated within the range of 1.2 to 6.42 and of 1.28 to 8.05 respectively by the moment method as the parameters for the analysis of runoff hydrograph based on linear time-invariant model. 2. Parameters for both linear time-invariant and linear time-variant models were calibrated with nine gaged watershed data, using a trial and error method. The resulting parameters including Gamma function argument, N and storage constant, K for linear time-invariant model were related statistically to watershed characteristic variables such as area, slope, length of main stream and the centroid length of the basin. 3. Average relative errors of the simulated peak discharge of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 0.75 and 5.42 percent respectively to the peak of observed runoff hydrographs. Correlation coefficients for the statistical analysis in the same condition were shown to be 0.999 and 0.978 with a high significance respectively. Therefore, it can be concluded that the accuracy of a linear time-variant model is approaching more closely to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 4. Average relative errors of the time to peak of calibrated runoff hydrographs by using linear time-variant and linear time-invariant models were shown to be 16.44 and 19.89 percent respectively to the time to peak of observed runoff hydrographs. Correlation coefficients in the same condition were also shown to be 0.999 and 0.886 with a high significance respectively. 5. It can be seen that the shape of simulated hydrograph based on a linear time- variant model is getting closer to the observed runoff hydrograph than that of a linear time-invariant model in the applied watersheds. 6. Two different models were verified with different rainfall-runoff events from data for the calibration by relative error and correlation analysis. Consequently, it can be generally concluded that verification results for the peak discharge and time to peak of simulated runoff hydrographs were in good agreement with those of calibrated runoff hydrographs.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2004년도 ICCAS
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• pp.1623-1628
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• 2004

In the 3-dimensional cyclic Lotka-Volterra equations, we show the solution on the invariant hyperplane. In addition, we show the existence of the invariant hyperplane by the center manifold theorem under the some conditions. With this result, we can lead the hyperplane of the n-dimensional cyclic Lotka-Volterra equaions. In other section, we study the 3- or 4-dimensional Hamiltonian Lotka-Volterra equations which satisfy the Jacobi identity. We analyze the solution of the Hamiltonian Lotka- Volterra equations with the functions called the split Liapunov functions by [4], [5] since they provide the Liapunov functions for each region separated by the invariant hyperplane. In the cyclic Lotka-Volterra equations, the role of the Liapunov functions is the same in the odd and even dimension. However, in the Hamiltonian Lotka-Volterra equations, we can show the difference of the role of the Liapunov function between the odd and the even dimension by the numerical calculation. In this paper, we regard the invariant hyperplane as the important item to analyze the motion of Lotka-Volterra equations and occur the chaotic orbit. Furtheremore, an example of the asymptoticaly stable and stable solution of the 3-dimensional cyclic Lotka-Volterra equations, 3- and 4-dimensional Hamiltonian equations are shown.

• 대한수학회지
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• 제26권1호
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• pp.143-157
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• 1989

• 한국산업정보학회논문지
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• 제9권2호
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• pp.81-88
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• 2004

잡음을 갖는 영상의 크기와 회전불변 패턴인식을 위한 광 웨이블릿 CHF-fSDF((wavelet circular harmonic function-filter modulation synthetic discriminant function, WCHF-fSDF) 필터를 제안하였다. 웨이블릿 CHF-fSDF 필터는 기준영상에 대하여 크기변화된 영상들을 웨이블릿 변환한 후, 이들로부터 추출한 단일 원형고조함수를 학습영상으로 사용하여 합성한다. 제안된 광 웨이블릿 CHF-fSDF 필터는 정합필터의 형태로서 전통적인 4f 광 상관기에 적용할 수 있도록 하였다. 컴퓨터 모의실험을 통하여 제안된 필터는 크기변화와 회전에 무관한 상관출력을 나타내며 특히 잡음환경하에서 유용함을 확인하였다.

• 대한수학회지
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• 제55권3호
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• pp.623-669
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• 2018

In Donaldson-Thomas theory, moduli spaces are locally the critical locus of a holomorphic function defined on a complex manifold. In this paper, we develop a theory of critical virtual manifolds which are the gluing of critical loci of holomorphic functions. We show that a critical virtual manifold X admits a natural semi-perfect obstruction theory and a virtual fundamental class $[X]^{vir}$ whose degree $DT(X)=deg[X]^{vir}$ is the Euler characteristic ${\chi}_{\nu}$(X) weighted by the Behrend function ${\nu}$. We prove that when the critical virtual manifold is orientable, the local perverse sheaves of vanishing cycles glue to a perverse sheaf P whose hypercohomology has Euler characteristic equal to the Donaldson-Thomas type invariant DT(X). In the companion paper, we proved that a moduli space X of simple sheaves on a Calabi-Yau 3-fold Y is a critical virtual manifold whose perverse sheaf categorifies the Donaldson-Thomas invariant of Y and also gives us a mathematical theory of Gopakumar-Vafa invariants.

• 대한전자공학회논문지
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• 제26권6호
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• pp.97-101
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• 1989

변형불변 패턴인식을 실현하기 위하여 크기와 회전변위에 대해 불변인 극-로가리즘 좌표변환을 이용하였고, 좌표 변환을 수행하기 위하여 Lee 방식의 투과함수를 갖는 CGH를 CAD용 포토(UV light)패턴 발생기에 의해 마스크로 제작하였다. 광학적으로 좌표변환된 입력패턴은 본 논문에서 제시한 광상관기에 입력되었으며, 실시간 홀로그래피에 의한 기록매질로서 $BaTiO_3$ 단결정을 정합필터로 사용하였다. 본 논문에서 제시한 광상관기를 사용하여 크기와 입력에 대한 자기상관값의 변화를 실험적으로 제시함으로서 변형불변 패턴인식을 증명하였다.