• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.159-169
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• 2005

An algorithmic approach to degree reduction of rational Bezier curves is presented. The algorithms are based on the degree reduction of polynomial Bezier curves. The method is introduced with the following steps: (a) convert the rational Bezier curve to polynomial Bezier curve by using homogenous coordinates, (b) reduce the degree of polynomial Bezier curve, (c) determine weights of degree reduced curve, (d) convert the Bezier curve obtained through step (b) to rational Bezier curve with weights in step (c).

• 충청수학회지
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• 제29권2호
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• pp.267-281
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• 2016

In this paper, we consider multi-degree reduction of $B{\acute{e}}zier$ curves with continuity of any (r, s) order with respect to $L_2$ norm. With help of matrix theory about generalized inverses we can use Lagrange multipliers to obtain the degree reduction matrix in a very simple form as well as the degree reduced control points. Also error analysis comparing with the least squares degree reduction without constraints is given. The advantage of our method is that the relationship between the optimal multi-degree reductions with and without constraints of continuity can be derived explicitly.

• 말소리와 음성과학
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• 제12권2호
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• pp.9-16
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• 2020

The present study examines the degree of suffix reduction that occurs when the Korean suffix [-nɨn] was attached to the root in spontaneous Seoul Korean speech. Specifically, it focuses on the degrees of reduction produced by individual speakers. The degree of reduction was assessed as the duration of the suffix [-nɨn] to clarify the continuum between the full and reduced forms. The results revealed that, first, the reduced forms of the suffix [-nɨn] were significantly distinguished from the full forms in the suffixation processes. Second, regarding parts of speech, the differences among individual speakers on the degrees of reduction were clearer when the suffix [-nɨn] was attached to verbs, rather than nouns and pronouns. Finally, the length of a root played a critical role in determining the degree of reduction of the suffix [-nɨn]. The degrees of reduction for individual speakers significantly differed when the suffix [-nɨn] was attached to two-syllable roots than three- and four-syllable roots. In conclusion, individual differences in the degrees of reduction were likely to occur when the roots are verbs and when two-syllable roots.

• 한국정보과학회논문지:시스템및이론
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• 제26권8호
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• pp.875-883
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• 1999

서로 다른 기하학적 모델링 시스템에 사용되는 곡선 및 곡면의 자료 교환에서, 시스템이 지원하는 그 곡선 및 곡면의 최대 차수에 제한이 있을 때, 낮은 차수로의 차수 감소가 필요하다. 본 논문에서는 근사 변환에 의한 B-spline 곡선의 차수 감소 방법을 제시한다. 기존의 Bzier 곡선의 차수감소 방법들을 적용하고, 그 방법들을 비교 분석한다. B-spline 곡선의 knot 제거 알고리즘이 자료 감소를 위해 차수 감소 과정에 적용된다.Abstract The degree reduction of B-splines is required in exchanging parametric curves and surfaces of the different geometric modeling systems because some systems limit the supported maximal degree. We propose an approximate degree reduction method of B-spline curves using the existing Bzier degree reduction methods. Knot removal algorithm is used to reduce data in the degree reduction process.

• 한국컴퓨터정보학회논문지
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• 제8권1호
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• pp.7-12
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• 2003

시스템이 지원하는 곡선 및 곡면의 최대 차수에 제한이 있을 때, 낮은 차수로의 차수 감소가 필요하다. 본 논문에서는 근사 변환의 한 방법으로써 NURBS 곡선의 차수 감소 방법을 소개한다. 이 방법은 기존 Eck의 B$\'{e}$zier 차수 감소 방법과 자료 감소를 위해 knot 제거 알고리즘이 적용된다. 제시하는 방법은 안정적일 뿐만 아니라 수학적으로도 단순하므로 이해와 구현이 용이하다.

• Journal of applied mathematics & informatics
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• 제26권3_4호
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• pp.605-614
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• 2008

In this paper, we find the matrix representation of multi-degree reduction by $L_{\infty}$ of $B{\acute{e}}zier$ curves with constraints of endpoints continuity. Using the basis transformation between Chebyshev polynomials and Bernstein polynomials we can derive the matrix representation of multi-degree reduction of $B{\acute{e}}zier$ with respect to $L_{\infty}$ norm.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.57-81
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• 2024

We introduce a new degree reduction method for homogeneous symmetric polynomials on binary variables that generalizes the conventional degree reduction methods on monomials introduced by Freedman and Ishikawa. We also design an degree reduction algorithm for general polynomials on binary variables, simulated on the graph coloring problem for random graphs, and compared the results with the conventional methods. The simulated results show that our new method produces reduced quadratic polynomials that contains less variables than the reduced quadratic polynomials produced by the conventional methods.

• 한국컴퓨터정보학회논문지
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• 제10권1호
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• pp.35-44
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• 2005

서로 다른 기하학적 모델링 시스템을 사용하는 곡선 및 곡면의 자료 교환에서, 시스템이 지원하는 B-spline 곡선 및 곡면의 최대 차수에 제한이 있을 때, 주어진 허용 오차 범위 내에서 낮은 차수로의 차수 감소가 필요하다 본 논문에서는 근사 변환의 한 방법인 B-spline 곡선의 차수 감소 방법을 적용한 실험적 결과를 제공한다. B-spline 곡선의 근사변환에서 기존의 $B\acute{e}zier$ 곡선의 차수감소 방법들을 차수 감소 과정에 적용하고. 그 방법들을 비교 분석한다 knot 제거 알고리즘도 자료 감소를 위하여 차수 감소과정에 적용한다

• Journal of applied mathematics & informatics
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• 제8권3호
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• pp.819-827
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• 2001

An algorithmic approach to degree reduction of B-spline curves is presented. The new algorithms are based on the blossoming spline curves are obtained by the generalized least square method. The computations are carried out by minimizing the $L_2$ distamce between the two curves.

• 한국환경보건학회지
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• 제27권1호
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• pp.14-19
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• 2001

The physical and chemical transformation and reduction degree of food waste were investigated in a food waste reduction machine using thermophilic bacteria. The first operation of the reduction machine for grain, vegetables, fishes and flesh wastes proceeded during three weeks. The first and second reduction percentages of the wastes were 98.3% and 93.2%, respectively. The residue of food waste was composed of fruits, fish, and vegetables. The temperature distribution of the reduction machine ranged between 30 and 6$0^{\circ}C$ appropriate for growth of thermophilic bacteria. At initial stage the pH in the reduction machine decreased with organic acids produced, but increased as the organic acids decomposed by different thermophilic bacteria. In the reduction machine, the moisture content of the food waste was reduced from 80-90% to 10-20% after 24 hours, and the salinity of residue was 0.29% after the second operation. The degree of odor was most high between 2 and 4 hours.