• 대한수학회지
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• 제53권3호
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• pp.583-595
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• 2016

In the present note, we deal with $L^2$ harmonic 1-forms on complete submanifolds with weighted $Poincar{\acute{e}}$ inequality. By supposing submanifold is stable or has sufficiently small total curvature, we establish two vanishing theorems for $L^2$ harmonic 1-forms, which are some extension of the results of Kim and Yun, Sang and Thanh, Cavalcante Mirandola and $Vit{\acute{o}}rio$.

• 한국멀티미디어학회논문지
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• 제8권1호
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• pp.34-45
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• 2005

본 논문은 3차원 얼굴 영상으로부터 추출된 표면 곡률에 대 하여, 깊이 값을 가중치로 하는 Hausdorff 거리를 이용한 얼굴 인식 알고리즘을 제안한다. Hausdorff 거리 방법은 두 개의 점 집합에 대한 일치성을 측정하는 방법이다. 먼저 객체와 배경을 분리하여 얼굴을 추출한 후 얼굴에서 가장 두드러진 형태인 코끝을 찾고, 회전에 대한 정규화를 실시한다. 3차원 얼굴 영상으로부터 표면 특성의 정보인 주 곡률, 평균 곡률 그리고 가우시안 곡률 값을 추출한다. 입력 영상과 데이터베이스 영상과의 유사도 비교를 위해 두 영상에 대하여 문턱치 값에 의한 이진 영상을 추출하여 각 점에 대한 깊이 값을 가중치로 하는 깊이 가중치 Hausdoff 거리(DWHD)를 이용하여 비교하였다. 제안된 방법으로 수행한 결과, 인식률은 픽셀의 분포가 가장 적은 주 곡률의 최소 곡률이 98%로 가장 높게 나타났다.

• 대한수의학회지
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• 제50권1호
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• pp.11-17
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• 2010

Linear and non-linear regressions were used to derive the calibration function for the measurement of roxithromycin plasma concentration. Their results were compared with weighted least squares regression by usual weight factors. In this paper the performance of a non-linear calibration equation with the capacity to account empirically for the curvature, y = ax$^{b}$ + c (b $\neq$ 1) is compared with the commonly used linear equation, y = ax + b, as well as the quadratic equation, y = ax$^{2}$+ bx + c. In the calibration curve (range of 0.01 to 10 ${\mu}g/mL$) of roxithromycin, both heteroscedasticity and nonlinearity were present therefore linear least squares regression methods could result in large errors in the determination of roxithromycin concentration. By the non-linear and weighted least squares regression, the accuracy of the analytical method was improved at the lower end of the calibration curve. This study suggests that the non-linear calibration equation should be considered when a curve is required to be fitted to low dose calibration data which exhibit slight curvature.

• Journal of Multimedia Information System
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• 제2권4호
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• pp.303-310
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• 2015

Vulnerable road users such as bike, motorcycle, small automobiles, and etc. are easily attacked or threatened with bigger vehicles than them. So this paper suggests a new approach two-wheelers detection system riding on people based on modified histogram of oriented gradients (HOGs) which is weighted by curvature and local correlation coefficient. This correlation coefficient between two variables, in which one is the person riding a bike and other is its background, can represent correlation relation. First, we extract edge vectors using the curvature of Gaussian and Histogram of Oriented Gradients (HOG) which includes gradient information and differential magnitude as cell based. And then, the value, which is calculated by the correlation coefficient between the area of each cell and one of bike, can be used as the weighting factor in process for normalizing the HOG cell. This paper applied the Adaboost algorithm to make a strong classification from weak classification. The experimental results validate the effectiveness of our proposed algorithm show higher than that of the traditional method and under challenging, such as various two-wheeler postures, complex background, and even conclusion.

• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.157-166
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• 2006

In order to model blending surfaces with curvature continuity, in this paper we apply sixth order partial differential equations (PDEs), which are solved with a composite power series based method. The proposed composite power series based approach meets boundary conditions exactly, minimises the errors of the PDEs, and creates almost as accurate blending surfaces as those from the closed form solution that is the most accurate but achievable only for some simple blending problems. Since only a few unknown constants are involved, the proposed method is comparable with the closed form solution in terms of computational efficiency. Moreover, it can be used to construct 3- or 4-sided patches through the satisfaction of continuities along all edges of the patches. Therefore, the developed method is simpler and more efficient than numerical methods, more powerful than the analytical methods, and can be implemented into an effective tool for the generation and manipulation of complex free-form surfaces.

• 대한수학회보
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• 제60권1호
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• pp.171-184
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• 2023

In this paper, we show that a complete translating soliton Σ^m in ℝⁿ for the mean curvature flow is stable with respect to weighted volume functional if Σ satisfies that the L^m norm of the second fundamental form is smaller than an explicit constant that depends only on the dimension of Σ and the Sobolev constant provided in Michael and Simon [12]. Under the same assumption, we also prove that under this upper bound, there is no non-trivial f-harmonic 1-form of L²_f on Σ. With the additional assumption that Σ is contained in an upper half-space with respect to the translating direction then it has only one end.

• 한국정보처리학회:학술대회논문집
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• 한국정보처리학회 2015년도 추계학술발표대회
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• pp.1579-1580
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• 2015

본 논문에서는 3차원 메쉬 모델의 중요 영역을 표현하는 메쉬 돌출맵(mesh saliency map)을 생성하기 위하여 다중 스케일 평균 곡률 (multi-scale mean curvature)을 기반으로 정의된 전역 희소치(global rarity)를 이용하는 방법을 제안한다. 제안 방법에서는 우선, 메쉬 모델의 지역 영역 특성을 정의하기 위하여 기존 관련 연구들에서 많이 사용하고 있는 가우시안 가중치 평균곡률(Gaussian-weighted mean curvature)을 5단계 서로 다른 스케일에서 정의하고, 메쉬의 각 정점(vertex)에 대하여 중심주변 연산자(center-surround operator)를 적용하여 5단계 지역 돌출특성(local saliency)을 정의한다. 주어진 메쉬 모델의 전역 희소치를 구하기 위하여 메쉬의 모든 정점쌍 (vertex pair)에 대하여 5단계 지역 돌출 특성 공간에서의 거리를 계산하고, 각 정점별로 5단계 지역 돌출 특성 공간에서의 다른 정점과의 거리의 합으로 전역 희소치를 정의한다. 이러한 전역 희소치를 각 정점의 메쉬 돌출치로 정의한다. 서로 다른 형태의 3차원 모델에 대하여 제안방법에 의한 메쉬 돌출맵과 지역 특성만을 고려한 기존 메쉬 돌출맵을 생성하여 중요 영역 표현 결과를 비교 분석한다.

• 한국재료학회지
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• 제33권5호
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• pp.205-213
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• 2023

This paper reports the results of an experimental examination using X-rays to test annealing materials for lapped bearing steel (STB2), to confirm the validity of the weighted averaging analysis method. The distribution behavior for the α_𝜓-sin²𝜓 diagram and the presence or absence of differences in the peak method, half-value breadth method, and centroid method were investigated. When lapping the annealed bearing steel (STB2) material, a residual stress state with a non-directional steep gradient appeared in the surface layer, and it was found that the weighted averaging analysis method was effective. If there is a steep stress gradient, the sin²𝜓 diagram is curved and the diffraction intensity distribution curve becomes asymmetric, resulting in a difference between the peak method, half-value breadth method, and centroid method. This phenomenon was evident when the stress gradient was more than 2~3 kg/mm²/㎛. In this case, if the position of the diffraction line is determined using the centroid method and the weighted averaging analysis method is applied, the stress value on the surface and the stress gradient under the surface can be obtained more accurately. When the stress gradient becomes a problem, since the curvature of the sin²𝜓 diagram appears clearly in the region of sin²𝜓 > 0.5, it is necessary to increase the inclination angle 𝜓 as much as possible. In the case of a lapping layer, a more accurate value can be obtained by considering 𝜎₃ in the weighted averaging analysis method. In an isotropic biaxial residual stress state, the presence or absence of 𝜎₃ can be determined as the presence or absence of strain for sin²𝜓≈0.4.

• 한국정밀공학회지
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• 제23권4호
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• pp.37-43
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• 2006

In this paper, an approach to adaptive finite element analysis of three-dimensional forging processes is presented with emphasis on remeshing. In the approach, an optimal tetrahedral element generation technique is employed and the mesh density is specified by the combination of the weighted normalized effective strain and the normalized effective strain rate as well as the weighted normalized curvature. The approach is applied to computer simulation of an enclosed die forging process of a bevel gear and its results are compared with its related experiments. It has been shown that the analyzed results are in good agreement with the experimental ones.