• 한국근적외분광분석학회:학술대회논문집
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• 한국근적외분광분석학회 2001년도 NIR-2001
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• pp.1041-1041
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• 2001

Removal of variability in spectra data before the application of chemometric modeling will generally result in simpler (and presumably more robust) models. Particularly for sparsely sampled data, such as typically encountered in diode array instruments, the use of Savitzky-Golay (S-G) derivatives offers an effective method to remove effects of shifting baselines and sloping or curving apparent baselines often observed with scattering samples. The application of these convolution functions is equivalent to fitting a selected polynomial to a number of points in the spectrum, usually 5 to 25 points. The value of the polynomial evaluated at its mid-point, or its derivative, is taken as the (smoothed) spectrum or its derivative at the mid-point of the wavelength window. The process is continued for successive windows along the spectrum. The original paper, published in 1964 [1] presented these convolution functions as integers to be used as multipliers for the spectral values at equal intervals in the window, with a normalization integer to divide the sum of the products, to determine the result for each point. Steinier et al. [2] published corrections to errors in the original presentation [1], and a vector formulation for obtaining the coefficients. The actual selection of the degree of polynomial and number of points in the window determines whether closely situated bands and shoulders are resolved in the derivatives. Furthermore, the actual noise reduction in the derivatives may be estimated from the square root of the sums of the coefficients, divided by the NORM value. A simple technique to evaluate the actual convolution factors employed in the calculation by the software will be presented. It has been found that some software packages do not properly account for the sampling interval of the spectral data (Equation Ⅶ in [1]). While this is not a problem in the construction and implementation of chemometric models, it may be noticed in comparing models at differing spectral resolutions. Also, the effects on parameters of PLS models of choosing various polynomials and numbers of points in the window will be presented.

• 대한수학회보
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• 제50권1호
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• pp.241-261
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• 2013

In this paper, we find the coefficients for the Weierstrass ${\wp}(x)$ and ${\wp}^{{\prime}{\prime}}(x)$($x=\frac{1}{2}$, $\frac{\tau}{2}$, $\frac{\tau+1}{2}$)-functions in terms of the arithmetic identities appearing in divisor functions which are proved by Ramanujan ([23]). Finally, we reprove congruences for the functions ${\mu}(n)$ and ${\nu}(n)$ in Hahn's article [11, Theorems 6.1 and 6.2].

• 한국컴퓨터그래픽스학회논문지
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• 제21권5호
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• pp.1-10
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• 2015

본 연구는 가상 조경을 구성하는 다양한 종류의 디지털 잎을 쉽고 직관적으로 제작할 수 있는 저작도구 개발방법을 제안한다. 제안하는 저작도구의 핵심 시스템은 영상 워핑기반의 잎몸 윤곽선 변형 방법, 잎맥의 절차적 모델링 그리고 잎의 색과 명암 등을 표현하기 위한 수리모델기반 시각화 방법으로 구성된다. 우선 잎 영상을 입력으로 받아 잎몸에 대한 윤곽선 정보를 찾고, 특징기반 영상 워핑을 활용하여 다양한 잎몸 형상을 직관적인 구조에서 쉽게 생성할 수 있는 잎몸 변형 방법을 설계한다. 그리고 계산된 잎몸 윤곽선을 기반으로 잎몸 형상에 적합한 자연스러운 잎맥 패턴을 생성하는 일반화된 절차적 모델링 방법을 저작도구에 맞게 구현한다. 마지막으로 약수 함수의 합성 기반의 수리모델을 활용하여 잎의 색, 명암 그리고 시간에 따른 변화를 표현할 수 있는 시각화 기능을 적용한다. 제안한 저작도구를 활용하여 제작된 디지털 잎이 다양한 3차원 디지털 콘텐츠 분야에 활용 가능하도록 텍스쳐 지원 기능을 제공한다.